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'''103edo''' is the [[EDO|equal division of the octave]] into 103 steps of size 11.6505 [[cent]]s each. It is a good [[Gamelismic_clan|miracle]] tuning, especially for the [[7-limit|7-]] and [[13-limit|13-]] limits and [[Gamelismic_clan|benediction]] and [[Gamelismic_clan|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_family#Marvel|marvel temperament]] as well as [[Gamelismic_clan#Miracle|benediction]] and [[Gamelismic_clan#Hemisecordite|hemisecordite]].
'''103edo''' is the [[EDO|equal division of the octave]] into 103 steps of size 11.6505 [[cent]]s each.  


103edo is the 27th [[prime_numbers|prime]] edo.
== Theory ==
103edo is a good [[miracle]] tuning, especially for the [[7-limit|7-]] and [[13-limit|13-]]limit and [[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 the 27th [[prime numbers|prime]] edo.
 
=== Prime harmonics ===
{{Primes in edo|103}}
{{Primes in edo|103}}


===13-limit temperaments===
== Intervals ==


{| class="wikitable"
{| class="wikitable center-1 right-2"
|-
| | Degree
| | cents
| | temperament
|-
| | 1
| | 11.6505
| |Marvel and Benediction
|-
| |2
| |23.301
| |Hemisecordite
|-
| |3
| |34.9515
| |Marvel and Benediction, Hemisecordite
|-
| |4
| |46.602
| |Marvel and Benediction
|-
| |5
| |58.252
| |Hemisecordite
|-
| |6
| |69.903
| |Marvel and Benediction
|-
| |7
| |81.553
| |Marvel and Benediction, Hemisecordite
|-
| |8
| |93.204
| |Hemisecordite
|-
| |9
| |104.854
| |Marvel and Benediction
|-
| |10
| |116.5045
| |Marvel and Benediction, Hemisecordite
|-
| |11
| |128.155
| |Marvel and Benediction
|-
| |12
| |139.806
| |Hemisecordite
|-
| |13
| |151.456
| |Marvel and Benediction, Hemisecordite
|-
| |14
| |163.107
| |Marvel and Benediction
|-
| |15
| |174.757
| |Hemisecordite
|-
| |16
| |186.408
| |Marvel and Benediction
|-
| |17
| |198.058
| |Marvel and Benediction, Hemisecordite
|-
| |18
| |209.708
| |Hemisecordite
|-
| |19
| |221.359
| |Marvel and Benediction
|-
| |20
| |233.010
| |Marvel and Benediction, Hemisecordite
|-
|-
| |21
! Degree
| |244.660
! Cents
| |Marvel and Benediction
! Temperament
|-
|-
| |22
| 1
| |256.311
| 11.6505
| |Hemisecordite
| Marvel and Benediction
|-
|-
| |23
| 2
| |267.961
| 23.301
| |Marvel and Benediction, Hemisecordite
| Hemisecordite
|-
|-
| |24
| 3
| |279.712
| 34.9515
| |Marvel and Benediction
| Marvel and Benediction, Hemisecordite
|-
|-
| |25
| 4
| |291.262
| 46.602
| |Hemisecordite
| Marvel and Benediction
|-
|-
| |26
| 5
| |303.013
| 58.252
| |Marvel and Benediction
| Hemisecordite
|-
|-
| |27
| 6
| |314.563
| 69.903
| |Marvel and Benediction, Hemisecordite
| Marvel and Benediction
|-
|-
| |28
| 7
| |326.214
| 81.553
| |Hemisecordite
| Marvel and Benediction, Hemisecordite
|-
|-
| |29
| 8
| |337.864
| 93.204
| |Marvel and Benediction
| Hemisecordite
|-
|-
| |30
| 9
| |349.615
| 104.854
| |Marvel and Benediction, Hemisecordite
| Marvel and Benediction
|-
|-
| |31
| 10
| |361.165
| 116.5045
