16/15: Difference between revisions
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Add more differences in lead section, add approximation section, add temperaments using 16/15 as a generator (merged from 1ed16/15) |
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The following [[linear temperament]]s are [[generate]]d by a [[~]]16/15: | The following [[linear temperament]]s are [[generate]]d by a [[~]]16/15: | ||
* [[Vavoom]] | * [[Vavoom]] | ||
* [[Stockhausenic]] | * [[Stockhausenic]] | ||
Revision as of 19:39, 5 August 2025
Interval information |
classic(al) diatonic semitone,
ptolemaic diatonic semitone
reduced,
reduced subharmonic
S6 × S7 × S8
[sound info]
The 5-limit superparticular interval 16/15 is the just diatonic semitone, classic(al) diatonic semitone or ptolemaic diatonic semitone[1].
It is the difference between:
- the major second 9/8 and the minor third 6/5;
- the major third 5/4 and the fourth 4/3;
- the perfect fifth 3/2 and the minor sixth 8/5;
- the major sixth 5/3 and the minor seventh 16/9;
- the major seventh 15/8 and the perfect octave 2/1.
Approximation
16/15 is very accurately approximated by 43edo (4\43).
Temperaments
When this ratio is taken as a comma to be tempered out, it produces father temperament, and lends itself the name father comma. In this exotemperament, 4/3 and 5/4 are equated, and major thirds and fifths become octave complements of each other. It is a Mersenne comma.
The following linear temperaments are generated by a ~16/15:
In addition, this fractional-octave temperaments are generated by a ~16/15:
Some 11th-octave temperaments treat ~16/15 as the period, including hendecatonic.
See also
- 15/8 – its octave complement
- 45/32 – its fifth complement
- 5/4 – its fourth complement
- 256/243 – the Pythagorean (3-limit) diatonic semitone
- Gallery of just intervals
- List of superparticular intervals
- 16/15 equal-step tuning – equal multiplication of this interval