Tonal analysis of musical works

Musical works encod­ed in the Bol Processor (using "sim­ple notes" accord­ing to English, Italian/Spanish/French and Indian con­ven­tions) can be analysed in terms of har­mon­ic or melod­ic intervals.

The musi­cal aspects are dis­cussed after a descrip­tion of the process.

In the final sec­tion, we present a one-click method for eval­u­at­ing the suit­abil­i­ty of all doc­u­ment­ed tun­ing sys­tems for a giv­en piece of music. A demo of this analy­sis can be found on the Bach well-tempered tonal analy­sis.

Basic process

This cal­cu­la­tion is start­ed by press­ing the ANALYZE INTERVALS but­ton at the bot­tom of the 'Data' window:

The machine found a '-to.tryTunigs' dec­la­ra­tion at the top of the data con­tent, indi­cat­ing that it should pick up the scale def­i­n­i­tions con­tained in this tonal­i­ty resource. These def­i­n­i­tions are only acces­si­ble if '-to.tryTunigs' was opened less than 24 hours ago: these files are stored in the 'temp_bolprocessor' fold­er which is auto­mat­i­cal­ly cleaned up of old stor­age. Click on the 'open' link if necessary.

The ana­lyt­i­cal process is demon­strat­ed using a sin­gle phrase of François Couperin's Les Ombres Errantes import­ed from a MusicXML score — see the Importing MusicXML scores page. This exam­ple is small enough to allow a visu­al check of the tech­ni­cal process, but too short to allow a mean­ing­ful musi­cal inter­pre­ta­tion of the result.

In Bol Processor nota­tion (English con­ven­tion), the musi­cal item reads as fol­lows — read the Polymetric struc­tures page:

-to.tryTunings

_scale(rameau_en_sib,0)
_rndtime(20) {_tempo(13/15) _vel(64){3, _legato(20) C5 _legato(0) {1/4,C5 B4 C5}{3/4,B4} _legato(20) Eb5,{1/2,Eb4}{5/2,G4 D4 F4 C4 Eb4},Eb4 D4 C4}} {_tempo(13/15) _vel(64){4, _legato(0) {1/4,Eb5 D5 Eb5}{3/4,D5} _legato(20) C5 _legato(0) {1/4,C5 B4 C5}{3/4,B4}{1/8,C5 B4}{7/8,C5},{4,B3 F4 Eb4 G4 D4 F4 C4 Eb4},B3 Eb4 D4 C4}}

Beginning of "Les Ombres Errantes"
Scale "Rameau en sib" (see full image)

The sound pro­duc­tion used the tonal­i­ty resource file '-to.tryTunings' which con­tains the tonal scale 'rameau_en_sib' — see the page Comparing tem­pera­ments. This scale prob­a­bly pro­vides the best tun­ing for this piece when played on a "harpsichord-like" Csound instrument.

The machine has picked up a def­i­n­i­tion of the tonal scale in a tem­po­rary copy of '-to.tryTunings'. The essen­tial con­tent of this def­i­n­i­tion is the set of tonal posi­tions in the scale shown in the image — see the Microtonality page.

Click on the ANALYZE INTERVALS but­ton and the fol­low­ing screen appears:

Analysis of melod­ic and har­mon­ic inter­vals in a short frag­ment of "Les Ombres errantes"

The table above gives a sum­ma­ry of match­ing inter­vals: pairs of notes played one after the oth­er (melod­ic) or one above the oth­er (har­mon­ic), dis­tin­guish­ing between ascend­ing and descend­ing melod­ic inter­vals. These match­es can be checked in the graph­i­cal rep­re­sen­ta­tion of this item:

Intervals are list­ed in descend­ing order of impor­tance. For exam­ple, the melod­ic inter­val 'C' to 'B' occurs in 20.3 beats, the high­est num­ber. Ascending melod­ic inter­vals 'B' to 'F' and 'D' to 'B' are the least fre­quent. Values less than 5% of the max­i­mum in the col­umn are ignored in the graph­i­cal display.

Harmonic (left) and melod­ic (right) intervals

Interestingly, the high­est scores of har­mon­ic inter­vals in this musi­cal phrase are minor thirds such as 'D'/'B' and 'C'/'Eb'. The fifth 'C'/'G' is scored only 1.6 beats, which is 18% of the high­est score.

The detec­tion of a "har­mon­ic inter­val" is based on the com­par­i­son of its start and end dates with options that can be mod­i­fied. Let $start1, $end1, $start2 and $end2 be the tim­ings of two notes. We assume $start2 >= $start1 due to a pre­lim­i­nary chrono­log­i­cal sort­ing of the list of notes. The matching_intervals() func­tion does the fol­low­ing to eval­u­ate har­mon­ic intervals:

$duration1 = $end1 - $start1;
$duration2 = $end2 - $start2;
$overlap = $end1 - $start2;
$smallest_duration = $duration1;
if($duration2 < $duration1) $smallest_duration = $duration2;


if($smallest_duration < $min_dur) return FALSE;
if($start1 + ($duration1 / 2.) < $start2) return FALSE;
if($overlap < ((1 - $ratio) * $smallest_duration)) return FALSE;
return TRUE;

This func­tion elim­i­nates brief over­laps of time inter­vals, such as those cre­at­ed by slurs inter­pret­ed as _legato() per­for­mance con­trols when import­ing MusicXML scores — see details. It also elim­i­nates notes with dura­tions less than $min_dur, option­al­ly set to 500 mil­lisec­onds. For exam­ple, short notes such as 'C5', 'B4', 'Eb5', etc., are dis­card­ed. Finally, it checks that $overlap is greater than a frac­tion of the small­est dura­tion, with $ratio set to 0.25 by default. Another option, not shown here, is the max­i­mum tonal dis­tance between two notes, which is set to 11 semi­tones by default.

The con­di­tions for match­ing melod­ic inter­vals are similar:

if($start2 > ($end1 + $max_gap)) return FALSE;
if($start1 + ($duration1 / 2.) >= $start2) return FALSE;
if($overlap >= ($ratio * $smallest_duration)) return FALSE;
return TRUE;

The $max_gap para­me­ter (typ­i­cal­ly 300 mil­lisec­onds) is the max­i­mum delay between the end of the first note and the begin­ning of the next one.

All para­me­ters can be changed before the process is restart­ed. These set­tings are dis­cussed later:

Default set­tings for tonal analysis

Calculations

Detailed tonal analysis

To check the sequence of time inter­vals in great detail it is pos­si­ble to acti­vate the "Display all dates" option yield­ing a detailed analysis.

All match­ing inter­vals will be list­ed. It is not prac­ti­cal to use this option on large pieces of music…

Dates are in sec­onds, round­ed to 0.1s, although more accu­rate val­ues are used. In fact, all time cal­cu­la­tions are based on whole num­bers, as in the Bol Processor console.

The result is always debat­able. For exam­ple, some melod­ic or har­mon­ic inter­vals may appear "acci­den­tal" rather than significant.

For this and oth­er rea­sons, it may be nec­es­sary to explore oth­er options relat­ed to musi­cal and per­for­mance styles.

Graphic display

Melodic and har­mon­ic tonal inter­vals are dis­played against the back­ground of the tonal scale used for the per­for­mance. Here it would be 'rameau_en_sib', although by default an equal-tempered scale is used.

Clicking on the links to the har­mon­ic inter­val pic­tures (see image above) will bring up the fol­low­ing three graphs — in sep­a­rate and resiz­able windows:

Display of har­mon­ic inter­vals. The 'rameau_en_sib' scale is in the middle.

Intervals are shown as gold high­lights with widths pro­por­tion­al to their rel­a­tive val­ues. In the left-hand image, these gold­en seg­ments are drawn behind the fifths, major and minor thirds marked on the scale. For this rea­son, the yel­low high­light­ing of the link between Eb and G, behind the green link of a har­mon­ic major third, is less vis­i­ble in the full image.

Minor thirds (ratio 6/5) have been added to the set­tings. For this rea­son, those avail­able in this scale are shown as black seg­ments. These addi­tion­al ratios are list­ed at the top right of each image.

Restricted analysis

If a MusicXML file has been import­ed along with bar num­bers (notat­ed [—1—], [—2—] etc.), these can be used to restrict the analy­sis to a sub­set of the score.

Below is the set­ting of bars #1 to #32 (the Aria) in J.S. Bach's Goldberg Variations:

Restricting the tonal analy­sis to the Aria in the Goldberg Variations makes sense because oth­er vari­a­tions, due to their high speed, do not show har­mon­ic inter­vals longer than the min­i­mum dura­tion fixed in the set­tings (500 ms).

Musicological discussion

Tonal analy­sis with the Bol Processor aims to help choose the most appro­pri­ate tun­ing sys­tem for a piece of music — a tem­pera­ment as defined by Baroque musi­cians. This top­ic is cov­ered on the page Comparing tem­pera­ments.

We first describe a visu­al method for esti­mat­ing (rather than mea­sur­ing) the ade­qua­cy of a tun­ing sys­tem for the per­for­mance of musi­cal works import­ed from MusicXML scores — read the page on this top­ic. In the next sec­tion, we will show how to auto­mat­i­cal­ly com­pare all can­di­date scales, tak­ing into account the rel­e­vant para­me­ters revealed in this section.

Take, for exam­ple, J.S. Bach's Prelude 1 in C major for which some his­tor­i­cal infor­ma­tion (report­ed by Asselin, 2000 p. 142) sug­gests the choice of a Kirnberger tem­pera­ment. Which one?

Harmonic tonal inter­vals of Bach's 1st pre­lude ver­sus Kirnberger II and Kirnberger III tun­ing systems

The full rep­re­sen­ta­tion of the har­mon­ic inter­vals is shown above and com­pared with two dif­fer­ent scales described by Kirnberger (Asselin, 2000 p. 90, 93). The match looks bet­ter on the right (Kirnberger III). For exam­ple, the inter­val 'D' - 'A' is clos­er to a "pure" fifth (702 cents) on Kirnberger III (697) than on Kirnberger II (691). Another sig­nif­i­cant match is the har­mon­ic major third 'F' - 'A'. Other inter­vals are sim­i­lar in terms of these scales.

A care­ful lis­ten­ing to both ver­sions might con­firm this mechan­i­cal analysis:

Kirnberger II
Kirnberger III

For François Couperin's Les Ombres Errantes, the same crude analy­sis yields no sig­nif­i­cant result. Harmonic inter­val analy­sis may be less rel­e­vant because this piece is more gen­er­al­ly per­ceived as a sequence of melod­ic inter­vals, includ­ing minor thirds and major sec­onds. This can be seen in the graph of melod­ic intervals:

Melodic inter­vals of "Les Ombres Errantes" (full performance)

Comparing this graph with the 'rameau_en_sib' scale does not reveal any inter­est­ing pat­terns, for the sim­ple rea­son that nei­ther minor thirds nor major sec­onds have been tak­en into account in this scale in terms of "just into­na­tion" — see page Just into­na­tion: a gen­er­al frame­work. Although we can assume that a Pythagorean major sec­ond (ratio 9/8) sounds more "con­so­nant" than a har­mon­ic one (ratio 10/9), there is no rea­son to sys­tem­at­i­cal­ly claim that the har­mon­ic minor third (ratio 6/5) is "bet­ter" than the Pythagorean one (ratio 32/27).

The pic­ture on the left shows that the fre­quent melod­ic inter­vals of major thirds empha­sise the har­mon­ic major thirds (ratio 5/4) of this scale.

We need to check inter­vals small­er than the major third in the tonal scales. If we tell the machine to check inter­vals close (with­in ± 10 cents) to the har­mon­ic minor third (ratio 6/5), the above graphs will look like this:

Melodic inter­vals of "Les Ombres Errantes" (full per­for­mance) with black mark­ings of "good" minor thirds (6/5) on a ‘rameau_en_sib’ temperament

The pic­ture on the left side shows that all the minor thirds used in this per­for­mance coin­cide with­in ± 10 cents with the har­mon­ic minor thirds (ratio 6/5) of the scale, which is an incen­tive to admit that the 'rameau_en_sib' scale would be a fair (per­haps the best) tun­ing option for Les Ombres Errantes.

A counter-example is the match­ing of Les Ombres Errantes with a pure-minor-thirds tem­pera­ment designed dur­ing in 16th cen­tu­ry (Asselin 2000 p. 82, see fig­ure). Below are the graphs of the match­ing melod­ic (left) and har­mon­ic (right) inter­vals, with black lines mark­ing the har­mon­ic minor thirds (ratio 6/5):

Melodic (left) and har­mon­ic (right) inter­vals of "Les Ombres Errantes" against a pure-minor-thirds temperament
"Les Ombres Errantes" with a pure minor thirds tem­pera­ment (16th century)

The main draw­back of this 'pure_minor_thirds' tem­pera­ment is the very low posi­tion of 'Ab' which is sup­posed to pro­duce a con­so­nant sequence of minor thirds: 'Ab' - 'B' - 'D' - 'F'. However, 'Ab' - 'B' is not a melod­ic inter­val found in this piece, nor are 'Db' - 'E' and 'E' - 'G', which are well rep­re­sent­ed by the 'pure_minor_thirds' tem­pera­ment. There are also dis­crep­an­cies in the har­mon­ic inter­vals, which are easy to hear. We can con­clude that the pure minor thirds tem­pera­ment is nei­ther the best nor the worst tun­ing sys­tem for this musi­cal work, although the com­par­i­son of sound pro­duc­tions sug­gests that it is sig­nif­i­cant­ly less good than the 'rameau_en_sib' scale.

➡ Comparing graphs is easy with the detached resiz­able pic­tures pro­duced by the Bol Processor.

A "deaf musicologist's" approach

The analy­sis shown so far has replaced a com­par­i­son of sound ren­der­ing — see the page Comparing tem­pera­ments — with a visu­al prob­lem of pattern-matching. We have shown that Baroque musi­cians and tuners sought to achieve con­so­nance in terms of sim­ple fre­quen­cy ratios for fifths (close to 3/2) and har­mon­ic major thirds (close to 5/4). This approach and its under­ly­ing assump­tions are dis­cussed on the page Just into­na­tion: a gen­er­al frame­work.

Furthermore, one might be tempt­ed to claim that a "just into­na­tion" minor third should be har­mon­ic (ratio close to 6/5), but the deci­sion should remain open. To this end, it is pos­si­ble to enter an addi­tion­al set of melod­ic and har­mon­ic inter­vals that the ana­lyst con­sid­ers sig­nif­i­cant for the eval­u­a­tion of tonal scales. Each inter­val is defined by an inte­ger ratio — which can be as com­plex as necessary.

Comparative pat­tern match­ing assigns a numer­i­cal score to each scale that has been eval­u­at­ed for its fit with the musi­cal work. This allows the can­di­date scales to be sort­ed. However, two sep­a­rate scores are required, one for melod­ic inter­vals and one for har­mon­ic inter­vals. A weight­ed sum of scores is there­fore used to sort the list of scales.

This method has been imple­ment­ed in the Tonal analy­sis process. We have com­pared all the scales defined in '-to.tryTunings' — includ­ing in par­tic­u­lar all the tem­pera­ments doc­u­ment­ed by Pierre-Yves Asselin — in terms of their suit­abil­i­ty for the ren­der­ing of melod­ic and tonal inter­vals in François Couperin's Les Ombres Errantes:

Matching scales for "Les Ombres Errantes"

Great result! The machine con­firms that the scale 'rameau_en_sib' is the best can­di­date for the inter­pre­ta­tion of Les Ombres Errantes. Its scores are sig­nif­i­cant­ly bet­ter for both melod­ic and har­mon­ic inter­vals. (A total of 45 tun­ing schemes were tried.)

By default, the eval­u­a­tion of melod­ic and har­mon­ic inter­vals con­sid­ers only per­fect fifths (3/2) and har­mon­ic major thirds (5/4) as "good" inter­vals, with weights of 2 and 1 respec­tive­ly, and wolf fifths (40/27), wolf fourths (320/243) and Pythagorean major thirds (81/64) as "bad" inter­vals, with weights of -2, -2 and -1 respec­tive­ly. All these weights can be mod­i­fied as shown in the image above.

We repeat the com­par­i­son with the addi­tion­al option of har­mon­ic minor thirds (6/5) as melod­ic intervals:

Matching scales, includ­ing har­mon­ic minor thirds (ratio close to 6/5) for melod­ic intervals

As expect­ed, all the melod­ic val­ues increased, but the win­ner remained. If we add the Pythagorean major sec­ond (ratio close to 9/8), we get the following:

Matching scales, includ­ing ratios 6/5 and 9/8 for melod­ic intervals

The 'rameau_en_sib' scale is now chal­lenged by 'sauveur' for melod­ic inter­vals, but its har­mon­ic score remains higher.

Note that scales Abmaj and Cmin are iden­ti­cal, which explains their equal scores.

A visu­al com­par­i­son of scales with melod­ic inter­val mark­ings shows that there is lit­tle dif­fer­ence between these tem­pera­ments in terms of the per­for­mance of Les Ombres Errantes. Since the 'sauveur' tem­pera­ment was designed in 1701 by the (hearing-impaired?) French math­e­mati­cian Joseph Sauveur, it is not unlike­ly that it was used for the com­po­si­tion of Les Ombres Errantes in 1730.

Comparison of 'rameau_en_sib' and 'sauveur' tem­pera­ments for melod­ic inter­vals in "Les Ombres Errantes", with addi­tion­al ratios 6/5 and 9/8 dis­played as black lines.

The scale 'rameau_en_sib' again scores as good as 'sauveur' when the Pythagorean minor third (ratio close to 32/27) is tried as a melod­ic inter­val (both ascend­ing and descend­ing) in place of the ratio 6/5… This is due to the use of 'F' - 'Ab', which is ren­dered as a Pythagorean minor third by 'rameau_en_sib', but not by 'sauveur'.

Many more checks can be made by chang­ing the weights assigned to the occur­rences of melod­ic and har­mon­ic ratios. Finding the best set­tings requires a thor­ough study of the musi­cal score — this is where human musi­col­o­gists come in!

Ears (plus expert knowl­edge of the score) could make the final decision:

"Les Ombres Errantes", Rameau en sib temperament
"Les Ombres Errantes", Sauveur temperament

The ana­lyt­i­cal process we are fol­low­ing is a kind of reverse engi­neer­ing… Obviously, com­posers did not search for a suit­able tem­pera­ment after cre­at­ing a musi­cal work. It is more real­is­tic to assume that they com­posed works on exist­ing instru­ments, with the effect that sets of pieces pro­duced by the same com­pos­er (using the same instru­ment) at a giv­en time obeyed implic­it melod­ic and har­mon­ic con­straints that best suit­ed the tun­ing of their instrument(s).

Comparative study

Let us look again at J.S. Bach's Prelude 1 in C major, for which Kirnberger III was cho­sen (visu­al­ly) as a bet­ter match than Kirnberger II. Including the ratios 6/5 and 9/8 as pos­si­ble melod­ic up/down inter­vals, and 6/5 as a har­mon­ic inter­val, the fol­low­ing clas­si­fi­ca­tion of tun­ing schemes emerges:

Classification of scales for the inter­pre­ta­tion of J.S. Bach's Prelude 1 in C major

The win­ner is undoubt­ed­ly 'sauveur' although the har­mon­ic score is iden­ti­cal for six tem­pera­ments, but 'kirnberger_3' scores much lower.

Note that this was achieved by declar­ing ratios close to 6/5 as pos­si­ble con­so­nant melod­ic and har­mon­ic inter­vals. For a dis­cus­sion of this hypoth­e­sis, see Bach well-tempered tonal analy­sis for a dis­cus­sion of this hypothesis.

Sauveur's tem­pera­ment is the best suit­ed because of its high pro­fi­cien­cy in har­mon­ic minor thirds (6/5) and Pythagorean major sec­onds (9/8). It also has a com­plete set of per­fect fourths and fifths (3/2) except for the wolf fourth 'D#' - 'G#', which is almost 477 cents (instead of 498). Fortunately, this inter­val is nev­er used in Bach's piece:

Matching the melod­ic inter­vals of J.S. Bach's Prelude 1 in C major with Sauveur's temperament
J.S. Bach's Prelude 1 in C major played by the Bol Processor + Csound with Sauveur's temperament

This ren­der­ing can be com­pared (in terms of tune­ful­ness) with a human per­for­mance on a real harpsichord:

J.S. Bach's Prelude 1 in C major played on the copy of an instru­ment built by Hans Moerman in Antwerpen (1584). Source: Wikipedia licence CC BY-SA.

Unsurprisingly, J.S. Bach's Fugue 1 in C major shares the same pref­er­ence for 'sauveur', with oth­er tun­ing schemes fol­low­ing in a dif­fer­ent order. All of the fugues in this series of works (books I and II) are asso­ci­at­ed with pre­ludes in the same key.

The tonal analy­sis of J.S. Bach's Prelude 2 in C minor again selects 'sauveur' using the same eval­u­a­tion cri­te­ria — includ­ing the ratios 6/5 (melod­ic and har­mon­ic) and 9/8 (melod­ic up/down). The scor­ing is com­plete­ly dif­fer­ent, but the win­ner is unchanged, although it is chal­lenged by 'rameau_en_sib' for its har­mon­ic score.

J.S. Bach's Prelude 2 in C minor played by the Bol Processor + Csound with Sauveur's temperament

Note that the Cmin scale has a bad rate because of the melod­ic inter­vals. It beats Sauveur's tem­pera­ment in terms of har­mon­ic inter­vals, but these are rel­a­tive­ly rare in this pre­lude. This clas­si­fi­ca­tion could be quite dif­fer­ent if some ratios (such as 9/8) were ignored for the eval­u­a­tion of melod­ic inter­vals. Even ratios close to Pythagorean thirds (81/64) may sound accept­able in fast melod­ic move­ments — see the page on Bach well-tempered tonal analy­sis.

J.S. Bach's Fugue 2 in C minor again favours 'sauveur'.

We get the same result with J.S. Bach's Prelude 6 in D minor (ran­dom choice). Note the strik­ing­ly high melod­ic scores of 'sauveur':

J.S. Bach's Prelude 6 in D minor played by theBol Processor + Csound with Sauveur's temperament

J.S. Bach once claimed that he could play his entire reper­toire on the instru­ment he had tuned by him­self. This sounds like squar­ing the cir­cle, and many hypothe­ses have been put for­ward to solve this prob­lem for das Wohltemperierte Clavier.

These exam­ples sug­gest that Sauveur's tem­pera­ment may have been Bach's choice. Although there is lit­tle chance that the German com­pos­er (1685-1750) would have heard of the research work of the French physi­cian (1653-1716), the sys­tem­at­ic con­struc­tion of this tem­pera­ment — a sin­gle sequence of fifths dimin­ished by 1/5 com­ma (see image and read Asselin, 2000 p. 80) — sug­gests that any com­pos­er could have worked it out independently.

To test (and chal­lenge) this hypoth­e­sis, we have under­tak­en a tonal analy­sis of 24 pre­ludes and fugues from books I and II of The Well-Tempered Clavier using the same set­tings. Read the Bach Well-tempered tonal analy­sis page. This large spec­trum analy­sis requires a batch pro­cess­ing device, which we will now describe.

Batch processing

To analyse the tonal­i­ty of a large num­ber of musi­cal works, we need to cre­ate a Data page con­tain­ing the names of all the pages con­tain­ing the Bol Processor scores of these items. For exam­ple, the page “-da.index_preludes_book_I” is as follows:

// All Bach preludes

-se.Bach_preludes
-to.tryTunings

-da.Bach_1st_prelude
-da.Bach_2nd_prelude
-da.Bach_3d_prelude
-da.Bach_4th_prelude
-da.Bach_5th_prelude
-da.Bach_6th_prelude
-da.Bach_7th_prelude
-da.Bach_8th_prelude
-da.Bach_9th_prelude
-da.Bach_10th_prelude
-da.Bach_11th_prelude
-da.Bach_12th_prelude
-da.Bach_13th_prelude
-da.Bach_14th_prelude
-da.Bach_15th_prelude
-da.Bach_16th_prelude
-da.Bach_17th_prelude
-da.Bach_18th_prelude
-da.Bach_19th_prelude
-da.Bach_20th_prelude
-da.Bach_21st_prelude
-da.Bach_22nd_prelude
-da.Bach_23d_prelude
-da.Bach_24th_prelude

When read­ing this page, the Tonal analy­sis pro­ce­dure opens each data file and picks up the Bol Processor score it con­tains. To facil­i­tate this, the Batch pro­cess­ing option can be checked in the settings.

In the batch-processing mode, the machine will not dis­play the full set of scales for each piece of music analysed. If the score con­tains a spec­i­fi­ca­tion for a tonal scale — a _scale(some_scale, 0) instruc­tion — the list of pre­ferred scales will be dis­played down to the spec­i­fied one. If the spec­i­fied scale is the first in the rank­ing, then the next two fol­low­ing scales are list­ed. If no scale is giv­en, only the 10 best match­ing scales are listed:

Batch pro­cess­ing of “-da.index_preludes_book_I
Items #2 and #3 con­tain the spec­i­fi­ca­tions of tonal scales sauveur and Dbmaj respec­tive­ly.
This pref­er­ence is con­firmed by the analy­sis of item #2 but it is not the case with item #3.

At the bot­tom of the page, a SHOW RESULTS but­ton dis­plays a down­load­able HTML file con­tain­ing all the results:

End of batch pro­cess­ing. Clicking on SHOW RESULTS dis­plays the entire result set.

The HTML page also shows the set­tings for the analy­sis, and can be down­loaded, along with a CVS file of the same fig­ures, which is suit­able for sta­tis­ti­cal graphing.

The results of the analy­sis of all the pre­ludes and fugues of The Well-tempered Clavier are pub­lished and dis­cussed on the page Bach well-tempered tonal analy­sis.

Does it apply to western classical music?