| |Marvel and Benediction
| Marvel and Benediction, Hemisecordite
|-
|-
| |32
| 11
| |372.816
| 128.155
| |Hemisecordite
| Marvel and Benediction
|-
|-
| |33
| 12
| |384.466
| 139.806
| |Marvel and Benediction, Hemisecordite
| Hemisecordite
|-
|-
| |34
| 13
| |396.117
| 151.456
| |Marvel and Benediction
| Marvel and Benediction, Hemisecordite
|-
|-
| |35
| 14
| |407.767
| 163.107
| |Hemisecordite
| Marvel and Benediction
|-
|-
| |36
| 15
| |419.4175
| 174.757
| |Marvel and Benediction
| Hemisecordite
|-
|-
| |37
| 16
| |431.068
| 186.408
| |Marvel and Benediction, Hemisecordite
| Marvel and Benediction
|-
|-
| |38
| 17
| |442.708
| 198.058
| |Hemisecordite
| Marvel and Benediction, Hemisecordite
|-
|-
| |39
| 18
| |454.369
| 209.708
| |Marvel and Benediction
| Hemisecordite
|-
|-
| |40
| 19
| |466.019
| 221.359
| |Marvel and Benediction, Hemisecordite
| Marvel and Benediction
|-
|-
| |41
| 20
| |477.670
| 233.010
| |Marvel and Benediction
| Marvel and Benediction, Hemisecordite
|-
|-
| |42
| 21
| |489.320
| 244.660
| |Hemisecordite
| Marvel and Benediction
|-
|-
| |43
| 22
| |500.971
| 256.311
| |Marvel and Benediction, Hemisecordite
| Hemisecordite
|-
|-
| |44
| 23
| |512.621
| 267.961
| |Marvel and Benediction
| Marvel and Benediction, Hemisecordite
|-
|-
| |45
| 24
| |524.272
| 279.712
| |Hemisecordite
| Marvel and Benediction
|-
|-
| |46
| 25
| |535.922
| 291.262
| |Marvel and Benediction
| Hemisecordite
|-
|-
| |47
| 26
| |547.573
| 303.013
| |Marevel and Benediction, Hemisecordite
| Marvel and Benediction
|-
|-
| |48
| 27
| |559.223
| 314.563
| |Hemisecordite
| Marvel and Benediction, Hemisecordite
|-
|-
| |49
| 28
| |570.874
| 326.214
| |Marvel and Benediction
| Hemisecordite
|-
|-
| |50
| 29
| |582.524
| 337.864
| |Marvel and Benediction, Hemisecordite
| Marvel and Benediction
|-
|-
| |52
| 30
| |605.825
| 349.615
| |Marvel and Benediction, Hemisecordite
| Marvel and Benediction, Hemisecordite
|-
|-
| |53
| 31
| |617.476
| 361.165
| |Marvel and Benediction, Hemisecordite
| Marvel and Benediction
|-
|-
| |54
| 32
| |629.126
| 372.816
| |Marvel and Benediction
| Hemisecordite
|-
|-
| |55
| 33
| |640.777
| 384.466
| |Hemisecordite
| Marvel and Benediction, Hemisecordite
|-
|-
| |56
| 34
| |652.427
| 396.117
| |Marvel and Benediction, Hemisecordite
| Marvel and Benediction
|-
|-
| |57
| 35
| |664.078
| 407.767
| |Marvel and Benediction
| Hemisecordite
|-
|-
| |58
| 36
| |675.728
| 419.4175
| |Hemisecordite
| Marvel and Benediction
|-
|-
| |59
| 37
| |687.379
| 431.068
| |Marvel and Benediction
| Marvel and Benediction, Hemisecordite
|-
|-
| |60
| 38
| |699.029
| 442.708
| |Marvel and Benediction, Hemisecordite
| Hemisecordite
|-
|-
| |61
| 39
| |710.677
| 454.369
| |Hemisecordite
| Marvel and Benediction
|-
|-
| |62
| 40
| |722.330
| 466.019
| |Marvel and Benediction
| Marvel and Benediction, Hemisecordite
|-
|-
| |63
| 41
| |733.981
| 477.670
| |Marvel and Benediction, Hemisecordite
| Marvel and Benediction
|-
|-
| |64
| 42
| |745.631
