Xenharmonic Wiki

72edo: Difference between revisions

← Older edit
VisualWikitext
→Theory: rework and expand on its 19-limit capability
→Music: Add Tolgahan Çoğulu's ''Ne ağlarsın benim zülfü siyahım'' (2026) – transcription by Stephen Weigel
 
(10 intermediate revisions by 4 users not shown)
Line 92: Line 92:
| 10
| 10
| 166.7
| 166.7
| [[11/10]]
| [[11/10]], [[21/19]]
| {{UDnote|step=10}}
| {{UDnote|step=10}}
|-
|-
Line 142: Line 142:
| 20
| 20
| 333.3
| 333.3
| [[17/14]], [[39/32]], [[40/33]]
| [[17/14]], ''[[39/32]]'', [[40/33]]
| {{UDnote|step=20}}
| {{UDnote|step=20}}
|-
|-
Line 302: Line 302:
| 52
| 52
| 866.7
| 866.7
| [[28/17]], [[33/20]], [[64/39]]
| [[28/17]], [[33/20]], ''[[64/39]]''
| {{UDnote|step=52}}
| {{UDnote|step=52}}
|-
|-
Line 352: Line 352:
| 62
| 62
| 1033.3
| 1033.3
| [[20/11]]
| [[20/11]], [[38/21]]
| {{UDnote|step=62}}
| {{UDnote|step=62}}
|-
|-
Line 409: Line 409:
=== Proposed interval names and solfèges ===
=== Proposed interval names and solfèges ===
{| class="wikitable center-all right-2 left-4 left-7 mw-collapsible mw-collapsed"
{| class="wikitable center-all right-2 left-4 left-7 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Table of proposed interval names and solfèges
|+ style="font-size: 105%; white-space: nowrap;" | Table of proposed interval names and solfèges
|-
|-
! #
! #
Line 1,285: Line 1,285:


== Notation ==
== Notation ==
=== Ups and downs 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}}
[[Alternative symbols for ups and downs notation#Sharp-6| Alternative ups and downs]] have sharps and flats with arrows borrowed from extended [[Helmholtz–Ellis notation]]:
{{Sharpness-sharp6}}
If double arrows are not desirable, arrows can be attached to quarter-tone accidentals:
{{Sharpness-sharp6-qt}}


=== Sagittal notation ===
=== Sagittal notation ===
Line 1,326: Line 1,327:


=== 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 [[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]]
[[File:plot72.png|alt=plot72.png|plot72.png]]
Line 1,669: Line 1,670:
| 516.7
| 516.7
| 27/20
| 27/20
| [[Marvo]] / [[zarvo]]
| [[Gravity]] / [[marvo]] / [[zarvo]]
|-
|-
| 1
| 1
Line 1,741: Line 1,742:
| 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
Line 1,773: Line 1,774:
| [[Gamelstearn]]
| [[Gamelstearn]]
|}
|}
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[normal lists|minimal form]] in parentheses if distinct
<nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct


== Octave stretch or compression ==
== Octave stretch or compression ==
Line 1,990: Line 1,991:


== 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)
Line 1,998: Line 2,002:


; [[Jake Freivald]]
; [[Jake Freivald]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/Lazy%20Sunday.mp3 ''Lazy Sunday'']{{dead link}} in the [[lazysunday]] scale
* [https://web.archive.org/web/20201127014336/http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/Lazy%20Sunday.mp3 ''Lazy Sunday''] in the [[lazysunday]] scale


{{Wikipedia|In vain (Haas)}}
{{Wikipedia|In vain (Haas)}}
Line 2,009: Line 2,013:


; [[Claudi Meneghin]]
; [[Claudi Meneghin]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-72-edo.mp3 ''Twinkle canon – 72 edo'']{{dead link}}
* [https://web.archive.org/web/20201127015744/http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-72-edo.mp3 ''Twinkle canon – 72 edo'']
* [https://www.youtube.com/watch?v=zR0NDgh4944 ''The Miracle Canon'', 3-in-1 on a Ground]
* [https://www.youtube.com/watch?v=zR0NDgh4944 ''The Miracle Canon'', 3-in-1 on a Ground]
* [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]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Rodgers/drum12a-c-t9.mp3 ''June Gloom #9'']{{dead link}}
* [https://web.archive.org/web/20201127012907/http://micro.soonlabel.com/gene_ward_smith/Others/Rodgers/drum12a-c-t9.mp3 ''June Gloom #9'']


; [[Gene Ward Smith]]
; [[Gene Ward Smith]]
* [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)


Retrieved from "https://en.xen.wiki/w/72edo"