The analy­sis of tonal inter­vals and their cor­re­spon­dence to doc­u­ment­ed tun­ing sys­tems (tem­pera­ments) makes sense in the con­text of Baroque music, assum­ing that com­posers and instru­ment tuners sought to achieve max­i­mum con­so­nance in the per­for­mance of their musi­cal reper­toire. The ques­tion remains whether it is equal­ly reli­able (and use­ful) for the analy­sis of musi­cal works from more recent periods.

Matching Beethoven’s Fugue in B flat major against doc­u­ment­ed scales

The best score — once again — is that of Sauveur's tem­pera­ment, main­ly because of the ascend­ing melod­ic inter­vals. If per­form­ers are try­ing to achieve ratios 9/8, 6/5, 5/4 and 3/2, then ‘sauveur’ may be the best rep­re­sen­ta­tion of the "tun­ing scheme" they have in mind.

The equal tem­pera­ment scale comes last, with scores of 3529, 1680 and 240 for ascend­ing melod­ic, descend­ing melod­ic and har­mon­ic inter­vals respec­tive­ly. Part of the expla­na­tion lies in the com­par­i­son of the two scales as a back­ground to the har­mon­ic intervals:

Comparison of the equal tem­pera­ment scale (left) and Sauveur's tem­pera­ment (right) for the per­for­mance of Beethoven's Fugue in B flat major.

The most obvi­ous dif­fer­ence is the use of almost per­fect har­mon­ic major thirds (ratio 5/4) on Sauveur's scale (see image) instead of Pythagorean major thirds (approx­i­mate­ly ratio 81/64) on the equal tem­pered scale (see image). The for­mer have been assigned weights (+1) and the lat­ter (-1). Yellow back­ground lines indi­cate that these inter­vals are used quite frequently.

Melodic inter­vals in Beethoven’s Fugue in B flat major

One draw­back of Sauveur's scale is the wolf fourth 'D#' - 'G#' (approx. 477 cents), but this inter­val does not occur fre­quent­ly in the score.

Many oth­er obser­va­tions could be made, com­par­ing the val­ues of the melod­ic inter­vals, and the whole process (which took almost 8 min­utes) could be start­ed again with dif­fer­ent set­tings of the weights, giv­ing more or less impor­tance to cer­tain inter­vals. After all, we do not know whether an expert play­er of a string instru­ment would play minor thirds at inter­vals of 6/5, 32/27, tem­pered, or some oth­er val­ue, and even more so, whether these val­ues depend on the harmonic/melodic con­text of each musi­cal phrase.

This sug­gests that we shouldn't get too excit­ed about a (still prim­i­tive) tonal analy­sis tool when it comes to sophis­ti­cat­ed tonal material…

Reference

Asselin, P.-Y. Musique et tem­péra­ment. Paris, 1985, repub­lished in 2000: Jobert. Soon avail­able in English.

➡ Musicians inter­est­ed in con­tin­u­ing this research and relat­ed devel­op­ment can use the cur­rent ver­sion of Bol Processor BP3 to process musi­cal works and imple­ment fur­ther tun­ing pro­ce­dures. Follow the instruc­tions on the Bol Processor ‘BP3’ and its PHP inter­face page to install BP3 and learn its basic operation.

Time resolution and quantization

   

These para­me­ters are saved in '-se' set­tings files asso­ci­at­ed with gram­mars and data. They are expressed in milliseconds.

Time res­o­lu­tion is the min­i­mum dif­fer­ence of dates between two events sent to a MIDI device or writ­ten on a Csound score. By default is is set to 10 ms but in some cas­es it may be nec­es­sary to dimin­ish this val­ue. This is already a type of quan­ti­za­tion because sev­er­al events occur­ing with time off­sets low­er than the res­o­lu­tion will be sent or writ­ten with iden­ti­cal dates.

Time quan­ti­za­tion is an option allow­ing the poly­met­ric expan­sion algo­rithm to reduce the size of the phase dia­gram con­struct­ed to frame out the sym­bol­ic tim­ing of events — in fact, rela­tions of prece­dence or simul­tane­ity. Read page Complex ratios in poly­met­ric expres­sions for a detailed expla­na­tion. In brief, it is a method for sav­ing mem­o­ry space and speed­ing up the computation.

In many cas­es, the pro­duc­tion of a piece would sim­ply be impos­si­ble with a quan­ti­za­tion reduced to the time res­o­lu­tion. This is due to the fact that all Bol Processor time cal­cu­la­tions are per­formed with inte­ger ratios to reach the best accu­ra­cy com­pat­i­ble with lim­i­ta­tions of the machine. However, for instance, stor­ing two notes dis­tant by a few mil­lisec­onds requires two dis­tinct columns on the phase dia­gram although (in gen­er­al) this dif­fer­nce is not audible.

Even though it is pos­si­ble to set the time quan­ti­za­tion to a val­ue low­er than the time res­o­lu­tion, it would increase the size of the phase dia­gram (i.e. mem­o­ry and com­pu­ta­tion time) with no effect on the out­put because the time res­o­lu­tion is the low­est val­ue of the actu­al quan­ti­za­tion. This incon­sis­ten­cy is sig­naled on the Data or Grammar window:

👉  Be aware that using a very short quan­ti­za­tion (typ­i­cal­ly less than 10 ms) on a large item can increase mem­o­ry usage to the point where the MAMP or XAMPP dri­ver hangs with­out warning.

Randomisation of dates

The Bol Processor has a per­for­mance tool notat­ed "_rndtime(x)" for ran­dom­iz­ing the dates of events, in which 'x' is half the range in mil­lisec­onds. For instance, fol­low­ing "_rndtime(100)", all dates will be recal­cu­lat­ed with­in a ± 100 ms range.

Randomisation is often used by poor com­po­si­tion devices to "human­ize" computer-made pieces. This is a ridicu­lous approach based on the belief that human inter­preters must be will­ing­ly impre­cise in their per­for­mance… or that music is implic­it­ly a "fuzzy" construction.

The _rndtime tool may oth­er­wise be used to com­pen­sate unwant­ed effects when sev­er­al dig­i­tal­ly syn­the­sized sounds are super­posed, as explained on page Importing MusicXML scores. In this case, the range is very small and the val­ue of the time res­o­lu­tion may need to be adjust­ed accord­ing­ly. For instance, "_rndtime(20)" should be asso­ci­at­ed with a time res­o­lu­tion of 1 mil­lisec­ond so that 40 dif­fer­ent val­ues will be ran­dom­ly picked up in a ± 20 ms range. Note that this has no inci­dence on the time quan­ti­za­tion.

The effect of a ± 20 ms time ran­domi­sa­tion can be noticed by care­ful­ly lis­ten­ing to the fol­low­ing two examples:

Non-randomized begin­ning of “Les Ombres Errantes”
20 mil­lisec­ond ran­dom­ized begin­ning of “Les Ombres Errantes”

Flags in grammars

Flags can be used in gram­mars to activate/deactivate rules accord­ing to sim­ple numer­i­cal and log­i­cal evaluations.

Let us look at the ‘-gr.tryFlags’ gram­mar:

-al.abc
// First create string of ‘a’
gram#1[1] S --> X /Num_total = 20/
gram#1[2] /Num_total - 1/ X --> a X
--------
// Create flags counting 'a' and 'b'
gram#2[1] X --> lambda /Num_a = 20/ /Num_b = 0/
--------
// Now replace 'a' with 'b' until they are in equal numbers
gram#3[1] /Num_a > Num_b/ a --> b /Num_b + 1/ /Num_a - 1/

This gram­mar pro­duces a string of 20 ter­mi­nal sym­bols (Num_total) con­tain­ing an equal num­ber of (ran­dom­ly posi­tioned) 'a' and 'b'. For example:

b b a a a b a a b a b a b b b a b b a a

In a gram­mar rule, flags are enclosed in '/'. The first occur­rence of a flag usu­al­ly sets its ini­tial val­ue (an inte­ger num­ber), for exam­ple /Num_total = 20/.

Additive/subtractive oper­a­tions (on inte­gers) can then be per­formed to increase or decrease the val­ues of the flags, e.g. /Num_b + 1/ or /Num_a - 1/.

Flags that appear before the left argu­ment of a rule are eval­u­at­ed and used to con­trol the rule. For example,

/myflag/ X --> Y

will only be a can­di­date rule if 'myflag' is strict­ly pos­i­tive. This eval­u­a­tion can also be a check of the val­ues of two flags. For exam­ple, rule:

/flag1 > flag2/ /flag3 = flag2/ /flag4 = 50/ X --> Y

will only remain a can­di­date as long as the three con­di­tions are met.

This tech­nique can be com­bined with oth­er con­trol tech­niques, such as (positive/negative, proximate/remote, left/right) con­texts, rule weights etc. An exam­ple of the use of flags can be found in "-gr.trial.mohanam", com­bined with rule weights and pat­tern con­texts. Read the page Computing ‘ideas’.

➡ Note that the oper­a­tors '≤', '≥' and '≠' are not yet accept­ed in the cur­rent ver­sion of BP3 as it does not han­dle multi-byte Unicode characters.

Au cœur des rythmes indiens

Entretien avec James Kippen
➡ English ver­sion

Par Antoine Bourgeau 

James Kippen est un des spé­cial­istes incon­tourn­ables de la musique hin­dous­tanie. Sa ren­con­tre en 1981 avec Afaq Hussain, alors doyen d’une des grandes lignées de joueur de tablā, est le point de départ d’importantes recherch­es sur cet instru­ment et sur les rythmes indi­ens. Il a occupé de 1990 à 2019 la chaire d’ethnomusicologie de la Faculty of Music de l’Université de Toronto (Canada). Formé à l’école de John Blacking et de John Baily, il acquiert par­al­lèle­ment au cours de ses recherch­es la maîtrise de cer­taines langues indo-persanes. Cette habil­ité lui per­met l’analyse de pre­mière main de nom­breuses sources (traités de musique, man­u­scrits de musi­ciens, généalo­gies, icono­gra­phies…) et d’appréhender les dif­férents con­textes socio-culturels indi­ens et leurs muta­tions depuis le XVIIIe siè­cle (cours indo-persanes, empire colo­nial bri­tan­nique, mon­tée du nation­al­isme, post-colonialisme).  Son tra­vail (voir la liste de ses pub­li­ca­tions en fin d’entretien) s’impose comme une con­tri­bu­tion majeure à la com­préhen­sion des pra­tiques rel­a­tives au rythme et au mètre en Inde. J’ai com­mencé à cor­re­spon­dre avec James Kippen lors de mes pro­pres recherch­es sur le tablā à la fin des années 1990. Toujours prompt à partager ses con­nais­sances et son expéri­ence avec ent­hou­si­asme, il me don­na de nom­breux con­seils et encour­age­ments et ce fût un grand hon­neur de le compter par­mi les mem­bres de mon jury de thèse lors de ma sou­te­nance en 2004. C’est avec la même envie de trans­met­tre qu’il a répon­du favor­able­ment à ma propo­si­tion d’entretien. Réalisé à dis­tance entre juil­let et décem­bre 2020, cet échange, à l’origine en anglais, relate près de quar­ante années de recherch­es ethnomusicologiques.

Traduction : Olivia Levingston et Antoine Bourgeau – Octobre 2021.

➡ Source = doi:10.13140/RG.2.2.26071.80804
➡ English ver­sion = doi:10.13140/RG.2.2.12650.03522
or https://bolprocessor.org/kippen-interview/

La voie de l’Inde et du tablā

Comment en es-tu venu à t’intéresser aux musiques de l’Inde et au tablā en particulier ?

J’ai gran­di à Londres, et déjà enfant j'étais fasciné par les dif­férentes langues et cul­tures qui étaient intro­duites pro­gres­sive­ment en Grande-Bretagne par les immi­grants. J’étais par­ti­c­ulière­ment séduit par les petites épiceries regorgeant de pro­duits exo­tiques et par les restau­rants indi­ens qui dégageaient des arômes épicés alléchants. Mon père me par­lait sou­vent de ses aven­tures pen­dant les sept années qu'il avait passées en Inde en tant que jeune sol­dat, et j'ai donc dévelop­pé une image très attrayante, bien qu’orientaliste, du sous-continent indi­en. Pendant ma licence de musique à l'Université de York (1975-78), mon ami et cama­rade Francis Silkstone m'a fait con­naître le sitār. J'ai égale­ment eu la chance de suiv­re un cours inten­sif de musique hin­dous­tanie avec le con­férenci­er Neil Sorrell, qui avait étudié la sāraṅgī avec le renom­mé Ram Narayan. La lit­téra­ture disponible à cette époque était rel­a­tive­ment rare, mais deux textes en par­ti­c­uli­er étaient tout de même très influ­ents : « Tabla in Perspective » de Rebecca Stewart (UCLA, 1974), qui a nour­ri en moi un intérêt musi­cologique pour les var­iétés et les com­plex­ités du rythme et le jeu des per­cus­sions et « The Cultural Structure and Social Organization of Musicians in India : the Perspective from Delhi » de Daniel Neuman (Université de l'Illinois, Urbana-Champaign, 1974), un aperçu socio-anthropologique du monde des musi­ciens tra­di­tion­nels et hérédi­taires indi­ens et de leurs points de vue.

 J’ai donc com­mencé à appren­dre le tablā à par­tir des dis­ques 33 tours et des livrets de Robert Gottlieb appelés « 42 Lessons for Tabla », et après quelques mois, j'avais appris suff­isam­ment de tech­niques de base pour accom­pa­g­n­er F. Silkstone lors d’un réc­i­tal. J'ai ensuite été l’élève de Manikrao Popatkar, un excel­lent joueur de tablā pro­fes­sion­nel qui venait d’immigrer en Grande-Bretagne. J'étais « accro » ! De plus, la pen­sée que je pour­rais entr­er dans ce monde socio-musical du tablā en Inde en qual­ité de participant-observateur m'a motivée à chercher des pro­grammes d'études supérieures où je pour­rais dévelop­per mes con­nais­sances et com­pé­tences tout en com­bi­nant les approches musi­cologiques et anthro­pologiques de R. Stewart et D. Neuman. Sur les con­seils de N. Sorrell, j'ai donc écrit à John Blacking au sujet de la pos­si­bil­ité d'étudier à l'Université Queen's de Belfast, et John a été très encour­ageant, en m'offrant une entrée directe au pro­gramme de doc­tor­at. Il a égale­ment souligné que son col­lègue John Baily avait récem­ment écrit un texte : « Krishna Govinda's Rudiments of Tabla Playing ». J'avais trou­vé le pro­gramme d'études supérieures idéal et des guides parfaits.

Approches méthodologiques

« How Musical Is Man » de J. Blacking est un texte fon­da­men­tal paru en 1973, à contre-courant de la pen­sée de l’époque, refu­sant les fron­tières entre musi­colo­gie et eth­no­mu­si­colo­gie ain­si que les oppo­si­tions stériles entre les tra­di­tions musi­cales. J. Blacking avance égale­ment l’idée essen­tielle que la musique, même si ce mot n’existe pas partout, est présente à tra­vers toutes les cul­tures humaines, en ce qu’elle résulte du « son humaine­ment organ­isé ». Sais-tu s’il con­nais­sait les pro­pos d’E. Varèse ? Voulant lui aus­si se démar­quer de la sig­ni­fi­ca­tion occi­den­tale du con­cept de « musique », bien que pour d’autres raisons, il avait avancé en 1941 l’expression de « son organisé ».

Je ne me sou­viens pas que J. Blacking ait men­tion­né Varèse ou ses réflex­ions sur la nature de la musique. John était par con­tre un excel­lent musi­cien et pianiste qui avait sans doute ren­con­tré et étudié beau­coup de musique d'art occi­den­tal, et il est donc pos­si­ble qu'il ait con­nu la déf­i­ni­tion de Varèse. Cependant, alors que la philoso­phie de Varèse est née de la con­vic­tion que les machines et les tech­nolo­gies seraient capa­bles d'organiser le son, J. Blacking a voulu porter l’attention sur la musique comme fait social : une activ­ité où la mul­ti­tude des façons dont les êtres humains pro­duisent leurs sons, à la fois comme inter­prètes et surtout comme audi­teurs, per­me­t­trait de révéler beau­coup de choses sur leur struc­ture sociale.

En quoi tes études uni­ver­si­taires ont-elles ori­en­té tes recherches ?

J'ai eu la chance d'avoir non pas un mais deux men­tors : J. Blacking et J. Baily, tous deux très dif­férents. J. Blacking regorgeait d’idées, grandes et inspi­rantes, qui ont défié et révo­lu­tion­né la façon dont on pense la musique et la société, tan­dis que J. Baily a mis l'accent sur une approche plus méthodique et empirique fondée sur la per­for­mance musi­cale et sur la ges­tion scrupuleuse de l'acquisition et la doc­u­men­ta­tion des données.

Il ne faut pas oubli­er que j'étais jeune et inex­péri­men­té lorsque j'ai entre­pris ce tra­vail de ter­rain, et donc l'exemple de J. Baily, axé sur la musique et la col­lecte de don­nées, m’a servi de guide pra­tique dans ma vie quo­ti­di­enne pen­dant mes années en Inde. Et lorsque j’avais en ma pos­ses­sion un énorme cor­pus de don­nées, j'ai pu pren­dre du recul et, inspiré par J. Blacking, j’ai pu iden­ti­fi­er cer­tains des grands mod­èles que ces don­nées met­taient en lumière. J'ai donc été frap­pé par le réc­it cohérent du déclin cul­turel lié à la nos­tal­gie d'un passé glo­rieux et artis­tique­ment abon­dant, et la tra­di­tion musi­cale du tablā de Lucknow était l'un des derniers liens vivants avec ce monde per­du. Cela est devenu l'un des thèmes clés de ma thèse de doc­tor­at et de cer­tains des autres travaux qui ont suivi. Quant à ma car­rière d'enseignant, j'ai essayé au fil des ans de com­bin­er les meilleures qual­ités de mes deux maîtres, tout en pro­mou­vant tou­jours l'idée que, dans les recherch­es por­tant sur la musique et la vie musi­cale, la théorie devrait naître à par­tir de don­nées solides et ne jamais ignor­er le dia­logue avec la réal­ité ethno­graphique afin de préserv­er ain­si sa valeur heuristique.

Dans « Working with the Masters » (2008), tu décris avec détails et fran­chise (ce qui est assez rare dans la pro­fes­sion !…) ton expéri­ence de ter­rain dans les années 1980 avec Afaq Hussain. Cette expéri­ence, et le réc­it que tu en fais, appa­rais­sent comme un mod­èle pour toute recherche en eth­nolo­gie et en eth­no­mu­si­colo­gie avec la par­tic­u­lar­ité de l’apprentissage musi­cal. Tu rends compte ain­si des phas­es d’approche, de ren­con­tre, de test et, enfin (et heureuse­ment dans ton cas) d’acceptation au sein de l’environnement étudié et de la con­fi­ance accordée per­me­t­tant de déploy­er pleine­ment ses inten­tions de recherche et d’apprentissage musi­cal. Tu abor­des aus­si les réflex­ions éthiques et déon­tologiques indis­pens­ables au chercheur : rela­tion aux autres, con­flits de loy­auté résul­tant des pos­si­bles dis­so­nances entre le rap­port à l’informateur et les objec­tifs ethno­graphique, respon­s­abil­ités vis à vis du savoir récolté et place du chercheur-musicien dans la réal­ité musi­cale de la tra­di­tion étudiée. Au-delà des par­tic­u­lar­ités du con­texte musi­cal, y a-t-il des spé­ci­ficités indi­ennes que les chercheurs occi­den­taux doivent avoir en tête pour entre­pren­dre (et espér­er réus­sir) une étude eth­nologique en Inde ?

La société sud-asiatique a énor­mé­ment changé au cours des 40 années qui se sont écoulées, c’est une évi­dence, et ce depuis que j'ai com­mencé à men­er des recherch­es ethno­graphiques. Mais cer­tains principes, ceux qui devraient guider le proces­sus d'enquête,  demeurent inébran­lables. C’est le cas du pro­fond respect pour la dimen­sion de l'ancienneté, qu’elle soit sociale ou cul­turelle. Naturellement, l'accès à une com­mu­nauté est la clef de voute, et il n'y a pas de meilleur « gate­keep­er » ou « spon­sor » (pour utilis­er les ter­mes anthro­pologiques) qu'une fig­ure d'autorité au sein de la sous-culture que l'on étudie, puisque la per­mis­sion que l'on reçoit se réper­cute sur la hiérar­chie sociale et famil­iale. Le dan­ger, dans une société forte­ment patri­ar­cale comme celle de l'Inde, est que l'on se retrou­ve avec une vision hiérar­chique descen­dante de la vie musi­cale. Si j'avais l'occasion de repren­dre mes recherch­es dans ce domaine, j'accorderais une plus grande atten­tion à ceux qui se trou­vent à dif­férents niveaux de cette hiérar­chie, en par­ti­c­uli­er aux femmes et à la musi­cal­ité quo­ti­di­enne de la vie dans la sphère domes­tique. En se con­cen­trant unique­ment sur les aspects les plus raf­finés de la pro­duc­tion cul­turelle, on peut pass­er à côté de ce qui a de la valeur dans la for­ma­tion des idées, de l'esthétique et des mécan­ismes de sou­tien néces­saires à la survie et à l'épanouissement d'une tra­di­tion artistique.

 Sur une note plus prag­ma­tique (et qui con­cerne plus sou­vent il me sem­ble les aspects relat­ifs au tra­vail sur le ter­rain), j'ai trou­vé que les entre­tiens formels enreg­istrés étaient rarement très fructueux parce qu'ils étaient ressen­tis comme intim­i­dants et étaient accom­pa­g­nés d'attentes élevées. En out­re, une sen­si­bil­ité accrue aux ram­i­fi­ca­tions poli­tiques – micro et macro – nous engageant à par­ler selon nos con­vic­tions, représen­tait sou­vent un obsta­cle à la col­lecte d'informations. En vérité, offi­cieuse­ment et dans des cir­con­stances déten­dues, moins je demandais et plus j'écoutais, plus l'information que je rece­vais était utile et intéres­sante. La mise en garde est que pour fonc­tion­ner de cette manière, il faut dévelop­per un niveau de patience que la plu­part des Occidentaux auraient du mal à accepter.

Fig. 1 : Séance d’enregistrement d’Afaq Hussain chez James Kippen, Lucknow, 1982,  pho­to de James Kippen

Tu adoptes dans les années 1980 l’« approche dialec­tique » enseignée par J. Blacking en y asso­ciant l’informatique et un pro­gramme d’IA. Le but était d’analyser les fonde­ments du jeu impro­visé des joueurs de tablā. Peux-tu revenir sur la genèse et l’évolution de cette approche ?

J. Blacking était par­ti­c­ulière­ment intéressé par le tra­vail de Noam Chomsky sur les gram­maires trans­for­ma­tion­nelles. Il théori­sait sur le fait que l'on pou­vait créer des ensem­bles de règles pour la musique – une gram­maire – avec plusieurs « couch­es » ; la pre­mière décrirait com­ment ces struc­tures sonores de sur­face étaient organ­isées. Les autres plus pro­fondes, com­prendraient des règles abor­dant des principes de plus en plus généraux sur l'organisation musi­cale et, au niveau le plus pro­fond, la gram­maire for­malis­erait les règles régis­sant les principes de l'organisation sociale. Si le but ultime d'un eth­no­mu­si­co­logue est de reli­er la struc­ture sociale à la struc­ture sonore, ou vice ver­sa, alors c'était cette idée que J. Blacking défendait pour attein­dre cet objectif.

L’été 1981, j'ai fui la chaleur intense des plaines du nord de l'Inde et me suis réfugié près de Mussoorie dans les con­tre­forts de l'Himalaya. J'avais con­venu de retrou­ver mon ami F. Silkstone, qui à l'époque étu­di­ait le sitār avec Imrat Khan et le dhru­pad avec Fahimuddin Dagar à Calcutta. Francis est arrivé avec Fahimuddin et l'un des étu­di­ants améri­cains de Fahim, Jim Arnold. Jim et Bernard Bel (un infor­mati­cien et math­é­mati­cien qui vivait à l'époque à New Delhi) tra­vail­laient ensem­ble pour un pro­jet expéri­men­tal sur l'intonation dans le rāga. Bernard est alors arrivé à Mussoorie, égale­ment pour échap­per à la chaleur, et pen­dant env­i­ron un mois nous avons tous vécu ensem­ble dans un envi­ron­nement riche et fer­tile de musique et d'idées. C'est là que Bernard et moi avons dis­cuté pour la pre­mière fois de la notion des gram­maires socio-musicales de J. Blacking, ain­si que de ma fas­ci­na­tion pour un type de com­po­si­tion des joueurs de tablā, avec une struc­ture offrant un thème et des vari­a­tions, con­nues sous le nom de qāi­da. J’étais très curieux d’apprendre que Bernard pou­vait con­cevoir un pro­gramme infor­ma­tique capa­ble de mod­élis­er le proces­sus de créa­tion de vari­a­tions à par­tir d'un thème donné.

L'année suiv­ante, Bernard et moi nous sommes ren­con­trés à plusieurs repris­es : il en a appris beau­coup plus sur le fonc­tion­nement du tablā et j'ai beau­coup appris sur la lin­guis­tique math­é­ma­tique. Ensemble, nous avons créé des ensem­bles de règles – des gram­maires trans­for­ma­tion­nelles – qui ont généré des vari­a­tions à par­tir d'un thème de qāi­da et traité des vari­a­tions exis­tantes pour déter­min­er si nos règles pou­vaient en tenir compte. Mais il était évi­dent que les con­nais­sances mod­élisées étaient les miennes et non celles de musi­ciens experts. Alors nous avons dévelop­pé une stratégie pour impli­quer ces experts en tant que « col­lab­o­ra­teurs et ana­lystes » (une expres­sion sou­vent util­isée par J. Blacking) dans un échange dialec­tique. Après tout, un « sys­tème expert » était des­tiné à mod­élis­er les con­nais­sances d'experts, et il n'y avait pas de meilleur expert qu'Afaq Hussain.

