Comparing temperaments

Images of tem­pered scales cre­at­ed by the Bol Processor

The fol­low­ing are Bol Processor + Csound inter­pre­ta­tions of Bach’s Prelude 1 in C major (BWV 846) using scales con­struct­ed with mean­tone tem­pera­ments (Asselin 2000). Names and tun­ing pro­ce­dures fol­low Asselin’s instruc­tions (pages 67-126). 

The con­struc­tion of these scales is explained on page Microtonality.

We hope to pub­lish bet­ter sound demos after receiv­ing a set of well-designed Csound instru­ments (“orc” files). This is an apol­o­gy to harp­si­chord play­ers and their designers!

Start lis­ten­ing to the piece in equal tem­pera­ment which is the most com­mon tun­ing of instru­ments in mod­ern times:

Equal tem­pera­ment (p. 123) ➡ Image

The fol­low­ing are tra­di­tion­al mean­tone tem­pera­ments, each of which has been designed at a par­tic­u­lar peri­od in response to the con­straints of musi­cal reper­toires en vogue (Asselin 2000 p. 139-180).

H.A. Kellner’s BACH (p. 101) ➡ Image
Barka in 1786 (p. 106) ➡ Image
Bethisy in 1764 (p. 121) ➡ Image
Chaumont in 1696 (p. 109) ➡ Image
Corrette in 1753 (p. 111) ➡ Image
D’Alambert-Rousseau 1752-1767 (p. 119) ➡ Image
Kirnberger II in 1771 (p. 90) ➡ Image
Kirnberger III in 1779 (p. 106) ➡ Image
Marpurg in 1756 (p. 117) ➡ Image
Pure minor thirds in 16th cen­tu­ry (p. 82) ➡ Image
Rameau en do in 1726 (p. 106) ➡ Image
Sauveur in 1701 (p. 80) ➡ Image
Tartini-Vallotti in mid. 18th cen­tu­ry (p. 104) ➡ Image
Werckmeister III in 1691 (p. 194) ➡ Image
Werckmeister IV in 1691 (p. 96) ➡ Image
Werckmeister V in 1691 (p. 199) ➡ Image
Zarlino in 1558 (p. 85) ➡ Image

The last exam­ple is Zarlino’s mean­tone tem­pera­ment which should not be con­fused with the pop­u­lar Zarlino’s “nat­ur­al scale”, an instance of just into­na­tion:

Zarlino’s “nat­ur­al scale” ➡ Image


Comparing tem­pera­ments on a sin­gle piece is a very lim­it­ed exer­cise aimed at high­light­ing dif­fer­ences in the var­i­ous pro­pos­als and their ade­qua­cy to cre­ate a pleas­ant effect when lis­ten­ing to this par­tic­u­lar piece.

J.S. Bach’s dis­ci­ple Johann Kirnberg (1721-1723) - (source)

In real­i­ty, Bach’s Well-Tempered Clavier (BWV 846–893) is a col­lec­tion of two sets of pre­ludes and fugues in all 24 major and minor keys. To assess the valid­i­ty of a tun­ing scheme it would there­fore be nec­es­sary to lis­ten to all pieces. Fortunately, there are clues to an opti­mal choice: Friedrich Wilhelm Marpurg received infor­ma­tion from Bach’s sons and pupils and Johann Kirnberger, one of those pupils, designed a tun­ing (Kirnberger II) which he claimed to rep­re­sent his mas­ter’s idea of “well-tempered”.

Chapter VIII of Pierre-Yves Asselin’s book (2000 p. 139-180) con­tains exam­ples of musi­cal works high­light­ing the rel­e­vance of spe­cif­ic tem­pera­ments. Given that the scores of many (if not all) Baroque and clas­si­cal mas­ter­pieces are avail­able in dig­i­tal for­mat MusicXML, we may use Bol Processor’s Importing MusicXML scores to transcode them and play these excerpts with the sug­gest­ed temperaments.

Musicians inter­est­ed in con­tin­u­ing this research may use Bol Processor BP3’s beta ver­sion to process musi­cal works and cre­ate new tun­ing pro­ce­dures. Follow instruc­tions on page Bol Processor ‘BP3’ and its PHP inter­face to install BP3 and learn its basic oper­a­tion. Download and install Csound from its dis­tri­b­u­tion page.


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

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