BudjarnLambeth at 03:18, 16 August 2025

2025-08-16T03:18:13Z

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	'''~~127~~''', the 127th [[zeta peak index]], is a [[Octave stretching\|stretched-octaves]] version of [[31edo]]. It can be thought of as '''31ed1200.84c''' or as '''38.737cet'''.		'''127zpi''', the 127th [[zeta peak index]], is a [[Octave stretching\|stretched-octaves]] version of [[31edo]]. It can be thought of as '''31ed1200.84c''' or as '''38.737cet'''.

	It has a step size of 38.737 [[cent]]s, and the [[octave]] ([[2/1]]) is tuned slightly impurely to 1200.84 cents.		It has a step size of 38.737 [[cent]]s, and the [[octave]] ([[2/1]]) is tuned slightly impurely to 1200.84 cents.

BudjarnLambeth: Created page with "{{Editable user page}} '''127''', the 127th zeta peak index, is a stretched-octaves version of 31edo. It can be thought of as '''31ed1200.84c''' or as '''38.737cet'''. It has a step size of 38.737 cents, and the octave (2/1) is tuned slightly impurely to 1200.84 cents. 31edo tunes most simple harmonics slightly flat by roughly the same amount, so 127zpi is one possible way of correcting for this. ==Prime harmonics== {{Ha..."

2025-08-16T03:17:49Z

Created page with "{{Editable user page}} '''127''', the 127th zeta peak index, is a stretched-octaves version of 31edo. It can be thought of as '''31ed1200.84c''' or as '''38.737cet'''. It has a step size of 38.737 cents, and the octave (2/1) is tuned slightly impurely to 1200.84 cents. 31edo tunes most simple harmonics slightly flat by roughly the same amount, so 127zpi is one possible way of correcting for this. ==Prime harmonics== {{Ha..."

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{{Editable user page}}

'''127''', the 127th [[zeta peak index]], is a [[Octave stretching|stretched-octaves]] version of [[31edo]]. It can be thought of as '''31ed1200.84c''' or as '''38.737cet'''.

It has a step size of 38.737 [[cent]]s, and the [[octave]] ([[2/1]]) is tuned slightly impurely to 1200.84 cents.

31edo tunes most simple [[harmonic]]s slightly flat by roughly the same amount, so 127zpi is one possible way of correcting for this.

==Prime harmonics==
{{Harmonics in cet|38.737|columns=10|intervals=prime|title=Approximation of prime harmonics in 127zpi}}

For [[prime]]s up to 29:

127zpi approximates these with less than 4 cents error (<10% relative error):
* 2, 3, 5, 7

...these with 4-8 cents error (10-21% relative error):
* 11, 23

...these with 8-16 cents error (21-41% relative error):
* 13, 17, 19

...and these with more than 16 cents error (>41% relative error):
* 29

This makes it usable as a full [[23-limit]] tuning, or as a more accurate full [[11-limit]] tuning.

==Scales==
Any [[31edo#Scales|scales from 31edo]] should also be useable here.

==Instruments==
All instruments listed under [[31edo#Instruments]] also work for 127zpi.

[[Category:Zeta peak indexes]] [[Category:31edo]]

User:BudjarnLambeth/127zpi - Revision history

BudjarnLambeth at 03:18, 16 August 2025