User:BudjarnLambeth/435zpi: Difference between revisions

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~~'''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.~~

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

'''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 [[harmonic]]s slightly sharp by roughly the same amount, so 435zpi is one possible way of correcting for this.

==Prime harmonics==

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{{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):

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* 43

This makes it usable as a [[41-limit]] tuning, or as a more accurate 2.3.5.11 or 2.3.5.11.19 [[subgroup]] tuning.

This makes it usable as a full [[41-limit]] tuning, or as a more accurate 2.3.5.11 or 2.3.5.11.19 [[subgroup]] tuning.

==Scales==

All [[80edo#Scales|scales from 80edo]] also occur in 435zpi.

==Instruments==

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: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]]

@@ Line 1: / Line 1: @@
-'''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.
+{{Editable user page}}
-edo tunes almost all simple harmonics slightly sharp by roughly the same amount, so 435zpi is one possible way of correcting for this.
+'''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.
+edo 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==
@@ Line 7: / Line 11: @@
 {{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:
 zpi approximates these with less than 3 cents error (<20% relative error):
@@ Line 18: / Line 22: @@
 * 43
-This makes it usable as a [[41-limit]] tuning, or as a more accurate 2.3.5.11 or 2.3.5.11.19 [[subgroup]] tuning.
+This makes it usable as a full [[41-limit]] tuning, or as a more accurate 2.3.5.11 or 2.3.5.11.19 [[subgroup]] tuning.
+==Scales==
+All [[80edo#Scales|scales from 80edo]] also occur in 435zpi.
+==Instruments==
+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: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]]