➡ Pour plus d’informations sur ces expéri­ences, voir : https://bolprocessor.org/bp1-in-real-musical-context/

Avais-tu con­nais­sance d’autres types de démarch­es inter­ac­tives comme celle du re-recording dévelop­pée un peu plus tôt par S. Arom ?

J'étais au courant des méth­odes inter­ac­tives de S. Arom pour obtenir les pro­pres per­spec­tives des musi­ciens sur ce qui se pas­sait dans leur musique, tout comme j'étais au courant des travaux en anthro­polo­gie cog­ni­tive visant à déter­min­er les caté­gories cog­ni­tives sig­ni­fica­tives pour les per­son­nes que nous étudi­ions. La thèse de S. Arom selon laque­lle les don­nées cul­turelles devaient être validées par nos inter­locu­teurs a cer­taine­ment été très influ­ente. Je ne con­nais­sais pas d'autres approches. Les exi­gences de notre sit­u­a­tion expéri­men­tale par­ti­c­ulière nous ont oblig­és à inven­ter notre pro­pre méthodolo­gie unique pour ce proces­sus d’interaction homme-machine.

On con­naît la crainte des maîtres indi­ens d’une dif­fu­sion de leurs savoirs au-delà de leur gharānā, et en par­ti­c­uli­er cer­taines tech­niques et com­po­si­tions. Quelles étaient l’attitude et l’implication d’Afaq Hussain dans cette démarche qui met­tait à jour les struc­tures des qāida ?

Afaq Hussain n'était pas du tout préoc­cupé par les révéla­tions con­cer­nant le qāi­da puisque l'art de les jouer dépendait de sa capac­ité à impro­vis­er. En d’autres ter­mes, il s’agissait d’une activ­ité axée sur les proces­sus et donc en con­stante évo­lu­tion. A l’inverse, les com­po­si­tions fix­es, en par­ti­c­uli­er celles trans­mis­es de généra­tion en généra­tion au sein de la famille, ne changeaient pas. Celles-ci étaient con­sid­érées comme des atouts pré­cieux et étaient soigneuse­ment gardées.

 Lorsque je repense aux expéri­ences sci­en­tifiques, je m'étonne que Bernard ait pu créer une gram­maire généra­tive aus­si puis­sante pour un ordi­na­teur (d'abord un Apple II avec 64k RAM, puis le portable 128k Apple IIc) avec une puis­sance de traite­ment et un espace aus­si lim­ité. Afaq Hussain s'est égale­ment éton­né qu'une machine « puisse penser », pour repren­dre son expres­sion. Nous avons com­mencé par une gram­maire de base pour un qāi­da don­né, puis généré quelques vari­a­tions, et je les ai ensuite lues à voix haute en util­isant la langue syl­labique, les bols pour tablā. De nom­breux résul­tats étaient prévis­i­bles, cer­tains étaient inhab­ituels mais néan­moins accept­a­bles, et d'autres ont été jugés erronés – tech­nique­ment et esthé­tique­ment. Nous avons ensuite demandé à Afaq Hussain de pro­pos­er ses pro­pres vari­a­tions ; celles-ci ont été intro­duites dans l'ordinateur (j’ai effec­tué la saisie en util­isant un sys­tème de cor­réla­tion de clés pour gag­n­er en rapid­ité) et « analysées » pour déter­min­er si les règles de notre gram­maire pou­vaient en tenir compte. De sim­ples ajuste­ments aux règles étaient pos­si­bles in situ, mais lorsqu'une repro­gram­ma­tion plus com­plexe était néces­saire, nous pas­sions à un deux­ième exem­ple et reve­nions à l’exemple d'origine dans une ses­sion ultérieure.

Fig. 2 : James Kippen, Afaq Hussain et son fils Ilmas Hussain, Lucknow, 1982, pho­to de James Kippen

Est-ce que ces recherch­es ont con­cerné d’autres types de com­po­si­tion comme les gat ou les tukra ?

Non. L'avantage d’observer une struc­ture de thème et de vari­a­tions comme celle des qāi­da est fondé sur le fait que chaque com­po­si­tion est un sys­tème fer­mé où les vari­a­tions (vistār) sont lim­itées aux élé­ments présen­tés dans le thème. Le but est donc de com­pren­dre les règles non écrites pour créer des vari­a­tions. Les com­po­si­tions fix­es comme les gat, ṭukṛā, paran, etc., com­pren­nent une var­iété d'éléments beau­coup plus large et plus imprévis­i­ble, et seraient ain­si très dif­fi­ciles à mod­élis­er. Cependant, nous avons pu expéri­menter sur le type de com­po­si­tion appelé tihāī : la phrase répétée trois fois qui agit comme une cadence ryth­mique finale. Cette dernière peut être mod­élisée math­é­ma­tique­ment afin d’obtenir une for­mule arith­mé­tique dans laque­lle on peut pro­pos­er des phras­es ryth­miques, puis être appliquée soit à un qāi­da (un frag­ment de son thème ou l'une de ses vari­a­tions), soit à des com­po­si­tions fix­es comme par exem­ple le ṭukṛā.

Est-ce que cer­taines phras­es ryth­miques générées par l’ordinateur et validées par Afaq Hussain ont inté­gré le réper­toire du gharānā de Lucknow ?

C'est une ques­tion dif­fi­cile. Lorsque nous étions au milieu d'une péri­ode inten­sive d'expérimentation avec le « Bol Processor », une sorte de dia­logue se met­tait en bran­le où Afaq Hussain alter­nait des phras­es ryth­miques générées par ordi­na­teur avec des ensem­bles de vari­a­tions qui lui étaient pro­pres. Tant de com­po­si­tions ont été générées et alternées de cette manière qu'il était sou­vent dif­fi­cile de savoir si le réper­toire qu'il jouait en con­cert prove­nait de l'ordinateur ou pas. Pourtant, alors que cer­tains enseignants et inter­prètes dévelop­pent un réper­toire de vari­a­tions fix­es provenant d’un thème, Afaq Hussain lui l'a rarement fait, s'appuyant plutôt sur son imag­i­na­tion « dans l'instant ». C'est aus­si l'approche qu'il a encour­agée en nous. Par con­séquent, je doute que le matériel généré par ordi­na­teur soit devenu une par­tie per­ma­nente du répertoire.

Est-ce que ce type d’approche spé­ci­fique util­isant l’IA en eth­no­mu­si­colo­gie a été pour­suivi par d’autres ?

Le terme « Intelligence Artificielle » a fait l'objet d'un change­ment rad­i­cal dans les années 1980-1990 grâce au développe­ment de l'approche « con­nex­ion­niste » (les neu­rones arti­fi­ciels) et de tech­niques d'apprentissage à par­tir d'exemples capa­bles de traiter une grande masse de don­nées. Avec le Bol Processor (BP) nous étions au stade de la mod­éli­sa­tion symbolique-numérique de déci­sions humaines représen­tées par des gram­maires formelles, ce qui exigeait une con­nais­sance appro­fondie, bien qu'intuitive, des mécan­ismes de décision.

Pour cette rai­son, les approches symboliques-numériques n'ont pas été repris­es par d'autres équipes à ma con­nais­sance. Par con­tre, nous avions aus­si abor­dé l'apprentissage automa­tique (de gram­maires formelles) à l'aide du logi­ciel QAVAID écrit sous Prolog II. Nous avons ain­si mon­tré que la machine devait col­lecter des infor­ma­tions en dia­loguant avec le musi­cien pour effectuer une seg­men­ta­tion cor­recte des phras­es musi­cales et amorcer un tra­vail de général­i­sa­tion par inférence induc­tive. Mais ce tra­vail n'a pas été pour­suivi car les machines étaient trop lentes et nous ne dis­po­sions pas de cor­pus assez grands pour con­stru­ire un mod­èle cou­vrant une grande var­iété de mod­èles d'improvisation.

Il se peut que des chercheurs indi­ens fassent appel à de l'apprentissage à par­tir d'exemples – qu'on appelle aujourd'hui « Intelligence Artificielle » – pour traiter de grandes mass­es de don­nées pro­duites par des per­cus­sion­nistes. Cette approche « big data » a le défaut de man­quer de pré­ci­sion dans un domaine où la pré­ci­sion est un mar­queur d'expertise musi­cale, et de ne pas pro­duire des algo­rithmes com­préhen­si­bles qui con­stitueraient une « gram­maire générale » de l'improvisation sur un instru­ment de per­cus­sion. Notre ambi­tion ini­tiale était de con­tribuer à la con­struc­tion de cette gram­maire, mais nous avons seule­ment prou­vé, avec la tech­nolo­gie de l'époque, que ce serait réalisable.

Fig. 3 : Bhupal Ray Chowdhury (dis­ci­ple de Wajid Hussain et son fils Afaq Hussain) et J. Kippen en séance d’expérimentation avec le Bol Processor, Calcutta, 1984, pho­to de James Kippen

Dans les ver­sions ultérieures, ce logi­ciel a pu pro­cur­er égale­ment de la matière et des out­ils pour le tra­vail de com­po­si­tion en musique et en danse au-delà du con­texte indi­en. On fêtera en 2021 les 40 ans de ce logi­ciel avec une nou­velle ver­sion. Quels sont les artistes qui ont util­isé le logiciel ? 

Des com­po­si­tions ryth­miques pro­gram­mées sur BP2 et inter­prétées sur un syn­thé­tiseur Roland D50 ont été util­isées pour l'œuvre choré­graphique CRONOS dirigée par Andréine Bel et pro­duite en 1994 au NCPA de Bombay. Voir par exem­ple https://bolprocessor.org/shapes-in-rhythm/.

A la fin des années 1990, le com­pos­i­teur néer­landais H. Visser a util­isé BP2 pour con­tribuer au développe­ment d'opérateurs per­me­t­tant la com­po­si­tion de musique sérielle. Voir par exem­ple https://bolprocessor.org/harm-vissers-examples/.

Nous avons eu des retours et deman­des d'universitaires européens et améri­cains qui utilisent BP2 comme out­il péd­a­gogique pour l'enseignement de la com­po­si­tion musi­cale. Mais nous n'avons jamais fait de cam­pagne « pub­lic­i­taire » à grande échelle pour agrandir la com­mu­nauté d'utilisateurs, étant intéressés en pri­or­ité par le développe­ment du sys­tème et la recherche musi­cologique qui lui est associée.

La prin­ci­pale lim­ite de BP2 était son fonc­tion­nement exclusif dans l'environnement Mac. C'est pourquoi la ver­sion BP3 en cours de développe­ment est mul­ti­plate­forme. Elle sera vraisem­blable­ment mise en ser­vice en ver­sion « Cloud » ren­du pos­si­ble par son inter­ac­tion étroite avec le logi­ciel Csound. Ce logi­ciel per­met de pro­gram­mer des algo­rithmes per­for­mants de pro­duc­tion sonore et de tra­vailler avec des mod­èles d'intonation micro­tonale que nous avons dévelop­pés, aus­si bien pour la musique har­monique que pour le raga indi­en – voir https://bolprocessor.org/category/related/musicology/.

Etudes de la notation, du mètre, du rythme et de leurs évolutions

Au fil de ton tra­vail, la ques­tion de la nota­tion musi­cale occupe une place impor­tante autant sur le plan de la méthodolo­gie que sur celui de la réflex­ion à pro­pos de son usage. Tu as mis en place ton pro­pre sys­tème afin de représen­ter le plus rigoureuse­ment pos­si­ble tes analy­ses des com­po­si­tions de tablā et de pakhā­vaj. Peux-tu nous par­ler de cet aspect de ton travail ? 

Toutes les nota­tions écrites sont des approx­i­ma­tions incom­plètes et leur con­tri­bu­tion au proces­sus de trans­mis­sion est lim­ité. Les représen­ta­tions orales, comme les suites de syl­labes énon­cées (bols) représen­tant des frappes de per­cus­sion, trans­met­tent sou­vent des infor­ma­tions plus pré­cis­es sur la musi­cal­ité inhérente aux mod­èles, tels que l’accentuation, l'inflexion, le phrasé et la vari­abil­ité micro-rythmique. De même, une fois intéri­or­isées, ces syl­labes sont indélé­biles. Nous savons que les sys­tèmes oraux favorisent une bonne mémoire musi­cale, ce qui est par­ti­c­ulière­ment impor­tant dans le con­texte de la per­for­mance musi­cale en Inde où les inter­prètes ne com­men­cent qu'avec une feuille de route très générale, mais pren­nent ensuite toutes sortes de détours inat­ten­dus. Dans cette per­spec­tive, on pour­rait se deman­der pourquoi écrire quoi que ce soit ?

À par­tir des années 1860, il y a eu un essor des nota­tions musi­cales en Inde, inspiré il me sem­ble par la prise de con­science que la musique occi­den­tale pos­sé­dait un sys­tème de nota­tion effi­cace, et sus­cité aus­si par l'augmentation con­stante de l'apprentissage insti­tu­tion­nal­isé et d’un besoin appar­ent de textes péd­a­gogiques et de réper­toires. Pourtant, il n'y a jamais eu de con­sen­sus sur la façon de not­er, et chaque nou­veau sys­tème dif­férait grande­ment des autres. La nota­tion conçue en 1903 par Gurudev Patwardhan était sans doute la plus détail­lée et la plus pré­cise jamais créée pour les per­cus­sions comme le tablā et le pakhā­vaj, mais elle était sûre­ment trop com­pliquée pour que les étu­di­ants la lisent comme une par­ti­tion. Son objec­tif pre­mier était donc davan­tage d'être un ouvrage de référence qui préser­vait le réper­toire et four­nis­sait un pro­gramme pour un appren­tis­sage structuré.

Nous vivons dans un monde de l’écrit et les musi­ciens recon­nais­sent que leurs élèves ne con­sacrent plus leurs journées entières à la pra­tique. Comme d'autres pro­fesseurs, Afaq Hussain nous a tous encour­agés à écrire le réper­toire qu'il enseignait pour qu'il ne soit pas oublié. Pour moi, il était par­ti­c­ulière­ment impor­tant de saisir deux aspects dans mes pro­pres cahiers : la pré­ci­sion ryth­mique et les doigtés pré­cis. En ce qui con­cerne ce dernier, par exem­ple, face à la phrase keṛe­na­ga tirak­iṭa takata­ka tirak­iṭa, je m’assurais de not­er cor­recte­ment le doigté pré­cis dans la douzaine de tech­niques pos­si­bles pour takata­ka, sans par­ler des var­iétés de keṛe­na­ga, et j’indiquais égale­ment que les deux ver­sions de tirak­iṭa avaient été jouées légère­ment différemment.

Afaq Hussain a gardé ses pro­pres cahiers rangés en toute sécu­rité dans une armoire ver­rouil­lée. Il les con­sul­tait par­fois. Je pense qu'il avait con­science du fait que le réper­toire dis­parais­sait effec­tive­ment avec la tra­di­tion orale. Après tout, il y a des cen­taines, voire des mil­liers de morceaux de musique. Son grand-père, Abid Hussain (1867-1936) fut le pre­mier pro­fesseur de tablā au Bhatkhande Music College de Lucknow. Lui aus­si a noté des com­po­si­tions de tablā, et j'ai en ma pos­ses­sion des cen­taines de pages qu'il a écrites sans aucun doute pour être pub­liées sous forme de texte péd­a­gogique. Cependant, il n'a pas indiqué de rythmes ou de doigtés pré­cis, et l'interprétation de sa musique est donc prob­lé­ma­tique, même pour le fils d'Afaq Hussain, Ilmas Hussain, avec qui j'ai passé tout son réper­toire au peigne fin. Une nota­tion pré­cise a donc de la valeur, si elle est accom­pa­g­née d'une tra­di­tion orale qui peut ajouter toutes les infor­ma­tions néces­saires pour don­ner vie à la musique.

Avec tes recherch­es récentes sur de nom­breux textes indo-persans des XVIIIe et XIXe siè­cles, tu mets en évi­dence l’évolution de la représen­ta­tion de la métrique en Inde. Ces recherch­es illus­trent l’importance de l’approche his­torique et met­tent en évi­dence pleine­ment les mécan­ismes d’évolution des faits cul­turels. Quels sont les con­cepts que tu utilis­es pour décrire ces phénomènes ?

Une facette impor­tante de notre for­ma­tion anthro­pologique était d'apprendre à fonc­tion­ner dans la langue de ceux avec qui nous nous sommes engagés dans nos recherch­es, non seule­ment pour gér­er la vie au quo­ti­di­en, mais aus­si pour avoir accès à des con­cepts qui sont sig­ni­fi­cat­ifs dans la cul­ture étudiée. Deux ter­mes sont impor­tants à cet égard, l'un dont l'importance est à mon avis exagérée, l'autre sous-estimée. Premièrement, gharānā, qui depuis sa pre­mière appari­tion dans les années 1860 sig­nifi­ait « famille » mais qui, au fil du temps, en est venu à englober toute per­son­ne qui croit partager cer­tains élé­ments de tech­nique, de style ou de réper­toire avec une per­son­ne dom­i­nante du passé. Deuxièmement, sil­si­la, un terme com­mun dans le soufisme qui sig­ni­fie « chaîne, con­nex­ion ou suc­ces­sion », et qui a une per­ti­nence spé­ci­fique dans le cas de l’enseignement dans une lignée de musi­ciens. C'est cette sil­si­la plus pré­cise qui détient, selon moi, la clé de la trans­mis­sion de la cul­ture musi­cale, et pour­tant le para­doxe est que la chaîne porte en elle une direc­tive implicite pour explor­er l’individualité créa­trice. C'est pourquoi, par exem­ple, lorsque l'on exam­ine la lignée des joueurs de tablā de Delhi à par­tir du milieu du XIXe siè­cle, on con­state des dif­férences majeures de tech­nique, de style et de réper­toire d'une généra­tion à l'autre. Il en va de même pour mon pro­fesseur Afaq Hussain, dont le jeu dif­férait grande­ment de celui de son père et enseignant Wajid Hussain. Chaque indi­vidu hérite d'une cer­taine essence musi­cale dans la sil­si­la, bien sûr, mais il doit s'engager et opér­er dans un monde en con­stante évo­lu­tion où la survie artis­tique néces­site une adap­ta­tion. Il est donc d'une impor­tance vitale lors de l'étude de toute époque musi­cale de recueil­lir autant d'informations que pos­si­ble sur le milieu socio­cul­turel observé.

Comme je viens de le démon­tr­er, il est impératif de s'engager avec des con­cepts de la cul­ture, de les expli­quer et de les utilis­er sans recourir à la tra­duc­tion. Un autre excel­lent exem­ple est celui du terme tāla, qui est le plus sou­vent traduit par mètre ou cycle métrique. Et pour­tant, il y a une dif­férence fon­da­men­tale entre les deux. Le mètre est implicite : c'est un motif qui est dérivé des rythmes de sur­face d'une pièce, et se com­pose d'une impul­sion sous-jacente qui est organ­isée en une séquence hiérar­chique récur­rente de bat­te­ments forts et faibles. Mais, par con­traste, tāla est explicite : c'est un motif récur­rent de bat­te­ments non hiérar­chiques se man­i­fes­tant par des gestes de la main con­sis­tant en des claps, des mou­ve­ments silen­cieux de la main et des comptes sur les doigts, ou comme une séquence rel­a­tive­ment fixe de frappes de per­cus­sion. Utiliser le terme « mètre » dans le con­texte indi­en est donc trompeur, et j'encourage donc l'utilisation de terme tāla avec une expli­ca­tion mais sans traduction.

Tu tra­vailles actuelle­ment sur un ouvrage con­cer­nant les sources du XVIIIe et XIXe siè­cles, quel est ton objectif ?

Mon objec­tif est de retrac­er les orig­ines et l'évolution du sys­tème du tāla actuelle­ment util­isé dans la musique hin­dous­tanie en rassem­blant autant d'informations que pos­si­ble à par­tir de sources con­tem­po­raines de la fin du XVIIe siè­cle jusqu’au début du XXe siè­cle et de l'ère de l’enregistrement. Le prob­lème est que les infor­ma­tions disponibles sont frag­men­taires et sou­vent rédigées dans un lan­gage obscur : la tâche s'apparente à un puz­zle où la plu­part des pièces man­quent. De plus, les sources que l'on trou­ve ne sont pas néces­saire­ment directe­ment con­nec­tées, et donc j’ai plutôt l’impression de tra­vailler avec deux ou plusieurs puz­zles à la fois. En bref, après une analyse minu­tieuse, des déduc­tions et des hypothès­es, je pense qu'il y a eu une con­ver­gence des sys­tèmes ryth­miques au XVIIIe siè­cle qui a don­né nais­sance au sys­tème du tāla d'aujourd'hui.

 Les pra­tiques musi­cales et les con­textes soci­aux des divers­es com­mu­nautés (les Kalāwant qui chan­taient le dhru­pad, les Qawwāl qui chan­taient le khayāl, le tarā­na et le qaul, ain­si que la com­mu­nauté des Ḍhāḍhī qui accom­pa­g­naient tous ces gen­res musi­caux), doivent impéra­tive­ment être pris en compte pour com­pren­dre com­ment et pourquoi la musique et le rythme en par­ti­c­uli­er, ont évolués comme ils l'ont fait. Pourtant, il y a tant d'autres aspects impor­tants dans cette his­toire : le rôle des femmes instru­men­tistes dans les espaces privés de la vie mog­hole au XVIIIe siè­cle, et leur dis­pari­tion pro­gres­sive au XIXe siè­cle, le colo­nial­isme, le statut et l'influence des textes anciens, les tech­niques d'impression et la dif­fu­sion de nou­veaux textes péd­a­gogiques à la fin du XIXe siè­cle, pour n'en citer que quelques-uns.

Quelles sont les sources intéres­santes à con­sid­ér­er pour com­pren­dre l’évolution des pra­tiques et des représen­ta­tions ryth­miques de la musique hindoustanie ?

Le nord de l'Inde a tou­jours été ouvert aux échanges cul­turels, et cela était par­ti­c­ulière­ment le cas sous les Moghols. Il est impératif de com­pren­dre qui se rendait dans ces cours, d'où ils venaient et ce qu'ils jouaient. Il est tout aus­si impor­tant de com­pren­dre les doc­u­ments écrits disponibles ain­si que les dis­cours intel­lectuels de l'époque, car la con­nais­sance de la musique était cru­ciale pour l'étiquette mog­hole. Ainsi, quand on sait que le traité de musique très influ­ent Kitāb al-adwār, du théoricien du XIIIe siè­cle Safi al-Din al-Urmawi al-Baghdadi, était large­ment disponible en Inde en arabe et en tra­duc­tion per­sane, et que des exem­plaires se trou­vaient dans la col­lec­tion des nobles de Delhi à par­tir du XVIIe siè­cle, on com­prend mieux pourquoi le rythme indi­en était expliqué en util­isant les principes de la prosodie arabe à la fin du XVIIIe siè­cle. Mon argu­ment est que la prosodie arabe, appliquée à la musique, était un out­il plus puis­sant que les méth­odes tra­di­tion­nelles de prosodie san­skrite, et qu’elle était donc plus effi­cace pour décrire les change­ments qui se pro­dui­saient dans la pen­sée et la pra­tique ryth­mique à cette époque.

Ces recherch­es ethno-historiques bous­cu­lent par­fois les croy­ances de cer­tains musi­ciens et chercheurs, notam­ment sur les ques­tions d’ancienneté et d’« authen­tic­ité » des tra­di­tions. Penses-tu que les musi­ciens d’aujourd’hui sont davan­tage enclins à accepter les évi­dences de la nature com­plexe des tra­di­tions musi­cales, for­mées de mul­ti­ples apports et en per­pétuelles transformations ?

Certains le sont, mais cer­tains ne le sont pas. Il y a tou­jours eu un petit nom­bre de chercheurs en Inde qui menaient des recherch­es pré­cieuses et factuelles sur la musique. Pourtant, je suis déçu de con­stater qu'il y en a beau­coup d'autres qui reposent sur le rabâchage et la dif­fu­sion d'opinions non fondées et non savantes. Ce qui me sur­prend peut-être le plus, c'est le manque de for­ma­tion sci­en­tifique rigoureuse dans les uni­ver­sités de musique en Inde et la per­sis­tance d'idées et d'informations réfutées ou dis­créditées en dépit de tant d'excellentes recherch­es pub­liées indi­quant le contraire.

Fig. 4 : J. Kippen, 2017, Université de Toronto. Photo de James Kippen

Depuis les années 1990, on con­state le ren­force­ment d’un nation­al­isme hin­dou au sein de la société indi­enne. Notes-tu un impact par­ti­c­uli­er sur le monde de la musique hin­dous­tanie et sur celui de la recherche ?

Il s’agit là d’un sujet com­plexe et sen­si­ble. Le nation­al­isme hin­dou n'est pas nou­veau, loin de là, et comme je l'ai démon­tré dans mon livre sur Gurudev Patwardhan, il a con­sti­tué une par­tie impor­tante de la rai­son d'être de la vie et de l'œuvre de Vishnu Digambar Paluskar au début du XXe siè­cle. Comme de nom­breux chercheurs l'ont souligné, ce nation­al­isme avait ses racines dans le colo­nial­isme et s'est dévelop­pé en tant que mou­ve­ment anti­colo­nial axé sur la poli­tique iden­ti­taire hin­doue. Ce réc­it, basé sur des notions inven­tées d'un passé hin­dou glo­rieux, a min­imisé les con­tri­bu­tions de la cul­ture mog­hole et des grandes lignées de musi­ciens musul­mans (sans par­ler des femmes). Depuis ce temps, l'identité musul­mane indi­enne dans le domaine de la musique a con­nu un cer­tain déclin. Les chercheurs ont pris note de cette chute et ont ten­té de retrac­er cer­tains des contre-récits qui ont jusqu'à présent été ignorés, comme l'excellent livre de Max Katz Lineage of Loss (Wesleyan University Press, 2017) sur une grande famille de musiciens-savants musul­mans, nom­mée Shahjahanpur-Lucknow gharānā. Je pense que dans de nom­breuses études actuelles qui por­tent sur la musique en Inde se trou­ve une forte moti­va­tion de ne pas omet­tre ces réc­its cul­turels impor­tants, de les réanimer et de les replac­er dans le grand réc­it de l'histoire de l'Asie du Sud.

