37edo: Difference between revisions
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== Notation == | == Notation == | ||
=== | === Stein–Zimmermann–Gould notation === | ||
37edo can be notated using [[Kite's ups and downs notation|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 === | |||
37edo can also be notated using [[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. | |||
{{Sharpness-sharp6a}} | {{Sharpness-sharp6a}} | ||
Half-sharps and half-flats can be used to avoid triple arrows: | Half-sharps and half-flats can be used to avoid triple arrows: | ||
{{Sharpness-sharp6b}} | {{Sharpness-sharp6b}} | ||
=== Ivan Wyschnegradsky's notation === | === Ivan Wyschnegradsky's notation === | ||
Since a sharp raises by six steps, Wyschnegradsky accidentals borrowed from [[72edo]] can also be used: | Since a sharp raises by six steps, Wyschnegradsky accidentals borrowed from [[72edo]] can also be used: | ||
{{Sharpness-sharp6-iw}} | {{Sharpness-sharp6-iw}} | ||
| Line 624: | Line 624: | ||
default [[File:37-EDO_Evo-SZ_Sagittal.svg]] | default [[File:37-EDO_Evo-SZ_Sagittal.svg]] | ||
</imagemap> | </imagemap> | ||
== Approximation to JI == | == Approximation to JI == | ||
=== Interval mappings === | === Interval mappings === | ||
| Line 707: | Line 708: | ||
| 6\37 | | 6\37 | ||
| 194.6 | | 194.6 | ||
| [[Hemiwürschmidt]] / [[hemiwur | | [[Hemiwürschmidt]] / [[hemiwur]] | ||
| [[Hemithirds]] (37b, out-of-tune) | | [[Hemithirds]] (37b, out-of-tune) | ||
|- | |- | ||
| Line 752: | Line 753: | ||
| 15\37 | | 15\37 | ||
| 486.5 | | 486.5 | ||
| [[Ultrapyth | | [[Ultrapyth]] | ||
| | | | ||
|- | |- | ||
| Line 762: | Line 763: | ||
| 17\37 | | 17\37 | ||
| 551.4 | | 551.4 | ||
| [[Freivald]] | | [[Freivald]], [[emka]] | ||
| | | | ||
|- | |- | ||
| Line 778: | Line 779: | ||
''See also: [[MOS Scales of 37edo]], [[Chromatic pairs#Roulette|Roulette scales]]'' | ''See also: [[MOS Scales of 37edo]], [[Chromatic pairs#Roulette|Roulette scales]]'' | ||
=== [[MOS scale]]s === | |||
* [[Ammonite]][21]: 1 3 1 3 1 1 3 1 1 3 1 3 1 1 3 1 1 3 1 3 1 | * [[Ammonite]][21]: 1 3 1 3 1 1 3 1 1 3 1 3 1 1 3 1 1 3 1 3 1 | ||
* [[Beatles]][7]: 4 7 4 7 4 7 4 | * [[Beatles]][7]: 4 7 4 7 4 7 4 | ||
* Beatles[10]: 4 3 4 4 3 4 4 4 3 4 | * Beatles[10]: 4 3 4 4 3 4 4 4 3 4 | ||
* Beatles[17]: 3 1 3 1 3 3 1 3 1 3 1 3 3 1 3 1 3 | * Beatles[17]: 3 1 3 1 3 3 1 3 1 3 1 3 3 1 3 1 3 | ||
* | * Ultrapyth[5] (quasi-[[equipentatonic]]): 7 8 7 8 7 (''recommended mode: 8 7 7 8 7'') | ||
* Ultrapyth[7]: 7 1 7 7 7 1 7 | |||
* | * Ultrapyth[12]: 1 6 1 6 1 6 1 1 6 1 6 1 | ||
* | * Ultrapyth[17]: 1 5 1 1 1 5 1 1 5 1 1 5 1 1 1 5 1 (''great as a [[dual-fifth]] scale'') | ||
* | * Ultrapyth[22]: 1 1 4 1 1 1 4 1 1 1 1 4 1 1 1 4 1 1 1 4 1 1 (''great as a [[dual-fifth]] scale'') | ||
* | |||
* Passion[9]: 13 3 3 3 3 3 3 3 3 | * Passion[9]: 13 3 3 3 3 3 3 3 3 | ||
* Passion[12]: 3 3 3 3 3 3 4 3 3 3 3 3 | * Passion[12]: 3 3 3 3 3 3 4 3 3 3 3 3 | ||
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* Porcupine[15]: 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 | * Porcupine[15]: 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 | ||
* Porcupine[22]: 2 1 2 2 1 2 2 1 2 2 1 2 2 2 1 2 2 1 2 2 1 2 | * Porcupine[22]: 2 1 2 2 1 2 2 1 2 2 1 2 2 2 1 2 2 1 2 2 1 2 | ||
* Twothirdtonic[7]: 13 4 4 4 4 4 4 | * Twothirdtonic[7]: 13 4 4 4 4 4 4 | ||
* Twothirdtonic[8]: 9 4 4 4 4 4 4 4 | * Twothirdtonic[8]: 9 4 4 4 4 4 4 4 | ||
