28/15: Difference between revisions
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== Terminology == | == 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]]. | 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 == | ||
Revision as of 07:49, 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 |