Xenharmonic Wiki

63edo: Difference between revisions

← Older edit
VisualWikitext
URL (talk | contribs)
114 edits
m Bolded stuff
→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
 
(59 intermediate revisions by 16 users not shown)
Line 1: Line 1:
The <b>63 equal division</b> or <b>63-EDO</b> divides the octave into 63 equal parts of 19.048 cents each. It tempers out 3125/3072 in the 5-limit and 875/864, 225/224 and 245/243 in the 7-limit, so that it supports magic temperament. In the 11-limit it tempers out 100/99, supporting 11-limit magic, plus 896/891, 385/384 and 640/539. In the 13-limit it tempers put 275/273, 169/168, 640/637, 352/351, 364/363 and 676/675. It provides the optimal patent val for the 29&amp;63 temperament in the 7-, 11- and 13-limit. It is divisible by 3, 7, 9 and 21.
{{Infobox ET}}
{{ED intro}}


63 is also a fascinating division to look at in the 23-limit, as its regular augmented fourth (+6 fifths) is less than 0.3c sharp of 23/16, therefore tempering out 729/726. Although it doesn't deal as well with primes 5, 17, and 19, it excels in the 2.3.7.11.13.23 group, and is a great candidate for a rank-1 or rank-2 gentle tuning. As a fifths-system, the diesis after 12 fifths can represent 32:33, 27:28, 88:91, and more, making chains of fifths 12 or longer very useful in covering harmonic and melodic ground while providing a lot of different colour in different keys. A 17-tone fifths chain looks on the surface a little similar to [[17edo|17edo]], but as -17 fifths gets us to 64/63, observing the comma becomes an essential part in progressions favouring prime 7.
== 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.  


=Music:=
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.


[https://soundcloud.com/camtaylor-1/63edobosanquetaxis-8thjuly2016-237111323-seconds-and-otonal-shifts Seconds and Otonal Shifts] by Cam Taylor
63 is also a fascinating division to look at in the [[47-limit]]. Although it does not deal as well with primes 5, 17, 19, 37 and 41, it excels in the 2.3.7.11.13.23.29.31.43.47 [[subgroup]], and is a great candidate for a [[gentle]] tuning. Its regular augmented fourth (+6 fifths) is less than 0.3 cents sharp of [[23/16]], therefore tempering out [[736/729]]. Its diesis (+12 fifths) can represent [[33/32]], [[32/31]], [[30/29]], [[29/28]], [[28/27]], as well as [[91/88]], and more, so it is very versatile, making chains of fifths of 12 tones or longer very useful in covering harmonic and melodic ground while providing a lot of different colour in different keys. We can take advantage of the representation of 27:28:29:30:31:32:33, which splits [[11/9]] into six "small dieses" as a result; here it can be seen more clearly why these are not regular quarter-tones so are best distinguished from such with the qualifier "large", as otherwise we would expect to see some flavour of minor third after six of them.


[https://soundcloud.com/cam-taylor-2-1/17-out-of-63edo-wurly-those-early-dreams those early dreams] by Cam Taylor
A 17-tone fifths chain looks on the surface a little similar to [[17edo]], but as −17 fifths gets us to [[64/63]], observing the comma becomes an essential part in progressions favouring prime 7. Furthermore, its prime 5 is far from unusable; although [[25/16]] is barely inconsistent, this affords the tuning supporting 7-limit magic, which may be considered interesting or desirable in of itself. And if this was not enough, if you really want to, it offers reasonable approximations to some yet higher primes too; namely [[43/32]], [[47/32]], and [[53/32]]; see the tables below.


[https://archive.org/details/17_63EDOEarlyDreamsTwo Early Dreams 2] by Cam Taylor
=== Prime harmonics ===
{{Harmonics in equal|63|columns=12}}
{{Harmonics in equal|63|start=13|columns=12|collapsed=1|title=Approximation of prime harmonics in 63edo (continued)}}


[https://soundcloud.com/cam-taylor-2-1/12tone63edo1 Improvisation in 12-tone fifths chain in 63EDO] by Cam Taylor
=== Subsets and supersets ===
Since 63 factors into primes as {{nowrap| 3<sup>2</sup> × 7 }}, 63edo has subset edos {{EDOs| 3, 7, 9, and 21 }}.
 
