The phrase temperament ordinaire (French tempérament ordinaire, meaning literally "ordinary temperament" or "usual temperament") is a term for musical intonation, particularly the tempered tuning of keyboard instruments. In modern usage, it usually refers to temperaments falling within the range (as understood broadly) of tunings now known as "well-tempered". The expression occurs primarily in French-language works of the 17th and 18th centuries concerning theory and practice of musical intonation with regard to keyboard instruments. It is discussed again, in the same or a similar musical application, in modern literature concerned with historical practices relating to keyboard instruments and performance. 17th-century usage and application One of the early historical documents in which the phrase was used is Christiaan Huygens' "Lettre touchant le cycle harmonique", ("Letter concerning the harmonic cycle") of 1691. This refers several times, in a comparative way, to "temperament ordinaire". The main purpose of Huygens' letter was to describe and discuss an unconventional 31-fold division of the octave. He did this by first recapitulating a conventional known temperament of his time, and then he compared that with his new scheme (which actually had been approximately conceived before, albeit without Huygens' mathematical precision); and he discussed the differences. Huygens' description of the conventional arrangement was quite precise, and it is clearly identifiable with what is now classified as (quarter-comma) meantone temperament. (A little calculation is needed to see the matching correspondence between, on the one hand, the figures in the right hand column of Huygens' table of 1691, which is headed 'Division of the octave following the temperament ordinaire', and on the other hand, the interval-values in the quarter-comma mean-tone scale. Huygens' figures are in base-10 logarithms, but in the inverse sense, and offset by 5: they range from 5 at the lower C, to (5-log10(2)) at the C an octave above. If H is Huygens' number for any note, then in modern terms, the number of cents in the interval that it makes with the lower C is ( 1200 / log10(2) ) * (5-H), and its frequency-ratio with the lower C is antilog10( 5-H ). Thus Huygens' value for G natural, 4.8252574989, corresponds to ~696.578... cents, and to a ratio of 1.495348...; and so on.) Huygens referred to this conventional arrangement, variously, in the course of his comparisons, as "the Temperament that I have just explained", "the Temperament", "the ordinary Temperament" (temperament ordinaire), "the Ordinary Temperament" (with both words