User:BudjarnLambeth/161zpi
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161zpi, the 161th zeta peak index, is a compressed-octaves version of 37edo. It can be thought of as 37ed1199.1c or as 32.408cET.
It has a step size of 32.408 cents, and the octave (2/1) is tuned slightly impurely to 1199.1 cents.
37edo tunes almost all simple harmonics slightly sharp by roughly the same amount, so 161zpi is one possible way of correcting for this.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.9 | +10.1 | +0.8 | +1.6 | -3.1 | -0.6 | -11.3 | -9.5 | -16.1 |
| Relative (%) | -2.8 | +31.2 | +2.4 | +5.0 | -9.5 | -1.9 | -35.0 | -29.2 | -49.8 | |
| Step | 37 | 59 | 86 | 104 | 128 | 137 | 151 | 157 | 167 | |
For primes up to 23:
161zpi approximates these with less than 4 cents error (<12% relative error):
- 2, 5, 7, 11, 13
...these with 4-12 cents error (12-36% relative error):
- 3, 17, 19
...and these with more than 12 cents error (>36% relative error):
- 23
This makes it usable as a full 19-limit tuning, or as a more accurate no-3s 13-limit tuning.
Scales
Any scales from 37edo should also be useable here.
Instruments
All instruments listed under 37edo#Instruments also work for 149zpi.