Well Temperament - Origins

Origins

"Well tempered" means that the twelve notes per octave of the standard keyboard are tuned in such a way that it is possible to play music in most major or minor keys and it will not sound perceptibly out of tune. In most tuning systems used before 1700, one or more intervals on the twelve-note keyboard were so far from any pure interval that they were unusable in harmony and were called a "wolf". Until about 1650 the most common keyboard temperament was quarter-comma meantone, in which the fifths were narrowed to the extent that they were just usable, and would thereby produce justly tuned thirds. The syntonic comma was distributed between four intervals, with most of the comma accommodated in the sol♯ to mi♭ diminished sixth, which expands to nearly a minor sixth. It is this interval that is usually called the "wolf", because it is so far out of consonance. The term "mean tone", the basis for meantone temperament, refers to the mathematical averaging of thirds, in which the middle note (for example the D between C and E) is in the "mean" position between the notes making the third. Another example of this is equal temperament (which is actually eleventh-comma meantone if seen in the perspective as to how to divide the comma between the fifths).

The wolf was not a problem if music was played in a small number of keys (or to be more precise, transposed modes) with few accidentals, but it prevented players from transposing and modulating freely. Some instrument-makers sought to remedy the problem by introducing more than twelve notes per octave, producing enharmonic keyboards which could provide, for example, a D♯ and an E♭ with different pitches so that the thirds B–D♯ and E♭–G could both be euphonious.

However, Werckmeister realised that these "subsemitonia", as he called them, were unnecessary, and even counterproductive in music with chromatic progressions and extensive modulations. He described a series of tunings where enharmonic notes had the same pitch: in other words, the same note was used as both (say) E♭ and D♯, thereby "bringing the keyboard into the form of a circle". This refers to the fact that the notes or keys may be arranged in a circle of fifths and it is possible to modulate from one key to another unrestrictedly.

According to Sinologist Robert K. G. Temple, the well temperament was first invented by the Chinese prince of the Ming dynasty Chu Tsai-Yü in 1584 and came in contact with Western culture during exchange fairs organized by the Cantonese viceroy in that time. How exactly it travelled to Europe is not documented, but it is likely that Jesuits in China brought the knowledge over to Europe (Temple 2007,). Other scholars, however, state that Prince Chu accurately calculated not a well temperament but equal temperament—though only in his second treatise, Lii Lu Ching I, written in 1595–96 and probably first published in 1606 did he achieve the full chromatic complement of 12 notes (Kutter 1975, 166–67). However, at just the same time, the Flemish mathematician Simon Stevin (1548–1620) wrote an essay containing the correct mathematical formulation of equal temperament for the first time in Western musical theory, though his manuscript remained unpublished until long after the author's death (Kutter 1975, 167–68; Stevin 1884).