A la suite de R. Stewart, tu as mis en évi­dence l’intrication com­plexe des approches ryth­miques et métriques dans le jeu des joueurs de tablā en mon­trant qu’il résulte de divers apports cul­turels qui se sont suc­cédés dans le temps. Avec l’intensification des échanges cul­turels mon­di­aux depuis la fin du XXe siè­cle, as-tu observé une ou des ten­dances évo­lu­tives dans le jeu des joueurs de tablā ?

Depuis l'inclusion du tablā dans la musique pop des années 1960, l’exaltante fusion jazz du groupe Shakti de John McLaughlin dans les années 1970 et l'omniprésence aujourd’hui du tablā dans la musique sous toutes ses formes, il sem­ble tout naturel que les joueurs de tablā du monde entier aient envie d’explorer et d’expérimenter ses sons mag­iques. Zakir Hussain a mon­tré la voie en démon­trant la flex­i­bil­ité et l'adaptabilité de cet instru­ment, ain­si que la véloc­ité vis­cérale et pal­pi­tante de ses motifs rythmiques.

Quant au tablā, dans le con­texte de la musique de con­cert hin­dous­tanie, j'ai remar­qué que nom­breux sont ceux qui ten­tent d'injecter ce même sen­ti­ment d'exaltation, ren­for­cé de plus en plus, semble-t-il, par une ampli­fi­ca­tion si forte qu'elle déforme le son et heurte les tym­pa­ns du pub­lic jusqu'à la soumis­sion.  J'irais jusqu'à dire que c'est mal­heureuse­ment devenu la norme. À cet égard, je me con­sid­ère comme une sorte de puriste qui aspire à un retour à une pra­tique où le joueur de tablā main­tient un rôle sub­til, dis­cret mais de sou­tien, et com­plète la ligne du soliste, en restant mod­este et sans domin­er la scène lorsqu'il est invité à faire une petite appari­tion ou un court solo. De la même manière, je désire un retour aux soli de tablā qui regor­gent de con­tenu plutôt que d’« effets sonores ». Par « con­tenu », j'entends des com­po­si­tions tra­di­tion­nelles de car­ac­tère, dotées de tech­niques spé­cial­isées, dont les com­pos­i­teurs sont nom­més et ain­si hon­orés. Et pour­tant, il est douloureuse­ment évi­dent qu'un tel « con­tenu » n'atteint pas beau­coup de jeunes joueurs de nos jours.

Ethnomusicologie

Comme évo­qué, tes recherch­es met­tent en avant l’importance des sources his­toriques aus­si bien que la prise en compte des phénomènes plus large comme l’orientalisme ou le nation­al­isme pour com­pren­dre le présent des pra­tiques musi­cales indi­ennes. En même temps tu es très atten­tif aux intens­es phénomènes tran­scul­turels actuels et à la néces­sité de les appréhen­der. Dans la pro­fes­sion, le con­cept d’« eth­no­mu­si­colo­gie » ne fait pas tou­jours con­sen­sus. Quelle est ta posi­tion par rap­port à cette appel­la­tion et à l’objet de cette dis­ci­pline en ce début du XXIe siècle ?

Je n'ai jamais été par­ti­c­ulière­ment à l'aise avec l'étiquette d’« eth­no­mu­si­colo­gie ». Comme dis­ait J. Blacking, toute musique est de la « musique eth­nique », et par con­séquent, il ne devrait pas y avoir de dis­tinc­tion entre les études sur le tablā, le game­lan, le hip-hop et celles sur Bach, Beethoven ou Brahms. Nous nous enga­geons tous dans un « dis­cours sur la musique », une « musi­colo­gie ». L'avantage de ter­mes comme « anthro­polo­gie » ou « soci­olo­gie » de la musique est qu'ils impliquent une gamme plus large d'approches théoriques et méthodologiques qui nous rap­pel­lent que la musique est un fait social. Pourtant, nous devons recon­naître que le champ des études eth­no­mu­si­cologiques a évolué et que, de nos jours, une atten­tion bien plus grande est accordée à des phénomènes comme le bruit ou les sons de la vie quo­ti­di­enne. Par con­séquent (sans vouloir paraître trop cynique) bien que dans cer­tains milieux les « sound stud­ies » soient traitées avec un cer­tain mépris, ce terme très général est peut-être la déf­i­ni­tion la plus hon­nête et la plus pré­cise de ce que nous (nous tous) faisons. Je recon­nais toute­fois qu'il serait dom­mage de rejeter com­plète­ment le terme « musique », et donc j’aime con­cevoir l'ethnomusicologie, la musi­colo­gie et la théorie musi­cale se réu­nis­sant sous la rubrique « musique et sound stud­ies ».

Enseignement

Après une courte péri­ode à Belfast, tu as enseigné à Toronto, peux tu nous par­ler de ton expéri­ence d’enseignement ?

Toronto est une ville mer­veilleuse et, selon la plu­part des témoignages, c'est la ville la plus mul­ti­cul­turelle de la planète. Elle offre un envi­ron­nement musi­cal très riche et stimulant.

Miecyzslaw Kolinski a enseigné à l'Université de Toronto de 1966 à 1978. Ses intérêts eth­no­mu­si­cologiques ont été façon­nés par sa for­ma­tion auprès de Hornbostel et Sachs, et par la vision d’un monde, partagée par tant de géants de notre dis­ci­pline. Ses pub­li­ca­tions por­tent sur les bases sci­en­tifiques de l'harmonie et de la mélodie et il a dévelop­pé des méth­odes d'analyse inter­cul­turelle. Son approche a été caté­gorique­ment rejetée dans ma pro­pre for­ma­tion avec John Blacking qui a tou­jours défendu avec véhé­mence le rel­a­tivisme cul­turel, tout comme cela était en con­tra­dic­tion avec la for­ma­tion de Tim Rice à l'Université de Washington. Tim a été embauché en 1974 et est par­ti pour l'UCLA en 1987. Comme moi à mes débuts, Tim a eu du mal à con­va­in­cre ses col­lègues de l'importance de l'approche eth­no­mu­si­cologique et de la néces­sité de traiter notre dis­ci­pline avec le respect qu'elle mérite et les ressources qu'elle néces­site. Nous avons tous les deux beau­coup lut­té. Tim a créé un pro­gramme qui est devenu con­nu sous ma direc­tion sous le nom « The World Music Ensembles », et pour ma part j'ai acquis un game­lan bali­nais en 1993, aidé par mon épouse, l'ethnomusicologue Annette Sanger, anci­enne col­lègue de J. Blacking. De plus, Tim et moi avons réus­si à inté­gr­er davan­tage les cours d'ethnomusicologie au cœur du pro­gramme pour nous assur­er que tous les étu­di­ants en musique, quels que soient leurs intérêts, soient exposés à notre approche et com­pren­nent la valeur et l'importance d'une vision sociale­ment fondée de toute musique. J’ai créé un cours d'introduction d'un an inti­t­ulé Music as Culture que j'ai co-enseigné pen­dant quelques années avec un col­lègue de musi­colo­gie : nous avons alterné nos cours, illus­trant et croisant notre cor­pus et nos obser­va­tions sur nos canons occi­den­taux et le vaste monde de la musique au-delà. Mon cours Introduction to Music & Society est devenu emblé­ma­tique. Mon approche étant essen­tielle­ment mod­u­laire, les thèmes choi­sis ont changé et se sont adap­tés au fil du temps pour refléter des préoc­cu­pa­tions plus con­tem­po­raines, notam­ment la musique et l'identité, l'expérience religieuse, la migra­tion, le genre, la guéri­son et les sound stud­ies.

Dans mes fonc­tions d’enseignant, j'ai conçu et enseigné une var­iété de cours : Hindustani music, Music & Islam, Theory & Method in Ethnomusicology, The Beatles, Anthropology of Music, Fieldwork, Music, Colonialism & Postcolonialism, Rhythm & Metre in Cross-Cultural Perspective, Transcription, Notation & Analysis, etc. J'ai tra­vail­lé avec la com­mu­nauté sud-asiatique de Toronto pour organ­is­er des con­certs du chanteur Pandit Jasraj. Ils ont attiré des spon­sors générant des bours­es d'études fiables pour des étu­di­ants dont les recherch­es por­taient sur la musique hin­dous­tanie. J'ai aidé à met­tre en place un pro­gramme d'artiste en rési­dence, invi­tant des musi­ciens du monde entier à pass­er un trimestre avec nous à enseign­er et à jouer. J'ai con­tribué à la refonte de nos pro­grammes d'études supérieures axés sur la musi­colo­gie et j'ai intro­duit dans le pro­gramme d’étude une maîtrise et un doc­tor­at en eth­no­mu­si­colo­gie. Mais les deux réal­i­sa­tions dont je suis sans doute le plus fier sont pre­mière­ment les nom­breux et mer­veilleux doc­tor­ants que j'ai encadrés, dont beau­coup ont eux-mêmes pour­suivi une car­rière dans le milieu uni­ver­si­taire, et deux­ième­ment le suc­cès de mon ini­tia­tive d’élargissement de notre représen­ta­tion : nous sommes passés d'un seul poste de pro­fesseur à qua­tre tit­u­laires à plein-temps en ethnomusicologie.

Quelle est ta place au sein du gharānā de Lucknow ?

J'ai beau­coup appré­cié appren­dre et jouer du tablā dans ma vie et je me con­sid­ère extrême­ment chanceux d'avoir eu un lien aus­si étroit et pro­duc­tif avec l'un des joueurs de tablā les plus remar­quables de l'histoire : Afaq Hussain. J'ai la chance d'avoir une bonne mémoire et j'ai donc encore dans ma tête un vaste réper­toire de com­po­si­tions mer­veilleuses remon­tant aux pre­miers mem­bres de la lignée Lucknow qui ont prospéré à la fin du XVIIIe et au début du XIXe siè­cle. Je suis par­ti­c­ulière­ment intéressé par la tech­nique et j'ai passé beau­coup de temps à étudi­er les mécan­ismes du jeu. Cependant, je suis avant tout un éru­dit et, en pra­tique, je ne me fais aucune illu­sion d’être guère plus qu’un ama­teur. En effet, mon intérêt pour le jeu m'a fourni des aperçus extra­or­di­naires de l'instrument et de son histoire.

Quant à ma place ou mon rôle au sein du gharānā de Lucknow, je dirais deux choses. Tout d'abord, je con­tin­ue à faire par­tie de l'échange d'idées et de réper­toire avec mes pairs aux côtés desquels j'ai étudié le tablā et qui font par­tie main­tenant, comme moi, des grandes fig­ures de la sil­si­la, la lignée directe de l’enseignement d'Afaq Hussain. Ils me con­sid­èrent comme un pro­fes­sion­nel avisé,  une autorité dans mon domaine. Parfois, on me demande si je me sou­viens d'une com­po­si­tion rare sur laque­lle il y a eu débat, et par­fois j'introduis dans notre dia­logue des infor­ma­tions et des ques­tions issues de mes recherch­es qui sus­ci­tent un vif intérêt. Par exem­ple, le fils d'Afaq Hussain, Ilmas Hussain, et moi-même avons tra­vail­lé ensem­ble pour ressus­citer les cahiers de son arrière-grand-père Abid Hussain et les plac­er dans leur con­texte, non seule­ment celui de leur tra­di­tion mais aus­si celui de la fin des années 1920 et du début des années 1930, années durant lesquelles Abid Hussain incar­nait le tout pre­mier pro­fesseur de tablā au Bhatkhande College de Lucknow. Enfin, je pense que mes travaux ont su attir­er une plus grande atten­tion sur la lignée de Lucknow. Quand je suis arrivé à la porte d'Afaq Hussain en jan­vi­er 1981, il était affaib­li – psy­chologique­ment et finan­cière­ment – et son avenir était incer­tain. D'autres étu­di­ants étrangers ont suivi mon exem­ple et ont rejoint un nom­bre tou­jours crois­sant de dis­ci­ples indi­ens venus pour appren­dre. Mon livre, The Tabla of Lucknow, ain­si que d'autres facettes de mes recherch­es ont donc bien con­tribué à attir­er l'attention nationale et inter­na­tionale sur Afaq Hussain, son fils Ilmas et toute leur tradition.

Liste des publications

Ouvrages         

2006                   Gurudev’s Drumming Legacy : Music, Theory and Nationalism in the Mrdang aur Tabla Vadanpaddhati of Gurudev Patwardhan. Aldershot : Ashgate (SOAS Musicology Series).

2005                   The Tabla of Lucknow : A Cultural Analysis of a Musical Tradition. New Delhi : Manohar (Nouvelle édi­tion avec nou­velle préface).

1988                   The Tabla of Lucknow : A Cultural Analysis of a Musical Tradition. Cambridge : Cambridge University Press (Cambridge Studies in Ethnomusicology).

Direction d’ouvrage          

2013                   avec Frank Kouwenhoven, Music, Dance and the Art of Seduction. Delft : Eburon Academic Publishers.

Direction de revue

1994-1996        Bansuri (A year­ly jour­nal devot­ed to the music and dance of India, pub­lished by Raga Mala Performing Arts of Canada). Volume 13, 1996 (60 pp), vol­ume 12, 1995 (60 pp), vol­ume 11, 1994 (64 pp).

Articles, chapitres d’ouvrages

À paraître           « Weighing ‘The Assets of Pleasure’: Interpreting the Theory and Practice of Rhythm and Drumming in the Sarmāya-i ‘Ishrat, a Pivotal 19th Century Text. », in Katherine Schofield, dir. : Hindustani Music Between Empires : Alternative Histories, 1748-1887. Éditeur à préciser.

À paraître           « An Extremely Nice, Fine and Unique Drum : A Reading of Late Mughal and Early Colonial Texts and Images on Hindustani Rhythm and Drumming. », in Katherine Schofield, Julia Byl et David Lunn, dir. : Paracolonial Soundworlds : Music and Colonial Transitions in South and Southeast Asia. Éditeur à préciser.

2021                   « Ethnomusicology at the Faculty of Music, University of Toronto. » MUSICultures (Journal of the Canadian Society for Traditional Music). Vol. 48.

2020                   « Rhythmic Thought and Practice in the Indian Subcontinent. » in Russell Hartenberger & Ryan McClelland, dir. : The Cambridge Companion to Rhythm. Cambridge University Press : 241-60.

2019                   « Mapping a Rhythmic Revolution Through Eighteenth and Nineteenth Century Sources on Rhythm and Drumming in North India. » In Wolf, Richard K., Stephen Blum, & Christopher Hasty, dir. : Thought and Play in Musical Rhythm: Asian, African, and Euro-American Perspectives. Oxford University Press : 253-72.

2013                   « Introduction. » In Frank Kouwenhoven & James Kippen, dir. : Music, Dance and the Art of Seduction. Delft : Eburon Academic Publishers : i-xix.

2012                   « On the con­tri­bu­tions of Pt. Sudhir V. Mainkar to our under­stand­ing of the tabla.” Souvenir Volume in Honour of Sudhir Vishnu Mainkar. Sharda Sangeet Vidyalaya : Mumbai.

2010                   « The History of Tabla. » In Joep Bor, Françoise ‘Nalini’ Delvoye, Jane Harvey and Emmie te Nijenhuis, dir. : Hindustani Music, Thirteenth to Twentieth Centuries. New Delhi : Manohar : 459-78.

2008                   « Working with the Masters. » In Gregory Barz and Timothy Cooley, dir. : Shadows in the Field : New Perspectives for Fieldwork in Ethnomusicology (2nd Edition révisée). Oxford University Press : 125–40.

2008                   « Hindustani Tala : An Introduction. » Concise Garland Encyclopedia of World Music. New York : Garland [ver­sion con­den­sée de la pub­li­ca­tion de 2000].

 2007                  « The Tal Paddhati of 1888 : An Early Source for Tabla. » Journal of the Indian MusicologicalSociety, 38 : 151–239.

2005                   « Lucknow » Encyclopedia of Popular Music of the World, Part 2, Vol. 5, Locations: Asia & Oceania. London : Continuum : 109–110.

2003                   « Le rythme: Vitalité de l'Inde. » In Gloire des princes, louange des dieux: Patrimoine musi­cal de l'Hindoustan du XIVe au XXe siè­cle. Paris : Cité de la musique et Réunion des Musées Nationaux 2003 :152–73.

2002                   « Wajid Revisited : A Reassessment of Robert Gottlieb’s Tabla Study, and a new Transcription of the Solo of Wajid Hussain Khan of Lucknow. » Asian Music, 33, 2 : 111–74.

2001                   « Asian Music [in Ontario]. » Garland Encyclopedia of World Music, Volume 3, The United States and Canada. New York : Garland Publishing : 1215–17.

2001                   « Folk Grooves and Tabla Tals. » ECHO: a music-centered jour­nal.  III: 1 (Spring 2001). En Ligne http://www.echo.ucla.edu/article-folk-grooves-and-tabla-tal-s-by-james-kippen/

2000                   « Hindustani Tala. » Garland Encyclopedia of World Music, Volume 5, South Asia: The Indian Subcontinent. New York : Garland Publishing : 110–37.

1998                   « What’s Wrong With Hindustani Music ? » Sruti (Madras), no.160 (réédi­tion de l’article parut dans Kala, 1996).

1998                   « Musings on Dhrupad, and an Interview with Falguni Mitra. » Kala, Volume 2, no.1 : 4.

1997                   « The Musical Evolution of Lucknow. » In Violette Graff, dir., Lucknow : Memories of a City. New Delhi : Oxford University Press : 181–95.

1996                   « A la recherche du temps musi­cal. » Temporalistes, 34 : 11-22 En ligne : http://temporalistes.socioroom.org/spip.php?article228

1996                   avec Andréine Bel « Lucknow Kathak Dance. » Bansuri (Journal of the Raga Mala Performing Arts of Canada), 13 : 42–50.

1996                   « What’s Wrong With Hindustani Music? » Kala, Volume 1, no.2, 1996 : 4–7.

1995                   Réponse à « Theory of Participatory Discrepancies » de Charles Keil Ethnomusicology, 39, 1 : 77–78.

1994                   « Computers, Composition, and the Challenge of ‘New Music’ in Modern India. » Leonardo Music Journal, 4 : 79–84.
https://hal.archives-ouvertes.fr/hal-00143124

1992                   « Tabla Drumming and the Human-Computer Interaction. » The World of Music, 34, 3 : 72–98.

1992                   « Music and the Computer : Some Anthropological Considerations. » Interface, 21, 3-4 : 257–62.

1992                   « Where Does The End Begin ? Problems in Musico-Cognitive Modelling. » Minds & Machines, 2, 4 : 329–44.

1992                   « Identifying Improvisation Schemata with QAVAID. » In Walter B. Hewlett & Eleanor Selfridge-Field, dir. : Computing in Musicology : An International Directory of Applications, Volume 8. Center for Computer Assisted Research in the Humanities :115–19.

1992                   « Bol Processor Grammars. » In M. Balaban, K. Ebcioglu, & O. Laske, dir. : Understanding AI with Music, AAAI Press : 367–400.
https://hal.archives-ouvertes.fr/hal-00256386

1992                   avec Bernard Bel « Modelling Music with Grammars : Formal Language Representation in the Bol Processor. » In A. Marsden & A. Pople, dir. : Computer Representations and Models in Music. London, Academic Press : 207–38.
https://halshs.archives-ouvertes.fr/halshs-00004506

1991                   avec Bernard Bel  « From Word-Processing to Automatic Knowledge Acquisition : A Pragmatic Application for Computers in Experimental Ethnomusicology. » in Ian Lancashire, dir. : Research in Humanities Computing I : Papers from the 1989 ACH-ALLC Conference, Oxford University Press : 238–53.

1991                   « Changes in the Social Status of Tabla Players. » Bansuri, 8 : 16–27, 1991. (réédi­tion de la pub­li­ca­tion de JIMS, 1989)

1990                   « Music and the Computer: Some Anthropological Considerations. » In B. Vecchione & B. Bel, dir. : Le Fait Musical — Sciences, Technologies, Pratiques, pré­fig­u­ra­tion des actes du col­loque Musique et Assistance Informatique, CRSM-MIM, Marseille, France, 3-6 Octobre : 41–50.

1989                   « Changes in the Social Status of Tabla Players. » Journal of the Indian Musicological Society, 20, 1 & 2 : 37–46.

1989                   « Can a Computer Help Resolve the Problem of Ethnographic Description? » Anthropological Quarterly, 62, 3 : 131–44.
https://hal.archives-ouvertes.fr/hal-00275429

1989                   Avec Bernard Bel « The Identification and Modelling of a Percussion ‘Language’, and the Emergence of Musical Concepts in a Machine-Learning Experimental Set-Up. » Computers and the Humanities, 23, 3 : 199–214.
https://halshs.archives-ouvertes.fr/halshs-00004505

1989                   « Computers, Fieldwork, and the Analysis of Cultural Systems. » Bulletin of Information on Computing and Anthropology, 7, 1989 : 1–7. En ligne : http://lucy.ukc.ac.uk/bicaweb/b7/kippen.html

1988                   « Computers, Fieldwork, and the Problem of Ethnomusicological Analysis. » International Council for Traditional Music (UK Chapter) Bulletin, 20 : 20–35.

1988                   Avec Bernard Bel « Un mod­èle d’inférence gram­mat­i­cale appliquée à l’apprentissage à par­tir d’exemples musi­caux. » Neurosciences et Sciences de l’Ingénieur, 4e Journées CIRM, Luminy, 3–6 Mai 1988. 

1988                   « On the Uses of Computers in Anthropological Research. » Current Anthropology, 29, 2 : 317–20.

1987                   « An Ethnomusicological Approach to the Analysis of Musical Cognition. » Music Perception 5, 2 : 173–95.

1987                   Avec Annette Sanger « Applied Ethnomusicology : the Use of Balinese Gamelan in Recreational and Educational Music Therapy. » British Journal of Music Education 4, 1 : 5–16.

1986                   Avec Annette Sanger « Applied Ethnomusicology : the Use of Balinese Gamelan in Music Therapy. » International Council for Traditional Music (UK Chapter) Bulletin, 15 : 25–28.

1986                   « Computational Techniques in Musical Analysis. » Bulletin of Information on Computing and Anthropology (University of Kent at Canterbury), 4 : 1–5.

1985                   « The Dialectical Approach : a Methodology for the Analysis of Tabla Music. » International Council for Traditional Music (UK Chapter) Bulletin, 12 : 4–12.

1984                   « Linguistic Study of Rhythm: Computer Models of Tabla Language. » International Society for Traditional Arts Research Newsletter, 2 : 28–33.

1984                   « Listen Out for the Tabla. » International Society for Traditional Arts Research Newsletter, 1 : 13–14.

Comptes ren­dus    

2012                   Elliott, Robin and Gordon E. Smith, dir. : Music Traditions, Cultures and Contexts, Wilfrid Laurier University Press,  in « Letters in Canada 2010 », University of Toronto Quarterly, 81: 3 :779–80.

2006                   McNeil, Adrian Inventing the Sarod : A Cultural History. Calcutta : Seagull Press, 2004. Yearbook for Traditional Music, 38 : 133–35.

1999                   Myers, Helen, Music of Hindu Trinidad : Songs from the India Diaspora. Chicago Studies in Ethnomusicology. Chicago : University of Chicago Press, 1998. Notes : 427–29.

1999                   Marshall, Wolf, The Beatles Bass. Hal Leonard Corporation, 1998. Beatlology, 5.

1997                   Widdess, Richard, The Ragas of Early Indian Music: Music, Modes, Melodies, and Musical Notations from the Gupta Period to c.1250. Oxford Monographs on Music. Oxford : Clarendon Press, 1995. Journal of the American Oriental Society, 117, 3 : 587.

1994                   Rowell, Lewis, Music and Musical Thought in Early India. Chicago Studies in Ethnomusicology, edit­ed by Philip V. Bohlman and Bruno Nettl. Chicago and London : The University of Chicago Press, 1992. Journal of the American Oriental Society, 114, 2 : 313.

1992                   Compte ren­du CD : « Bengal : chants des ‘fous’ », par Georges Luneau & Bhaskar Bhattacharyya, and « Inde du sud : musiques rit­uelles et théâtre du Kerala », par Pribislav Pitoëff. Asian Music 23, 2 :181–84.

1992                   Witmer, Robert, dir. : “Ethnomusicology in Canada : Proceedings of the First Conference on Ethnomusicology in Canada.” (CanMus Documents, 5) Toronto, Institute for Canadian Music, 1990. Yearbook for Traditional Music, 24 : 170–71.

1992                   Neuman, Daniel M. The Life of Music in North India: The Organization of an Artistic Tradition. Chicago, University of Chicago Press, 1990. Journal of the American Oriental Society, 112, 1 : 171.

1988                   Qureshi, Regula Burckhardt. Sufi Music of India and Pakistan : Sound, Context and Meaning in the Qawwali. Cambridge Studies in Ethnomusicology. Cambridge : CUP, 1986. International Council for Traditional Music (UK Chapter) Bulletin, 20 : 40–45.

1986                   Wade, Bonnie C. Khyal : Creativity with­in North India’s Classical Music Tradition. Cambridge Studies in Ethnomusicology. Cambridge : CUP. Journal of the Royal Asiatic Society : 144–46.

Enregistrements

1999                   Honouring Pandit Jasraj at Convocation Hall, University of Toronto. 2 CD set. Foundation for the Indian Performing Arts, FIPA002.

1995                   Pandit Jasraj Live at the University of Toronto. 2 CD set. Foundation for the Indian Performing Arts, FIPA001.

Livrets d’album musical

2009                   Liner notes for Mohan Shyam Sharma (pakhavaj): Solos in Chautal and Dhammar. India Archive Music CD, New York.

