The following are Bol Processor + Csound interpretations of J.-S. Bach’s Prelude 1 in C major (1722) and François Couperin’s Les Ombres Errantes (1730) — both near the end of the Baroque period — using scales constructed with temperaments (Asselin 2000). The names and tuning procedures follow Asselin’s instructions (p. 67-126). Images of the scales have been created by the Bol Processor.
➡ We hope to publish better sound demos after receiving a set of well-designed Csound instruments (“orc” files). Apologies to harpsichord players, tuners and designers!
Bach’s Prelude 1 in C major (1722)
Let us start listening to the piece in equal temperament, the popular tuning of instruments in electronic times. Uneducated musicians believe that “well-tempered” equates “equal-tempered”…
➡ Don’t hesitate to click “Image” links to display circular graphic representations of scale intervals highlighting consonance and dissonance.
The following are traditional temperaments, each of which has been designed at a particular time to meet the specificities of musical repertoires en vogue (Asselin 2000 p. 139-180).
J.S. 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, dated 1722. To assess the validity of a tuning scheme it would be necessary to listen to all pieces. Readers impatient to know more may be interested in a “computational” approach of this subject, read Bach well-tempered tonal analysis and listen to results on page The Well-tempered Clavier.
Fortunately, there are historical clues to optimal choices: Friedrich Wilhelm Marpurg received information from Bach’s sons and pupils and Johann Kirnberger, one of these pupils, designed tunings which he claimed to represent his master’s idea of “well-tempered”.
On page Tonal analysis of musical items we show that the analysis of tonal intervals tends to suggest the choice of Kirnberger III rather than Kirnberger II. However, the temperament designed in 1701 by French physician Joseph Sauveur also seemed to be a better fit in terms on melodic intervals — and indeed it sounds beautfiful… This may in turn be challenged by the systematic matching of all works in books I and II against tuning schemes implemented on the Bol Processor — read page Bach well-tempered tonal analysis.
François Couperin’s Les Ombres Errantes (1730)
Again, apologies to harpsichord players, tuners and manufacturers!
This piece is part of François Couperin’s Quatrième livre published in 1730 ➡ read the full score (Creative Commons licence CC0 1.0 Universal). We used it to illustrate the interpretation of mordents when importing MusicXML files.
Since a few of the following temperaments have been designed (or described?) after 1730, these were unlikely to be used by the composer. Let us try them all anyway, and find the winner!
The best temperament for this piece might be Rameau en sib designed by Couperin’s contemporary Jean-Philippe Rameau for musical works with flats in their key signature (Asselin, 2000 p. 149) — such as the present one. Read page Tonal analysis of musical items for the description of a systematic (automated) analysis confirming this choice.
We may end up listening to François Couperin’s Le Petit Rien (Ordre 14e de clavecin in D major, 1722) with two sharps in the key signature suggesting the use of a Rameau en do temperament.
This choice is also confirmed by the method described on page Tonal analysis of musical items.
Work in progress
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 Baroque and classical masterpieces are available in digital format MusicXML, we hope to use Bol Processor’s Importing MusicXML scores to transcode them and play these fragments with the suggested temperaments.
Despite the limitation of comparing temperaments on only two musical examples, the aim of this page is to illustrate the notion of “perfection” in sets of tonal intervals — and music at large. Read the discussion: Just intonation: a general framework. At least, we hope to convince readers that equal-temperament is not the “perfect” solution!
Musicians interested in continuing this research and related development 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.