63edo: Difference between revisions
Sort the information so that the general tuning profile is presented before the commas and temps |
→Rank-2 temperaments: 81/80 can't be the associated ratio for 1\63 in Sevond, because 63edo maps 81/80 inconsistently to 2\63; I think 64/63 fits the bill, but better check on that |
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== Theory == | == Theory == | ||
63edo is almost consistent to the [[15-odd-limit]]; the only inconsistency is that [[10/9]] is mapped to 9\63 (1\7, the same as what [[11/10]] is mapped to consistently) so that it is almost 11{{cent}} out of tune. This corresponds to 63edo exaggerating the syntonic comma, [[81/80]], to two steps, so that it finds a somewhat flat mean-tone between ~10/9 and ~9/8. | 63edo is almost [[consistent]] to the [[15-odd-limit]]; the only inconsistency is that [[10/9]] is mapped to 9\63 (1\7, the same as what [[11/10]] is mapped to consistently) so that it is almost 11{{cent}} out of tune. This corresponds to 63edo exaggerating the syntonic comma, [[81/80]], to two steps, so that it finds a somewhat flat mean-tone between ~10/9 and ~9/8. | ||
As an equal temperament, it [[tempering out|tempers out]] [[3125/3072]] in the 5-limit and [[225/224]], [[245/243]], and [[875/864]] in the 7-limit, so that it [[support]]s [[magic]] temperament. In the 11-limit it tempers out [[100/99]], supporting 11-limit magic, plus [[385/384]] and [[540/539]], [[896/891]]. In the 13-limit it tempers out [[169/168]], [[275/273]], [[640/637]], [[352/351]], [[364/363]] and [[676/675]]. It provides the [[optimal patent val]] for [[immune]], the {{nowrap| 29 & 34d }} temperament in the 7-, 11- and 13-limit. | As an equal temperament, it [[tempering out|tempers out]] [[3125/3072]] in the 5-limit and [[225/224]], [[245/243]], and [[875/864]] in the 7-limit, so that it [[support]]s [[magic]] temperament. In the 11-limit it tempers out [[100/99]], supporting 11-limit magic, plus [[385/384]] and [[540/539]], [[896/891]]. In the 13-limit it tempers out [[169/168]], [[275/273]], [[640/637]], [[352/351]], [[364/363]] and [[676/675]]. It provides the [[optimal patent val]] for [[immune]], the {{nowrap| 29 & 34d }} temperament in the 7-, 11- and 13-limit. | ||
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| 10 | | 10 | ||
| 190.5 | | 190.5 | ||
| [[29/26]], [[39/35]], [[49/44]] | | [[19/17]], [[29/26]], [[39/35]], [[49/44]] | ||
|- | |- | ||
| 11 | | 11 | ||
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| 53 | | 53 | ||
| 1009.5 | | 1009.5 | ||
| [[52/29]], [[70/39]], [[88/49]] | | [[34/19]], [[52/29]], [[70/39]], [[88/49]] | ||
|- | |- | ||
| 54 | | 54 | ||
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== Notation == | == Notation == | ||
=== Ups and downs notation === | |||
63edo can be notated using [[ups and downs notation|ups and downs]]. Trup is equivalent to quudsharp, trudsharp is equivalent to quup, etc. | |||
{{Sharpness-sharp7a}} | |||
Alternatively, sharps and flats with arrows borrowed from [[Helmholtz–Ellis notation]] can be used: | |||
{{Sharpness-sharp7}} | |||
=== Sagittal notation === | === Sagittal notation === | ||
This notation uses the same sagittal sequence as [[56edo #Sagittal notation|56edo]]. | This notation uses the same sagittal sequence as [[56edo #Sagittal notation|56edo]]. | ||
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default [[File:63-EDO_Revo_Sagittal.svg]] | default [[File:63-EDO_Revo_Sagittal.svg]] | ||
</imagemap> | </imagemap> | ||
== Approximation to JI == | == Approximation to JI == | ||
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=== Zeta peak index === | === Zeta peak index === | ||
{ | {{ZPI | ||
| | | zpi = 321 | ||
| steps = 63.0192885705350 | |||
| step size = 19.0417890652143 | |||
| tempered height = 6.768662 | |||
| pure height = 6.534208 | |||
| integral = 1.049023 | |||
| gap = 15.412920 | |||
| octave = 1199.63271110850 | |||
| consistent = 8 | |||
| distinct = 8 | |||
}} | |||
| 19.0417890652143 | |||
| 6.768662 | |||
| 1.049023 | |||
| 15.412920 | |||
| | |||
| 8 | |||
| 8 | |||
== Regular temperament properties == | == Regular temperament properties == | ||
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| 26\63<br>(1\63) | | 26\63<br>(1\63) | ||
| 495.24<br>(19.05) | | 495.24<br>(19.05) | ||
| 4/3<br>( | | 4/3<br>(64/63) | ||
| [[Sevond]] | | [[Sevond]] | ||
|- | |- | ||
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* Timeywimey (original/default tuning): 16 10 7 4 11 5 10 | * Timeywimey (original/default tuning): 16 10 7 4 11 5 10 | ||
* Sandcastle (original/default tuning): 8 10 8 11 8 8 10 | * Sandcastle (original/default tuning): 8 10 8 11 8 8 10 | ||
== Instruments == | |||
* [[Lumatone mapping for 63edo]] | |||
* [[Skip fretting system 63 3 17]] | |||
== Music == | == Music == | ||
; [[Bryan Deister]] | |||
* [https://www.youtube.com/shorts/IYLzF4ogl_w ''microtonal improvisation in 63edo''] (2025) | |||
; [[Cam Taylor]] | ; [[Cam Taylor]] | ||
* [https://soundcloud.com/cam-taylor-2-1/12tone63edo1 ''Improvisation in 12-tone fifths chain''] (2015) | * [https://soundcloud.com/cam-taylor-2-1/12tone63edo1 ''Improvisation in 12-tone fifths chain''] (2015) | ||