21/19: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = | | 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 ''' | 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 |
undevicesimal submajor second,
undevicesimal supraneutral second
[sound info]
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 | 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 |