2007                   Liner notes for Anand Badamikar (tabla): Tabla Solo in Tintal. India Archive Music (IAM•CD 1084), New York.

2002                   Pandit Shankar Ghosh : Tabla Solos in Nasruk Tal and Tintal. CD, India Archive Recordings (IAM•CD1054), New York.

2001                   Shujaat Khan, Sitar : Raga Bilaskhani Todi & Raga Bhairavi. CD, India Archive Recordings (IAM•CD1046), New York.

1998                   Pandit Bhai Gaitonde : Tabla Solo in Tintal. CD, India Archive Recordings (IAM•CD1034), New York.

1995                   Ustad Amjad Ali Khan : Rag Bhimpalasi & Rag “Tribute to America”. CD, India Archive Recordings (IAM•CD1019), New York.

1994                   Ustad Nizamuddin Khan : Tabla Solo in Tintal. CD, India Archive Recordings (IAM•CD1014), New York.

1992                   Rag Bageshri & Rag Zila Kafi, played by Tejendra Narayan Majumdar (sar­od) and Pandit Kumar Bose (tabla). CD, India Archive Recordings (IAM•CD 1008), New York.

Hommage

1990                   « In Memoriam : Afaq Husain (1930-1990). » Ethnomusicology 34, 3 : 429–30.

1990                   « In Memoriam : John Blacking (1928-1990). » Ethnomusicology 34, 2 : 263–6.


➡ A new ver­sion of Bol Processor com­pli­ant with var­i­ous sys­tems (MacOS, Windows, Linux…) is under devel­op­ment. We invite soft­ware design­ers to join the team and con­tribute to the devel­op­ment of the core appli­ca­tion and its client appli­ca­tions. Please join the BP open dis­cus­sion forum and/or the BP devel­op­ers list to stay in touch with work progress and dis­cus­sions of relat­ed the­o­ret­i­cal issues.

At the heart of Indian rhythms and their evolution

An inter­view with James Kippen
➡ Version française

by Antoine Bourgeau

James Kippen is one of the key fig­ures in the study of Hindustani music. His encounter in 1981 with Afaq Hussain, at the time the doyen of one of the great tablā-play­ing lin­eages, was the start­ing point for major research into both the instru­ment and Indian rhythm. From 1990 to 2019 he was the head of eth­no­mu­si­col­o­gy at the Faculty of Music in the University of Toronto in Canada. Trained under John Blacking and John Baily, he also acquired over the course of his research a mas­tery of sev­er­al Indo-Persian lan­guages. This abil­i­ty has allowed him to analyse first-hand numer­ous sources (trea­tis­es on music, musi­cians' own writ­ings, genealo­gies, icono­graph­ic mate­ri­als…) and to under­stand the chang­ing socio­cul­tur­al con­texts in which they were pro­duced (the Indo-Persian courts, the colo­nial British Empire, the rise of Indian Nationalism, and the post-colonial state). His work (see the select list of pub­li­ca­tions at the end of this inter­view) stands out as a major con­tri­bu­tion to the under­stand­ing of the the­o­ry and prac­tice of rhythm and metre in India.

I began cor­re­spond­ing with James Kippen dur­ing my own research on tablā at the end of the 1990s. Always quick to share his knowl­edge and his expe­ri­ence with enthu­si­asm, he gave me a lot of advice and encour­age­ment, and it was a great hon­our to count him among the mem­bers of my the­sis jury dur­ing my defence in 2004. It was with that same will­ing­ness to share that he respond­ed favourably to my pro­pos­al to inter­view him. Carried out remote­ly between July and December 2020, this exchange cov­ers near­ly 40 years of eth­no­mu­si­co­log­i­cal research.

➡ Source = doi:10.13140/RG.2.2.12650.03522
➡ Version française = doi:10.13140/RG.2.2.26071.80804
ou https://bolprocessor.org/kippen-interview-fr/

The path to India and to the tablā

– How did you become inter­est­ed in the musics of India, and in the tablā in particular?

As a child grow­ing up in London, I was fas­ci­nat­ed by the dif­fer­ent lan­guages and cul­tures that were increas­ing­ly being intro­duced by immi­grants to Britain. I was par­tic­u­lar­ly enchant­ed by the lit­tle Indian cor­ner shops brim­ming with exot­ic goods and the Indian restau­rants that emit­ted allur­ing, spicy aro­mas. My father reg­u­lar­ly regaled me with sto­ries of his adven­tures from the sev­en years he spent in India as a young sol­dier, and I devel­oped an entire­ly favourable though admit­ted­ly Orientalist impres­sion of the sub­con­ti­nent. During my music degree at the University of York (1975-78), I was intro­duced by my friend and fel­low stu­dent Francis Silkstone to the sitār. I also had the good for­tune to take an inten­sive course in Hindustani music with lec­tur­er Neil Sorrell, who had stud­ied sāraṅgī with the great Ram Narayan. The avail­able lit­er­a­ture at that time was rel­a­tive­ly sparse, but two texts in par­tic­u­lar were high­ly influ­en­tial: Rebecca Stewart's Tablā in Perspective (UCLA, 1974), which nur­tured in me a musi­co­log­i­cal inter­est in the vari­eties and com­plex­i­ties of rhythm and drum­ming, and Daniel Neuman's The Cultural Structure and Social Organization of Musicians in India: the Perspective from Delhi (University of Illinois, Urbana-Champaign, 1974), which offered social-anthropological insights into both the worlds and the world­views of tra­di­tion­al, hered­i­tary musicians.

Thus, I began learn­ing tablā from Robert Gottlieb's LP record­ings and book­lets called 42 Lessons for Tabla, and after a few months I had learnt enough basic mate­r­i­al to accom­pa­ny Francis Silkstone in a recital. I lat­er stud­ied in per­son under Manikrao Popatkar, an excel­lent pro­fes­sion­al tablā play­er who had recent­ly immi­grat­ed to Britain. I was hooked. Moreover, the thought that I might enter that socio-musical world of tablā in India and become a participant-observer moti­vat­ed me to look at grad­u­ate pro­grams where I would be able to devel­op the knowl­edge and skills to com­bine the musi­co­log­i­cal and anthro­po­log­i­cal approach­es of Stewart and Neuman. On Neil Sorrell's advice I wrote to John Blacking about the pos­si­bil­i­ty of study­ing at The Queen's University of Belfast, and John was most encour­ag­ing, offer­ing me entry direct­ly to the doc­tor­al pro­gram. He also point­ed out that his col­league John Baily had recent­ly writ­ten a text: Krishna Govinda's Rudiments of Tabla Playing. It seemed I had found the ide­al grad­u­ate pro­gram and the per­fect mentors.

Methodological approaches

– The book How Musical Is Man? by John Blacking is a fun­da­men­tal text that appeared in 1973 that ran counter to the think­ing of the time and refused to recog­nise the bar­ri­ers between musi­col­o­gy and eth­no­mu­si­col­o­gy, as well as the fruit­less dif­fer­ences between musi­cal tra­di­tions. Blacking also put for­ward the essen­tial idea that music, even if that word does not exist every­where, is present in all human cul­tures, result­ing in his def­i­n­i­tion of “human­ly organ­ised sound.” Do you know if he knew of Edgar Varèse's expres­sion “organ­ised sound,” which Varèse put for­ward in 1941 in an attempt to dis­tance him­self from the Western con­cept of “music,” albeit for oth­er reasons?

I have no per­son­al rec­ol­lec­tion of Blacking ever men­tion­ing Varèse or his thoughts on the nature of music. Nonetheless, Blacking was an excel­lent musi­cian and pianist who had doubt­less encoun­tered and stud­ied a great deal of Western Art Music, and so it is pos­si­ble he knew of Varèse's def­i­n­i­tion. However, where­as Varèse's phi­los­o­phy was born out of a con­vic­tion that machines and tech­nolo­gies would be capa­ble of organ­is­ing sound, Blacking want­ed to re-centre music as a social fact: an activ­i­ty where the myr­i­ad ways in which human beings organ­ised sound both as per­form­ers and, impor­tant­ly, as lis­ten­ers promised to reveal a great deal about their social structure.

– How did your stud­ies at uni­ver­si­ty guide your research?

I was lucky enough to have not one but two men­tors in John Blacking and John Baily, and they were very dif­fer­ent from one anoth­er. Blacking was full of grand and inspir­ing ideas that chal­lenged and rev­o­lu­tion­ized the way one thinks about music and soci­ety, where­as Baily empha­sized a more method­i­cal and empirically-based approach ground­ed in per­for­mance and the care­ful acqui­si­tion and doc­u­men­ta­tion of data. One should remem­ber that I was young and inex­pe­ri­enced when I under­took field­work, and so Baily's exam­ple, focussed on doing music and on gath­er­ing data, served as a prac­ti­cal guide in my dai­ly life dur­ing my years in India; yet once I was armed with a huge cor­pus of infor­ma­tion I was able to stand back and, hope­ful­ly like Blacking, see some of the grand pat­terns which that data spelled out. I was struck there­fore by the con­sis­tent nar­ra­tive of cul­tur­al decline linked to a nos­tal­gia for a glo­ri­ous and artistically-abundant past, and the tablā music of Lucknow was one of the last liv­ing links to that lost world. This became one of the key themes in my doc­tor­al dis­ser­ta­tion, and in some of the oth­er work that fol­lowed. As for my career as a teacher, I have tried over the years to com­bine the best qual­i­ties of both my men­tors, always pro­mot­ing the idea that the­o­ry should grow out of sol­id data about music and musi­cal lives so that it does not lose its heuris­tic val­ue by aban­don­ing its dia­logue with ethno­graph­ic reality.

– In Working with the Masters (2008), you describe in detail and with frank­ness (some­thing that is fair­ly rare in the pro­fes­sion!) your field­work expe­ri­ence with Afaq Hussain in the 1980s. This expe­ri­ence, and your account of it, appear to be a mod­el for any research in eth­nol­o­gy and eth­no­mu­si­col­o­gy, par­tic­u­lar­ly as it applies to learn­ing music. Thus, you account for the phas­es of approach­ing, meet­ing, being test­ed and, final­ly (and for­tu­nate­ly in your case), accep­tance with­in the research con­text; the trust you were grant­ed allowed you to pur­sue in full your research and music-learning goals. You also tack­le the eth­i­cal and deon­to­log­i­cal con­sid­er­a­tions essen­tial to any researcher: one's rela­tion­ship to oth­ers, con­flicts of loy­al­ty result­ing from pos­si­ble incon­sis­ten­cies between that rela­tion­ship and one's ethno­graph­ic objec­tives, respon­si­bil­i­ty to the gath­ered knowl­edge, and the place of the researcher-musician with­in the musi­cal real­i­ty of the tra­di­tion stud­ied. Beyond the par­tic­u­lar­i­ties of the musi­cal con­text, are there any spe­cif­ic fea­tures of Indian cul­ture that Western researchers need to bear in mind in order to under­take (and hope­ful­ly suc­ceed with) an eth­no­log­i­cal study in India?

It goes with­out say­ing that South Asian soci­ety has changed enor­mous­ly in the 40 years since I first began con­duct­ing ethno­graph­ic research, but cer­tain prin­ci­ples stead­fast­ly remain that should guide the inves­tiga­tive process, such as a deeply ingrained respect for social and cul­tur­al senior­i­ty. Naturally, access to a com­mu­ni­ty is key, and there is no bet­ter “gate­keep­er” or “spon­sor” (to use the anthro­po­log­i­cal terms) than an author­i­ty fig­ure with­in the sub­cul­ture one is study­ing, since the per­mis­sion one receives trick­les down through the social and famil­ial hier­ar­chy. The dan­ger, in a heav­i­ly patri­ar­chal soci­ety like India's, is that one ends up with a top-down view of musi­cal life. If I had an oppor­tu­ni­ty to revis­it my field I would pay greater atten­tion to those at dif­fer­ent lev­els with­in that hier­ar­chy, espe­cial­ly to women and to the every­day musi­cal­i­ty of life in the domes­tic sphere. By focussing only on the most refined aspects of cul­tur­al pro­duc­tion, one may miss much that is of val­ue in the for­ma­tion of ideas, of aes­thet­ics, and in the sup­port mech­a­nisms nec­es­sary for an artis­tic tra­di­tion to sur­vive and thrive.

Fig.1: Recording ses­sion with Afaq Hussain at the home of James Kippen. Lucknow, 1982. Photo by James Kippen.

On a more prac­ti­cal note – some­thing that applies I think rather more gen­er­al­ly in the field­work endeav­our – I found that for­mal, record­ed inter­views were rarely very insight­ful because they were felt to be intim­i­dat­ing and were accom­pa­nied by lofty expec­ta­tions. Furthermore, a height­ened sen­si­tiv­i­ty to the polit­i­cal ram­i­fi­ca­tions – micro and macro – of speak­ing one's mind on record was also often an imped­i­ment to gath­er­ing infor­ma­tion. In truth, the less I asked and the more I lis­tened – off the record and in relaxed cir­cum­stances – the more use­ful and insight­ful the infor­ma­tion I received. The caveat is that to oper­ate in that way one must devel­op a lev­el of patience that would be dif­fi­cult for most Westerners to accept.

– In the 1980s you adopt­ed the “dialec­ti­cal approach” taught by John Blacking and com­bined it with com­put­er sci­ence and an Artificial Intelligence pro­gram. The aim was to analyse the fun­da­men­tals of impro­vi­sa­tion by tablā play­ers. Can you go over the gen­e­sis and evo­lu­tion of this approach?

John Blacking was par­tic­u­lar­ly inter­est­ed in Noam Chomsky's work on trans­for­ma­tion­al gram­mars. He the­o­rized that one could cre­ate sets of rules for music – a gram­mar – with the top­most lay­er describ­ing how those sur­face sound struc­tures were organ­ised. At deep­er lev­els the lay­ers of rules would address increas­ing­ly more gen­er­al prin­ci­ples of musi­cal organ­i­sa­tion, and at the very deep­est lev­el the gram­mar would for­malise rules gov­ern­ing prin­ci­ples of social organ­i­sa­tion. If an ethnomusicologist's ulti­mate aim is to relate social struc­ture to sound struc­ture, or vice ver­sa, then this was Blacking's idea of how one might achieve that goal.

In the sum­mer of 1981, I escaped the intense heat of the North Indian plains and head­ed to Mussoorie in the foothills of the Himalayas. I had agreed to meet up again with my friend Francis Silkstone, who at the time was study­ing sitār with Imrat Khan and dhru­pad vocal music with Fahimuddin Dagar in Calcutta. Francis arrived with Fahimuddin and one of Fahim's American stu­dents named Jim Arnold. Jim was col­lab­o­rat­ing on some exper­i­men­tal work on rāga into­na­tion with Bernard Bel, who at that time was liv­ing in New Delhi. Bernard then arrived in Mussoorie, also to escape the heat, and for about a month we all lived togeth­er in a rich and fer­tile envi­ron­ment of music and ideas. It was there that Bernard and I first dis­cussed Blacking's notion of socio-musical gram­mars as well as my fas­ci­na­tion with tablā's theme-and-variations struc­tures known as qāi­da. I was intrigued when Bernard sug­gest­ed that he could design a com­put­er pro­gram capa­ble of mod­el­ling the process of cre­at­ing vari­a­tions from a giv­en theme.

Over the fol­low­ing year, Bernard and I met sev­er­al times: he learnt much more about how tablā works and I learnt much more about math­e­mat­i­cal lin­guis­tics. Together we cre­at­ed sets of rules – trans­for­ma­tion­al gram­mars – that gen­er­at­ed vari­a­tions from a qāi­da theme and processed exist­ing vari­a­tions to deter­mine if our rules could account for them. Yet it was also clear that the knowl­edge being mod­elled was my own and not that of expert musi­cians. Therefore, we devel­oped a strat­e­gy to involve those experts as “co-workers and ana­lysts” (a phrase Blacking often used) in a dialec­ti­cal exchange. After all, an “expert sys­tem” was intend­ed to mod­el expert knowl­edge, and there was no bet­ter expert than Afaq Hussain.

➡ For more infor­ma­tion about these exper­i­ments, vis­it: https://bolprocessor.org/bp1-in-real-musical-context/

– Were you aware of oth­er types of inter­ac­tive approach­es, such as Simha Arom's “re-recording” devel­oped a few years earlier?

I was aware of Simha Arom's inter­ac­tive meth­ods of elic­it­ing musi­cians' own per­spec­tives on what was hap­pen­ing in their music, much as I was aware of work in cog­ni­tive anthro­pol­o­gy aimed at deter­min­ing cog­ni­tive cat­e­gories mean­ing­ful to the peo­ple we stud­ied. Arom's insis­tence that cul­tur­al data had to be val­i­dat­ed by our inter­locu­tors was cer­tain­ly very influ­en­tial. I did not know of oth­er approach­es. The exi­gen­cies of our par­tic­u­lar exper­i­men­tal sit­u­a­tion forced us to invent our own unique method­ol­o­gy for this human-computer interaction.

– We know of the fear Indian mas­ters have of their knowl­edge being spread beyond their own gharānā, in par­tic­u­lar, cer­tain tech­niques and com­po­si­tions. What was Afaq Hussain's atti­tude regard­ing this, and what was his involve­ment in this method that updat­ed the soft­ware for exam­in­ing qāi­da structures?

Afaq Hussain was not remote­ly con­cerned about rev­e­la­tions regard­ing qāi­da since the art of play­ing them depend­ed on one's abil­i­ty to impro­vise. In oth­er words, this was a process-oriented and there­fore ever-changing endeav­our. On the con­trary, play­ing fixed com­po­si­tions, espe­cial­ly those hand­ed down over gen­er­a­tions with­in the fam­i­ly, were product-oriented, and the pieces did not change. Those were con­sid­ered pre­cious assets, and were care­ful­ly guarded.

Fig.2: James Kippen, Afaq Hussain, and his son Ilmas
Hussain. Lucknow, 1982. Photo by James Kippen.

 When I reflect on the exper­i­ments, I mar­vel that Bernard Bel was able to cre­ate such a pow­er­ful gen­er­a­tive gram­mar for a com­put­er (first­ly an Apple II with 64k RAM, then the portable 128k Apple IIc) with such lim­it­ed pro­cess­ing pow­er and space. Afaq Hussain also mar­velled that a machine could “think,” as he put it. We began with a basic gram­mar for a giv­en qāi­da, gen­er­at­ed some vari­a­tions, and I then read those out loud using the syl­lab­ic lan­guage, the bols, for tablā. Many results were pre­dictable, some were unusu­al but nonethe­less accept­able, and oth­ers were deemed to be wrong – tech­ni­cal­ly, aes­thet­i­cal­ly. We then asked Afaq Hussain to offer a few vari­a­tions of his own; these were fed into the com­put­er (I typed using a key-correlation sys­tem for rapid entry) and “analysed” to deter­mine if the rules of our gram­mar could account for them. Simple adjust­ments to the rules were pos­si­ble in situ, but when more com­plex repro­gram­ming was required we would move on to a sec­ond exam­ple and return to the orig­i­nal exam­ple in a lat­er session.

Did this research ever involve oth­er types of com­po­si­tion such as gat or ṭukṛā?

No. The advan­tage of look­ing at a theme-and-variations struc­ture like qāi­da is that each com­po­si­tion is a closed sys­tem where vari­a­tions (vistār) are restrict­ed to the mate­r­i­al pre­sent­ed in the theme. Relā (rapidly-articulated strings of strokes) is anoth­er struc­ture that fol­lows sim­i­lar prin­ci­ples. The aim is there­fore to under­stand the unwrit­ten rules for cre­at­ing vari­a­tions. Fixed com­po­si­tions such as gat, ṭukṛā, paran, etc., com­prise a far wider and more unpre­dictable vari­ety of ele­ments, and would be very hard to mod­el. However, one thing we did exper­i­ment with was the tihāī, the thrice-repeated phrase that acts as a final rhyth­mic cadence. These can be mod­elled math­e­mat­i­cal­ly and applied to a qāi­da (based on frag­ments of its theme or one of its vari­a­tions) or to fixed com­po­si­tions like, say, ṭukṛā as an arith­metic for­mu­la into which one can pour rhyth­mic phrases.

– Did any of the rhyth­mic phras­es gen­er­at­ed by the com­put­er and val­i­dat­ed by Afaq Hussain Khan make it into the reper­toire of the Lucknow gharānā?

That is a hard ques­tion to answer. When we were in the mid­dle of an inten­sive peri­od of exper­i­men­ta­tion with the Bol Processor, there would devel­op a kind of dia­logue where Afaq Hussain would play mate­r­i­al gen­er­at­ed by the com­put­er and then respond with sets of vari­a­tions of his own. So many were gen­er­at­ed and exchanged in this way that it was often hard to tell whether some­thing he played in con­cert orig­i­nat­ed in the com­put­er. Yet, where­as some teach­ers and per­form­ers devel­op a reper­toire of fixed vari­a­tions for a theme, Afaq Hussain rarely did, rely­ing instead on his imag­i­na­tion “in the moment.” This is also the approach he encour­aged in us. Therefore, I doubt computer-generated mate­r­i­al became a per­ma­nent part of the repertoire.

Fig.3: Bhupal Ray Chowdhury (a dis­ci­ple of Wajid Hussain and his son Afaq Hussain) and James Kippen in an exper­i­men­tal ses­sion with the Bol Processor. Calcutta, 1984. Photo by James Kippen.

– Has this spe­cif­ic type of approach using Artificial Intelligence in eth­no­mu­si­col­o­gy been pur­sued by others?

The term “Artificial Intelligence” under­went a rad­i­cal change in the years 1980-1990 thanks to the devel­op­ment of the “con­nec­tion­ist” approach (arti­fi­cial neu­rons) and learn­ing tech­niques from exam­ples with the capa­bil­i­ty of pro­cess­ing a large amount of data. With the Bol Processor (BP) we were at the stage of symbolic-numerical mod­el­ling of human deci­sions rep­re­sent­ed by for­mal gram­mars, which required in-depth, although intu­itive, knowl­edge of deci­sion mechanisms.

 For this rea­son, symbolic-numerical approach­es have not to my knowl­edge been tak­en up by oth­er teams. On the oth­er hand, we had also tack­led machine learn­ing (of for­mal gram­mars) using the QAVAID soft­ware writ­ten in Prolog II. We also showed that the machine had to col­lect infor­ma­tion by dia­logu­ing with the musi­cian in order to car­ry out a cor­rect seg­men­ta­tion of musi­cal phras­es and to begin gen­er­al­is­ing by induc­tive infer­ence. But this work was dis­con­tin­ued because the machines were too slow and we did not have a large enough body of data to build a mod­el capa­ble of cov­er­ing a wide vari­ety of impro­vi­sa­tion models.

It is pos­si­ble that Indian researchers will use learn­ing from exam­ples – now called Artificial Intelligence – to process large amounts of data pro­duced by per­cus­sion­ists. This “big data” approach has the draw­back of lack­ing pre­ci­sion in a field where pre­ci­sion is a mark­er of musi­cal exper­tise, and it does not pro­duce under­stand­able algo­rithms which would con­sti­tute a “gen­er­al gram­mar” of impro­vi­sa­tion on a per­cus­sion instru­ment. Our ini­tial ambi­tion was to con­tribute to the con­struc­tion of this gram­mar, but we only proved, using the tech­nol­o­gy avail­able at the time, that it would be feasible.

In lat­er ver­sions, this soft­ware was also able to pro­vide mate­r­i­al and tools for music and dance com­po­si­tion beyond the Indian con­text. We will be cel­e­brat­ing 40 years of this soft­ware next year with a new ver­sion. Who are the artists that have used this software?

Rhythmic com­po­si­tions pro­grammed on BP2 and per­formed on a Roland D50 syn­the­sis­er were used for the chore­o­graph­ic work CRONOS direct­ed by Andréine Bel and pro­duced in 1994 at the NCPA in Bombay. See, for exam­ple, https://bolprocessor.org/shapes-in-rhythm/.

At the end of the 1990s, the Dutch com­pos­er Harm Visser used BP2 to help devel­op oper­a­tors for ser­i­al music com­po­si­tion. See, for exam­ple, https://bolprocessor.org/harm-vissers-examples/.

We have had feed­back (and requests) from European and American aca­d­e­mics who use BP2 as an edu­ca­tion­al tool for teach­ing musi­cal com­po­si­tion. However, we have nev­er car­ried out a large-scale adver­tis­ing cam­paign to enlarge the user com­mu­ni­ty because we are pri­mar­i­ly inter­est­ed in the devel­op­ment of the sys­tem itself and in the musi­co­log­i­cal research asso­ci­at­ed with it.

The main lim­i­ta­tion of BP2 was its exclu­sive oper­a­tion with­in the Macintosh envi­ron­ment. This is why the BP3 ver­sion under devel­op­ment is cross-platform. It will prob­a­bly be imple­ment­ed in a Cloud ver­sion made pos­si­ble by its close inter­ac­tion with Csound soft­ware. This soft­ware makes it pos­si­ble to pro­gram high-performance sound pro­duc­tion algo­rithms and to work with micro­ton­al into­na­tion mod­els that we have devel­oped, both for har­mon­ic music and for Indian rāga. See, for exam­ple, https://bolprocessor.org/category/related/musicology/.

Studies of notation, metre, rhythm, and their evolution

– Over the course of your work, the ques­tion of musi­cal nota­tion has occu­pied an impor­tant place both in terms of method­ol­o­gy and also in con­sid­er­a­tions of how it is used. Can you speak to this aspect of your work?

All writ­ten nota­tions are incom­plete approx­i­ma­tions, and their con­tri­bu­tion to the trans­mis­sion process is lim­it­ed. Oral rep­re­sen­ta­tions, like the spo­ken strings of syl­la­bles rep­re­sent­ing drum strokes, often con­vey more accu­rate infor­ma­tion about the musi­cal­i­ty inher­ent in pat­terns, such as stress, inflec­tion, phras­ing, and micro-rhythmic vari­abil­i­ty. By the same token, once inter­nalised, those spo­ken strings are indeli­ble. We know that oral sys­tems pro­mote a healthy musi­cal mem­o­ry, which is par­tic­u­lar­ly impor­tant in the con­text of the per­for­mance of music in India where per­form­ers begin with only a very gen­er­al road map but then take all man­ner of unex­pect­ed twists and turns along the way. That being the case, one might ask why write any­thing down at all?