Its representation of the 2.3.5.7.13 subgroup (no-11's 13-limit) can uniquely be described in terms of accurate approximations contained in its main subsets of [[7edo]] and [[9edo]]:
* 1\9 = [[14/13]]~[[13/12]], implying the much more accurate 2\9 = ~[[7/6]] ([[septiennealic]])
* 2\7 = [[39/32]]~[[128/105]], via [[4096/4095]] and the [[akjaysma]] (which are naturally paired)
If we avoid equating 14/13 and 13/12 (which is by far the highest damage equivalence) so that we achieve {{nowrap| 7/6 {{=}} 2\9 }} directly, we get the {{nowrap| 63 & 441 }} microtemperament in the same subgroup.
 
== Intervals ==
{| class="wikitable center-all right-2 left-3"
|-
! Degree
! Cents
! Approximate ratios*
|-
| 0
| 0.0
| [[1/1]]
|-
| 1
| 19.0
| ''[[50/49]]'', ''[[55/54]]'', [[64/63]], [[65/64]], [[91/90]], [[105/104]]
|-
| 2
| 38.1
| [[45/44]], [[46/45]], [[49/48]], ''[[56/55]]'', ''[[66/65]]'', ''[[81/80]]''
|-
| 3
| 57.1
| ''[[25/24]]'', [[28/27]], [[29/28]], [[30/29]], [[31/30]], [[32/31]], [[33/32]], [[36/35]]
|-
| 4
| 76.2
| [[22/21]], [[23/22]], [[24/23]], [[26/25]], ''[[27/26]]''
|-
| 5
| 95.2
| ''[[21/20]]'', [[35/33]]
|-
| 6
| 114.3
| [[15/14]], [[16/15]]
|-
| 7
| 133.3
| [[13/12]], [[14/13]]
|-
| 8
| 152.4
| [[12/11]]
|-
| 9
| 171.4
| ''[[10/9]]'', [[11/10]], [[31/28]], [[32/29]]
|-
| 10
| 190.5
| [[19/17]], [[29/26]], [[39/35]], [[49/44]]
|-
| 11
| 209.5
| [[9/8]]
|-
| 12
| 228.6
| [[8/7]]
|-
| 13
| 247.6
| [[15/13]]
|-
| 14
| 266.7
| [[7/6]]
|-
| 15
| 285.7
| [[13/11]]
|-
| 16
| 304.8
| [[31/26]]
|-
| 17
| 323.8
| [[6/5]]
|-
| 18
| 342.9
| [[11/9]], [[28/23]], [[39/32]]
|-
| 19
| 361.9
| [[16/13]], [[26/21]], [[27/22]]
|-
| 20
| 381.0
| [[5/4]]
|-
| 21
| 400.0
| [[29/23]], [[44/35]], [[49/39]]
|-
| 22
| 419.0
| [[14/11]]
|-
| 23
| 438.1
| [[9/7]]
|-
| 24
| 457.1
| [[13/10]]
|-
| 25
| 476.2
| [[21/16]]
|-
| 26
| 495.2
| [[4/3]]
|-
| 27
| 514.3
| [[35/26]]
|-
| 28
| 533.3
| [[15/11]], ''[[27/20]]''
|-
| 29
| 552.4
| [[11/8]]
|-
| 30
| 571.4
| [[18/13]], [[32/23]]
|-
| 31
| 590.5
| [[7/5]]
|-
| 32
| 609.5
| [[10/7]]
|-
| 33
| 628.6
| [[13/9]], [[23/16]]
|-
| 34
| 647.6
| [[16/11]]
|-
| 35
| 666.7
| [[22/15]]
|-
| 36
| 685.7
| [[52/35]]
|-
| 37
| 704.8
| [[3/2]]
|-
| 38
| 723.8
| [[32/21]]
|-
| 39
| 742.9
| [[20/13]]
|-
| 40
| 761.9
| [[14/9]]
|-
| 41
| 781.0
| [[11/7]]
|-
| 42
| 800.0
| [[35/22]], [[46/29]]
|-
| 43
| 819.0
| [[8/5]]
|-
| 44
| 838.1
| [[13/8]], [[21/13]], [[44/27]]
|-
| 45
| 857.1
| [[18/11]], [[23/14]], [[64/39]]
|-
| 46
| 876.2
| [[5/3]]
|-
| 47
| 895.2
| [[52/31]]
|-
| 48
| 914.3
| [[22/13]]
|-
| 49
| 933.3
| [[12/7]]
|-
| 50
| 952.4
| [[26/15]]
|-
| 51
| 971.4
| [[7/4]]
|-
| 52
| 990.5
| [[16/9]]
|-
| 53
| 1009.5
| [[34/19]], [[52/29]], [[70/39]], [[88/49]]
|-
| 54
| 1028.6
| ''[[9/5]]'', [[20/11]], [[29/16]], [[56/31]]
|-
| 55
| 1047.6
| [[11/6]]
|-
| 56
| 1066.7
| [[13/7]], [[24/13]]
|-
| 57
| 1085.7
| [[15/8]], [[28/15]]
|-
| 58
| 1104.8
| ''[[40/21]]'', [[66/35]]
|-
| 59
| 1123.8
| [[21/11]], [[23/12]], [[25/13]], [[44/23]], ''[[52/27]]''
|-
| 60
| 1142.9
| [[27/14]], [[29/15]], [[31/16]], [[35/18]], ''[[48/25]]'', [[56/29]], [[60/31]], [[64/33]]
|-
| 61
| 1161.9
| [[45/23]], ''[[55/28]]'', [[88/45]], [[96/49]], ''[[160/81]]''
|-
| 62
| 1181.0
| ''[[49/25]]'', [[63/32]], [[65/33]], ''[[108/55]]'', [[180/91]], [[208/105]]
|-
| 63
| 1200.0
| [[2/1]]
|}
<nowiki>*</nowiki> As a 2.3.5.7.11.13.23.29.31-subgroup (no-17 no-19 31-limit) temperament, inconsistent intervals in ''italics''
 
