72edo: Difference between revisions

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=== Zeta properties ===

72edo is the ninth [[zeta integral edo]], as well as being a peak and gap edo, and the maximum value of the [[~~the Riemann zeta function and tuning#The Z function|~~Z function]] in the region near 72 occurs at 71.9506, giving an octave of 1200.824 cents, the stretched octaves of the zeta tuning. Below is a plot of Z in the region around 72.

72edo is the ninth [[zeta integral edo]], as well as being a peak and gap edo, and the maximum value of the [[Z function]] in the region near 72 occurs at 71.9506, giving an octave of 1200.824 cents, the stretched octaves of the zeta tuning. Below is a plot of Z in the region around 72.

[[File:plot72.png|alt=plot72.png|plot72.png]]

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| [[~~Marvo~~]] / [[zarvo]]

| [[Gravity]] / [[marvo]] / [[zarvo]]

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== Music ==

; [[Tolgahan Çoğulu]]

* [https://www.youtube.com/watch?v=BItT4f8MOiI ''Ne ağlarsın benim zülfü siyahım''] (from the UnTwelving 2026 convention) – transcription by [[Stephen Weigel]]

; [[Bryan Deister]]

* [https://www.youtube.com/shorts/VwVp3RVao_k ''microtonal improvisation in 72edo''] (2025)

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* [https://www.youtube.com/watch?v=w6Bckog1eOM ''Sicilienne in Miracle'']

* [https://www.youtube.com/watch?v=QKeZLtFHfNU ''Arietta with 5 Variations'', for Organ] (2024)

; [https://www.youtube.com/@Mintsoda_15/videos Mintsoda_15]

* [https://www.youtube.com/watch?v=eA8S746K9_A ''Quarter-tone Impromptu-72 TET''] (2022)

; [[Prent Rodgers]]

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* [https://www.archive.org/details/Kotekant ''Kotekant''] [https://www.archive.org/download/Kotekant/kotekant.mp3 play] (2010)

;[[Ivan Wyschnegradsky]]

; [[Ivan Wyschnegradsky]]

* [https://www.youtube.com/watch?v=RCcJHCkYQ6U ''Arc-en-ciel, for 6 pianos in twelfth tones, Op. 37''] (1956)

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 === Zeta properties ===
-edo is the ninth [[zeta integral edo]], as well as being a peak and gap edo, and the maximum value of the [[the Riemann zeta function and tuning#The Z function|Z function]] in the region near 72 occurs at 71.9506, giving an octave of 1200.824 cents, the stretched octaves of the zeta tuning. Below is a plot of Z in the region around 72.
+edo is the ninth [[zeta integral edo]], as well as being a peak and gap edo, and the maximum value of the [[Z function]] in the region near 72 occurs at 71.9506, giving an octave of 1200.824 cents, the stretched octaves of the zeta tuning. Below is a plot of Z in the region around 72.
 [[File:plot72.png|alt=plot72.png|plot72.png]]
@@ Line 1,670: / Line 1,670: @@
 | 516.7
 | 27/20
-| [[Marvo]] / [[zarvo]]
+| [[Gravity]] / [[marvo]] / [[zarvo]]
 |-
 | 1
@@ Line 1,991: / Line 1,991: @@
 == Music ==
+; [[Tolgahan Çoğulu]]
+* [https://www.youtube.com/watch?v=BItT4f8MOiI ''Ne ağlarsın benim zülfü siyahım''] (from the UnTwelving 2026 convention) – transcription by [[Stephen Weigel]]
 ; [[Bryan Deister]]
 * [https://www.youtube.com/shorts/VwVp3RVao_k ''microtonal improvisation in 72edo''] (2025)
@@ Line 2,014: / Line 2,017: @@
 * [https://www.youtube.com/watch?v=w6Bckog1eOM ''Sicilienne in Miracle'']
 * [https://www.youtube.com/watch?v=QKeZLtFHfNU ''Arietta with 5 Variations'', for Organ] (2024)
+; [https://www.youtube.com/@Mintsoda_15/videos Mintsoda_15]
+* [https://www.youtube.com/watch?v=eA8S746K9_A ''Quarter-tone Impromptu-72 TET''] (2022)
 ; [[Prent Rodgers]]
@@ Line 2,021: / Line 2,027: @@
 * [https://www.archive.org/details/Kotekant ''Kotekant''] [https://www.archive.org/download/Kotekant/kotekant.mp3 play] (2010)
-;[[Ivan Wyschnegradsky]]
+; [[Ivan Wyschnegradsky]]
 * [https://www.youtube.com/watch?v=RCcJHCkYQ6U ''Arc-en-ciel, for 6 pianos in twelfth tones, Op. 37''] (1956)