| 489.320
| |Marvel and Benediction
| Hemisecordite
|-
|-
| |65
| 43
| |757.282
| 500.971
| |Hemisecordite
| Marvel and Benediction, Hemisecordite
|-
|-
| |66
| 44
| |768.932
| 512.621
| |Marvel and Benediction, Hemisecordite
| Marvel and Benediction
|-
|-
| |67
| 45
| |780.583
| 524.272
| |Marvel and Benediction
| Hemisecordite
|-
|-
| |68
| 46
| |792.233
| 535.922
| |Hemisecordite
| Marvel and Benediction
|-
|-
| |69
| 47
| |803.883
| 547.573
| |Marvel and Benediction
| Marevel and Benediction, Hemisecordite
|-
|-
| |70
| 48
| |815.534
| 559.223
| |Marvel and Benediction, Hemisecordite
| Hemisecordite
|-
|-
| |71
| 49
| |827.185
| 570.874
| |Hemisecordite
| Marvel and Benediction
|-
|-
| |72
| 50
| |838.835
| 582.524
| |Marvel and Benediction
| Marvel and Benediction, Hemisecordite
|-
|-
| |73
| …
| |850.385
| …
| |Marvel and Benediction. Hemisecordite
| …
|-
| |74
| |862.156
| |Marvel and Benediction
|-
| |75
| |873.786
| |Hemisecordite
|-
| |76
| |885.537
| |Marvel and Benediction, Hemisecordite
|-
| |77
| |896.987
| |Marvel and Benediction
|-
| |78
| |908.638
| |Hemisecordite
|-
| |79
| |920.388
| |Marvel and Benediction, Hemisecordite
|-
| |80
| |932.039
| |Marvel and Benediction
|-
| |81
| |943.689
| |Hemisecordite
|-
| |82
| |955.34
| |Marvel and Benediction
|-
| |83
| |966.99
| |Marvel and Benediction, Hemisecordite
|-
| |84
| |978.641
| |Marvel and Benediction
|-
| |85
| |990.291
| |Hemisecordite
|-
| |86
| |1001.942
| |Marvel and Benediction, Hemisecordite
|-
| |87
| |1013.592
| |Marvel and Benediction
|-
| |88
| |1025.243
| |Hemisecordite
|-
| |89
| |1036.893
| |Marvel and Benediction
|-
| |90
| |1048.544
| |Marvel and Benediction, Hemisecordite
|-
| |91
| |1060.194
| |Hemisecordite
|-
| |92
| |1071.845
| |Marvel and Benediction
|-
| |93
| |1083.495
| |Marvel and Benediction, Hemisecordite
|-
| |94
| |1095.146
| |Marvel and Benediction
|-
| |95
| |1106.796
| |Hemisecordite
|-
| |96
| |1118.447
| |Marvel and Benediction, Hemisecordite
|-
| |97
| |1130.097
| |Marvel and Benediction
|-
| |98
| |1141.748
| |Hemisecordite
|-
| |99
| |1153.398
| |Marvel and Benediction
|-
| |100
| |1165.0485
| |Marvel and Benediction, Hemisecordite
|-
| |101
| |1176.609
| |Hemisecordite
|-
| |102
| |1188.3495
| |Marvel and Benediction
|}
|}
Since 103edo has a step of 11.6505 cents, it also allows one to use its MOS scales as circulating temperaments.
 
== Scales ==
Since 103edo has a step of 11.6505 cents, it also allows one to use its MOS scales as circulating temperaments{{clarify}}.
{| class="wikitable"
{| class="wikitable"
|+Circulating temperaments in 103edo
|+Circulating temperaments in 103edo
Line 673: Line 480:
|}
|}


===13-limit temperaments===
=== 13-limit temperaments ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 1,183: Line 990:
|
|
|}
|}
[[Category:Benediction]]
[[Category:Benediction]]
[[Category:Equal divisions of the octave]]
[[Category:Equal divisions of the octave]]
Retrieved from "https://en.xen.wiki/w/103edo"