21/19: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Name = large neutral undevicesimal second
| Name = hendrix major second, undevicesimal submajor second, undevicesimal supraneutral second
| Color name = 19uz2, nuzo 2nd
| Color name = 19uz2, nuzo 2nd
| Sound = ji-21-19-csound-foscil-220hz.mp3
| Sound = ji-21-19-csound-foscil-220hz.mp3
}}
}}


'''21/19''' is the '''large neutral undevicesimal second'''. Its [[octave complement]] is the minor neutral undevicesimal seventh [[38/21]].
In [[19-limit]] [[just intonation]], '''21/19''' is the '''hendrix major second''', also known as the '''undevicesimal submajor second''' or '''undevicesimal supraneutral second''', named for falling short of the [[9/8|Pythagorean major second (9/8)]] by a [[57/56|hendrix comma (57/56)]]. In [[counterpyth]] systems, it is equated to the diminished third (the interval formed by two [[256/243|limmas (256/243)]]). It can also be considered to approximate the [[tetracot]] generator.
 
== Approximation ==
{{Interval edo approximation|21/19}}
== See also ==
== See also ==
* [[38/21]] – its [[octave complement]]
* [[38/21]] – its [[octave complement]]
* [[19/14]] – its [[fifth complement]]
* [[Gallery of just intervals]]
* [[Gallery of just intervals]]


[[Category:Second]]
[[Category:Second]]
[[Category:Neutral second]]
[[Category:Neutral second]]
[[Category:Equable heptatonic]]
[[Category:Tetracot]]
[[Category:Hendrix]]

Latest revision as of 13:07, 3 November 2025

Interval information
Ratio 21/19
Factorization 3 × 7 × 19-1
Monzo [0 1 0 1 0 0 0 -1
Size in cents 173.2679¢
Names hendrix major second,
undevicesimal submajor second,
undevicesimal supraneutral second
Color name 19uz2, nuzo 2nd
FJS name [math]\displaystyle{ \text{M2}^{7}_{19} }[/math]
Special properties reduced
Tenney norm (log2 nd) 8.64024
Weil norm (log2 max(n, d)) 8.78463
Wilson norm (sopfr(nd)) 29

[sound info]
Open this interval in xen-calc

In 19-limit just intonation, 21/19 is the hendrix major second, also known as the undevicesimal submajor second or undevicesimal supraneutral second, named for falling short of the Pythagorean major second (9/8) by a hendrix comma (57/56). In counterpyth systems, it is equated to the diminished third (the interval formed by two limmas (256/243)). It can also be considered to approximate the tetracot generator.

Approximation

Edo approximations for 21/19 (173.27 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
7 1\7 171.43 -1.84 -1.07
14 2\14 171.43 -1.84 -2.15
21 3\21 171.43 -1.84 -3.22
28 4\28 171.43 -1.84 -4.29
34 5\34 176.47 +3.20 +9.07
35 5\35 171.43 -1.84 -5.36
41 6\41 175.61 +2.34 +8.00
42 6\42 171.43 -1.84 -6.44
48 7\48 175.00 +1.73 +6.93
49 7\49 171.43 -1.84 -7.51
55 8\55 174.55 +1.28 +5.86
56 8\56 171.43 -1.84 -8.58
62 9\62 174.19 +0.93 +4.78
63 9\63 171.43 -1.84 -9.66
69 10\69 173.91 +0.65 +3.71
76 11\76 173.68 +0.42 +2.64

See also