From the 1860s onwards, there was a bur­geon­ing of musi­cal nota­tions in India inspired, I believe, by an aware­ness that Western music pos­sessed an effi­cient nota­tion sys­tem, and prompt­ed too by the steady increase in insti­tu­tion­alised learn­ing and the per­ceived need for ped­a­gog­i­cal texts and asso­ci­at­ed reper­toire. Yet there was nev­er any con­sen­sus on how to notate, and each new sys­tem dif­fered great­ly from the oth­ers. The nota­tion devised in 1903 by Gurudev Patwardhan was arguably the most detailed and pre­cise ever cre­at­ed for drum­ming, yet it was sure­ly too com­pli­cat­ed for stu­dents to read as a score. Therefore, its pur­pose was more as a ref­er­ence work that pre­served reper­toire and pro­vid­ed a syl­labus for struc­tured learning.

We live in a lit­er­ate age, and musi­cians recog­nise that their stu­dents no longer devote their wak­ing hours to prac­tis­ing. Like oth­er teach­ers, Afaq Hussain encour­aged us all to write down the reper­toire he taught so that it would not be for­got­ten. For me, it was espe­cial­ly impor­tant to cap­ture two aspects in my own note­books: rhyth­mic accu­ra­cy and pre­cise fin­ger­ing. Regarding the lat­ter, for exam­ple, when faced with the phrase – keṛe­na­ga tirak­iṭa takata­ka tirak­iṭa – I want­ed to ensure that I notat­ed the cor­rect intend­ed fin­ger­ing from the dozen or so pos­si­ble tech­niques for takata­ka, not to men­tion the vari­eties of keṛe­na­ga, and I would also indi­cate that the two instances of tirak­iṭa were played slight­ly differently.

Afaq Hussain kept his own note­books safe­ly stored in a locked cup­board. He some­times con­sult­ed them. I think he recog­nised that reper­toire does indeed dis­ap­pear in the oral tra­di­tion – after all, there are many hun­dreds, if not thou­sands of pieces of music. His grand­fa­ther, Abid Hussain (1867-1936) was the first pro­fes­sor of tablā at the Bhatkhande Music College in Lucknow. He too notat­ed tablā com­po­si­tions, and I have hun­dreds of pages he wrote that were almost cer­tain­ly intend­ed to be pub­lished as a ped­a­gog­i­cal text. However, he did not indi­cate pre­cise rhythms or fin­ger­ings, and so inter­pret­ing his music is prob­lem­at­ic, even for Afaq Hussain's son Ilmas Hussain with whom I combed through the mate­r­i­al. A pre­cise nota­tion, then, does have val­ue, but only along­side an oral tra­di­tion that can add the nec­es­sary lay­ers of infor­ma­tion that can bring the music to life.

– In your recent research on numer­ous Indo-Persian texts from the 18th and 19th cen­turies, you high­light the evo­lu­tion of the rep­re­sen­ta­tion of musi­cal metre in India. This research illus­trates the impor­tance of the his­tor­i­cal approach and ful­ly demon­strates the mech­a­nisms of the evo­lu­tion of cul­tur­al facts. What con­cepts do you use to describe these phenomena?

An impor­tant facet of our anthro­po­log­i­cal train­ing was learn­ing to func­tion in the lan­guage of those we engaged with in our research, not mere­ly to man­age life on a day-to-day basis but rather to have access to con­cepts that are mean­ing­ful with­in the cul­ture stud­ied. Two terms are sig­nif­i­cant in this regard, one whose impor­tance is, I think, over­stat­ed, the oth­er under­stat­ed. Firstly, gharānā, which from its first appear­ance in the 1860s orig­i­nal­ly meant “fam­i­ly” but which over time has come to encom­pass any­one who believes they share some ele­ments of tech­nique, style, or reper­toire with an api­cal fig­ure of the past. Secondly, sil­si­la, a term com­mon in Sufism which means chain, con­nec­tion, or suc­ces­sion, has spe­cif­ic rel­e­vance to a direct teach­ing lin­eage. It is this more pre­cise sil­si­la that I believe holds the key to the trans­mis­sion of musi­cal cul­ture, and yet the para­dox is that the chain car­ries with­in it an implic­it direc­tive to explore one's cre­ative indi­vid­u­al­i­ty. That is why, for exam­ple, when one exam­ines, say, the lin­eage of Delhi tablā play­ers from the mid 19th cen­tu­ry onwards, one finds major dif­fer­ences in tech­nique, style, and reper­toire from gen­er­a­tion to gen­er­a­tion. The same is true for my teacher Afaq Hussain, whose play­ing dif­fered great­ly from that of his father and teacher Wajid Hussain. Each indi­vid­ual inher­its some musi­cal essence in the sil­si­la, for sure, but they must engage with and oper­ate in an ever-changing world where artis­tic sur­vival requires adap­ta­tion. It is there­fore vital­ly impor­tant when study­ing any musi­cal era to gath­er as much infor­ma­tion about the socio-cultural milieu as possible.

 As I have shown above, it is imper­a­tive to engage with native con­cepts, and to explain and use them with­out recourse to trans­la­tion. Another prime exam­ple is tāla, which most com­mon­ly gets trans­lat­ed as metre or met­ric cycle. And yet there is a fun­da­men­tal dif­fer­ence. Metre is implic­it: it is a pat­tern that is abstract­ed from the sur­face rhythms of a piece, and con­sists of an under­ly­ing pulse that is orga­nized into a recur­ring hier­ar­chi­cal sequence of strong and weak beats. On the oth­er hand, tāla is explic­it: it is a recur­ring pat­tern of non-hierarchical beats man­i­fest­ed as hand ges­tures con­sist­ing of claps, silent waves, and fin­ger counts, or as a rel­a­tive­ly fixed sequence of drum strokes. To use metre in the Indian con­text is there­fore mis­lead­ing, and I there­fore encour­age the use of tāla with an accom­pa­ny­ing expla­na­tion but with­out translation.

– You are cur­rent­ly work­ing on a book about 18th and 19th cen­tu­ry sources. What is your goal?

My goal is to trace the ori­gins and evo­lu­tion of the tāla sys­tem cur­rent­ly in use in Hindustani music by gath­er­ing as much infor­ma­tion as pos­si­ble from con­tem­po­rary sources begin­ning in the late 17th cen­tu­ry through to the ear­ly 20th cen­tu­ry and the era of record­ed sound. The prob­lem is that the avail­able infor­ma­tion is frag­men­tary and often couched in obscure lan­guage: the task is akin to doing a jig­saw puz­zle where most of the pieces are miss­ing. Moreover, the pieces one does find are not nec­es­sar­i­ly direct­ly con­nect­ed, and so the task might be bet­ter described as work­ing with two or more puz­zles. In brief, through care­ful analy­sis, infer­ence, and some guess­work, I believe that there was a con­ver­gence of rhyth­mic sys­tems in the 18th cen­tu­ry that gave rise to the tāla sys­tem of today.

The musi­cal prac­tices and social con­texts of the com­mu­ni­ties of Kalāwants who sang dhru­pad and Qawwāls who sang khayāl, tarā­na, and qaul, along with the Ḍhāḍhī com­mu­ni­ty that accom­pa­nied all these gen­res, are cru­cial to under­stand­ing how and why music – and rhythm in par­tic­u­lar – evolved the way it did. Yet there are so many oth­er impor­tant aspects to this sto­ry: the role of women instru­men­tal­ists in the pri­vate spaces of Mughal life in the 18th cen­tu­ry, and their grad­ual dis­ap­pear­ance in the 19th cen­tu­ry; colo­nial­ism; the sta­tus and influ­ence of ancient texts; print­ing tech­nol­o­gy and the dis­sem­i­na­tion of new ped­a­gog­i­cal texts in the late 19th cen­tu­ry – to name but a few.

– What are some of the inter­est­ing sources to con­sid­er in order to under­stand the evo­lu­tion of prac­tices and rhyth­mic rep­re­sen­ta­tions of Hindustani music?

Northern India has always been open to cul­tur­al exchange, and this was espe­cial­ly true under the Mughals. It is imper­a­tive that we under­stand who trav­elled to the courts, from where, and what they played. It is equal­ly impor­tant to under­stand the writ­ten mate­ri­als avail­able as well as the intel­lec­tu­al dis­cours­es of the time, for knowl­edge of music was cru­cial to Mughal eti­quette. Thus, to know that the high­ly influ­en­tial music trea­tise Kitāb al-adwār, by the 13th cen­tu­ry the­o­rist Safi al-Din al-Urmawi al-Baghdadi was wide­ly avail­able in India both in Arabic and Persian trans­la­tion, and that copies were in the col­lec­tion of Delhi nobles from the 17th cen­tu­ry onwards, helps us to under­stand why Indian rhythm was explained using the prin­ci­ples of Arabic prosody in the late 18th cen­tu­ry. I have argued that, as applied to music, Arabic prosody was a more pow­er­ful tool than the tra­di­tion­al meth­ods of Sanskrit prosody, and thus it was more effec­tive in describ­ing the changes that were occur­ring in rhyth­mic thought and prac­tice in that period.

This ethno-historical research some­times clash­es with the beliefs of cer­tain musi­cians and researchers, espe­cial­ly on ques­tions of the age and “authen­tic­i­ty” of tra­di­tions. Do you think the younger gen­er­a­tions are more inclined to accept the obvi­ous facts of the com­plex nature of musi­cal tra­di­tions made up of mul­ti­ple con­tri­bu­tions and in per­pet­u­al transformation?

Some are, but some are not. There has always been a small num­ber of schol­ars in India who con­duct valu­able, evidence-based research on music. Yet it dis­ap­points me to note there are many more that rely on the regur­gi­ta­tion and prop­a­ga­tion of unfound­ed, unschol­ar­ly opin­ion. What per­haps sur­pris­es me most is the lack of rig­or­ous schol­ar­ly train­ing in Indian music col­leges and the per­sis­tence of dis­proven or dis­cred­it­ed ideas and infor­ma­tion in spite of so much excel­lent pub­lished research to the contrary.

Fig 4: James Kippen, University of Toronto, 2017. Photo by James Kippen.

– Since the 1990s, one notices the strength­en­ing of a Hindu nation­al­ism with­in Indian soci­ety. Have you not­ed a par­tic­u­lar impact on the world of Hindustani music and on research?

This is a com­plex and sen­si­tive top­ic. Hindu nation­al­ism is not new, far from it, and as I demon­strat­ed in my book on Gurudev Patwardhan, it formed a sig­nif­i­cant part of the ratio­nale for the life and work of Vishnu Digambar Paluskar in the ear­ly 20th cen­tu­ry. As many schol­ars have point­ed out, it had roots in colo­nial­ism, and devel­oped as an anti-colonial move­ment focussed on Hindu iden­ti­ty pol­i­tics. That nar­ra­tive, based on invent­ed notions of a glo­ri­ous Hindu past, down­played the con­tri­bu­tions of Mughal cul­ture and the great lin­eages of Muslim musi­cians (not to men­tion women), and Indian Muslim iden­ti­ty with­in the sphere of music has suf­fered a decline ever since. Scholars have tak­en note of this dynam­ic and have attempt­ed to trace some of the coun­ternar­ra­tives that have hith­er­to been ignored, such as Max Katz's excel­lent book Lineage of Loss (Wesleyan University Press, 2017) about an impor­tant fam­i­ly of Muslim scholar-musicians, the so-called Shāhjahānpūr-Lucknow gharānā. I sus­pect that a moti­va­tion­al force in much mod­ern schol­ar­ship on music in India is the desire not to omit impor­tant cul­tur­al nar­ra­tives but to ani­mate them and frame them with­in the grand sweep of South Asia's history.

– Following on from Rebecca Stewart's work, you too have high­light­ed the com­plex inter­weav­ing of rhyth­mic and met­ric approach­es in tablā play­ing by show­ing that it results from var­i­ous cul­tur­al con­tri­bu­tions which have fol­lowed one anoth­er over time. With the inten­si­fi­ca­tion of glob­al cul­tur­al exchanges since the end of the 20th cen­tu­ry, have you observed one or more evolv­ing trends in tablā playing?

Since the inclu­sion of tablā in pop music in the 1960s, the excit­ing jazz fusion of John McLaughlin's group Shakti in the 1970s, and the ubiq­ui­ty of tablā ever since in music of every kind, it seems only nat­ur­al that tablā play­ers the world over should explore and exper­i­ment with its mag­i­cal sounds. Zakir Hussain has led the way in demon­strat­ing the flex­i­bil­i­ty and adapt­abil­i­ty of these drums, and the thrilling, vis­cer­al veloc­i­ty of its rhyth­mic pat­terns. As for tablā with­in the con­text of Hindustani con­cert music, I have noticed that there are many who attempt to inject that same sense of excite­ment, enhanced increas­ing­ly, it seems, by ampli­fi­ca­tion so loud that it dis­torts the sound and beats the audience's eardrums into sub­mis­sion. I would go so far as to say that this has unfor­tu­nate­ly become the norm.

In this regard, I count myself as some­thing of a purist who longs for a return to a prac­tice where the tablā play­er main­tains a sub­tle, under­stat­ed yet sup­port­ive role, com­ple­ments the mate­r­i­al pre­sent­ed by the soloist, and is mod­est and not over­pow­er­ing when invit­ed to con­tribute a short flour­ish or cameo solo. By the same token, I crave a return to tablā solos that are packed with con­tent rather than “sound effects.” By “con­tent,” I mean tra­di­tion­al, char­ac­ter­ful com­po­si­tions fea­tur­ing spe­cialised tech­niques, whose com­posers are named and thus hon­oured. And yet it is painful­ly obvi­ous that such “con­tent” is not reach­ing many younger play­ers these days.

Ethnomusicology

– As men­tioned, your research high­lights the impor­tance of his­tor­i­cal sources as well as the con­sid­er­a­tion of broad­er phe­nom­e­na such as Orientalism or Nationalism in order to under­stand Indian musi­cal prac­tices in the present. At the same time, you are very atten­tive to the intense cur­rent tran­scul­tur­al phe­nom­e­na and to the need to com­pre­hend them. In the pro­fes­sion, the con­cept of “eth­no­mu­si­col­o­gy” does not always achieve con­sen­sus. What is your posi­tion with regard to this name and the sub­ject of this dis­ci­pline at the start of the 21st century?

I have nev­er been par­tic­u­lar­ly com­fort­able with the label “eth­no­mu­si­col­o­gy.” As John Blacking used to say, all music is “eth­nic music,” and there­fore there should be no dis­tinc­tion between stud­ies of tablā, game­lan, or hip-hop and those of Bach, Beethoven, or Brahms. We all engage in a “dis­course on music”: in oth­er words, “musi­col­o­gy.” The advan­tage of terms like the “anthro­pol­o­gy” or “soci­ol­o­gy” of music is that they imply a broad­er slate of the­o­ret­i­cal and method­olog­i­cal approach­es that remind us that music is a social fact. Yet we must recog­nise that the purview of eth­no­mu­si­co­log­i­cal stud­ies has evolved, and nowa­days far greater atten­tion is paid to phe­nom­e­na like noise or the mun­dane sounds of every­day life. Therefore – with­out wish­ing to sound too cyn­i­cal – although in some quar­ters the term “sound stud­ies” is treat­ed with a degree of con­tempt, per­haps that very gen­er­al term is the most hon­est and accu­rate def­i­n­i­tion of what we (all of us) do. However, I acknowl­edge that it would be a shame to reject the term “music” alto­geth­er, and so I could imag­ine eth­no­mu­si­col­o­gy, musi­col­o­gy, and music the­o­ry com­ing togeth­er under the rubric “music and sound studies.”

Teaching

– After a short peri­od in Belfast, you taught in Toronto. Can you tell us about your teach­ing experience?

Yes, Toronto is a won­der­ful city, and by most accounts it is the most multi-cultural city on this plan­et. It offers a very rich and stim­u­lat­ing musi­cal environment.

 Miecyzslaw Kolinski taught at the University of Toronto from 1966 until 1978. His eth­no­mu­si­co­log­i­cal inter­ests were shaped by his train­ing under Hornbostel and Sachs, and by the world­view shared by so many of the ear­ly giants of our dis­ci­pline. He pub­lished on the sci­en­tif­ic basis of har­mo­ny and melody, and devel­oped meth­ods for cross-cultural analy­sis – an approach emphat­i­cal­ly reject­ed in my own train­ing with John Blacking who argued vehe­ment­ly for cul­tur­al rel­a­tivism, much as it was at odds with Tim Rice's train­ing at the University of Washington. Tim was hired in 1974 and left for UCLA in 1987. Like me dur­ing my ear­ly days, Tim strug­gled to per­suade col­leagues of the impor­tance of the eth­no­mu­si­co­log­i­cal approach and the need to treat our dis­ci­pline with the respect it deserved and the resources it required. We both fought hard. Tim intro­duced a pro­gram that came to be known under my watch as the World Music Ensembles, and I acquired a Balinese game­lan in 1993, which was taught by my wife, eth­no­mu­si­col­o­gist Dr Annette Sanger, for­mer­ly a col­league of John Blacking. Moreover, both Tim and I suc­ceed­ed in draw­ing eth­no­mu­si­col­o­gy class­es fur­ther into the core of the cur­ricu­lum to ensure that all music stu­dents, what­ev­er their inter­ests, were exposed to our approach and under­stood the val­ue and impor­tance of a socially-grounded view of all music. One ini­tia­tive I cre­at­ed was a year-long intro­duc­to­ry course called Music as Culture which for a few years I co-taught with a musi­col­o­gy col­league: we alter­nat­ed our pre­sen­ta­tions, illus­trat­ing and cross-referencing our mate­r­i­al and obser­va­tions from the Western canon and the vast world of music beyond. Later incar­na­tions of this course includ­ed our flag­ship Introduction to Music & Society. Essentially mod­u­lar in approach, the cho­sen themes shift­ed and adapt­ed over time to reflect more con­tem­po­rary con­cerns, includ­ing music and iden­ti­ty, reli­gious expe­ri­ence, migra­tion, gen­der, heal­ing, and sound studies.

I devised and taught a vari­ety of cours­es dur­ing my time: Hindustani music; Music & Islam; Theory & Method in Ethnomusicology; The Beatles; Anthropology of Music; Fieldwork; Music, Colonialism & Postcolonialism; Rhythm & Metre in Cross-Cultural Perspective; Transcription, Notation & Analysis, etc. I worked with the South Asian com­mu­ni­ty in Toronto to put on con­certs by vocal­ist Pandit Jasraj that drew spon­sor­ship that gen­er­at­ed healthy schol­ar­ships for stu­dents study­ing Hindustani music. I helped insti­tute an Artist-in-Residence pro­gram, invit­ing musi­cians from all over the world to spend a term with us teach­ing and per­form­ing. I helped to over­haul our musicology-oriented grad­u­ate pro­grammes and intro­duced an MA and PhD in eth­no­mu­si­col­o­gy. But per­haps the two achieve­ments of which I am most proud are first­ly the many won­der­ful doc­tor­al stu­dents I men­tored, many of whom have them­selves gone on pur­sue to careers in acad­e­mia, and sec­ond­ly my suc­cess in expand­ing our rep­re­sen­ta­tion from a sin­gle fac­ul­ty posi­tion to four full-time posi­tions in ethnomusicology.

– What is your posi­tion with­in the Lucknow gharānā?

I have great­ly enjoyed learn­ing and play­ing tablā in my life, and I con­sid­er myself extreme­ly for­tu­nate to have had such a close and pro­duc­tive asso­ci­a­tion with one of the most remark­able tablā play­ers in his­to­ry: Afaq Hussain. I am blessed with a good mem­o­ry and there­fore still have in my head a vast reper­toire of won­der­ful com­po­si­tions dat­ing all the way back to the ear­ly mem­bers of the Lucknow lin­eage who flour­ished in the late 18th and ear­ly 19th cen­turies. I am par­tic­u­lar­ly inter­est­ed in tech­nique, and have spent a good deal of time study­ing the mechan­ics of play­ing. However, I am first and fore­most a schol­ar, and in prac­ti­cal mat­ters I have no illu­sions about being any­thing more than a tablā hob­by­ist. Indeed, my inter­est in play­ing has pro­vid­ed me with extra­or­di­nary insights into the instru­ment and its history.

As for my place or role with­in the Lucknow gharānā, I would say two things. Firstly, I con­tin­ue to be part of the exchange of ideas and reper­toire with my peers along­side whom I stud­ied tablā and who now are, like me, senior fig­ures with­in the sil­si­la, the direct teach­ing lin­eage of Afaq Hussain. I am con­sid­ered by them to be knowl­edge­able: an author­i­ty, if you will. On occa­sions I am asked if I remem­ber a rare com­po­si­tion over which there has been some debate, and some­times I intro­duce into our dia­logue infor­ma­tion and ques­tions aris­ing from my research that spark a live­ly inter­est. For exam­ple, Afaq Hussain's son Ilmas Hussain and I have been work­ing togeth­er to res­ur­rect the note­books of his great-grandfather Abid Hussain, and place them in the con­text not only of his tra­di­tion but also of the ear­ly years of Lucknow's Bhatkhande College where Abid Hussain served as the first pro­fes­sor of tablā in the late 1920s and ear­ly 1930s. Secondly, I believe that my work has brought greater atten­tion to the Lucknow lin­eage. When I arrived at Afaq Hussain's doorstep in January 1981 he was frankly at a low ebb in his life – psy­cho­log­i­cal­ly and finan­cial­ly – and much about the future was uncer­tain. Other for­eign stu­dents fol­lowed my lead and joined an ever-growing num­ber of Indian dis­ci­ples who came to learn. My book, The Tabla of Lucknow, as well as oth­er facets of my research helped to bring nation­al and inter­na­tion­al atten­tion to Afaq Hussain, his son Ilmas, and their entire tradition.

When I came to Toronto I made a deci­sion not to teach tablā out­side of my duties at the University of Toronto, since I did not wish to risk depriv­ing local tablā play­ers (of whom there were sev­er­al very good ones) of the oppor­tu­ni­ty to earn income. Within the uni­ver­si­ty itself, I did run occa­sion­al work­shops and cours­es for stu­dents, plus indi­vid­ual lessons, and some of them (par­tic­u­lar­ly per­cus­sion­ists) became quite com­pe­tent players.

List of publications

Books               

2006                   Gurudev’s Drumming Legacy: Music, Theory and Nationalism in the Mrdang aur Tabla Vadanpaddhati of Gurudev Patwardhan. Aldershot: Ashgate (SOAS Musicology Series).

2005                   The Tabla of Lucknow: A Cultural Analysis of a Musical Tradition. New Delhi: Manohar (New edi­tion with new preface).

1988                   The Tabla of Lucknow: A Cultural Analysis of a Musical Tradition. Cambridge: Cambridge University Press (Cambridge Studies in Ethnomusicology).

Edited books   

2013                   with Frank Kouwenhoven, Music, Dance and the Art of Seduction. Delft: Eburon Academic Publishers.

Edited jour­nals       

1994-1996        Bansuri, vol­umes 11-13 (A year­ly jour­nal devot­ed to the music and dance of India, pub­lished by Raga Mala Performing Arts of Canada).

Articles, chap­ters in books

Forthcoming     “Weighing ‘The Assets of Pleasure’: Interpreting the Theory and Practice of Rhythm and Drumming in the Sarmāya-i ‘Ishrat, a Pivotal 19th Century Text” in Katherine Schofield, ed.: Hindustani Music Between Empires: Alternative Histories, 1748-1887. Publisher TBA.

Forthcoming     “An Extremely Nice, Fine and Unique Drum: A Reading of Late Mughal and Early Colonial Texts and Images on Hindustani Rhythm and Drumming” in Katherine Schofield, Julia Byl et David Lunn, eds: Paracolonial Soundworlds: Music and Colonial Transitions in South and Southeast Asia. Publisher TBA.

2021                   “Ethnomusicology at the Faculty of Music, University of Toronto.” MUSICultures (Journal of the Canadian Society for Traditional Music): Vol.48.

2020                   “Rhythmic Thought and Practice in the Indian Subcontinent” in Russell Hartenberger & Ryan McClelland, eds: The Cambridge Companion to Rhythm. Cambridge University Press: 241-60.

2019                   “Mapping a Rhythmic Revolution Through Eighteenth and Nineteenth Century Sources on Rhythm and Drumming in North India” in Wolf, Richard K., Stephen Blum, & Christopher Hasty, eds: Thought and Play in Musical Rhythm: Asian, African, and Euro-American Perspectives. Oxford University Press: 253-72.

2013                   “Introduction” in Frank Kouwenhoven & James Kippen, eds: Music, Dance and the Art of Seduction. Delft: Eburon Academic Publishers: i-xix.

2010                   “The History of Tabla” in Joep Bor, Françoise ‘Nalini’ Delvoye, Jane Harvey and Emmie te Nijenhuis, eds: Hindustani Music, Thirteenth to Twentieth Centuries. New Delhi: Manohar: 459-78.

2008                   “Working with the Masters” in Gregory Barz and Timothy Cooley, eds:Shadows in the Field: New Perspectives for Fieldwork in Ethnomusicology (2nd revised edi­tion). Oxford University Press: 125–40.

2007                   “The Tal Paddhati of 1888: An Early Source for Tabla.” Journal of The Indian Musicological Society, 38: 151–239.

2003                   “Le rythme: Vitalité de l'Inde.” Gloire des princes, louange des dieux: Patrimoine musi­cal de l'Hindoustan du XIVe au XXe siè­cle. Paris: Cité de la musique et Réunion des Musées Nationaux 2003:152–73.

