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== Theory ==
== Theory ==
103edo is a good [[miracle]] tuning, especially for the [[7-limit|7-]], and for [[Gamelismic clan #Miracle|benediction]] and [[Gamelismic clan #Miracle|hemisecordite]], two of the [[13-limit]] extensions of miracle. It [[tempering out|tempers out]] [[78732/78125]] in the [[5-limit]]; [[225/224]], [[1029/1024]] and [[2401/2400]] in the 7-limit; [[243/242]], [[441/440]] and [[540/539]] in the [[11-limit]]; [[351/350]] and [[847/845]] in the 13-limit. In the 13-limit it provides the [[optimal patent val]] for [[marvel]] temperament as well as benediction and hemisecordite.
103edo is a good [[miracle]] tuning, especially for the [[7-limit]], and for [[Gamelismic clan #Miracle|benediction]] and [[Gamelismic clan #Miracle|hemisecordite]], two of the [[13-limit]] extensions of miracle. It [[tempering out|tempers out]] [[78732/78125]] in the [[5-limit]]; [[225/224]], [[1029/1024]] and [[2401/2400]] in the 7-limit; [[243/242]], [[441/440]] and [[540/539]] in the [[11-limit]]; [[351/350]] and [[847/845]] in the 13-limit. In the 13-limit it provides the [[optimal patent val]] for [[marvel]] temperament as well as benediction and hemisecordite.


