16/15: Difference between revisions

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'''16/15'''
{{Infobox Interval
|4 -1 -1>
| Icon =
| Ratio = 16/15
| Monzo = 4 -1 -1
| Cents = 111.73129
| Name = diatonic semitone, <br/> classic minor second
| Color name = g2, gu 2nd
| Sound = jid_16_15_pluck_adu_dr220.mp3
}}


111.73129 cents
The [[5-limit]] just diatonic semitone is the [[superparticular]] interval '''16/15''' -- the difference between the major third [[5/4]] and the fourth [[4/3]], and between [[3/2]] and [[8/5]].


[[File:jid_16_15_pluck_adu_dr220.mp3]] [[:File:jid_16_15_pluck_adu_dr220.mp3|sound sample]]
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.


The 5-limit just diatonic semitone is the [[superparticular|superparticular]] interval 16/15 -- the difference between the major third [[5/4|5/4]] and the fourth [[4/3|4/3]], and between [[3/2|3/2]] and [[8/5|8/5]].
== See also ==
* [[15/8]] its [[inverse interval]]
* [[Gallery of Just Intervals]]


When this ratio is taken as a comma to be tempered, it produces [[Father|father]] temperament, where 4/3 and 5/4 are equated. In this temperament, major thirds and fifths become octave-inverses of each other.
[[Category:5-limit]]
[[Category:5-limit]]
[[Category:interval]]
[[Category:Interval]]
[[Category:just_interval]]
[[Category:Just interval]]
[[Category:ratio]]
[[Category:Ratio]]
[[Category:semitone]]
[[Category:Sound example]]
[[Category:Semitone]]
[[Category:Superparticular]]

Revision as of 22:47, 26 October 2018

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

[sound info]
Open this interval in xen-calc

The 5-limit just diatonic semitone is the superparticular interval 16/15 -- the difference between the major third 5/4 and the fourth 4/3, and between 3/2 and 8/5.

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.

See also