* Twothirdtonic[10]: 4 4 4 4 1 4 4 4 4 4 | * Twothirdtonic[10]: 4 4 4 4 1 4 4 4 4 4 | ||
* Twothirdtonic[19]: 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 | * Twothirdtonic[19]: 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 | ||
=== Scales by individuals === | |||
{| class="wikitable mw-collapsible mw-collapsed" | |||
|+[[Budjarn Lambeth]]'s scales | |||
|'''Contains [[Template:Idiosyncratic|idiosyncratic terms]].''' | |||
* Opalised ammonite{{idio}} (modmos of Ammonite[8]): 5 4 6 5 2 5 4 6 | |||
* [[User:BudjarnLambeth/Antechinus|Antechinus]]{{idio}} (''nonoctave period'') | |||
* [[Maeve Gutierrez#Gutierrez-Lambeth quasi-subharmonic pentatonic|Gutierrez-Lambeth quasi-subharmonic pentatonic]]{{idio}} (''octave-reduced ver.: 5 3 13 9 7'') | |||
* Approximated [[pelog]] lima: 4 5 12 4 12 | |||
* Flattened ionian pentatonic: 12 3 6 12 4 | |||
* Flattened major: 6 6 3 6 6 6 4 | |||
* Flattened major pentatonic: 6 6 9 6 10 | |||
* Sharpened natural minor: 7 3 6 6 3 6 6 | |||
* Sharpened harmonic minor: 7 3 6 6 3 9 3 | |||
* Sharpened pentatonic minor: 10 6 6 9 6 | |||
* Superharmonic minor pentatatonic I: 7 3 12 13 2 | |||
* Superharmonic minor pentatatonic II: 10 6 6 13 2 | |||
* Flattened hexatonic minor: 6 3 6 6 9 7 | |||
* Flattened phrygian dominant: 2 9 4 6 3 6 7 | |||
* Sharpened blues aeolian hexatonic: 10 6 3 3 3 12 | |||
* Flattened blues aeolian pentatonic: 9 6 6 3 13 | |||
* Sharpened blues aeolian pentatonic: 10 12 3 6 6 | |||
* Sharpened blues dorian hexatonic: 10 6 6 6 3 6 | |||
* Extrasharp blues dorian hexatonic: 10 6 6 6 4 5 | |||
* Roughened augmented: 10 2 10 2 11 2 | |||
* Flattened cosmic: 15 6 3 6 7 (''approximated from [[32afdo]]'') | |||
* Sharpened Hirajoshi: 7 3 12 3 12 | |||
* Sharpened Akebono I: 7 3 12 6 9 | |||
* Roughened Javanese pentachordal: 2 8 9 2 16 | |||
* Sharpened underpass: 10 12 7 2 6 (''approximated from [[10afdo]]'') | |||
* ''The scales listed in: [[User:BudjarnLambeth/Quasipelog theory]]'' | * ''The scales listed in: [[User:BudjarnLambeth/Quasipelog theory]]'' | ||
* ''The scales listed in: [[Oceanfront scales]]'' (not all Budjarn's) | |||
|} | |||
=== Equally spaced scales === | |||
* [[37ed4]] (''every 2 steps''): 2 2 2... | |||
* [[Square root of 13 over 10]] (''every 7 steps''): 7 7 7... | |||
* ''Every 8 steps (see below)'' | |||
=== Every 8 steps of 37edo === | === Every 8 steps of 37edo === | ||
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== Music == | == Music == | ||
=== Modern renderings === | |||
; {{W|Alessandro Marcello}} and {{w|Johann Sebastian Bach}} | |||
* [https://www.youtube.com/watch?v=HTAobydvC20 ''Oboe Concerto in D minor'', BWV 974] (1715) – arranged for oboe & organ by [[Claudi Meneghin]] (2022) | |||
; {{W|Pietro Domenico Paradies}} | |||
* [https://www.youtube.com/watch?v=AJ2sa-fRqbE "Toccata" from ''Harpsichord Sonata in A major''] – arranged for organ by Claudi Meneghin (2023) | |||
=== 21st century === | |||
; [[Beheld]] | ; [[Beheld]] | ||
* [https://www.youtube.com/watch?v=IULi2zSdatA ''Mindless vibe''] (2023) | * [https://www.youtube.com/watch?v=IULi2zSdatA ''Mindless vibe''] (2023) | ||
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* [https://www.youtube.com/shorts/m9hmiH8zong ''37edo jam''] (2025) | * [https://www.youtube.com/shorts/m9hmiH8zong ''37edo jam''] (2025) | ||
* [https://www.youtube.com/shorts/mVRbcB2hoBU ''37edo prelude''] (2026) | * [https://www.youtube.com/shorts/mVRbcB2hoBU ''37edo prelude''] (2026) | ||