See the below section for a machine-generated table including higher-limit ratios selected with a mind towards higher accuracy.
 
=== Higher-accuracy interpretations ===
 
The following table was created using [[User:Godtone#My python 3 code|Godtone's code]] with the command <code><nowiki>interpret_edo(63,ol=53,no=[5,17,19,25,27,37,41,51],add=[73,75,87,89,91,93,105],dec="''",wiki=23)</nowiki></code> (run in a Python 3 interactive console) plus manual correction of the order of some inconsistent intervals, removal of unsimplified intervals of 75, and adding of (the inconsistent but simple) 10/9, 21/20 and their octave-complements.
 
As the command and description indicates, it is a(n accurate) "no-5's"* no-17's no-19's no-25's no-27's no-37's no-41's 49-odd-limit add-53 add-63 add-73 add-87 add-89 add-91 add-93 add-105 interpretation, tuned to the strengths of 63edo. * Note that because of the cancellation of factors, some odd harmonics of 5 (the simpler/more relevant ones) are present, EG {{nowrap|75/3 {{=}} 25}}, {{nowrap|45/3 {{=}} 15}}, {{nowrap|105/75 {{=}} 7/5}}, {{nowrap| 75/35/2 {{=}} 15/14}}, and {{nowrap|45/9 {{=}} 5}}, so it isn't really "no-5's", just has a de-emphasized focus.
 
Intervals are listed in order of size, so that one can know their relative order at a glance and deem the value of the interpretation for a harmonic context, and [[23-limit]] intervals are highlighted for navigability as [[13-limit]] intervals are more likely to already have pages, and as we are excluding primes 17 and 19, we are only adding prime 23 to the 13-limit.
 
Inconsistent intervals are ''in italics''.
 
