72edo: Difference between revisions
→Music: fix dead links |
→Music: Add Tolgahan Çoğulu's ''Ne ağlarsın benim zülfü siyahım'' (2026) – transcription by Stephen Weigel |
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== Notation == | == Notation == | ||
=== | === Stein–Zimmermann–Gould notation === | ||
72edo can be notated with ups and downs, spoken as up, dup, trup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, trud, dupflat etc. | [[Stein–Zimmermann–Gould notation]] uses sharps and flats combined with quartertone accidentals and arrows: | ||
{{Sharpness-sharp6-szg}} | |||
If double arrows are not desirable, arrows can be attached to quarter-tone accidentals: | |||
{{Sharpness-sharp6-qt-szg}} | |||
=== Kite's ups and downs notation === | |||
72edo can also be notated with [[Kite's ups and downs notation|Kite's ups and downs]], spoken as up, dup, trup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, trud, dupflat etc. | |||
{{Ups and downs sharpness}} | {{Ups and downs sharpness}} | ||
Half-sharps and half-flats can be used to avoid triple arrows: | Half-sharps and half-flats can be used to avoid triple arrows: | ||
{{Ups and downs sharpness|72|true}} | {{Ups and downs sharpness|72|true}} | ||
=== Sagittal notation === | === Sagittal notation === | ||
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=== Zeta properties === | === Zeta properties === | ||
72edo is the ninth [[zeta integral edo]], as well as being a peak and gap edo, and the maximum value of the [[ | 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]] | [[File:plot72.png|alt=plot72.png|plot72.png]] | ||
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| 516.7 | | 516.7 | ||
| 27/20 | | 27/20 | ||
| [[ | | [[Gravity]] / [[marvo]] / [[zarvo]] | ||
|- | |- | ||
| 1 | | 1 | ||
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| 316.7<br>(50.0) | | 316.7<br>(50.0) | ||
| 6/5<br>(36/35) | | 6/5<br>(36/35) | ||
| [[Ennealimmal]] / ennealimnic | | [[Ennealimmal]] / ennealimnic / ennealiminal | ||
|- | |- | ||
| 9 | | 9 | ||
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== Music == | == 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]] | ; [[Bryan Deister]] | ||
* [https://www.youtube.com/shorts/VwVp3RVao_k ''microtonal improvisation in 72edo''] (2025) | * [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=w6Bckog1eOM ''Sicilienne in Miracle''] | ||
* [https://www.youtube.com/watch?v=QKeZLtFHfNU ''Arietta with 5 Variations'', for Organ] (2024) | * [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]] | ; [[Prent Rodgers]] | ||
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* [https://www.archive.org/details/Kotekant ''Kotekant''] [https://www.archive.org/download/Kotekant/kotekant.mp3 play] (2010) | * [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) | * [https://www.youtube.com/watch?v=RCcJHCkYQ6U ''Arc-en-ciel, for 6 pianos in twelfth tones, Op. 37''] (1956) | ||