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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.
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 ...
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 intervals of 5-limit just intonation (prime limit, not odd limit) are ratios involving only the powers of 2, 3, and 5. The fundamental intervals are the superparticular ratios 2/1 (the octave), 3/2 (the perfect fifth) and 5/4 (the major third). That is, the notes of the major triad are in the ratio 1:5/4:3/2 or 4:5:6.
Isomorphic keyboards expose the invariant properties of the meantone tunings of the syntonic temperament isomorphically (that is, for example, by exposing a given interval with a single consistent inter-button shape in every octave, key, and tuning) because both the isomorphic keyboard and temperament are two-dimensional (i.e., rank 2) entities ...
A chain of three tones spaced in equal-sized fifths (reduced to the octave) generates a whole tone (e.g. C G D). A sequence of six tones spaced in fourths generates a semitone in the same way (e.g. E A D G C F). A sequence of five tones spaced in fifths (e.g. C G D A E) generates a major third, consisting of two whole tones.