2002                   “Wajid Revisited: A Reassessment of Robert Gottlieb’s Tabla Study, and a new Transcription of the Solo of Wajid Hussain Khan of Lucknow.” Asian Music, 33, 2: 111–74.

2001                   “Folk Grooves and Tabla Tals.” ECHO: a music-centered jour­nal.  III: 1 (Spring 2001).

2000                   “Hindustani Tala.” Garland Encyclopedia of World Music, Volume 5, South Asia: The Indian Subcontinent. New York: Garland Publishing: 110–37.

1997                   “The Musical Evolution of Lucknow” in Violette Graff, dir., Lucknow: Memories of a City. New Delhi: Oxford University Press: 181–95.

1996                   “A la recherche du temps musi­cal.” Temporalistes, 34: 11-22

1994                   “Computers, Composition, and the Challenge of ‘New Music’ in Modern India.” Leonardo Music Journal, 4: 79–84. https://hal.archives-ouvertes.fr/hal-00143124

1992                   “Tabla Drumming and the Human-Computer Interaction.” The World of Music, 34, 3: 72–98.

1992                   “Music and the Computer: Some Anthropological Considerations.” Interface, 21, 3-4: 257–62.

1992                   “Where Does The End Begin ? Problems in Musico-Cognitive Modelling.” Minds & Machines, 2, 4: 329–44.

1992                   “Identifying Improvisation Schemata with QAVAID” in Walter B. Hewlett & Eleanor Selfridge-Field, eds: Computing in Musicology: An International Directory of Applications, Volume 8. Center for Computer Assisted Research in the Humanities:115–19.

1992                   “Bol Processor Grammars” in M. Balaban, K. Ebcioglu, & O. Laske, eds: Understanding AI with Music, AAAI Press: 367–400. https://hal.archives-ouvertes.fr/hal-00256386

1992                   with Bernard Bel “Modelling Music with Grammars: Formal Language Representation in the Bol Processor” in A. Marsden & A. Pople, eds: Computer Representations and Models in Music. London, Academic Press: 207–38. https://halshs.archives-ouvertes.fr/halshs-00004506

1991                   with Bernard Bel “From Word-Processing to Automatic Knowledge Acquisition: A Pragmatic Application for Computers in Experimental Ethnomusicology” in Ian Lancashire, ed.: Research in Humanities Computing I: Papers from the 1989 ACH-ALLC Conference, Oxford University Press: 238–53.

1990                   “Music and the Computer: Some Anthropological Considerations” in B. Vecchione & B. Bel, eds: Le Fait Musical – Sciences, Technologies, Pratiques, pré­fig­u­ra­tion des actes du col­loque Musique et Assistance Informatique, CRSM-MIM, Marseille, France, 3-6 Octobre: 41–50.

1990                   “In Memoriam: Afaq Husain (1930-1990).” Ethnomusicology 34, 3: 429–30.

1990                   “In Memoriam: John Blacking (1928-1990).” Ethnomusicology 34, 2: 263–6.

1989                   “Changes in the Social Status of Tabla Players.” Journal of the Indian Musicological Society, 20, 1 & 2: 37–46.

1989                   “Can a Computer Help Resolve the Problem of Ethnographic Description?” Anthropological Quarterly, 62, 3: 131–44. https://hal.archives-ouvertes.fr/hal-00275429

1989                   with Bernard Bel “The Identification and Modelling of a Percussion ‘Language’, and the Emergence of Musical Concepts in a Machine-Learning Experimental Set-Up.” Computers and the Humanities, 23, 3: 199–214. https://halshs.archives-ouvertes.fr/halshs-00004505

1988                   with Bernard Bel “Un mod­èle d’inférence gram­mat­i­cale appliquée à l’apprentissage à par­tir d’exemples musi­caux.” Neurosciences et Sciences de l’Ingénieur, 4e Journées CIRM, Luminy, 3–6 Mai 1988. 

1987                   “An Ethnomusicological Approach to the Analysis of Musical Cognition.” Music Perception 5, 2: 173–95.

1987                   with Annette Sanger “Applied Ethnomusicology: the Use of Balinese Gamelan in Recreational and Educational Music Therapy.” British Journal of Music Education 4, 1: 5–16.

1986                   with Annette Sanger “Applied Ethnomusicology: the Use of Balinese Gamelan in Music Therapy.” International Council for Traditional Music (UK Chapter) Bulletin, 15: 25–28.

1986                   “Computational Techniques in Musical Analysis.” Bulletin of Information on Computing and Anthropology (University of Kent at Canterbury), 4: 1–5.

1985                   “The Dialectical Approach: a Methodology for the Analysis of Tabla Music.” International Council for Traditional Music (UK Chapter) Bulletin, 12: 4–12.

1984                   “Linguistic Study of Rhythm: Computer Models of Tabla Language.” International Society for Traditional Arts Research Newsletter, 2: 28–33.

1984                   “Listen Out for the Tabla.” International Society for Traditional Arts Research Newsletter, 1: 13–14.

Reviews           

2012                   Elliott, Robin and Gordon E. Smith, eds: Music Traditions, Cultures and Contexts, Wilfrid Laurier University Press,  in “Letters in Canada 2010”, University of Toronto Quarterly, 81: 3:779–80.

2006                   McNeil, Adrian Inventing the Sarod: A Cultural History. Calcutta: Seagull Press, 2004. Yearbook for Traditional Music, 38: 133–35.

1999                   Myers, Helen, Music of Hindu Trinidad: Songs from the India Diaspora. Chicago Studies in Ethnomusicology. Chicago: University of Chicago Press, 1998. Notes: 427–29.

1999                   Marshall, Wolf, The Beatles Bass. Hal Leonard Corporation, 1998. Beatlology, 5.

1997                   Widdess, Richard, The Ragas of Early Indian Music: Music, Modes, Melodies, and Musical Notations from the Gupta Period to c.1250. Oxford Monographs on Music. Oxford: Clarendon Press, 1995. Journal of the American Oriental Society, 117, 3: 587.

1994                   Rowell, Lewis, Music and Musical Thought in Early India. Chicago Studies in Ethnomusicology, edit­ed by Philip V. Bohlman and Bruno Nettl. Chicago and London: The University of Chicago Press, 1992. Journal of the American Oriental Society, 114, 2: 313.

1992                   CD: review “Bengal: chants des ‘fous’”, par Georges Luneau & Bhaskar Bhattacharyya, and “Inde du sud: musiques rit­uelles et théâtre du Kerala”, par Pribislav Pitoëff. Asian Music 23, 2:181–84.

1992                   Witmer, Robert, ed.: “Ethnomusicology in Canada: Proceedings of the First Conference on Ethnomusicology in Canada.” (CanMus Documents, 5) Toronto, Institute for Canadian Music, 1990. Yearbook for Traditional Music, 24: 170–71.

1992                   Neuman, Daniel M. The Life of Music in North India: The Organization of an Artistic Tradition. Chicago, University of Chicago Press, 1990. Journal of the American Oriental Society, 112, 1: 171.

1988                   Qureshi, Regula Burckhardt. Sufi Music of India and Pakistan: Sound, Context and Meaning in the Qawwali. Cambridge Studies in Ethnomusicology. Cambridge: CUP, 1986. International Council for Traditional Music (UK Chapter) Bulletin, 20: 40–45.

1986                   Wade, Bonnie C. Khyal: Creativity with­in North India’s Classical Music Tradition. Cambridge Studies in Ethnomusicology. Cambridge: CUP. Journal of the Royal Asiatic Society: 144–46.

Recordings

1999                   Honouring Pandit Jasraj at Convocation Hall, University of Toronto. 2 CD set. Foundation for the Indian Performing Arts, FIPA002.

1995                   Pandit Jasraj Live at the University of Toronto. 2 CD set. Foundation for the Indian Performing Arts, FIPA001.

Liner notes

2009                   Mohan Shyam Sharma (pakhavaj): Solos in Chautal and Dhammar. India Archive Music CD, New York.

2007                   Anand Badamikar (tabla): Tabla Solo in Tintal. India Archive Music (IAM•CD 1084), New York.

2002                   Pandit Shankar Ghosh: Tabla Solos in Nasruk Tal and Tintal. CD, India Archive Recordings (IAM•CD1054), New York.

2001                   Shujaat Khan, Sitar: Raga Bilaskhani Todi & Raga Bhairavi. CD, India Archive Recordings (IAM•CD1046), New York.

1998                   Pandit Bhai Gaitonde: Tabla Solo in Tintal. CD, India Archive Recordings (IAM•CD1034), New York.

1995                   Ustad Amjad Ali Khan: Rag Bhimpalasi & Rag “Tribute to America”. CD, India Archive Recordings (IAM•CD1019), New York.

1994                   Ustad Nizamuddin Khan: Tabla Solo in Tintal. CD, India Archive Recordings (IAM•CD1014), New York.

1992                   Rag Bageshri & Rag Zila Kafi, played by Tejendra Narayan Majumdar (sar­od) and Pandit Kumar Bose (tabla). CD, India Archive Recordings (IAM•CD 1008), New York.

Obituaries

1990                   “In Memoriam: Afaq Husain (1930-1990).” Ethnomusicology 34, 3: 429–30.

1990                   “In Memoriam: John Blacking (1928-1990).” Ethnomusicology 34, 2: 263–6.


➡ A new ver­sion of Bol Processor com­pli­ant with var­i­ous sys­tems (MacOS, Windows, Linux…) is under devel­op­ment. We invite soft­ware design­ers to join the team and con­tribute to the devel­op­ment of the core appli­ca­tion and its client appli­ca­tions. Please join the BP open dis­cus­sion forum and/or the BP devel­op­ers list to stay in touch with work progress and dis­cus­sions of relat­ed the­o­ret­i­cal issues.

Towards a standalone application

   

The Bol Processor BP3 is cur­rent­ly com­prised of a con­sole (writ­ten in C lan­guage) and a set of PHP/HTML/CSS/Javascript files that act as its inter­face. A con­sole ver­sion of Csound can also be attached. For detailed instal­la­tion instruc­tions, please refer to the Bol Processor ‘BP3’ and its PHP inter­face page.

It all works beau­ti­ful­ly in a design that is com­pat­i­ble with mul­ti­ple 64-bit sys­tems: MacOS, Linux and Windows. However it does require the instal­la­tion of an Apache+PHP pack­age to run the inter­face: MAMP or XAMPP.

The next phase of the project is the cre­ation of a stand­alone appli­ca­tion replac­ing the web brows­er and its asso­ci­at­ed PHP/HTML/CSS files. The appli­ca­tion will be avail­able in three ver­sions, for Linux, MacOS and Windows.

This step is with­in our reach using the PHP Desktop plat­form. The MacOS ver­sion is ready — see the instal­la­tion. The Windows ver­sion is up and run­ning, but there are still a few issues that need to be resolved to reach the state of a distribution.

Rationalizing musical time: syntactic and symbolic-numeric approaches

Bernard Bel

A con­tri­bu­tion to The Ratio Symposium, 14-16 Dec. 1992, Den Haag (The Netherlands). Published in Barlow, Clarence (ed.) The Ratio Book. Den Haag: Royal Conservatory - Institute of Sonology. 2001: 86-101. This paper is ref­er­enced on HAL ⟨hal-00134179⟩ and quot­ed in Polymetric struc­tures.

Abstract

This paper deals with var­i­ous prob­lems of quan­ti­fy­ing musi­cal time that arise both in the analy­sis of tra­di­tion­al drum­ming and in computer-generated musi­cal pieces based on "sound-objects", i.e. sequences of code that con­trol a real-time sound processor.

Section 1 sug­gests that syn­tac­tic approach­es may be clos­er to the intu­itions of musi­cians and musi­col­o­gists than com­mon­ly advo­cat­ed numer­i­cal approach­es. Furthermore, symbolic-numerical approach­es lead to effi­cient and ele­gant solu­tions of con­straint sat­is­fac­tion prob­lems with respect to sym­bol­ic and phys­i­cal dura­tions, as illus­trat­ed in Sections 2 and 3, respectively.

Download this paper

Polymetric structures

Polymetric expres­sions are the basic rep­re­sen­ta­tion mod­el for the tim­ing of musi­cal data in the Bol Processor. The word is a mix­ture of polypho­ny and polyrhythm, the for­mer evok­ing super­im­posed streams of musi­cal events, and the lat­ter a met­ric adjust­ment of their durations.

This page illus­trates the syn­tax of sim­ple expres­sions and their inter­pre­ta­tion by the poly­met­ric expan­sion algo­rithm described in Two algo­rithms for the instan­ti­a­tion of struc­tures of musi­cal objects (Bel 1992). This process can be extreme­ly com­plex, since an entire musi­cal work — e.g. Beethoven's Fugue in B flat major — is treat­ed by the Bol Processor as a sin­gle poly­met­ric struc­ture: see exam­ple.

In this tuto­r­i­al, sim­ple notes ("C4", "D4" etc.) are used fol­low­ing the "English" con­ven­tion. All time-setting process­es could be illus­trat­ed using sound-objects or sim­ple notes in oth­er con­ven­tions: "Italian/Spanish/French" or "Indian".

Symbolic versus physical duration

Music nota­tion sys­tems (for humans) make use of sym­bol­ic rather than phys­i­cal dura­tions. Their units are beats rather than (milli)seconds.

Three quar­ter notes on a score
in west­ern con­ven­tion­al music notation

In west­ern con­ven­tion­al music nota­tion, notes and paus­es are rep­re­sent­ed by spe­cial signs indi­cat­ing their rel­a­tive durations.

For exam­ple, if the time sig­na­ture is 3/4, we will have 3 quar­ter notes (crotch­ets) in a bar (see pic­ture). A half note (min­im) lasts twice as long as a quar­ter note in the same con­text. Other rel­a­tive dura­tions are expressed in the same way.

To get the phys­i­cal dura­tion of a note we need an addi­tion­al piece of infor­ma­tion: the metronome val­ue, for exam­ple "mm = 100", which means 100 beats (quar­ter notes) per minute.

A metronome val­ue (60 bpm by default ) is declared in the set­tings file of a Grammar or Data page. With this set­ting, note "E4" on a Bol Processor score rep­re­sents an "E" of the 4th octave played in 1 beat with a phys­i­cal dura­tion of 1 second.

This con­ven­tion extends to arbi­trar­i­ly named sound-objects whose default dura­tions are set by the streams of MIDI events or sequences of Csound instruc­tions from which they are com­posed. The map­ping of sym­bol­ic to phys­i­cal time for the per­for­mance of sound-object struc­tures (with their met­ric and topo­log­i­cal prop­er­ties) is a sophis­ti­cat­ed process per­formed by a time-setting algo­rithm. A prac­ti­cal exam­ple is dis­cussed on the page Interactive impro­vi­sa­tion with sound-objects.

Polymetric expression

Typical forms of poly­met­ric expres­sions are:

  • field 1, field2 or {field 1, field2} indi­cates that field1 and field2 should be super­im­posed and the total sym­bol­ic dura­tion should be adjust­ed to that of field1;
  • field1 • field2 or {field1 • field2} indi­cates that field1 and field2 should be con­sec­u­tive and the sym­bol­ic dura­tion of each field should be adjust­ed to that of field1;
  • {expression} is equiv­a­lent to expression.

Curly braces '{' and '}' are used to cre­ate multi-level expressions.

➡ Periods writ­ten as bul­lets '' in the Data and Grammar win­dows are con­vert­ed to plain peri­ods before being sent to the con­sole, as the con­sole rejects some Unicode characters.

For exam­ple, {C4 D4, E4 F4 G4, E5} pro­duces the fol­low­ing time struc­ture with a metronome set to 60 beats per minute:

Item {C4 D4, E4 F4 G4, E5} on a sound-object graph
The dura­tion is 2 beats, as set by the first field "C4 D4"

The use of the first field to set the total dura­tion is high­light­ed by the fol­low­ing exam­ples where the fields appear in a reverse order:

{C4 D4 E4, F4 G4}
Duration of 3 beats
{F4 G4, C4 D4 E4}
Duration of 2 beats

Rests (silences) can be notat­ed with "-" for sin­gle unit rests, or with inte­ger num­bers and ratios. The fol­low­ing shows a sin­gle unit rest and a more com­plex rest of 2.5 beats:

{F4 - G4, C4 D4}
Duration of 3 beats
{F4 2 1/2 G4, C4 D4}
Duration of 4.5 beats
Fields in reverse order: {C4 D4, F4 2 1/2 G4}
Duration of 2 beats

Polymetric struc­tures can be multi-level, for example:

Multi-level poly­met­ric struc­ture:
{C4 D4, {E4 F4 G4, E5} B4}

The same time-setting rules apply to sequences where com­mas are replaced by peri­ods. For example:

Sequence F4 2 1/2 G4 • C4 D4 or {F4 2 1/2 G4 • C4 D4}
Duration is set by that of the first field "F4 2 1/2 G4"
= 4.5 beats applied to the sec­ond field

Superpositions and sequences can be com­bined (even in multi-level expres­sions), such as:

{F4 2 1/2 G4 • C4 D4, A4 B4, G4 A4 • F4}
Duration of 9 beats = twice that of "F4 2 1/2 G4"

Undetermined rests

Undetermined rests are a pow­er­ful fea­ture of poly­met­ric expres­sions used to avoid incon­ve­nient com­pu­ta­tions. The poly­met­ric expan­sion algo­rithm cal­cu­lates (sym­bol­ic) dura­tions that pro­duce the least com­plex expression.

They may be notat­ed as "" or "_rest" in Data or Grammars.

➡ Since the con­sole does not recog­nise the "" Unicode sym­bol, the PHP inter­face rewrites it as"_rest".

Let us start with a triv­ial exam­ple. In {C4 D4 E4, … F4 G4}, the unde­ter­mined rest "" is replaced by a sin­gle unit rest:

{C4 D4 E4, … F4 G4}
= {C4 D4 E4, _rest F4 G4}

This solu­tion gives the sim­plest poly­met­ric expres­sion. The same sim­ple case is that of {… C4 D4 E4, F4 G4}:

{… C4 D4 E4, F4 G4}
= {_rest C4 D4 E4, F4 G4}

If a field of the poly­met­ric expres­sion con­tains sev­er­al unde­ter­mined rests, these are assigned equal dura­tions — in such a way that the com­plex­i­ty of the struc­ture remains min­i­mal. For exam­ple, con­sid­er {… C4 D4 … E4, A4 F4 G4}:

{… C4 D4 … E4, A4 F4 G4}
= {_rest C4 D4 _rest E4, A4 F4 G4}

An unde­ter­mined rest may even be assigned dura­tion 0 in case this yields a sim­pler expres­sion. For exam­ple, in {… C4 D4 … E4, F4 G4} dura­tion 0 gives a "three in two" polyrhythm where­as dura­tion 1 would give "five in two". The cri­te­ri­on for eval­u­at­ing the com­plex­i­ty is to get the low­est com­mon mul­ti­ple (LCM) of the num­ber of units in each field, in fact 6 against 10. Therefore the solu­tion is:

{… C4 D4 … E4, A4 F4 G4}

Each field of a poly­met­ric expres­sion can con­tain unde­ter­mined rests. Consider for exam­ple {… C4 D4 E4, A4 B4 F4 … G4}. Again, assign­ing a dura­tion of zero to each unde­ter­mined rest gives the sim­plest struc­ture, since "four in three" (LCM = 12) is a bet­ter trade-off than "five in four" (LCM = 20).

{… C4 D4 E4, A4 B4 F4 … G4}

A more com­plex struc­ture is assigned to {C4 D4 E4, A4 B4 F4 … G4 A4, C5 … D5} with rests of 1 unit in the sec­ond and third fields. The LCM of 3 and 6 is 6, which is the low­est val­ue pos­si­ble for this structure.

{C4 D4 E4, A4 B4 F4 … G4 A4, C5 … D5}

Note that there is an equiv­a­lent solu­tion in terms of com­plex­i­ty: assign­ing dura­tion 0 to the rest in the third field. If more than one solu­tion is valid, the algo­rithm choos­es the one with the fewest zero-duration rests.

A sim­i­lar case is {C4 D4 E4, A4 B4 F4 … G4 A4, C5 … D5 E5}:

{C4 D4 E4, A4 B4 F4 … G4 A4, C5 … D5 E5}

Here, the first rest has been assigned 1 unit and the sec­ond one 3 units. This gives the LCM of 3 and 6 = 6. Another opti­mal (equiv­a­lent) solu­tion would be to assign 0 to the sec­ond rest, but this was dis­card­ed due to the heuris­tic of avoid­ing zero dura­tion rests.

Replacing com­mas with peri­ods gives the same struc­ture in a sequen­tial form:

"C4 D4 E4 • A4 B4 F4 … G4 A4 • C5 … D5 E5"
= {C4 D4 E4 • A4 B4 F4 … G4 A4 • C5 … D5 E5}
Duration of the first field "C4 D4 E4" is applied to the 2nd and 3d ones
which makes a final count of 3 x 3 = 9 beats

Tied notes, tied sound-objects

Sound-objects or sim­ple notes can be con­cate­nat­ed ("tied"). Consider, for example:

"C4 D4 C4 E4 C4 F4 E4"

and its vari­a­tion with ties notat­ed "&":

"C4& D4 &C4& E4& &C4 F4 &E4"

The time inter­val of a tied note/sound-object may cross the lim­its of (tree-shaped) poly­met­ric struc­tures. For example:

{C4 D4}{E4{2,E4,C4,G4}}
{C4& D4}{E4 {2,E4,&C4,G4}}

The chal­lenge of deal­ing with tied events is dis­cussed on the Tied notes page.

Real music is “polymetric”

The rules and heuris­tics asso­ci­at­ed with poly­met­ric expres­sions make sense when deal­ing with real musi­cal items. In par­tic­u­lar, they made it pos­si­ble to import MusicXML scores and inter­pret them as Bol Processor data (read page).

For exam­ple, check out Mozart’s musi­cal dice game, this "Charles Ames" exam­ple and Harm Visser's demos.

Further reading

Bel, Bernard. Rationalizing musi­cal time: syn­tac­tic and symbolic-numeric approach­es. In Barlow, Clarence (ed.) The Ratio Book. Den Haag: Royal Conservatory - Institute of Sonology. 2001: 86-101.

Bol Processor shares a few fea­tures, with respect to pat­tern rep­re­sen­ta­tion, with the TIDAL Pattern Language for the Live Encoding of Music (Alex McLean & Geraint Wiggins, 2010):

An Indian con­cep­tion of time can be seen most clear­ly in the ven­er­a­ble Bol Processor sys­tem for algo­rith­mic music, cre­at­ed by com­put­er sci­en­tist Bernard Bel from work on notat­ing tabla rhythms and devel­oped over forty years. Drawing from Indian clas­si­cal music, it includes an expres­sive approach to time set­ting that seems unique to the algo­rith­mic music field, in which sound events are orga­nized in terms of inter­re­la­tion­ships before being mapped to phys­i­cal time. Although not a live cod­ing sys­tem itself, it has been heav­i­ly influ­en­tial on the design of the TidalCycles sys­tem, par­tic­u­lar­ly its embed­ded “minino­ta­tion” lan­guage for describ­ing rhythm in the Bol Processor and more gen­er­al­ly its rep­re­sen­ta­tion of music based not on the dura­tion of events (as in staff nota­tion) but on the dura­tion of cycles.

Alan Blackwell, Emma Cocker, Geoff Cox, Thor Magnusson, Alex McLean, Live Coding: A User's Manual, MIT 2022, page 195.

Tied notes

This page is intend­ed for devel­op­ers of the Bol Processor BP3 (read instal­la­tion). It is not a for­mal descrip­tion of the algo­rithms car­ried by the console's C code, but rather an illus­tra­tion of their man­age­ment of musi­cal process­es, which may be use­ful for check­ing or extend­ing algorithms.

All exam­ples are includ­ed in the "ctests" fold­er of the dis­tri­b­u­tion. A set of cor­rect and incor­rect exam­ples is found in the "-da.checkTies" project.

Example of tied notes

Consider mea­sures #18 to #22 of Liszt's 14th Hungarian Rhapsody import­ed from a MusicXML file — see Importing MusicXML scores. The print­ed score of mea­sures #19 to #21 is as follows:

Measures #19 to #21 of Liszt's 14th Hungarian Rhapsody
Source: ManWithNoName in the MuseScore com­mu­ni­ty

Tied notes are vis­i­ble on this score. Slurs con­nect­ing notes at dif­fer­ent pitch­es are ignored by the Bol Processor. These could be inter­pret­ed using the _legato(x) per­for­mance con­trol, but set­ting an appro­pri­ate val­ue for 'x' would require a care­ful analy­sis of the con­text. Ties link the same pitch, such as "Ab1" (A flat in octave 1) at the bot­tom of the score lines. There are 3 occur­rences of tied "Ab1" in this sec­tion, the first one start­ing at the end of mea­sure #18 and the third one end­ing at mea­sure #21.