In 103edo, all intervals within the 17-odd-limit are [[consistent]], with the sole exception of 9/8 and its octave complement 16/9, which barely miss (relative error 50.2%).
In 103edo, all intervals within the 17-odd-limit are [[consistent]], with the sole exception of 9/8 and its octave complement 16/9, which barely miss (relative error 50.2%).
Line 186: Line 186:
| 7/5
| 7/5
| [[Neptune]]
| [[Neptune]]
|}
== Scales ==
=== 13-limit temperaments ===
{| class="wikitable"
|+
! colspan="3" | Marvel and Benediction
! colspan="3" | Hemisecordite
|-
! Degree
! cents
! Difference from 72edo
! Degree
! cents
! Difference from 62edo
|-
|1
|11.6505
| -5.016¢
|2
|23.301
|3.946¢
|-
|3
|34.9515
|1.618¢
|3
|34.9515
| -3.758¢
|-
|4
|46.602
| -3.398¢
|5
|58.252
|0.188¢
|-
|6
|69.903
|3.236¢
|7
|81.553
|4.134¢
|-
|7
|81.553
| -1.78¢
|8
|93.204
| -3.57¢
|-
|9
|104.854
|4.854¢
|10
|116.505
|0.376¢
|-
|10
|116.5045
| -0.162¢
|12
|139.806
|4.322¢
|-
|11
|128.155
| -5.178¢
|13
|151.456
| -3.382¢
|-
|13
|151.456¢
|1.456¢
|15
|174.757
|0.563¢
|-
|14
|163.107¢
| -3.56¢
|17
|198.058
|4.51¢
|-
|16
|186.408
|3.074¢
|18
|209.709
| -3.1945¢
|-
|17
|198.058
| -1.942¢
|20
|233.01
|0.751¢
|-
|19
|221.359
|4.693¢
|22
|256.311
|4.698¢
|-
|20
|233.01
| -0.324¢
|23
|267.961
| -3.007¢
|-
|21
|244.66
| -5.34¢
|25
|291.262
|0.94¢
|-
|23
|267.961
|1.2945¢
|27
|314.563
|4.886¢
|-
|24
|279.612
| -3.722¢
|28
|326.214
| -2.819¢
|-
|26
|302.913
|2.913¢
|30
|349.515
|1.1275¢
|-
|27
|314.563
| -2.104¢
|32
|372.8155
|5.074¢
|-
|29
|337.864
|4.531¢
|33
|384.466
| -2.631¢
|-
|30
|349.515
| -0.485¢
|35
|407.767
|1.315¢
|-
|31
|361.165
| -5.502¢
|37
|431.068
|5.2615¢
|-
|33
|384.466
|1.133¢
|38
|442.718
| -2.443¢
|-
|34
|396.1165
| -3.8835¢
|40
|466.0190
|1.503¢
|-
|36
|419.4175
|2.751¢
|42
|489.32
|5.449¢
|-
|37
|431.068
| -2.265¢
|43
|500.971
| -2.255¢
|-
|39
|454.369
|4.369¢
|45
|524.272
|1.691¢
|-
|40
|466.019
| -0.647¢
|47
|547.573
|5.637¢
|-
|41
|477.67
| -5.663¢
|48
|559.223
| -2.067¢
|-
|43
|500.971
|0.971¢
|50
|582.524
|1.879¢
|-
|44
|512.621¢
| -4.045¢
|52
|605.825
|5.825¢
|-
|46
|535.922¢
|2.589¢
|53
|617.476
| -1.879¢
|-
|47
|547.573¢
| -2.427¢
|55
|640.777¢
|2.067
|-
|49
|570.874¢
|4.207¢
|56
|652.427
| -5.637¢
|-
|50
|582.524
| -0.809¢
|58
|675.728
| -1.691
|-
|52
|605.825
|5.825¢
|60
|699.029
|2.255¢
|-
|53
|617.475
|0.809¢
|61
|710.68
| -5.449¢
|-
|54
|629.126¢
| -4.207¢
|63
|733.981
| -1.503¢
|-
|56
|652.427¢
|2.427¢
|65
|757.282
|2.443¢
|-
|57
|664.078
| -2.589¢
|66
|768.932
| -5.2615¢
|-
|59
|687.379
|4.045¢
|68
|792.233
| -1.315¢
|-
|60
|699.029
| -0.971¢
|70
|815.534
|2.631¢
|-
|62
|722.33
|5.663¢
|71
|827.1845
| -5.074¢
|-
|63
|733.981
|0.647¢
|73
|850.485
| -1.1275¢
|-
|64
|745.631
| -4.369¢
|75
|873.786
|2.819¢
|-
|66
|768.932
|2.265¢
|76
|885.437
| -4.886¢
|-
|67
|780.5825
| -2.751¢
|78
|908.738
| -0.94¢
|-
|69
|803.8835
|3.8835¢
|80
|932.039
|3.007¢
|-
|70
|815.534
| -1.133¢
|81
|943.689
| -4.698¢
|-
|72
|838.835
|5.501¢
|83
|966.99
| -0.752¢
|-
|73
|850.485
|0.485¢
|85
|990.291
|3.1945¢
|-
|74
|862.136
| -4.531¢
|86
|1001.942
| -4.51¢
|-
|76
|885.439
|2.104¢
|88
|1025.243
| -0.564¢
|-
|77
|897.087
| -2.913¢
|90
|1048.544
|3.382¢
|-
|79
|920.388
|3.722¢
|91
|1060.194
| -4.322¢
|-
|80
|932.039
| -1.2945¢
|93
|1083.495
| -0.376¢
|-
|82
|955.34
|5.34¢
|95
|1106.796
|3.57¢
|-
|83
|966.99
|0.324¢
|96
|1118.447¢
| -4.134¢
|-
|84
|978.641
| -4.693¢
|98
|1141.748
| -0.188¢
|-
|86
|1001.942
|1.942¢
|100
|1165.0485
|3.758¢
|-
|87
|1013.592
| -3.074¢
|101
|1176.699
| -3.946¢
|-
|89
|1036.893
|3.56¢
|
|
|
|-
|90
|1048.544
| -1.456¢
|
|
|
|-
|92
|1071.845
|5.178¢
|
|
|
|-
|93
|1083.495
|0.162¢
|
|
|
|-
|94
|1095.146
| -4.854¢
|
|
|
|-
|96
|1118.447
|1.78¢
|
|
|
|-
|97
|1130.097
| -3.236¢
|
|
|
|-
|99
|1153.398
|3.398¢
|
|
|
|-
|100
|1165.0485
| -1.618¢
|
|
|
|-
|102
|1188.3495
|5.016¢
|
|
|
|}
|}


== Music ==
== Music ==
; [[Francium]]
; [[Francium]]
* "Forest Tribe Dance" from ''Mysteries'' (2023) [https://open.spotify.com/track/0lPUfgduKoJliGbU3kcow0 Spotify] | [https://francium223.bandcamp.com/track/forest-tribe-dance Bandcamp] | [https://www.youtube.com/watch?v=5pbnmzXAFcM YouTube]
* "Forest Tribe Dance" from ''Mysteries'' (2023) – [https://open.spotify.com/track/0lPUfgduKoJliGbU3kcow0 Spotify] | [https://francium223.bandcamp.com/track/forest-tribe-dance Bandcamp] | [https://www.youtube.com/watch?v=5pbnmzXAFcM YouTube]


[[Category:Benediction]]
[[Category:Benediction]]
[[Category:Miracle]]
[[Category:Miracle]]
Retrieved from "https://en.xen.wiki/w/103edo"