Hkm at 01:32, 17 August 2025

2025-08-17T01:32:55Z

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	'''161zpi''', the 161th [[zeta peak index]], is a [[Octave shrinking\|compressed-octaves]] version of [[37edo]]. It can be thought of as '''37ed1199.1c''' or as '''32.~~408cet~~'''.		'''161zpi''', the 161th [[zeta peak index]], is a [[Octave shrinking\|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 [[cent]]s, and the [[octave]] ([[2/1]]) is tuned slightly impurely to 1199.1 cents.		It has a step size of 32.408 [[cent]]s, and the [[octave]] ([[2/1]]) is tuned slightly impurely to 1199.1 cents.

	37edo tunes almost all simple [[harmonic]]s slightly ~~flat~~ by roughly the same amount, so 161zpi is one possible way of correcting for this.		37edo tunes almost all simple [[harmonic]]s slightly sharp by roughly the same amount, so 161zpi is one possible way of correcting for this.

	==Prime harmonics==		==Prime harmonics==

BudjarnLambeth: Last one of these I'm making today and for the forseeable future

2025-08-16T06:34:04Z

Last one of these I'm making today and for the forseeable future

New page

{{Editable user page}}

'''161zpi''', the 161th [[zeta peak index]], is a [[Octave shrinking|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 [[cent]]s, and the [[octave]] ([[2/1]]) is tuned slightly impurely to 1199.1 cents.

37edo tunes almost all simple [[harmonic]]s slightly flat by roughly the same amount, so 161zpi is one possible way of correcting for this.

==Prime harmonics==
{{Harmonics in cet|32.408|columns=9|intervals=prime|title=Approximation of prime harmonics in 161zpi}}

For [[prime]]s 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 [[37edo#Scales|scales from 37edo]] should also be useable here.

==Instruments==
All instruments listed under [[37edo#Instruments]] also work for 149zpi.

[[Category:Zeta peak indexes]] [[Category:37edo]]

User:BudjarnLambeth/161zpi - Revision history

Hkm at 01:32, 17 August 2025

BudjarnLambeth: Last one of these I'm making today and for the forseeable future