22/15: Difference between revisions
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The '''undecimal diminished fifth''' of '''22/15''' is flat of [[3/2]] by [[45/44]], and is the interval between [[5/4]] and [[11/6]]. It is wider than [[16/11]] by exactly [[121/120]] and narrower than [[40/27]] by exactly [[100/99]]. Additionally, it is wider than [[352/243]] by exactly [[81/80]], which lends to it being called the '''undecimal acute ultra-diminished fifth'''. | The '''undecimal diminished fifth''' of '''22/15''' is flat of [[3/2]] by [[45/44]], and is the interval between [[5/4]] and [[11/6]]. It is wider than [[16/11]] by exactly [[121/120]] and narrower than [[40/27]] by exactly [[100/99]]. Additionally, it is wider than [[352/243]] by exactly [[81/80]], which lends to it being called the '''undecimal acute ultra-diminished fifth'''. | ||
5 steps of [[9edo]] is a good approximation of this interval. | 5 steps of [[9edo]] is a good approximation of this interval. | ||
== Approximation == | |||
{{Interval edo approximation|22/15}} | |||
== See also == | == See also == | ||
* [[15/11]] – its [[octave complement]] | * [[15/11]] – its [[octave complement]] | ||
Latest revision as of 13:13, 3 November 2025
| Interval information |
undecimal acute ultra-diminished fifth
[sound info]
The undecimal diminished fifth of 22/15 is flat of 3/2 by 45/44, and is the interval between 5/4 and 11/6. It is wider than 16/11 by exactly 121/120 and narrower than 40/27 by exactly 100/99. Additionally, it is wider than 352/243 by exactly 81/80, which lends to it being called the undecimal acute ultra-diminished fifth. 5 steps of 9edo is a good approximation of this interval.
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 9 | 5\9 | 666.67 | +3.62 | +2.71 |
| 11 | 6\11 | 654.55 | -8.50 | -7.80 |
| 18 | 10\18 | 666.67 | +3.62 | +5.43 |
| 20 | 11\20 | 660.00 | -3.05 | -5.08 |
| 27 | 15\27 | 666.67 | +3.62 | +8.14 |
| 29 | 16\29 | 662.07 | -0.98 | -2.37 |
| 38 | 21\38 | 663.16 | +0.11 | +0.34 |
| 47 | 26\47 | 663.83 | +0.78 | +3.06 |
| 49 | 27\49 | 661.22 | -1.82 | -7.45 |
| 56 | 31\56 | 664.29 | +1.24 | +5.77 |
| 58 | 32\58 | 662.07 | -0.98 | -4.74 |
| 65 | 36\65 | 664.62 | +1.57 | +8.48 |
| 67 | 37\67 | 662.69 | -0.36 | -2.02 |
| 76 | 42\76 | 663.16 | +0.11 | +0.69 |
| 78 | 43\78 | 661.54 | -1.51 | -9.82 |