* [https://www.youtube.com/shorts/Jt6_r6r3lGY ''37edo improv''] (2026) | |||
; [[Francium]] | ; [[Francium]] | ||
| Line 952: | Line 1,001: | ||
* [https://www.youtube.com/watch?v=ngxSiuVadls ''A Dark Era Arises''] (2023) – in Porcupine[15], 37edo tuning | * [https://www.youtube.com/watch?v=ngxSiuVadls ''A Dark Era Arises''] (2023) – in Porcupine[15], 37edo tuning | ||
* [https://www.youtube.com/watch?v=U93XFJJ1aXw ''Two Faced People''] (2025) – in Twothirdtonic[10], 37edo tuning | * [https://www.youtube.com/watch?v=U93XFJJ1aXw ''Two Faced People''] (2025) – in Twothirdtonic[10], 37edo tuning | ||
; [[groundfault]] | |||
* From ''Souvenirs of the Affliction'' (2025) – [https://groundfco.bandcamp.com/album/souvenirs-of-the-affliction Bandcamp] | [https://www.youtube.com/watch?v=rrjuGmmodn0 YouTube] | |||
** "The Life Unreachable" | |||
** "Not This Time" | |||
; [[Andrew Heathwaite]] | ; [[Andrew Heathwaite]] | ||
* [https://andrewheathwaite.bandcamp.com/ | * From [https://andrewheathwaite.bandcamp.com/album/newbeams ''Newbeams''] (2012) | ||
* | ** "Shorn Brown" | ||
** "Jellybear" | |||
; [[Aaron Krister Johnson]] | ; [[Aaron Krister Johnson]] | ||
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* [https://www.youtube.com/watch?v=taT1DClJ2KM ''Tyrian and Gold''] (2024) | * [https://www.youtube.com/watch?v=taT1DClJ2KM ''Tyrian and Gold''] (2024) | ||
; [[ | ; [[Fitzgerald Lee]] | ||
* [https://www.youtube.com/watch?v=Nr0cUJcL4SU ''Bittersweet End''] (2025) | * [https://www.youtube.com/watch?v=Nr0cUJcL4SU ''Bittersweet End''] (2025) | ||
| Line 971: | Line 1,026: | ||
; [[Claudi Meneghin]] | ; [[Claudi Meneghin]] | ||
* [https://www.youtube.com/watch?v=7dU8eyGbt9I ''Deck The Halls''] (2022) | * [https://www.youtube.com/watch?v=7dU8eyGbt9I ''Deck The Halls''] (2022) | ||
* [https://www.youtube.com/watch?v=hpjZZXFM_Fk ''Little Fugue on Happy Birthday''] (2022) – in Passion, 37edo tuning | * [https://www.youtube.com/watch?v=hpjZZXFM_Fk ''Little Fugue on Happy Birthday''] (2022) – in Passion, 37edo tuning | ||
* [https://www.youtube.com/watch?v=SgHY3snZ5bs ''Fugue on an Original Theme''] (2022) | * [https://www.youtube.com/watch?v=SgHY3snZ5bs ''Fugue on an Original Theme''] (2022) | ||
; [[Micronaive]] | ; [[Micronaive]] | ||
* [https:// | * [https://www.youtube.com/watch?v=TMVRYLvg_cA No.27.50] (2022) | ||
; [[Herman Miller]] | ; [[Herman Miller]] | ||
* | * [https://soundcloud.com/morphosyntax-1/luck-of-the-draw ''Luck of the Draw''] (2023) | ||
; [[Joseph Monzo]] | ; [[Joseph Monzo]] | ||
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; [[Mundoworld]] | ; [[Mundoworld]] | ||
* ''Reckless Discredit'' (2021) [https://www.youtube.com/watch?v=ovgsjSoHOkg YouTube] · [https://mundoworld.bandcamp.com/track/reckless-discredit Bandcamp] | * ''Reckless Discredit'' (2021) – [https://www.youtube.com/watch?v=ovgsjSoHOkg YouTube] · [https://mundoworld.bandcamp.com/track/reckless-discredit Bandcamp] | ||
; [[Ray Perlner]] | ; [[Ray Perlner]] | ||
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; [[Stephen Weigel]] | ; [[Stephen Weigel]] | ||
* [https://www.youtube.com/watch?v=71yBnSVBsJk ''Leap Day Cloo | * [https://www.youtube.com/watch?v=71yBnSVBsJk ''Leap Day Cloo''] (2025) | ||
; | ; [[Xeno*n*]] | ||
* | * [https://www.youtube.com/watch?v=_m5u4VviMXw ''Galantean Drift''] (2025) | ||
== See also == | == See also == | ||