1ed33/32
The equal multiplication of 33/32, the Alpharabian quarter-tone, results in an interesting nonoctave tuning, equivalent to 22.5255 EDO.
Lookalikes: 5ed7/6, 45ed4
Theory
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +25.3 | +15.9 | -16.1 | -12.6 | +4.0 | -18.9 | -3.8 | +16.7 | +5.6 | -22.8 | +21.5 |
| Relative (%) | +47.4 | +29.8 | -30.3 | -23.7 | +7.5 | -35.4 | -7.2 | +31.3 | +10.4 | -42.8 | +40.4 | |
| Step | 23 | 36 | 52 | 63 | 78 | 83 | 92 | 96 | 102 | 109 | 112 | |
In this tuning, 2 steps correspond to the parapotome 1089/1024, and 5 steps are approximately equal to 7/6, thus tempering out the quartisma if this equivalence is assumed.
Intervals with excellent approximation in this tuning are: 7/6, 18/11, 20/13. Other intervals with good approximation are: 6/5, 7/5, 9/5, 13/7, 13/9, 11/10, 19/12, 17/16, 17/15, 16/15.