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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.
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).
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 ]
Below is a comparison between the first 31 harmonics and the intervals of 12-tone equal temperament (12TET), octave displaced and compressed into the span of one octave. Tinted fields highlight differences greater than 5 cents ( 1 ⁄ 20 of a semitone), which is the human ear's " just noticeable difference " for notes played one after the other ...
Starting on a C, and using the standard system of tuning for Western music (12-tone equal temperament), the sequence is: C, G, D, A, E, B, F ♯ /G ♭, C ♯ /D ♭, G ♯ /A ♭, D ♯ /E ♭, A ♯ /B ♭, F, and C. This order places the most closely related key signatures adjacent to one another.
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).