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

Approximation of prime harmonics in 100zpi

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

Approximation of prime harmonics in 100zpi

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.