Musical temperament
The famous Well-Tempered Clavier by Johann Sebastian Bach takes full advantage of this breakthrough, with pieces written in all 24 major and minor keys.
Temperament, in music, the accommodation or adjustment of the imperfect sounds by transferring a part of their defects to the more perfect ones, in order to remedy, in some degree, the false intervals of those instruments, the sounds of which are fixed; as the organ, harpsichord, piano-forte, etc.Temperament is what the Italians call participatione, or system temperato, because it is founded on temperature; that is, on the diminution of some intervals and augmentation of others, by which it partakes of the diatonic and chromatic systems.
[7] If one of those pitches is adjusted slightly to deviate from the just interval, a trained ear can detect this change by the presence of beats, which are periodical oscillations in the note's intensity.
When two tones depart from exact integer ratios, the shape waveform[clarification needed] becomes erratic—a phenomenon that may be described as destabilization.
[9] Nevertheless, these relationships between differentials play a large role in determining which tunings create consonant sound.
Tempering an interval involves the deliberate use of such minor adjustments (accepting the related destabilization) to enable musical possibilities that are impractical using just intonation.
With the correct amount of tempering, the syntonic comma is reduced to a unison, bringing the major and minor thirds closer to their ratios in just intonation.
In meantone temperament, this effect is even more pronounced (the fifth over the break in the circle is known as the Wolf interval, as its intense beating was likened to a "howling").
This phenomenon gives rise to infinite shades of key-colors, which are lost in the modern standard version: 12-tone equal temperament (12-TET).
This freedom of modulation also allowed substantial use of more distant harmonic relationships, such as the Neapolitan chord, which became very important to Romantic composers in the 19th century.