{| class="wikitable center-all right-2 left-3 mw-collapsible mw-collapsed"
|-
! Degree
! Cents
! Approximate ratios<ref group="note">{{sg|limit=2.3.5.7.11.13.23.29.31.43.47.53.73.89-subgroup (no-17's no-19's no-37's no-41's 53-limit add-73 add-89 add-105)}} Note that due to the error on 5, only low-complexity intervals involving 5 are included here.</ref>
|-
| 0
| 0.0
| [[1/1]]
|-
| 1
| 19.05
| 106/105, [[105/104]], 94/93, 93/92, [[92/91]], [[91/90]], 90/89, 89/88, 88/87, 87/86, 73/72, [[65/64]], [[64/63]]
|-
| 2
| 38.1
| ''[[66/65]]'', 53/52, [[49/48]], 48/47, 47/46, 93/91, [[46/45]], 91/89, [[45/44]], 89/87, 44/43, 43/42
|-
| 3
| 57.14
| [[36/35]], [[33/32]], 32/31, 94/91, 31/30, 92/89, [[91/88]], 30/29, 89/86, 29/28, ''[[25/24]]''
|-
| 4
| 76.19
| [[26/25]], 49/47, 73/70, [[24/23]], 47/45, 93/89, [[23/22]], 91/87, 45/43, [[22/21]]
|-
| 5
| 95.24
| ''[[21/20]]'', 98/93, [[96/91]], 94/89, 56/53, 93/88, 92/87, 91/86, 89/84, [[35/33]], [[52/49]]
|-
| 6
| 114.29
| 33/31, [[49/46]], [[16/15]], 47/44, 78/73, 31/29, 46/43, [[15/14]]
|-
| 7
| 133.33
| [[14/13]], 96/89, 94/87, 93/86, 53/49, [[13/12]]
|-
| 8
| 152.38
| [[49/45]], [[12/11]], 47/43, [[35/32]], 58/53, [[23/21]]
|-
| 9
| 171.43
| [[11/10]], 98/89, 43/39, 32/29, 53/48, 116/105, 73/66, 52/47, 31/28, ''[[10/9]]''
|-
| 10
| 190.48
| [[49/44]], [[39/35]], 29/26, 48/43, 105/94, 104/93, 47/42
|-
| 11
| 209.52
| ''[[28/25]]'', [[9/8]], 98/87, 53/47, [[44/39]], 35/31, [[26/23]], 60/53, ''[[25/22]]''
|-
| 12
| 228.57
| 33/29, 49/43, 106/93, 73/64, 89/78, [[105/92]], [[8/7]]
|-
| 13
| 247.62
| 84/73, 53/46, [[15/13]], [[52/45]]
|-
| 14
| 266.67
| ''29/25'', 36/31, 106/91, [[7/6]], 104/89, 62/53
|-
| 15
| 285.71
| 73/62, 53/45, 86/73, [[33/28]], [[46/39]], 105/89, 124/105, [[13/11]], 58/49
|-
| 16
| 304.76
| 106/89, 56/47, 87/73, 31/26, [[105/88]], 43/36, 104/87
|-
| 17
| 323.81
| [[6/5]], 112/93, 53/44, 47/39, 88/73, 35/29, 64/53, 29/24, 52/43
|-
| 18
| 342.86
| 73/60, [[28/23]], 106/87, [[39/32]], [[128/105]], 89/73, 105/86, [[11/9]], [[60/49]]
|-
| 19
| 361.9
| 43/35, [[16/13]], 53/43, 90/73, 58/47, 89/72, [[26/21]]
|-
| 20
| 380.95
| 31/25, 36/29, 87/70, [[56/45]], 66/53, 91/73, 116/93, [[5/4]]
|-
| 21
| 400.0
| [[49/39]], [[44/35]], 39/31, 112/89, 73/58, 92/73, 29/23, 53/42, [[91/72]], 62/49
|-
| 22
| 419.05
| [[33/26]], 89/70, [[14/11]], 93/73, 116/91, 60/47, [[23/18]]
|-
| 23
| 438.1
| ''[[32/25]]'', [[9/7]], 112/87, 94/73, 58/45, 40/31, 31/24
|-
| 24
| 457.14
| [[13/10]], 56/43, 43/33, 116/89, 73/56, [[30/23]], 47/36, [[64/49]]
|-
| 25
| 476.19
| [[21/16]], [[46/35]], 96/73, 29/22, [[120/91]], 62/47, 70/53
|-
| 26
| 495.24
| 93/70, [[4/3]]
|-
| 27
| 514.29
| 98/73, 47/35, 43/32, 39/29, [[35/26]], [[66/49]], 31/23, 120/89, 89/66, 58/43
|-
| 28
| 533.33
| 42/31, 72/53, 53/39, 87/64, [[49/36]], 64/47, 124/91, [[15/11]]
|-
| 29
| 552.38
| [[48/35]], [[11/8]], 128/93, 73/53, 62/45, [[91/66]], 40/29, 29/21
|-
| 30
| 571.43
