28/15: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = septimal grave major seventh | |||
| Color name = zg8, zogu octave | |||
| Name = septimal | |||
| Color name = | |||
| Sound = jid_28_15_pluck_adu_dr220.mp3 | | Sound = jid_28_15_pluck_adu_dr220.mp3 | ||
}} | }} | ||
'''28/15''', the '''septimal | '''28/15''' is a [[7-limit]] [[just intonation]] interval of about 1080.6 [[cent]]s. It is well approximated by [[10edo]] (9\10). | ||
== Terminology == | |||
Despite being approximated by the major seventh in systems like [[septimal meantone]], and even being called the '''septimal grave major seventh''' by some musicians, 28/15 is a diminished octave in just intonation notation systems such as [[Sagittal notation]], [[Helmholtz-Ellis notation]] and the [[Functional Just System]], viewed as the Pythagorean diminished octave ([[4096/2187]]) altered by [[5120/5103]]. | |||
== Approximation == | |||
{{Interval edo approximation|28/15}} | |||
== See also == | == See also == | ||
* [[15/14]] – its [[octave complement]] | |||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
[[Category:Seventh]] | [[Category:Seventh]] | ||
[[Category:Major seventh]] | [[Category:Major seventh]] | ||
[[Category:Octave]] | |||
[[Category: | [[Category:Diminished octave]] | ||
[[Category: | {{todo|improve synopsis}} | ||
Latest revision as of 13:03, 3 November 2025
| Interval information |
[sound info]
28/15 is a 7-limit just intonation interval of about 1080.6 cents. It is well approximated by 10edo (9\10).
Terminology
Despite being approximated by the major seventh in systems like septimal meantone, and even being called the septimal grave major seventh by some musicians, 28/15 is a diminished octave in just intonation notation systems such as Sagittal notation, Helmholtz-Ellis notation and the Functional Just System, viewed as the Pythagorean diminished octave (4096/2187) altered by 5120/5103.
Approximation
| 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 |