28/15: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = septimal grave major seventh, aberschismic diminished octave | |||
| Color name = zg8, zogu octave | |||
| Name = septimal grave major seventh | |||
| Color name = | |||
| Sound = jid_28_15_pluck_adu_dr220.mp3 | | Sound = jid_28_15_pluck_adu_dr220.mp3 | ||
}} | }} | ||
'''28/15''' is an interval in [[7-limit]] [[just intonation]] measuring about 1080.6 [[cent]]s, traditionally known as the '''septimal grave major seventh''' for its proximity (and conflation in [[marvel]] tunings such as septimal [[meantone]]) with the classical major seventh [[15/8]]. However, it functions as a diminished octave, as is supported by [[Sagittal notation]], [[Helmholtz–Ellis notation]] and the [[Functional Just System]], viewed as the [[4096/2187|Pythagorean diminished octave]] flattened by an [[aberschisma]]. This gives rise to the more precise name '''aberschismic diminished octave'''. It arises from stacking various [[9-odd-limit]] consonances, including the stack consisting of [[6/5]] and [[14/9]], of [[7/6]] and [[8/5]], and of [[7/5]] and [[4/3]]. | |||
== Approximation == | |||
This interval is well approximated by [[10edo]] (9\10). | |||
{{Interval edo approximation|28/15}} | |||
== See also == | == See also == | ||
| Line 18: | Line 15: | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
[[Category:Seventh]] | [[Category:Seventh]] | ||
[[Category:Major seventh]] | [[Category:Major seventh]] | ||
[[Category:Octave]] | [[Category:Octave]] | ||
[[Category:Diminished octave]] | [[Category:Diminished octave]] | ||
Latest revision as of 10:46, 1 August 2026
| Interval information |
aberschismic diminished octave
[sound info]
28/15 is an interval in 7-limit just intonation measuring about 1080.6 cents, traditionally known as the septimal grave major seventh for its proximity (and conflation in marvel tunings such as septimal meantone) with the classical major seventh 15/8. However, it functions as a diminished octave, as is supported by Sagittal notation, Helmholtz–Ellis notation and the Functional Just System, viewed as the Pythagorean diminished octave flattened by an aberschisma. This gives rise to the more precise name aberschismic diminished octave. It arises from stacking various 9-odd-limit consonances, including the stack consisting of 6/5 and 14/9, of 7/6 and 8/5, and of 7/5 and 4/3.
Approximation
This interval is well approximated by 10edo (9\10).
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 10 | 9\10 | 1080.00 | -0.56 | -0.46 |
| 11 | 10\11 | 1090.91 | +10.35 | +9.49 |
| 20 | 18\20 | 1080.00 | -0.56 | -0.93 |
| 21 | 19\21 | 1085.71 | +5.16 | +9.02 |
| 30 | 27\30 | 1080.00 | -0.56 | -1.39 |
| 31 | 28\31 | 1083.87 | +3.31 | +8.56 |
| 40 | 36\40 | 1080.00 | -0.56 | -1.86 |
| 41 | 37\41 | 1082.93 | +2.37 | +8.10 |
| 50 | 45\50 | 1080.00 | -0.56 | -2.32 |
| 51 | 46\51 | 1082.35 | +1.80 | +7.63 |
| 60 | 54\60 | 1080.00 | -0.56 | -2.79 |
| 61 | 55\61 | 1081.97 | +1.41 | +7.17 |
| 70 | 63\70 | 1080.00 | -0.56 | -3.25 |
| 71 | 64\71 | 1081.69 | +1.13 | +6.70 |
| 80 | 72\80 | 1080.00 | -0.56 | -3.71 |