19683/16384: Difference between revisions
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The '''Pythagorean augmented 2nd''', '''19683/16384''', may be reached by stacking 9 3/2's and octave reducing. It differs from the classic minor third, [[6/5]], by the [[schisma]], and, as a result, the Pythagorean augmented second is in fact rather consonant. According to [[User:Aura|Aura]], while 19683/16384 may take the place of the classic minor third in chords, its status as an augmented second means that it has a different function in terms of voice-leading. | The '''Pythagorean augmented 2nd''', '''19683/16384''', may be reached by stacking 9 3/2's and octave reducing. It differs from the classic minor third, [[6/5]], by the [[schisma]], and, as a result, the Pythagorean augmented second is in fact rather consonant. According to [[User:Aura|Aura]], while 19683/16384 may take the place of the classic minor third in chords, its status as an augmented second means that it has a different function in terms of voice-leading. According to Vector, it is itself a minor third due to being within the range of other accepted minor thirds, and its status as an augmented second is only in the context of a Pythagorean diatonic system. | ||
== Temperaments == | == Temperaments == | ||
Revision as of 03:40, 13 July 2024
| Interval information |
Evadairean comma
reduced harmonic
The Pythagorean augmented 2nd, 19683/16384, may be reached by stacking 9 3/2's and octave reducing. It differs from the classic minor third, 6/5, by the schisma, and, as a result, the Pythagorean augmented second is in fact rather consonant. According to Aura, while 19683/16384 may take the place of the classic minor third in chords, its status as an augmented second means that it has a different function in terms of voice-leading. According to Vector, it is itself a minor third due to being within the range of other accepted minor thirds, and its status as an augmented second is only in the context of a Pythagorean diatonic system.
Temperaments
When this ratio is taken as a comma to be tempered out, it produces the tervenna temperament, and has been named the Evadairean comma (by analogy with the Pythagorean comma not sharing its name with compton temperament). Edos tempering it out include 9edo, as well as 18edo if its flat fifth is used. It can be used as a generator for hanson.