40/21: Difference between revisions
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+logical reasons for both d8 and M7 but let's just remove "small septimal diminished octave" since the term is out of nowhere |
Rewrite. De-highlight "septimal diminished octave" as major sources agree this is a major seventh |
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{{Infobox Interval | {{Infobox Interval | ||
| Name = septimal acute major seventh, aberschismic major seventh | |||
| Color name = ry7, ruyo 7th | |||
| Name = acute major seventh | |||
| Color name = | |||
| Sound = jid_40_21_pluck_adu_dr220.mp3 | | Sound = jid_40_21_pluck_adu_dr220.mp3 | ||
}} | }} | ||
'''40/21''', conventionally known as the '''septimal acute major seventh''', is an interval in [[7-limit]] [[just intonation]] measuring about 1115.5 [[cent]]s. Despite being approximated by the diminished octave in systems like septimal [[meantone]], and even being called the ''septimal diminished octave'' by some musicians due to analogy with [[21/20]] being called the "septimal chromatic semitone", 40/21 functions as a major seventh, as is supported by [[Sagittal notation]], [[Helmholtz–Ellis notation]] and [[Functional Just System]], viewed as the [[243/128|Pythagorean major seventh (243/128)]] altered by an [[aberschisma]]. This gives rise to the more precise name '''aberschismic major seventh'''. | |||
== Approximation == | |||
{{Interval edo approximation|40/21}} | |||
== See also == | == See also == | ||
| Line 16: | Line 13: | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
[[Category:Seventh]] | [[Category:Seventh]] | ||
[[Category:Major seventh]] | [[Category:Major seventh]] | ||
Latest revision as of 11:07, 1 August 2026
| Interval information |
aberschismic major seventh
[sound info]
40/21, conventionally known as the septimal acute major seventh, is an interval in 7-limit just intonation measuring about 1115.5 cents. Despite being approximated by the diminished octave in systems like septimal meantone, and even being called the septimal diminished octave by some musicians due to analogy with 21/20 being called the "septimal chromatic semitone", 40/21 functions as a major seventh, as is supported by Sagittal notation, Helmholtz–Ellis notation and Functional Just System, viewed as the Pythagorean major seventh (243/128) altered by an aberschisma. This gives rise to the more precise name aberschismic major seventh.
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 13 | 12\13 | 1107.69 | -7.84 | -8.49 |
| 14 | 13\14 | 1114.29 | -1.25 | -1.45 |
| 15 | 14\15 | 1120.00 | +4.47 | +5.58 |
| 27 | 25\27 | 1111.11 | -4.42 | -9.95 |
| 28 | 26\28 | 1114.29 | -1.25 | -2.91 |
| 29 | 27\29 | 1117.24 | +1.71 | +4.13 |
| 42 | 39\42 | 1114.29 | -1.25 | -4.36 |
| 43 | 40\43 | 1116.28 | +0.75 | +2.67 |
| 44 | 41\44 | 1118.18 | +2.65 | +9.71 |
| 56 | 52\56 | 1114.29 | -1.25 | -5.82 |
| 57 | 53\57 | 1115.79 | +0.26 | +1.22 |
| 58 | 54\58 | 1117.24 | +1.71 | +8.26 |
| 70 | 65\70 | 1114.29 | -1.25 | -7.27 |
| 71 | 66\71 | 1115.49 | -0.04 | -0.24 |
| 72 | 67\72 | 1116.67 | +1.13 | +6.80 |