16/15: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Icon =
| Ratio = 16/15
| Ratio = 16/15
| Monzo = 4 -1 -1
| Monzo = 4 -1 -1
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== Temperaments ==
== 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-inverses]] of each other.
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 complement]]s of each other.


== See also ==
== See also ==
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[[Category:5-limit]]
[[Category:5-limit]]
[[Category:Interval]]
[[Category:Just interval]]
[[Category:Ratio]]
[[Category:Listen]]
[[Category:Second]]
[[Category:Second]]
[[Category:Semitone]]
[[Category:Semitone]]

Revision as of 20:44, 12 December 2021

Interval information
Ratio 16/15
Factorization 24 × 3-1 × 5-1
Monzo [4 -1 -1
Size in cents 111.7313¢
Names classic/just diatonic semitone,
classic/just minor second
Color name g2, gu 2nd
FJS name [math]\displaystyle{ \text{m2}_{5} }[/math]
Special properties square superparticular,
reduced,
reduced subharmonic
Tenney height (log2 nd) 7.90689
Weil height (log2 max(n, d)) 8
Wilson height (sopfr(nd)) 16

[sound info]
Open this interval in xen-calc

The 5-limit superparticular interval 16/15 is the classic or just diatonic semitone – 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