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In Western music theory, an interval is named according to its number (also called diatonic number, interval size [6] or generic interval [7]) and quality. For instance, major third (or M3 ) is an interval name, in which the term major ( M ) describes the quality of the interval, and third ( 3 ) indicates its number.
Melodies can be based on a diatonic scale and maintain its tonal characteristics but contain many accidentals, up to all twelve tones of the chromatic scale, such as the opening of Henry Purcell's "Thy Hand, Belinda" from Dido and Aeneas (1689) with figured bass), which features eleven of twelve pitches while chromatically descending by half steps, [1] the missing pitch being sung later.
For example, for every generic interval of a second there are only two possible specific intervals: 1 semitone (a minor second) or 2 semitones (a major second). In diatonic set theory a generic interval is the number of scale steps between notes of a collection or scale. The largest generic interval is one less than the number of scale members ...
There exists another type of limit, the odd limit, a concept used by Harry Partch (bigger of odd numbers obtained after dividing numerator and denominator by highest possible powers of 2), but it is not used here. The term "limit" was devised by Partch. [1] By definition, every interval in a given limit can also be part of a limit of higher order.
As explained above, all major scales use the same interval sequence T–T–S–T–T–T–S. This interval sequence was called the Ionian mode by Glarean. It is one of the seven modern modes. From any major scale, a new scale is obtained by taking a different degree as the tonic. With this method it is possible to generate six other scales or ...
For the ordinary diatonic scales described here, the T-s are tones and the s-s are semitones which are half, or approximately half the size of the tone.But in the more general regular diatonic tunings, the two steps can be of any relation within the range between T = 171.43 ¢ (for s = T at the high extreme) and T = 240 ¢ (for s = 0 at the low extreme) in musical cents (fifth, p5, between 685 ...
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The class of the unison, Class(0), consists solely of multiples of Ω and is typically excluded from consideration, so that the number of generic intervals is ℘ − 1. Hence the generic intervals are numbered from 1 to ℘ − 1, and a scale is proper if for any two generic intervals i < j implies class(i) < class(j).