BudjarnLambeth at 06:05, 16 August 2025

2025-08-16T06:05:32Z

← Older revision		Revision as of 06:05, 16 August 2025
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	{{Editable user page}}		{{Editable user page}}

	'''100zpi''', the 100th [[zeta peak index]], is a [[Octave stretching\|stretched-octaves]] version of [[26edo]]. It can be thought of as '''~~31ed1202~~.975c''' or as '''46.268cet'''.		'''100zpi''', the 100th [[zeta peak index]], is a [[Octave stretching\|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 [[cent]]s, and the [[octave]] ([[2/1]]) is tuned slightly impurely to 1202.975 cents.		It has a step size of 46.268 [[cent]]s, and the [[octave]] ([[2/1]]) is tuned slightly impurely to 1202.975 cents.

BudjarnLambeth: /* Prime harmonics */

2025-08-16T06:04:22Z

Prime harmonics

← Older revision		Revision as of 06:04, 16 August 2025
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	* 11, 23		* 11, 23

	...and these with more than 16 cents error (>39% relative error):		...and these with more than 18 cents error (>39% relative error):
	* 31		* 31

BudjarnLambeth: Created page with "{{Editable user page}} '''100zpi''', the 100th zeta peak index, is a stretched-octaves version of 26edo. It can be thought of as '''31ed1202.975c''' 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==..."

2025-08-16T06:00:20Z

Created page with "{{Editable user page}} '''100zpi''', the 100th zeta peak index, is a stretched-octaves version of 26edo. It can be thought of as '''31ed1202.975c''' 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==..."

New page

{{Editable user page}}

'''100zpi''', the 100th [[zeta peak index]], is a [[Octave stretching|stretched-octaves]] version of [[26edo]]. It can be thought of as '''31ed1202.975c''' or as '''46.268cet'''.

It has a step size of 46.268 [[cent]]s, and the [[octave]] ([[2/1]]) is tuned slightly impurely to 1202.975 cents.

26edo tunes most simple [[harmonic]]s slightly flat by roughly the same amount, so 100zpi is one possible way of correcting for this.

==Prime harmonics==
{{Harmonics in cet|46.268|columns=6|intervals=prime|title=Approximation of prime harmonics in 100zpi}}
{{Harmonics in cet|46.268|columns=5|start=7|intervals=prime|title=Approximation of prime harmonics in 100zpi}}

For [[prime]]s 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 16 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 [[26edo#Scales|scales from 26edo]] should also be useable here.

==Instruments==
All instruments listed under [[26edo#Instruments]] also work for 100zpi.

[[Category:Zeta peak indexes]] [[Category:26edo]]

User:BudjarnLambeth/100zpi - Revision history

BudjarnLambeth at 06:05, 16 August 2025

BudjarnLambeth: /* Prime harmonics */