| [[18/13]], 43/31, 146/105, 89/64, [[32/23]], [[39/28]], 124/89, [[46/33]], 60/43
|-
| 31
| 590.48
| [[7/5]], 87/62, 73/52, 66/47, [[45/32]], [[128/91]], 31/22
|-
| 32
| 609.52
| 44/31, [[91/64]], [[64/45]], 47/33, 104/73, 124/87, [[10/7]]
|-
| 33
| 628.57
| 43/30, [[33/23]], 89/62, [[56/39]], [[23/16]], 128/89, 105/73, 62/43, [[13/9]]
|-
| 34
| 647.62
| 42/29, 29/20, [[132/91]], 45/31, 106/73, 93/64, [[16/11]], [[35/24]]
|-
| 35
| 666.67
| [[22/15]], 91/62, 47/32, [[72/49]], 128/87, 78/53, 53/36, 31/21
|-
| 36
| 685.71
| 43/29, 132/89, 89/60, 46/31, [[49/33]], [[52/35]], 58/39, 64/43, 70/47, 73/49
|-
| 37
| 704.76
| [[3/2]], 140/93
|-
| 38
| 723.81
| 53/35, 47/31, [[91/60]], 44/29, 73/48, [[35/23]], [[32/21]]
|-
| 39
| 742.86
| [[49/32]], 72/47, [[23/15]], 112/73, 89/58, 66/43, 43/28, [[20/13]]
|-
| 40
| 761.9
| 48/31, 31/20, 45/29, 73/47, 87/56, [[14/9]], ''[[25/16]]''
|-
| 41
| 780.95
| [[36/23]], 47/30, 91/58, 146/93, [[11/7]], 140/89, [[52/33]]
|-
| 42
| 800.0
| 49/31, [[144/91]], 84/53, 46/29, 73/46, 116/73, 89/56, 62/39, [[35/22]], [[78/49]]
|-
| 43
| 819.05
| [[8/5]], 93/58, 146/91, 53/33, [[45/28]], 140/87, 29/18, 50/31
|-
| 44
| 838.1
| [[21/13]], 144/89, 47/29, 73/45, 86/53, [[13/8]], 70/43
|-
| 45
| 857.14
| [[49/30]], [[18/11]], 172/105, 146/89, [[105/64]], [[64/39]], 87/53, [[23/14]], 120/73
|-
| 46
| 876.19
| 43/26, 48/29, 53/32, 58/35, 73/44, 78/47, 88/53, 93/56, [[5/3]]
|-
| 47
| 895.24
| 87/52, 72/43, [[176/105]], 52/31, 146/87, 47/28, 89/53
|-
| 48
| 914.29
| 49/29, [[22/13]], 105/62, 178/105, [[39/23]], [[56/33]], 73/43, 90/53, 124/73
|-
| 49
| 933.33
| 53/31, 89/52, [[12/7]], 91/53, 31/18, ''50/29''
|-
| 50
| 952.38
| [[45/26]], [[26/15]], 92/53, 73/42
|-
| 51
| 971.43
| [[7/4]], [[184/105]], 156/89, 128/73, 93/53, 86/49, 58/33
|-
| 52
| 990.48
| ''[[44/25]]'', 53/30, [[23/13]], 62/35, [[39/22]], 94/53, 87/49, [[16/9]], ''[[25/14]]''
|-
| 53
| 1009.52
| 84/47, 93/52, 188/105, 43/24, 52/29, [[70/39]], [[88/49]]
|-
| 54
| 1028.57
| ''[[9/5]]', 56/31, 47/26, 132/73, 105/58, 96/53, 29/16, 78/43, 89/49, [[20/11]]
|-
| 55
| 1047.62
| [[42/23]], 53/29, [[64/35]], 86/47, [[11/6]], [[90/49]]
|-
| 56
| 1066.67
| [[24/13]], 98/53, 172/93, 87/47, 89/48, [[13/7]]
|-
| 57
| 1085.71
| [[28/15]], 43/23, 58/31, 73/39, 88/47, [[15/8]], [[92/49]], 62/33
|-
| 58
| 1104.76
| [[49/26]], [[66/35]], 168/89, 172/91, 87/46, 176/93, 53/28, 89/47, [[91/48]], 93/49, ''[[40/21]]''
|-
| 59
| 1123.81
| [[21/11]], 86/45, 174/91, [[44/23]], 178/93, 90/47, [[23/12]], 140/73, 94/49, [[25/13]]
|-
| 60
| 1142.86
| ''[[48/25]]'', 56/29, 172/89, 29/15, [[176/91]], 89/46, 60/31, 91/47, 31/16, [[64/33]], [[35/18]]
|-
| 61
| 1161.9
| 84/43, 43/22, 174/89, [[88/45]], 178/91, [[45/23]], 182/93, 92/47, 47/24, [[96/49]], 104/53
|-
| 62
| 1180.95
| [[63/32]], 144/73, 172/87, 87/44, 176/89, 89/45, [[180/91]], [[91/46]], 184/93, 93/47, [[208/105]], 105/53
|-
| 63
| 1200.0
| [[2/1]]
|}
<references group="note" />
 
