User:BudjarnLambeth/149zpi
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149zpi, the 149th zeta peak index, is a compressed-octaves version of 35edo. It can be thought of as 35ed1202.564 or as 34.358cet.
It has a step size of 34.358 cents, and the octave (2/1) is tuned slightly impurely to 1202.564 cents.
35edo tunes almost all simple harmonics slightly flat by roughly the same amount, so 149zpi is one possible way of correcting for this.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | |
|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.5 | -12.3 | -3.3 | -1.7 | +6.0 | -8.3 | +8.2 |
| Relative (%) | +7.4 | -35.7 | -9.7 | -5.1 | +17.5 | -24.3 | +24.0 | |
| Step | 35 | 55 | 81 | 98 | 121 | 129 | 143 | |
| Harmonic | 19 | 23 | 29 | 31 | 37 | 41 | 43 | |
|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -12.5 | +0.3 | +11.3 | -1.1 | +1.8 | -4.1 | +16.5 |
| Relative (%) | -36.5 | +0.8 | +32.8 | -3.2 | +5.3 | -12.0 | +48.0 | |
| Step | 148 | 158 | 170 | 173 | 182 | 187 | 190 | |
For primes up to 43:
435zpi approximates these with less than 7 cents error (<20% relative error):
- 2, 5, 7, 11, 23, 31, 37, 41
...these with 7-14 cents error (20-40% relative error):
- 3, 13, 17, 19, 29
...and these with more than 14 cents error (>40% relative error):
- 43
This makes it usable as a full 41-limit tuning, or as a more accurate no-3s 11-limit tuning.
Scales
Any scales from 35edo should also be useable here.
Instruments
All instruments listed under 35edo#Instruments also work for 149zpi.