User:BudjarnLambeth/435zpi - Revision history

BudjarnLambeth: music

2025-08-19T04:37:37Z

music

← Older revision		Revision as of 04:37, 19 August 2025
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	==Instruments==		==Instruments==
	All instruments listed under [[80edo#Instruments]] also work for 435zpi.		All instruments listed under [[80edo#Instruments]] also work for 435zpi.

			==Music==
			; [[Budjarn Lambeth]]
			* [https://youtu.be/6N_8QM2UK5I Improvisation in compressed 80edo (435zpi)] (2025)

	[[Category:Zeta peak indexes]] [[Category:80edo]] [[Category:80-tone scales]] [[Category:15-tone scales]] [[Category:13-tone scales]] [[Category:12-tone scales]] [[Category:11-tone scales]]		[[Category:Zeta peak indexes]] [[Category:80edo]] [[Category:80-tone scales]] [[Category:15-tone scales]] [[Category:13-tone scales]] [[Category:12-tone scales]] [[Category:11-tone scales]]

2025-08-16T09:44:10Z

Scales

@@ Line 25: / Line 25: @@
 ==Scales==
-Any [[80edo#Scales|scales from 80edo]] should also be useable here.
+All [[80edo#Scales|scales from 80edo]] also occur in 435zpi.
 ==Instruments==

2025-08-15T07:11:18Z

← Older revision		Revision as of 07:11, 15 August 2025
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	; [[Equipentatonic]]		; [[Equipentatonic]]
	* 239.8 - 479.6 - 719.3 - 959.1 - 1198.9		* 239.8 - 479.6 - 719.3 - 959.1 - 1198.9

			==Instruments==
			All instruments listed under [[80edo#Instruments]] also work for 435zpi.

	[[Category:Zeta peak indexes]] [[Category:80edo]] [[Category:80-tone scales]] [[Category:15-tone scales]] [[Category:13-tone scales]] [[Category:12-tone scales]] [[Category:11-tone scales]]		[[Category:Zeta peak indexes]] [[Category:80edo]] [[Category:80-tone scales]] [[Category:15-tone scales]] [[Category:13-tone scales]] [[Category:12-tone scales]] [[Category:11-tone scales]]

2025-08-15T07:07:44Z

Combination product sets

← Older revision		Revision as of 07:07, 15 August 2025
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	===Combination product sets===		===Combination product sets===
	''See also: [[Combination product set]]		''See also: [[Combination product set]]


	; CPS (10 of 1 3 5 9 11 15 19 25 27 29 33)		; CPS (10 of 1 3 5 9 11 15 19 25 27 29 33)

2025-08-15T07:07:32Z

=Other scales

← Older revision		Revision as of 07:07, 15 August 2025
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	* 74.9 - 209.8 - 239.8 - 299.7 - 329.7 - 389.6 - 494.5 - 554.5 - 704.4 - 749.3 - 794.3 - 884.2 - 929.1 - 1049.0 - 1198.9		* 74.9 - 209.8 - 239.8 - 299.7 - 329.7 - 389.6 - 494.5 - 554.5 - 704.4 - 749.3 - 794.3 - 884.2 - 929.1 - 1049.0 - 1198.9

	===Other scales==		===Other scales===
	; [[Equipentatonic]]		; [[Equipentatonic]]
	* 239.8 - 479.6 - 719.3 - 959.1 - 1198.9		* 239.8 - 479.6 - 719.3 - 959.1 - 1198.9

	[[Category:Zeta peak indexes]] [[Category:80edo]] [[Category:80-tone scales]] [[Category:15-tone scales]] [[Category:13-tone scales]] [[Category:12-tone scales]] [[Category:11-tone scales]]		[[Category:Zeta peak indexes]] [[Category:80edo]] [[Category:80-tone scales]] [[Category:15-tone scales]] [[Category:13-tone scales]] [[Category:12-tone scales]] [[Category:11-tone scales]]