In Bol Processor nota­tion, this frag­ment results in a sequence of poly­met­ric struc­tures. For the sake of clar­i­ty, each mea­sure has been placed on its own paragraph:

#18 {_tempo(4/3) {4,{7/4,C4,C5}{1/4,C4,F4,Ab4,C5}{7/4,C4,F4,Ab4,C5}{1/4,Db4,F4,Ab4,Db5},{7/4,G4,Bb4}9/4,{7/4,E2,C3,G3,Bb3}{1/4,F2}{7/4,C3,F3,Ab3}{1/4, Ab1&}}

#19 {_tempo(4/3) {4,{15/4,Db4,F4,Ab4,Db5}1/8{1/8,C4,Gb4,B4,Eb5},{3/4,Ab2}{3,Db3 F3 Ab3 Db4 F4 Ab4 Db5 F5 Ab5 Db6 F6 Ab6}{1/4,- Ab1&}, &Ab1 ---}

#20 {_tempo(13/10) {33/8,{1/4,Db4& Gb4& A4& Eb5&}{7/2,&Db4,&Gb4,&A4,&Eb5}1/4{1/8,Fb4,Ab4,Cb5,Fb5},{3/4,Ab2}{13/4,Eb3 Gb3 A3 C4 G4 Bb4 Eb5 Gb5 A5 Eb6 Gb6 B6 -}{1/8, Ab1&}, &Ab1 25/8}}

#21 {_tempo(13/10) {33/8,{15/4,Fb4,Ab4,C5,Fb5}1/4{1/8,F4,Ab4,Db5,F5},{3/4,Ab2}{13/4,Fb3 Ab3 Cb4 F4 Ab4 C5 F5 Ab5 Cb6 Fb6 Ab6 Cb7 -}{1/8,B1&}, &Ab1 25/8}}

#22 {_tempo(4/3) {4,{7/2,F4,Ab4,Db5,F5}1/2,{3/4,B2}{13/4,F3 Ab3 Db4 F4 Ab4 Db5 F5 Ab5 Db6 F6 Ab6 Db7 -}, &B1 ---}}

The 3 occur­rences of tied "Ab1" and "B1" are shown in colour. "Ab1&" is the begin­ning of a tie and "&Ab1" is the end (of the same colour). Longer ties would occa­sion­al­ly require sequences such as "Ab1&" + "&Ab1&"+ "&Ab1".

These ties merge the (sym­bol­ic) time inter­vals of the begin­ning and end­ing occur­rence. For exam­ple, the score "C4& &C4" could be replaced by "C4 _ " or equiv­a­lent­ly "{2, C4}". The merg­ing of time inter­vals is done in the FillPhaseDiagram() pro­ce­dure of file "FillPhaseDiagram.c".

While pars­ing the com­pact poly­met­ric struc­ture to build the phase table — see Complex ratios in poly­met­ric expres­sions — the algo­rithm calls GetSymbolicDuration() (in "SetObjectFeatures.c") to cal­cu­late the sym­bol­ic dura­tion of a sound-object or sim­ple note. By default, this is easy to cal­cu­late. The ignorecon­cat flag is set to true if the sound-object or note is not fol­lowed by a '&'. The dura­tion is set by prodtem­po = Prod / tem­po.

If ignorecon­cat is false, GetSymbolicDuration() looks for the next accept­able occur­rence of the note or sound object pre­ced­ed by a '&'. Acceptability implies the fol­low­ing conditions:

  1. The note or sound-object should be on the same MIDI chan­nel or the same Csound instrument;
  2. The date of the next occur­rence should be lat­er than the on-set date.

The con­di­tions are read­i­ly appar­ent in the exam­ple. For exam­ple, "A1b&" can­not be paired with "&A1b" because the lat­ter occurs at an ear­li­er date. The next valid occur­rence is "&A1b". The same applies to pairs shown in oth­er colours. Each colour indi­cates a match­ing pair.

Once the dura­tion has been set, the algo­rithm calls PutZeros() to fill as many columns as nec­es­sary to set the total dura­tion of the pair of tied notes — as detailed in the page on Complex ratios in poly­met­ric expres­sions.

In addi­tion, when "&A1b" is parsed lat­er, it should be ignored because the dura­tion of the note has already been set by call­ing GetSymbolicDuration() and PutZeros() at the time of pars­ing "A1b&". Skipping these pro­ce­dures is ensured by the foundend­con­cate­na­tion flag.

Graphic display

The fol­low­ing is a sound-object graph of mea­sures #20 to #21 on which the bound­eries of inter­vals in tied notes are marked with dashed lines. The bounds of "Ab1& … &AB1" (red colour) are self-explanatory when com­pared with the musi­cal score shown above: each occur­rence is an instance of "{1/8, Ab1&} &Ab1".

Symbolic dura­tions can be checked against phys­i­cal time: since the tem­po is 13/10, the first part has a phys­i­cal dura­tion of 1/8 x 10 / 13 = 0.09 sec­onds and the sec­ond part 10/13 = 0.77 seconds.

Measures #20-21 of Liszt's 14th Hungarian Rhapsody on a sound-object graph

At the end of mea­sure #21 the begin­ning of the note "B1&" is linked to its occur­rence "&B1" in mea­sure #22. The bound­ary is marked by a dashed blue line. The piano roll of mea­sures #21-22 shows this con­nec­tion of "B1":

Measures #21-22 of Liszt's 14th Hungarian Rhapsody on a piano roll
Liszt's 14th Hungarian Rhapsody inter­pret­ed by the Bol Processor on a Pianoteq physical-model syn­the­sis­er
Source: ManWithNoName in the MuseScore community

Arpeggios

Arpeggio on chord
"{Db, Gb, Bbb, Eb}"
"Bbb" is inter­pret­ed as "A".

The green dashed lines belong to the poly­met­ric expres­sion {1/4,Db4& Gb4& A4& Eb5&}{7/2,&Db4,&Gb4,&A4,&Eb5}, the inter­pre­ta­tion of an arpeg­gio on the chord at the begin­ning of mea­sure #20. This inter­pre­ta­tion is con­struct­ed when import­ing MusicXML files — see the PHP code in the file "_musicxml.php".

A short sequence "Db4 Gb4 A4 Eb5" (dura­tion 1/4 beat) is played before the chord "{Db4, Gb4, A4, Eb5}" whose dura­tion is set to 7/2 beats. Each note in the sequence is tied to its occur­rence in the chord.

A sound exam­ple of an arpeg­gio can be found on the Importing MusicXML scores page.

More tied notes

A clear illus­tra­tion of the use of tied notes and unde­ter­mined rests is a short musi­cal phrase bor­rowed from a tuto­r­i­al by Charles Ames, a pio­neer­ing design­er of com­po­si­tion algo­rithms. The phrase is sup­plied as a musi­cal score but its inter­pre­ta­tion requires a care­ful analy­sis of the musi­cal struc­ture, result­ing in the fol­low­ing Bol Processor score:

{{2,-{2,F#3}, _rest {1,F5,A5}}{4,{ 1/2 ,G#3,E5,G5}{ 7/2 ,Bb4}}, _rest { 1/4 ,G#5&,C6,E6,B6&}{2,&G#5,&B6}}

To make things clear we need to look at the score in com­mon music nota­tion, divide it into blocks asso­ci­at­ed with vari­ables, and final­ly write a gram­mar "-gr.Ames" to build the struc­ture. Below are details of the analy­sis process and the result­ing graphs of sound-objects and piano roll:

In this gram­mar, unde­ter­mined rests have been writ­ten as "". In its cur­rent ver­sion, the Bol Processor con­sole no longer recog­nis­es the Unicode sym­bol for ellip­sis "". Therefore, it is auto­mat­i­cal­ly con­vert­ed it to "_rest" by the PHP interface.

Undetermined rests are a pow­er­ful fea­ture of poly­met­ric expres­sions used to avoid tedious cal­cu­la­tions. The poly­met­ric expan­sion algo­rithm com­putes (sym­bol­ic) dura­tions that pro­duce the least com­plex expres­sion. Read more in the Polymetric Structures tuto­r­i­al.

Tied notes are exact­ly the ones indi­cat­ed by links on the musi­cal score. The sound ren­der­ing is:

Rendering of "-gr.Ames" with metronome mm = 60

Error tracing

The con­struc­tion of suit­able time inter­vals for tied notes depends on the match­ing of pairs — e.g. "A4&" fol­lowed by "&A4" — in the Bol Processor score. Some pairs may remain incom­plete for one rea­son or another:

  1. The musi­cal item has been split into chunks, using the PLAY safe (instead of PLAY) option to speed up com­pu­ta­tion, and the two parts belong to sep­a­rate chunks;
  2. An error in the import­ed MusicXML score;
  3. An error in the algo­rithm — increas­ing­ly rare.
Unbound tie(s) sig­naled in a chunk

Case (1) is lim­it­ed by the method for chunk­ing items: each chunk is designed to con­tain the same num­ber of start and end ties. However, this is not guar­an­teed because the chunks are lim­it­ed in size.

Failure to bal­ance ties is indi­cat­ed below the PLAY safe but­ton (see image).

Errors are shown in colour on the track being played.. These may not cause any notice­able changes in per­for­mance. However, we rec­om­mend that you report any incor­rect data to the designers.

Below is an exam­ple of an error in a MusicXML score of Beethoven's Fugue in B flat major. A tie starts at note "Db5" (MIDI key #73) at the begin­ning of mea­sure #573 (part 2), but it ends nowhere:

Measures #573 to 575 (part 2) of Beethoven's Fugue in B flat major, with a never-ending tie start­ing at "Db5"

Read the MusicXML score frag­ment to check for this incon­sis­ten­cy. There are oth­er incon­sis­ten­cies in this score, such as a slur start­ing on note 'C4' of mea­sure #646 (part 3) that does not end. This makes it dif­fi­cult to inter­pret the slurs as legato.

Complex ratios in polymetric expressions

This page is intend­ed for devel­op­ers of the Bol Processor BP3 (read instal­la­tion). It is not a for­mal descrip­tion of the algo­rithms car­ried by the console's C code, but rather an illus­tra­tion of their man­age­ment of musi­cal process­es, which may be use­ful for check­ing or extend­ing algorithms.

All exam­ples are con­tained in the file "-da.checkPoly" in the "ctests" fold­er in the distribution.

Syntax of silences

In the Bol Processor's data/grammar syn­tax, silences (rests in con­ven­tion­al musi­cal ter­mi­nol­o­gy) are rep­re­sent­ed either by a hyphen '-' for a sin­gle unit dura­tion, or by inte­ger ratios to spec­i­fy a more com­plex duration:

  • "4" is a rest of 4 units duration
  • "5/3" is a rest of (approx­i­mate­ly) 1.666-unit duration
  • "3 1/2" is a rest of 3.5 units duration

For exam­ple, "C4 C5 3/2 D5 E5" results in the fol­low­ing piano roll with a rest of 3/2 (1.5) units start­ing on beat 2 and end­ing on beat 3.5:

Piano roll of item "C4 C5 3/2 D5 E5"

In this tuto­r­i­al we will use the default metronome val­ue = 60 beats per minute.

Another sim­ple exam­ple is {3 1/2, C3 D3 B2}, which is the sequence of notes "C3 D3 B2" con­strained to a total dura­tion of 3 1/2 (3.5) beats. This silence is the first field of the poly­met­ric expres­sion (explained below). This results in the fol­low­ing piano roll:

or equiv­a­lent­ly the sound-object graph:

Syntax of tempo

Any sequence of sym­bols con­form­ing to the syn­tax of Bol Processor is processed as a poly­met­ric expres­sion. Typical forms are:

  • field 1, field2 indi­cates that field1 and field2 should be super­im­posed and the total dura­tion should be that of field1;
  • field1.field2 indi­cates that field1 and field2 should be sequen­tial, with the dura­tion of each field being that of field1;
  • {expression} is equiv­a­lent to expression.

Brackets '{' and '}' are used to cre­ate multi-level expressions.

A num­ber of exam­ples of poly­met­ric expres­sions can be found in the Polymetric struc­tures tutorial.

For exam­ple, {{C4 D4, E4 F4 G4}, E5} gives the fol­low­ing structure:

Item {{C4 D4, E4 F4 G4}, E5} on a sound-object graph

In order to inter­pret this struc­ture, the Bol Processor needs to insert explic­it tem­po val­ues into the expres­sion. In fact, in this case, the most com­pact rep­re­sen­ta­tion would be with explic­it tem­po values:

*1/1 {{C4 D4,*2/3 E4 F4 G4} ,*2/1 E5}

Expressions such as "*2/3" indi­cate that the dura­tion of each note (or sound-object) should be mul­ti­plied by 2/3, regard­less of the pre­ced­ing state­ments. This means that the dura­tions of notes "E4", "F4" and "G4" should be 2/3 sec­onds as shown in the diagram.

Creating the com­pact rep­re­sen­ta­tion with its explic­it tem­po mark­ers may require recur­sive calls of a sophis­ti­cat­ed pro­ce­dure called PolyExpand() in the "Polymetric.c" file.

At this stage it is impor­tant not to con­fuse the notations:

  1. "2/3" is a silence of dura­tion 2/3 beats;
  2. "_tempo(2/3)" mul­ti­plies the cur­rent tem­po by 2/3. This is a rel­a­tive tem­po marker;
  3. "*2/3" sets the cur­rent dura­tion of the units to 2/3 of the metronome peri­od. This is an absolute tem­po mark­er. Similarly, "*4" mul­ti­plies dura­tions by 4, and "*1/5" or "/5" divides them by 5 — where­as "1/5" is a 1/5 beat silence.

The third syn­tax is the one used by the Bol Processor's time-setting algo­rithms. Despite its syn­tac­tic valid­i­ty, we do not rec­om­mend using it in gram­mars and data, as it can pro­duce con­flict­ing dura­tions in poly­met­ric struc­tures. For exam­ple, {*2/1 A4 B4, *3/1 A5 B5} makes no sense because it tries to force the first field to have a dura­tion of 2 x 2 = 4 beats and the sec­ond field to have a dura­tion of 3 x 2 = 6 beats. The cor­rect (nev­er con­tra­dic­to­ry) way to change a tem­po in data or gram­mars is to use the "_tempo(x)" per­for­mance tool.

Expanding a polymetric expression

In the pre­vi­ous para­graph we saw that {{C4 D4, E4 F4 G4}, E5} is inter­nal­ly rep­re­sent­ed as *1/1 {{C4 D4,*2/3 E4 F4 G4} ,*2/1 E5}. This inter­nal rep­re­sen­ta­tion is the most com­pact with explic­it tem­po mark­ings. Therefore, it is the one that is main­tained through all the steps of time setting.

Humans may pre­fer to see a more com­pre­hen­sive rep­re­sen­ta­tion called the expand­ed poly­met­ric expres­sion:

/3 {{C4_ _ D4_ _, E4_ F4_ G4_} , E5_ _ _ _ _}

This is done by click­ing the EXPAND but­ton on a data page. Underscores'_' rep­re­sent exten­sions of the dura­tion of the pre­vi­ous unit. These should not be con­fused with '-' (silence). To make things clear­er, let us replace a '_' with a '-':

/3 {{C4_ _ D4_ _, E4_ F4 - G4_}, E5_ _ _ _ _}

This results in the fol­low­ing struc­ture, where "F4" is not extended:

Item /3 {{C4_ _ D4_ _, E4_ F4 - G4_}, E5_ _ _ _ _}

The expand­ed poly­met­ric expres­sion may become too large for a human observ­er. In this case only the com­pact ver­sion will be returned.

In the code of the Bol proces­sor con­sole, sound objects (of all kinds) are iden­ti­fied by num­bers. The vari­able used to iden­ti­fy them in algo­rithms is always 'k' or 'kobj'. There is an option (in the code) to dis­play object iden­ti­fiers on a graph, which is set by the SHOWEVERYTHING con­stant. If set to true, this would be the pre­vi­ous sound object graph:

Item /3 {{C4_ _ D4_ _, E4_ F4 - G4_}, E5_ _ _ _ _}
in SHOWEVERYTHING mode

Notes "C4", "D4", etc. have iden­ti­fiers kobj = 2, 3, etc. The iden­ti­fi­er "0" is reserved for exten­sions '_' and "1" for silences "-", none of which are shown in the graph. An excep­tion is object #8, labelled <<->>, which is an out-time (zero dura­tion) "silence" mark­ing the end of the struc­ture to facil­i­tate its syn­chro­ni­sa­tion with the next item.

The phase diagram

Given a com­pact poly­met­ric struc­ture, time-setting algo­rithms require a table in which each col­umn is assigned a date (in phys­i­cal time). The cells of this phase dia­gram con­tain the iden­ti­fiers of the sound-objects, includ­ing "0" and "1". It is cre­at­ed by the pro­ce­dure FillPhaseDiagram() in the file "FillPhaseDiagram.c".

It is easy to imag­ine that the table would become very large if no com­pres­sion tech­niques were used. For exam­ple, Liszt's 14th Rhapsody would require no less than 9 x 1021 cells! The rea­son is that the Bol Processor cal­cu­lates sym­bol­ic dura­tions as inte­ger ratios. A sym­bol­ic dura­tion of 5/3 will nev­er be replaced by "1.666" for two rea­sons: (1) round­ings would accu­mu­late as notice­able errors, and (2) we don't know in advance how many dec­i­mals we need to keep. The phys­i­cal dura­tion of 5/3 beats depends on the metronome and the sequence of "_tempo(x)" con­trols that change the tempo.

Let us first con­sid­er an unprob­lem­at­ic case. The poly­met­ric expres­sion /3 {{C4_ _ D4_ _, E4_ F4 - G4_}, E5_ _ _ _ _} cre­ates the fol­low­ing phase diagram:

Phase dia­gram of
/3 {{C4_ _ D4_ _, E4_ F4 - G4_}, E5_ _ _ _ _}

In this exam­ple, if the metronome is set to 60 beats per minute, the phys­i­cal dura­tion assigned to each col­umn is 1/3 sec­ond = 333 ms. As the graph becomes larg­er, this phys­i­cal dura­tion may decrease beyond the lim­it. This is where quan­ti­za­tion comes in. It is set to 10 mil­lisec­onds by default, which means that two events occur­ring with­in 10 ms of each oth­er can be writ­ten into the same col­umn. To do this, the com­pact poly­met­ric struc­ture is rewrit­ten with a com­pres­sion rate (Kpress) that makes it fit into a phase dia­gram of suit­able size.

If the piece of music lasts 10 min­utes, we'll still get 10 x 60000 / 10 = 60000 columns in the table. Filling the phase dia­gram requires a very high com­pres­sion rate, for exam­ple more than 5 x 1012 for Beethoven's Fugue in B-flat major.

To make mat­ters worse, the algo­rithm has to deal with sequences of events that fall into the same col­umn. This sit­u­a­tion is sig­nalled by the vari­able toofast, which is obtained by com­par­ing the cur­rent tem­po with the max­i­mum tem­po accept­ed in the struc­ture. In the case of toofast, each event is writ­ten to a new row of the table in such a way as to respect the sequen­tial order of the stream.

So we end up with 12132 lines for the phase table of Beethoven's fugue, in which the longest toofast stream con­tains 625 events — notes or sound-objects. These 625 events, which occur with­in a sin­gle frame of 10 ms, actu­al­ly include '_' events which are exten­sions of notes belong­ing to the stream.

Dealing with complex ratios

In Bol Processor ter­mi­nol­o­gy, an inte­ger ratio p/q is "com­plex" if either 'p' or 'q' exceeds a lim­it that depends on the source code. The lim­it is ULONG_MAX, the max­i­mum val­ue of an unsigned long type, cur­rent­ly 18446744073709551616.

In the code of the Bol Processor con­sole, 'p' and 'q' are actu­al­ly cod­ed as dou­ble float­ing point num­bers whose man­tis­sa can con­tain as many dig­its as unsigned long inte­gers. Arithmetic oper­a­tions are per­formed on the frac­tions. Each result­ing frac­tion is checked for com­plex­i­ty by a pro­ce­dure called Simplify() in the "Arithmetic.c" file:

  1. While 'p' or 'q' is greater than ULONG_MAX, divide 'p' and 'q' by 10;
  2. Divide 'p' and 'q' by their great­est com­mon divi­sor (GCD).

Part (1) of the Simplify() pro­ce­dure gen­er­ates round­ing errors, but these rep­re­sent a few units of very large num­bers. In this way, the accu­ra­cy of sym­bol­ic dura­tions is main­tained through­out the com­pu­ta­tion of com­pli­cat­ed poly­met­ric structures.

Complex ratios in silences

Let us check the effect on quan­ti­za­tion by playing:

C4 C5 36001/24000 D5 E5

The ratio 36001/24000 can­not be sim­pli­fied. However, 1/24000 beat would take 0.04 ms which is much less than the 10 ms quan­ti­za­tion. So, the ratio can be approx­i­mat­ed to 36000/24000 and sim­pli­fied to 3/2. The final result is there­fore "C4 C5 3/2 D5 E5":

Item "C4 C5 36001/24000 D5 E5" sim­pli­fied as "C4 C5 3/2 D5 E5"

Let us now con­sid­er "C4 C5 35542/24783 D5 E5" which looks sim­i­lar, as 35542/24783 (1.43) is close to 1.5. However, the cal­cu­la­tion is more com­plex… Using the 10 ms quan­ti­za­tion, the ratio is reduced to 143/100 and the com­pact poly­met­ric expres­sion is:

/1 C4 C5 /100 - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ /1 D5 E5

The 143/100 silence is now rep­re­sent­ed as a sin­gle '-' (kobj = 1) fol­lowed by 142 '_' (kobj = 0). This sequence is toofast because tem­po­max, the max­i­mum tem­po accept­ed here, would be '50' instead of '100'. The com­pres­sion rate is Kpress = 2. A full expla­na­tion requires the poly­met­ric algo­rithm explained here.

The process of fill­ing the phase table can be found in "FillPhaseDiagram.c". We call 'ip' the index of the col­umn into which the next event is to be plot­ted. In the most com­mon sit­u­a­tion, e.g. writ­ing "C4 _ _" (object #2), two pro­ce­dures are called:

  • Plot() writes '2' (kobj) into col­umn ip
  • PutZeros() writes two zeros into the columns ip + 1 and ip +2.

So, "C4 _ _" will have a sym­bol­ic dura­tion of 3 units, as expected.

The case is dif­fer­ent with a silence of 143/100, because the toofast sit­u­a­tion requires that less than 142 '_' should be insert­ed after '-'. To this end, a (floating-point) vari­able part_of_ip is ini­tialised to 0 and gets incre­ment­ed by a cer­tain val­ue until it exceeds Kpress. Then Plot() and PutZeros() are called, part_of_ip is reset and a new cycle starts… until all 142 '_' of the com­pact poly­met­ric expres­sion have been read.

The incre­ment of part_of_ip in each cycle is:

part_of_ip += Kpress * tem­po­max / tempo;

In this sim­ple exam­ple, tem­po = 100, tem­po­max = 50 and Kpress =2. So the incre­ment is 1 and part_of_ip will reach the val­ue of Kpress after 2 cycles. This means that every oth­er '_' will be skipped.

Incrementing ip requires a more com­pli­cat­ed process. The algo­rithm keeps track of the col­umn num­bers in the table as it would be cre­at­ed with Kpress = 1. These num­bers are usu­al­ly much larg­er than those of the actu­al phase dia­gram. The large num­ber i is mapped to ip using the Class() function:

unsigned long Class(double i) {
unsigned long result;
if(Kpress < 2.) return((unsigned long)i);
result = 1L + ((unsigned long)(floor(i) / Kpress));
return(result);
}

So, each cycle of read­ing '_' in the toofast sit­u­a­tion ends up incre­ment­ing i and then updat­ing ip via the Class(i) func­tion. The incre­ment of i is:

prodtem­po - 1

in which:

prodtem­po = Prod / tempo

The vari­ables Prod and Kpress are cal­cu­lat­ed after the com­pact poly­met­ric expres­sion has been cre­at­ed. Prod is the low­est com­mon mul­ti­ple (LCM) of all tem­po val­ues, i.e. '100' in this example.

Let us use the inte­gers Pclock and Qclock to define the metronome val­ue as Qclock * 60 / Pclock. If the metronome is set to its default val­ue of 60 bpm, then Pclock = Qclock = 1.

The fol­low­ing (sim­pli­fied) code cal­cu­lates Kpress and updates Prod accordingly:

Kpress = 1. + (Quantization * Qclock * Prod) / Pclock / 1000.;
if(Kpress > 1.) {
s = LCM(Prod, Kpress) / Prod;
if(s > 1. && s < 10. && Prod < 1000000.) Prod = Round(s * Prod);
s = Round(Prod / Kpress);
if(s > 10.) Prod = Kpress * s;
}

As expect­ed, we get the fol­low­ing sound-object graph:

Sound-object graph of C4 35542/24783 D5.
The silence dura­tion is 35542/24783 = 1.43 beats.

A more complex structure

This is a phrase from Liszt's 14th Hungarian Rhapsody:

_tempo(80/39) {F1, C2} {2, F2} 667/480 {53/480, G1, G2} {1/2, Ab1, Ab2} {1/2, B1, B2}

The com­pact poly­met­ric expres­sion — with a some redun­dant ratios removed — is:

*39/80 {F1, C2} {F2 _} *13/12800 - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ *689/12800 {G1, G2} *39/160 {Ab1, Ab2} {B1, B2}

which gives the fol­low­ing sound-object graph:

_tempo(80/39){F1,C2}_tempo(80/39){2,F2}667/480 {53/480,G1,G2}{1/2,Ab1,Ab2}{1/2,B1,B2}
Metronome is set to 60 beats per minute.

Let us cal­cu­late the dura­tion of the silence between "F2" and "G1" in two ways:

  1. In the source poly­met­ric expres­sion, this silence is notat­ed as 667/480. Since the tem­po is 80/39, its dura­tion should be 667/480 * 39/80 = 0.67 beats (con­firmed by the graph).
  2. In the com­pact poly­met­ric expres­sion, we find one '-' object fol­lowed by 666 '_' pro­lon­ga­tions at a speed of *13/12800. The dura­tion is there­fore 667 * 13/12800 = 0.67 beats.

It would be dif­fi­cult to fol­low the algo­rithm step by step because Prod = 2496100 , Kpress = 24961 and tem­po­max = Prod / Kpress = 100. Within the silence, tem­po = 985 and the incre­ment of part_of_ip is 24961 * 100 / 985 = 2 534.11167… The num­ber of cycles before part_of_ip reach­es the val­ue of Kpress is ceil(9.85) = 10. This means that 9 out of 10 objects '_' have been skipped.

Conclusion

These exam­ples and expla­na­tions pro­vide insight into the code in the "FillPhaseDiagram.c" file of the con­sole code. We hope that it will be use­ful for future devel­op­ment or migra­tion of algorithms.

This is also a demon­stra­tion of the com­plex­i­ty of time cal­cu­la­tions when deal­ing with poly­met­ric struc­tures capa­ble of car­ry­ing all the details of real musi­cal works — see Importing MusicXML scores for "real life" examples.