16/15: Difference between revisions
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The [[5-limit]] [[superparticular]] interval '''16/15''' is the '''just''', '''classic(al)''' or '''ptolemaic diatonic semitone''' – the difference between the major third [[5/4]] and the fourth [[4/3]], and between [[3/2]] and [[8/5]]. | The [[5-limit]] [[superparticular]] interval '''16/15''' is the '''just''', '''classic(al)''' or '''ptolemaic diatonic semitone'''<ref>For reference, see [[5/4]]. </ref> – the difference between the major third [[5/4]] and the fourth [[4/3]], and between [[3/2]] and [[8/5]]. | ||
== Temperaments == | == Temperaments == | ||
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* [[45/32]] – its [[fifth complement]] | * [[45/32]] – its [[fifth complement]] | ||
* [[5/4]] – its [[fourth complement]] | * [[5/4]] – its [[fourth complement]] | ||
* [[256/243]] | * [[256/243]] – the Pythagorean (3-limit) diatonic semitone | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
* [[16/ | * [[16/15 equal-step tuning]] – equal multiplication of this interval | ||
== Notes == | |||
<references/> | |||
[[Category:Second]] | [[Category:Second]] | ||
[[Category:Semitone]] | [[Category:Semitone]] | ||
Revision as of 12:43, 12 January 2023
| Interval information |
classic(al) diatonic semitone,
ptolemaic diatonic semitone
reduced,
reduced subharmonic
[sound info]
The 5-limit superparticular interval 16/15 is the just, classic(al) or ptolemaic diatonic semitone[1] – the difference between the major third 5/4 and the fourth 4/3, and between 3/2 and 8/5.
Temperaments
When this ratio is taken as a comma to be tempered, it produces father temperament, where 4/3 and 5/4 are equated. In this temperament, major thirds and fifths become octave complements of each other.
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