23/22: Difference between revisions

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Created page with "{{Infobox Interval | Icon = | Ratio = 23/22 | Monzo = 3 1 0 0 0 0 0 0 -1 | Cents = {{subst:cents|23/22|5}} | Name = greater vicesimotertial semitone | Color name = 23o1u2, tw..."
 
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{{Infobox Interval
{{Infobox Interval
| Icon =
| Ratio = 23/22
| Monzo = 3 1 0 0 0 0 0 0 -1
| Cents = 76.95640
| Name = greater vicesimotertial semitone
| Name = greater vicesimotertial semitone
| Color name = 23o1u2, twenty-tholu 2nd
| Color name = 23o1u2, twetholu 2nd
| Sound = Ji-23-22-csound-foscil-220hz.mp3
| Sound = Ji-23-22-csound-foscil-220hz.mp3
| Comma = yes
}}
}}
'''23/22''', the '''greater vicesimotertial semitone''', is a [[23-limit]] interval. It is the first [[superparticular]] interval that is [[mapped interval|mapped]] to 0 steps in [[12edo]], which means it is treated as a [[comma]], although it is more than half the size of a 12edo [[semitone (interval size measure)|semitone]].
== Approximation ==
{{Interval edo approximation|23/22}}
== See also ==
* [[24/23]] – the lesser vicesimotertial semitone
* [[Gallery of just intervals]]


[[Category:23-limit]]
[[Category:Second]]
[[Category:Semitone]]
[[Category:Semitone]]
[[Category:Listen]]
[[Category:Commas named after their interval size]]


[[Category:Todo:expand]]
{{Todo|expand}}
[[Category:Todo:improve synopsis]]

Latest revision as of 13:08, 3 November 2025

Interval information
Ratio 23/22
Factorization 2-1 × 11-1 × 23
Monzo [-1 0 0 0 -1 0 0 0 1
Size in cents 76.9564¢
Name greater vicesimotertial semitone
Color name 23o1u2, twetholu 2nd
FJS name [math]\displaystyle{ \text{A1}^{23}_{11} }[/math]
Special properties superparticular,
reduced
Tenney norm (log2 nd) 8.98299
Weil norm (log2 max(n, d)) 9.04712
Wilson norm (sopfr(nd)) 36
Comma size medium

[sound info]
Open this interval in xen-calc

23/22, the greater vicesimotertial semitone, is a 23-limit interval. It is the first superparticular interval that is mapped to 0 steps in 12edo, which means it is treated as a comma, although it is more than half the size of a 12edo semitone.

Approximation

Edo approximations for 23/22 (76.96 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
15 1\15 80.00 +3.04 +3.80
16 1\16 75.00 -1.96 -2.61
17 1\17 70.59 -6.37 -9.02
30 2\30 80.00 +3.04 +7.61
31 2\31 77.42 +0.46 +1.20
32 2\32 75.00 -1.96 -5.22
46 3\46 78.26 +1.30 +5.00
47 3\47 76.60 -0.36 -1.41
48 3\48 75.00 -1.96 -7.83
61 4\61 78.69 +1.73 +8.80
62 4\62 77.42 +0.46 +2.39
63 4\63 76.19 -0.77 -4.02
77 5\77 77.92 +0.97 +6.20
78 5\78 76.92 -0.03 -0.22
79 5\79 75.95 -1.01 -6.63

See also