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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.
If all these commas are exactly of the same size, there results an octave of 5 tones + 2 diatonic semitones, 5 × 9 + 2 × 4 = 53 equal commas. Holder [ 18 ] attributes the division of the octave in 53 equal parts to Nicholas Mercator , [ c ] who himself had proposed that 1 / 53 part of the octave be named the "artificial comma".
[citation needed] Furthermore, every interval created by two sustained tones creates a third tone, called a differential (or resultant) tone. This third tone is equal to the lower pitch subtracted from the higher pitch. This third tone then creates intervals with the original two tones, and the difference between these is called a second ...
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 most popular bowed strings used nowadays belong to the violin family; together with their respective standard tunings, they are: Violin – G 3 D 4 A 4 E 5 (ascending perfect fifths, starting from G below middle C) Viola – C 3 G 3 D 4 A 4 (a perfect fifth below a violin's standard tuning) Cello – C 2 G 2 D 3 A 3 (an octave lower than ...
The first column gives the fraction of the systonic comma by which the perfect fifths are tempered in the meantone system. The second lists 5-limit rational intervals that occur within this tuning. The third gives the fraction of an octave, within the corresponding equitempered microinterval system, that best approximates the meantone fifth.
A semitone is thus made of two steps, and three steps make a three-quarter tone or neutral second, half of a minor third. The 8-TET scale is composed of three-quarter tones. Four steps make a whole tone. Quarter tones and intervals close to them also occur in a number of other equally tempered tuning systems.
The just perfect fifth can be heard when a violin is tuned: if adjacent strings are adjusted to the exact ratio of 3:2, the result is a smooth and consonant sound, and the violin sounds in tune. Keyboard instruments such as the piano normally use an equal-tempered version of the perfect fifth, enabling the instrument to play in all keys.