== 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 ===
This notation uses the same sagittal sequence as [[56edo #Sagittal notation|56edo]].
 
==== Evo flavor ====
<imagemap>
File:63-EDO_Evo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 639 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 120 106 [[64/63]]
rect 120 80 220 106 [[81/80]]
rect 220 80 340 106 [[33/32]]
default [[File:63-EDO_Evo_Sagittal.svg]]
</imagemap>
 
==== Revo flavor ====
<imagemap>
File:63-EDO_Revo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 705 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 120 106 [[64/63]]
rect 120 80 220 106 [[81/80]]
rect 220 80 340 106 [[33/32]]
default [[File:63-EDO_Revo_Sagittal.svg]]
</imagemap>
 
== Approximation to JI ==
=== Interval mappings ===
{{Q-odd-limit intervals}}
 
=== 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
}}
 
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{Monzo| 100 -63 }}
| {{Mapping| 63 100 }}
| -0.885
| 0.885
| 4.65
|-
| 2.3.5
| 3125/3072, 1638400/1594323
| {{Mapping| 63 100 146 }}
| +0.177
| 1.67
| 8.77
|-
| 2.3.5.7
| 225/224, 245/243, 51200/50421
| {{Mapping| 63 100 146 177 }}
| -0.099
| 1.52
| 8.00
|-
| 2.3.5.7.11
| 100/99, 225/224, 245/243, 1331/1323
| {{mapping| 63 100 146 177 218 }}
| -0.141
| 1.37
| 7.17
|-
| 2.3.5.7.11.13
| 100/99, 169/168, 225/224, 245/243, 275/273
| {{mapping| 63 100 146 177 218 233 }}
| -0.008
| 1.28
| 6.73
|}
 
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>ratio*
! Temperament
|-
| 1
| 2\63
| 38.10
| 49/48
| [[Slender]]
|-
| 1
| 13\63
| 247.62
| 15/13
| [[Immune]]
|-
| 1
| 19\63
| 361.90
| 16/13
| [[Submajor]]
|-
| 1
| 20\63
| 380.95
| 5/4
| [[Magic]]
|-
| 1
| 25\63
| 476.19
| 21/16
| [[Subfourth]]
|-
| 3
| 26\63<br>(5\63)
| 495.24<br>(95.24)
| 4/3<br>(21/20)
| [[Fog]]
|-
| 7
| 26\63<br>(1\63)
| 495.24<br>(19.05)
| 4/3<br>(64/63)
| [[Sevond]]
|-
| 9
| 13\63<br>(1\63)
| 247.62<br>(19.05)
| 15/13<br>(99/98)
| [[Enneaportent]]
|}
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[normal lists|minimal form]] in parentheses if distinct
 
== Scales ==
* Approximation of ''[[Pelog]] lima'': 6 9 21 6 21
* Timeywimey (original/default tuning): 16 10 7 4 11 5 10
* Sandcastle (original/default tuning): 8 10 8 11 8 8 10
 
== Instruments ==
* [[Lumatone mapping for 63edo]]
* [[Skip fretting system 63 3 17]]
 
== Music ==
; [[Bryan Deister]]
* [https://www.youtube.com/shorts/IYLzF4ogl_w ''microtonal improvisation in 63edo''] (2025)
 
; [[Cam Taylor]]
* [https://soundcloud.com/cam-taylor-2-1/12tone63edo1 ''Improvisation in 12-tone fifths chain''] (2015)
* [https://soundcloud.com/cam-taylor-2-1/17-out-of-63edo-wurly-those-early-dreams ''those early dreams''] (2016)
* [https://archive.org/details/17_63EDOEarlyDreamsTwo ''early dreams 2''] (2016)
* [https://soundcloud.com/camtaylor-1/63edobosanquetaxis-8thjuly2016-237111323-seconds-and-otonal-shifts ''Seconds and Otonal Shifts''] (2016)
 
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/63edo"