23/21: Difference between revisions

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Created page with "{{Infobox Interval | Icon = | Ratio = 23/21 | Monzo = 0 -1 0 -1 0 0 0 0 1 | Cents = {{subst:cents|23/21|5}} | Name = vicesimotertial neutral second | Color name = 23or2, twen..."
 
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{{Infobox Interval
{{Infobox Interval
| Icon =
| Name = large vicesimotertial neutral second
| Ratio = 23/21
| Color name = 23or2, twethoru 2nd
| Monzo = 0 -1 0 -1 0 0 0 0 1
| Cents = 157.49344
| Name = vicesimotertial neutral second
| Color name = 23or2, twenty-thoru 2nd
| Sound = Ji-23-21-csound-foscil-220hz.mp3
| Sound = Ji-23-21-csound-foscil-220hz.mp3
}}
}}
'''23/21''', the '''large vicesimotertial neutral second''' is a [[23-limit]] interval. It is mediant of two undecimal neutral seconds, [[11/10]] and [[12/11]]. Two of them fall short of [[6/5]] by [[2646/2645]].
== Approximation ==
{{Interval edo approximation|23/21}}
== See also ==
* [[42/23]] – its [[octave complement]]
* [[25/23]] – the small vicesimotertial neutral second
* [[Gallery of just intervals]]
* [[23-odd-limit]]


[[Category:23-limit]]
[[Category:Second]]
[[Category:Neutral second]]
[[Category:Neutral second]]
[[Category:Second]]
[[Category:Whole tone]]
[[Category:Whole tone]]
[[Category:Listen]]
[[Category:Todo:expand]]
[[Category:Todo:improve synopsis]]

Latest revision as of 13:02, 3 November 2025

Interval information
Ratio 23/21
Subgroup monzo 3.7.23 [-1 -1 1
Size in cents 157.4934¢
Name large vicesimotertial neutral second
Color name 23or2, twethoru 2nd
FJS name [math]\displaystyle{ \text{A1}^{23}_{7} }[/math]
Special properties reduced
Tenney norm (log2 nd) 8.91588
Weil norm (log2 max(n, d)) 9.04712
Wilson norm (sopfr(nd)) 33

[sound info]
Open this interval in xen-calc

23/21, the large vicesimotertial neutral second is a 23-limit interval. It is mediant of two undecimal neutral seconds, 11/10 and 12/11. Two of them fall short of 6/5 by 2646/2645.

Approximation

Edo approximations for 23/21 (157.49 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
7 1\7 171.43 +13.94 +8.13
8 1\8 150.00 -7.49 -5.00
15 2\15 160.00 +2.51 +3.13
16 2\16 150.00 -7.49 -9.99
23 3\23 156.52 -0.97 -1.86
30 4\30 160.00 +2.51 +6.27
31 4\31 154.84 -2.65 -6.86
38 5\38 157.89 +0.40 +1.27
45 6\45 160.00 +2.51 +9.40
46 6\46 156.52 -0.97 -3.72
53 7\53 158.49 +1.00 +4.40
54 7\54 155.56 -1.94 -8.72
61 8\61 157.38 -0.12 -0.59
68 9\68 158.82 +1.33 +7.54
69 9\69 156.52 -0.97 -5.59
76 10\76 157.89 +0.40 +2.54

See also