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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".
The names heptatonia prima and heptatonia secunda apply to seven-note scales that can be formed using five tones (t) and two semi-tones (s), (also called whole-steps and half-steps), but without two semi-tones in succession. Throughout history and to the present day, some have occurred much more commonly than others, namely Ionian (also called ...
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).
For this reason, notes an octave apart are given the same note name in the Western system of music notation—the name of a note an octave above A is also A. This is called octave equivalence , the assumption that pitches one or more octaves apart are musically equivalent in many ways, leading to the convention "that scales are uniquely defined ...
Major 13th (compound major 6th) inverts to a minor 3rd by moving the bottom note up two octaves, the top note down two octaves, or both notes one octave. A simple interval (i.e., an interval smaller than or equal to an octave) may be inverted by raising the lower pitch an octave or lowering the upper pitch an octave. For example, the fourth ...