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12 tone equal temperament chromatic scale on C, one full octave ascending, notated only with sharps. Play ascending and descending ⓘ. An equal temperament is a musical temperament or tuning system that approximates just intervals by dividing an octave (or other interval) into steps such that the ratio of the frequencies of any adjacent pair of notes is the same.
In musical tuning, a temperament is a tuning system that slightly compromises the pure intervals of just intonation to meet other requirements. Most modern Western musical instruments are tuned in the equal temperament system. Tempering is the process of altering the size of an interval by making it narrower or wider than pure.
The first is in equal temperament; the second is in just intonation. The pair of chords is repeated with a transition from equal temperament to just intonation between the two chords. In the equal temperament chords a roughness or beating can be heard at about 4 Hz and about 0.8 Hz. In the just intonation triad, this roughness is absent.
Quarter tones have their roots in the music of the Middle East and more specifically in Persian traditional music. [1] However, the first evidenced proposal of the equally-tempered quarter tone scale, or 24 equal temperament , was made by 19th-century music theorists Heinrich Richter in 1823 [ 2 ] and Mikhail Mishaqa about 1840. [ 3 ]
12-tone equal temperament chromatic scale on C, one full octave ascending, notated only with sharps. Play ascending and descending ⓘ. 12 equal temperament (12-ET) [a] is the musical system that divides the octave into 12 parts, all of which are equally tempered (equally spaced) on a logarithmic scale, with a ratio equal to the 12th root of 2 (≈ 1.05946).
Nowadays, with the advent of electronic isomorphic keyboards, equal temperament tunings with more than twelve notes per octave can be used to close the circle of fifths for other tunings. For example, 31-tone equal temperament closely approximates quarter-comma meantone, and 53-tone equal temperament closely approximates Pythagorean tuning.
In music, 15 equal temperament, called 15-TET, 15-EDO, or 15-ET, is a tempered scale derived by dividing the octave into 15 equal steps (equal frequency ratios). Each step represents a frequency ratio of 15 √ 2 (=2 (1/15) ), or 80 cents ( Play ⓘ ).
Figure 1: 19-TET on the syntonic temperament's tuning continuum at P5= 694.737 cents [1]. In music, 19 equal temperament, called 19 TET, 19 EDO ("Equal Division of the Octave"), 19-ED2 ("Equal Division of 2:1) or 19 ET, is the tempered scale derived by dividing the octave into 19 equal steps (equal frequency ratios).