User:BudjarnLambeth/435zpi
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435zpi, the 435th zeta peak index, is a compressed-octaves version of 80edo. It can be thought of as 80ed1198.9c or as 14.986cet.
80edo tunes almost all simple harmonics slightly sharp by roughly the same amount, so 435zpi is one possible way of correcting for this.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | |
|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.12 | +1.27 | +1.08 | +3.02 | -0.20 | -4.67 | -4.53 |
| Relative (%) | -7.5 | +8.5 | +7.2 | +20.2 | -1.3 | -31.2 | -30.3 | |
| Step | 80 | 127 | 186 | 225 | 277 | 296 | 327 | |
| Harmonic | 19 | 23 | 29 | 31 | 37 | 41 | 43 | |
|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.27 | -3.34 | -0.02 | +4.41 | -2.18 | -0.07 | +7.39 |
| Relative (%) | -15.2 | -22.3 | -0.2 | +29.4 | -14.6 | -0.5 | +49.3 | |
| Step | 340 | 362 | 389 | 397 | 417 | 429 | 435 | |
For primes up to 43:
435zpi approximates these with less than 3 cents error (<20% relative error):
- 2, 3, 5, 11, 19, 29, 37, 41
...these with 3-5 cents error (20-33% relative error):
- 7, 13, 17, 23, 31
...and these with more than 5 cents error (>33% relative error):
- 43