Sources of the Temperament Ordinaire: France, late 17th- to late 18th-century
Introduction
The tuning of harpsichords in the later Baroque period in France (which means Paris, so far as we have any documentary sources) began to deviate at some point from meantone. Mark Lindley has proposed (Journal of Music Theory, 1980) to trace this back to Mersenne's keyboard tuning instructions in Harmonie Universelle (1636), which contained a description of meantone starting from F, in which the intended narrowing of the "back-side" fifths F-Bb and Bb-Eb was confusingly described, so that readers could have read these two fifths as being wide rather than narrow.
This would not yet create a "temperament ordinaire" in the usual sense of a circulating tuning with no wolf fifth, since G#-Eb would still be very wide. But, as an interesting musical result, that the same note could be tolerable as D#, as leading-note of E minor for example, and at the same time Eb as minor third on C. Lindley has suggested that Louis Couperin's use of Eb/D# and Bb/A# may have reflected this type of modified meantone.
To the idea of (some of) the accidentals being compromises between sharps and flats, what was added was the requirement that there should be a true circle of fifths, with every interval tolerably tuned. This could be achieved by further alterations of notes away from regular meantone: with the result that fewer thirds were pure, but more keys were usable, given that their impure thirds were accepted. When and how this practice became common is unknown. Right through the Baroque and early Classical period, French writers (Denis 1643, Corrette 1753, Bedos 1766) describe meantone with slight, or no, modifications; the optional widening of F-Bb-Eb was mentioned by Chaumont (1695). Sources that give truly circular tunings (Rameau 1726, d'Alembert 1752, Rousseau 1767, Mercadier 1776) do not say how old the practice was - only that it was already usual at the time of writing.
Principal sources
For each source there is a short summary, and a link to a separate page with text and discussion.
Rameau gives two descriptions: one of the usual practice, and one of what he considers an ideal temperament. The usual tuning begins by establishing a meantone base with a major third "as pure as the ear demands"; then in the middle of the bearings, one starts to make the fifths progressively wider, until the last one. The starting note is not specified. The ideal temperament contains seven narrow tempered fifths producing four pure thirds: the remaining fifths are wider, with the last two apparently the widest. Rameau first describes this temperament starting on C (possibly for theoretical simplicity) then says that if one starts on Bb, the intervals in the commonest harmonies will keep as much purity as possible.
Rameau remarks on the musical effect of the wide fifths and consequently impure thirds. These occur in progressions that are little used, unless expressly chosen for an effect of "hardness", etc. The impression we receive from intervals differs, depending on how far they deviate from purity. The impurity of the intervals could be condemned, but for the expression that expert musicians derive from it.
Rameau's later writing (1737) introducing the supposed novelty of equal temperament refers to a harpsichord with the "falsest" temperament, which appears to be meantone.
d'Alembert, writing under Rameau's direct influence, promotes equal temperament in this textbook. However, in a footnote he notes that this deviates considerably from the usual practice, and gives a more precise description of this than in 1726. This is the first known text to use the expression "temperament ordinaire". One tunes C-E as meantone with a pure third; then from E through G# the fifths are less narrow, so that E-G# is only "nearly" pure. Starting again from C one tunes downward by fifths, making them all a little wide so as to meet up with the previously-tuned G# as Ab. By a curious mistake d'Alembert says that the last note to be tuned is Db, perhaps thinking of Eb = D#.
Concerning the musical effect, d'Alembert says that although [most] thirds are purer than in Mr. Rameau's temperament (meaning ET), there are five or six unbearable keys, in which one cannot perform anything; whereas in Mr. Rameau's temperament every key is equally perfect...
Rousseau's article sets out to summarize the mathematics and history of temperament. He describes a tuning which he says is regarded by organists and builders as the most perfect that one can use. Starting as usual with four fifths to make a pure third C-E, one continues by fifths, until on reaching the sharps one widens the fifths a little, although the thirds will suffer. G# should make a "pure or at least bearable" third with E. Starting again from C tuning downward fifths, one at first tunes narrow, then gradually widening the fifths until the circle is closed. Rousseau says that the last test is that Db, taken as C#, makes a good fifth with the previously-tuned G#: this is the same mistake as d'Alembert's, aggravated by Rousseau's fuller (but wronger) explanation.
On the musical effect, Rousseau says that Bb and Eb major are dark and even a little hard; but this is bearable if the tuning has been well done, and their thirds need not be used except by choice. The natural [diatonic] keys enjoy all the purity of harmony, whereas the less common transposed keys have great resources for more pronounced expression. In the article on "Ton" Rousseau explains key character as a result of (keyboard) temperament.
The "Temperament" article also mentions Rameau several times. Rousseau quotes some of his comments on the musical effect of ordinare from 1726, then says that he changed his tune later, and began to make claims for a new practice of equal temperament. But Rousseau notes that Mersenne had written about equal temperament in detail long ago, that [Francois] Couperin had tried and rejected it, and that musical practitioners do not like it.
Mercadier deals both with equal temperament and ordinaire, and also tries to construct a tuning which lies between the two (given in Lindley, Stimmung & Temperatur). His account of the "usual" tuning appears to have slight inconsistencies, or at least to derive from more than one previous source. His first description corresponds closely to d'Alembert, with the remark that E-G# should be "a little sharp", and correctly counts the fifths on the flat side from C back to Ab (which is to be tuned as G# and then not touched).
Later he gives a version of the sharp-side fifths which corresponds more to Rameau (1726), saying that commonly E-G# is almost pure, and only the fifth C#-G# is less narrow than the others. He says the usual practice on the flat side is to take F-C only a very little wide; then Bb-F a little more; until the last one Ab-Eb is the largest of all. This formula recalls Rousseau, though Rousseau implies that one starts off on the flat side with at least one narrow fifth.
Online references
Other references
- New Grove Dictionary, article "Temperament"
- M. Lindley, "Stimmung und Temperatur", in Hoeren, messen und rechnen in der fruehen Neuzeit, Frieder Zaminer (ed.), vol. 6 of Geschichte der Musiktheorie, Wissenschaftliche Buchgesellschaft, Darmstadt, 1987, pp. 109-331.
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