16/15: Difference between revisions

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Names
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{{Infobox Interval
{{Infobox Interval
| Name = classic/just diatonic semitone, classic/just minor second
| Name = just diatonic semitone, classic(al) diatonic semitone, ptolemaic diatonic semitone
| Color name = g2, gu 2nd
| Color name = g2, gu 2nd
| Sound = jid_16_15_pluck_adu_dr220.mp3
| Sound = jid_16_15_pluck_adu_dr220.mp3
}}
}}


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]].
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]].


== Temperaments ==
== Temperaments ==

Revision as of 12:42, 12 January 2023

Interval information
Ratio 16/15
Factorization 24 × 3-1 × 5-1
Monzo [4 -1 -1
Size in cents 111.7313¢
Names just diatonic semitone,
classic(al) diatonic semitone,
ptolemaic diatonic semitone
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 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.

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