User:BudjarnLambeth/100zpi
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100zpi, the 100th zeta peak index, is a stretched-octaves version of 26edo. It can be thought of as 26ed1202.975c or as 46.268cet.
It has a step size of 46.268 cents, and the octave (2/1) is tuned slightly impurely to 1202.975 cents.
26edo tunes most simple harmonics slightly flat by roughly the same amount, so 100zpi is one possible way of correcting for this.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | |
|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +3.0 | -5.0 | -10.2 | +8.7 | +12.8 | +1.2 |
| Relative (%) | +6.4 | -10.7 | -22.1 | +18.9 | +27.7 | +2.6 | |
| Step | 26 | 41 | 60 | 73 | 90 | 96 | |
| Harmonic | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.5 | -8.0 | -14.9 | +0.2 | -22.7 |
| Relative (%) | -1.2 | -17.4 | -32.2 | +0.4 | -49.1 | |
| Step | 106 | 110 | 117 | 126 | 128 | |
For primes up to 31:
100zpi approximates these with less than 6 cents error (<13% relative error):
- 2, 3, 13, 17, 29
...these with 6-12 cents error (13-26% relative error):
- 5, 7, 19
...these with 12-18 cents error (26-39% relative error):
- 11, 23
...and these with more than 18 cents error (>39% relative error):
- 31
This makes it usable as a full 31-limit tuning, or as a more accurate no-11s 19-limit tuning.
Scales
Any scales from 26edo should also be useable here.
Instruments
All instruments listed under 26edo#Instruments also work for 100zpi.