2025-08-15T07:07:23Z

Scales

← Older revision		Revision as of 07:07, 15 August 2025
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	Tempered to 435zpi:		Tempered to 435zpi:
	* 74.9 - 209.8 - 239.8 - 299.7 - 329.7 - 389.6 - 494.5 - 554.5 - 704.4 - 749.3 - 794.3 - 884.2 - 929.1 - 1049.0 - 1198.9		* 74.9 - 209.8 - 239.8 - 299.7 - 329.7 - 389.6 - 494.5 - 554.5 - 704.4 - 749.3 - 794.3 - 884.2 - 929.1 - 1049.0 - 1198.9

			===Other scales==
			; [[Equipentatonic]]
			* 239.8 - 479.6 - 719.3 - 959.1 - 1198.9

	[[Category:Zeta peak indexes]] [[Category:80edo]] [[Category:80-tone scales]] [[Category:15-tone scales]] [[Category:13-tone scales]] [[Category:12-tone scales]] [[Category:11-tone scales]]		[[Category:Zeta peak indexes]] [[Category:80edo]] [[Category:80-tone scales]] [[Category:15-tone scales]] [[Category:13-tone scales]] [[Category:12-tone scales]] [[Category:11-tone scales]]

2025-08-15T07:04:00Z

Prime harmonics

← Older revision		Revision as of 07:04, 15 August 2025
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	{{Harmonics in cet\|14.986\|columns=7\|start=8\|intervals=prime\|title=Approximation of prime harmonics in 435zpi}}		{{Harmonics in cet\|14.986\|columns=7\|start=8\|intervals=prime\|title=Approximation of prime harmonics in 435zpi}}

	For ~~primes~~ up to 43:		For [[prime]]s up to 43:

	435zpi approximates these with less than 3 cents error (<20% relative error):		435zpi approximates these with less than 3 cents error (<20% relative error):

2025-08-15T07:03:46Z

← Older revision		Revision as of 07:03, 15 August 2025
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	It has a step size of 14.986 [[cent]]s, and the [[octave]] ([[2/1]]) is tuned slightly impurely to 1198.9 cents.		It has a step size of 14.986 [[cent]]s, and the [[octave]] ([[2/1]]) is tuned slightly impurely to 1198.9 cents.

	80edo tunes almost all simple ~~harmonics~~ slightly sharp by roughly the same amount, so 435zpi is one possible way of correcting for this.		80edo tunes almost all simple [[harmonic]]s slightly sharp by roughly the same amount, so 435zpi is one possible way of correcting for this.

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

2025-08-15T07:03:22Z

← Older revision		Revision as of 07:03, 15 August 2025
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	'''435zpi''', the 435th [[zeta peak index]], is a [[Octave shrinking\|compressed-octaves]] version of [[80edo]]. It can be thought of as '''80ed1198.9c''' or as '''14.986cet'''.		'''435zpi''', the 435th [[zeta peak index]], is a [[Octave shrinking\|compressed-octaves]] version of [[80edo]]. It can be thought of as '''80ed1198.9c''' or as '''14.986cet'''.

	It has a step size of 14.986 [[cent]]s, and the [[octave]] (([[2/1]])) is tuned slightly impurely to 1198.9 cents.		It has a step size of 14.986 [[cent]]s, and the [[octave]] ([[2/1]]) is tuned slightly impurely to 1198.9 cents.

	80edo tunes almost all simple harmonics slightly sharp by roughly the same amount, so 435zpi is one possible way of correcting for this.		80edo tunes almost all simple harmonics slightly sharp by roughly the same amount, so 435zpi is one possible way of correcting for this.

2025-08-15T07:03:12Z

← Older revision		Revision as of 07:03, 15 August 2025
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	{{Editable user page}}		{{Editable user page}}

	'''435zpi''', the 435th [[zeta peak index]], is a compressed-octaves version of [[80edo]]. It can be thought of as 80ed1198.9c or as 14.986cet.		'''435zpi''', the 435th [[zeta peak index]], is a [[Octave shrinking\|compressed-octaves]] version of [[80edo]]. It can be thought of as '''80ed1198.9c''' or as '''14.986cet'''.

			It has a step size of 14.986 [[cent]]s, and the [[octave]] (([[2/1]])) is tuned slightly impurely to 1198.9 cents.

	80edo tunes almost all simple harmonics slightly sharp by roughly the same amount, so 435zpi is one possible way of correcting for this.		80edo tunes almost all simple harmonics slightly sharp by roughly the same amount, so 435zpi is one possible way of correcting for this.