32/31
| Interval information |
small tricesimoprimal quartertone
reduced,
reduced subharmonic
[sound info]
32/31 is the small tricesimoprimal quartertone measuring about 55 ¢. It differs from 33/32, the undecimal quartertone, by 1024/1023 (approx. 1.69 ¢). It differs from 31/30, another tricesimoprimal quartertone, by 961/960 (approx. 1.80 ¢); they together make 16/15.
Approximation
This interval is approximated well (about 0.4 ¢ off) by 1\22 and extremely closely (about 0.0025 ¢ off) by 6\131.
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 2 | 0\2 | 0.00 | -54.96 | -9.16 |
| 20 | 1\20 | 60.00 | +5.04 | +8.39 |
| 21 | 1\21 | 57.14 | +2.18 | +3.81 |
| 22 | 1\22 | 54.55 | -0.42 | -0.77 |
| 23 | 1\23 | 52.17 | -2.79 | -5.35 |
| 24 | 1\24 | 50.00 | -4.96 | -9.93 |
| 42 | 2\42 | 57.14 | +2.18 | +7.62 |
| 43 | 2\43 | 55.81 | +0.85 | +3.04 |
| 44 | 2\44 | 54.55 | -0.42 | -1.54 |
| 45 | 2\45 | 53.33 | -1.63 | -6.12 |
| 64 | 3\64 | 56.25 | +1.29 | +6.86 |
| 65 | 3\65 | 55.38 | +0.42 | +2.28 |
| 66 | 3\66 | 54.55 | -0.42 | -2.30 |
| 67 | 3\67 | 53.73 | -1.23 | -6.88 |
Notation
This interval is significant in Helmholtz–Ellis notation as the formal comma to translate a Pythagorean interval to a nearby tricesimoprimal (31-limit) interval. The symbols are adapted from Persian quartertones accidentals invented by Ali-Naqi Vaziri.
Temperaments
This interval can serve as a generator for the escapade temperament (which both 22 and 131edo, among others, support).