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37edo: Difference between revisions

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37 edo is also a very accurate equal tuning for Undecimation Temperament, which has a generator of about 519 cents; 2 generators lead to 29/16; 3 generators to 32/13; 6 generators to a 10 cent sharp 6/1; 8 generators to a very accurate 11/1 and 10 generators to 20/1. It has a 7L+2s nonatonic MOS, which in 37-edo scale degrees is 0, 1, 6, 11, 16, 17, 22, 27, 32, a scale structure reminiscent of mavila; as well as a 16 note MOS.
37 edo is also a very accurate equal tuning for Undecimation Temperament, which has a generator of about 519 cents; 2 generators lead to 29/16; 3 generators to 32/13; 6 generators to a 10 cent sharp 6/1; 8 generators to a very accurate 11/1 and 10 generators to 20/1. It has a 7L+2s nonatonic MOS, which in 37-edo scale degrees is 0, 1, 6, 11, 16, 17, 22, 27, 32, a scale structure reminiscent of mavila; as well as a 16 note MOS.
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Line 55: Line 56:
! | Degrees of 37edo
! | Degrees of 37edo
! | Cents Value
! | Cents Value
!pions
!7mus
! | Approximate Ratios
! | Approximate Ratios


Line 76: Line 79:
|-
|-
| | 0
| | 0
| | 0.00
| colspan="3"| 0.00
| | 1/1
| | 1/1
| |  
| |  
Line 85: Line 88:
| | 1
| | 1
| | 32.43
| | 32.43
|34.38
|41.51 (29.83<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 92: Line 97:
|-
|-
| | 2
| | 2
| | 64.86
| | 64.865
|68.76
|83.03 (53.07<sub>16</sub>)
| | 28/27, 27/26
| | 28/27, 27/26
| |  
| |  
Line 100: Line 107:
|-
|-
| | 3
| | 3
| | 97.30
| | 97.3
|103.135
|124.54 (7C.8B<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 109: Line 118:
| | 4
| | 4
| | 129.73
| | 129.73
|137.51
|166.05 (A6.0E<sub>16</sub>)
| | 14/13
| | 14/13
| | 13/12
| | 13/12
Line 117: Line 128:
| | 5
| | 5
| | 162.16
| | 162.16
|171.89
|207.57 (CF.91<sub>16</sub>)
| | 11/10
| | 11/10
| | 12/11
| | 12/11
Line 124: Line 137:
|-
|-
| | 6
| | 6
| | 194.59
| | 194.595
|206.27
|249.08 (F9.14<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 133: Line 148:
| | 7
| | 7
| | 227.03
| | 227.03
|240.65
|290.595 (122.98<sub>16</sub>)
| | 8/7
| | 8/7
| |  
| |  
Line 141: Line 158:
| | 8
| | 8
| | 259.46
| | 259.46
|275.03
|332.11 (14C.1C<sub>16</sub>)
| |  
| |  
| | 7/6
| | 7/6
Line 149: Line 168:
| | 9
| | 9
| | 291.89
| | 291.89
|309.405
|373.63 (175.9F<sub>16</sub>)
| | 13/11, 32/27
| | 13/11, 32/27
| |  
| |  
Line 157: Line 178:
| | 10
| | 10
| | 324.32
| | 324.32
|343.78
|415.135 (19F.23<sub>16</sub>)
| |  
| |  
| | 6/5
| | 6/5
Line 165: Line 188:
| | 11
| | 11
| | 356.76
| | 356.76
|378.16
|456.65 (1C8.A6<sub>16</sub>)
| | 16/13, 27/22
| | 16/13, 27/22
| |  
| |  
Line 173: Line 198:
| | 12
| | 12
| | 389.19
| | 389.19
|412.54
|498.16 (1F2.298<sub>16</sub>)
| | 5/4
| | 5/4
| |  
| |  
Line 181: Line 208:
| | 13
| | 13
| | 421.62
| | 421.62
|446.92
|539.68 (21B.AD<sub>16</sub>)
| | 14/11
| | 14/11
| |  
| |  
Line 189: Line 218:
| | 14
| | 14
| | 454.05
| | 454.05
|481.3
|581.19 (245.3<sub>16</sub>)
| | 13/10
| | 13/10
| |  
| |  
Line 197: Line 228:
| | 15
| | 15
| | 486.49
| | 486.49
|515.68
|622.7 (26E.B4<sub>16</sub>)
| |  
| |  
| | 4/3
| | 4/3
Line 205: Line 238:
| | 16
| | 16
| | 518.92
| | 518.92
|550.05
|664.22 (298.37<sub>16</sub>)
| | 27/20
| | 27/20
| |  
| |  
Line 213: Line 248:
| | 17
| | 17
| | 551.35
| | 551.35
|584.43
|705.73 (2C1.BB<sub>16</sub>)
| | 11/8
| | 11/8
| |  
| |  
Line 221: Line 258:
| | 18
| | 18
| | 583.78
| | 583.78
|618.81
|747.24 (2EB.3E<sub>16</sub>)
| | 7/5
| | 7/5
| |  
| |  
Line 229: Line 268:
| | 19
| | 19
| | 616.22
| | 616.22
|653.19
|788.76 (314.C2<sub>16</sub>)
| | 10/7
| | 10/7
| |  
| |  
Line 237: Line 278:
| | 20
| | 20
| | 648.65
| | 648.65
|687.57
|830.27 (33E.45<sub>16</sub>)
| | 16/11
| | 16/11
| |  
| |  
Line 245: Line 288:
| | 21
| | 21
| | 681.08
| | 681.08
|721.95
|871.78 (367.C9<sub>16</sub>)
| | 40/27
| | 40/27
| |  
| |  
Line 253: Line 298:
| | 22
| | 22
| | 713.51
| | 713.51
|756.32
|913.3 (391.4C<sub>16</sub>)
| |  
| |  
| | 3/2
| | 3/2
Line 261: Line 308:
| | 23
| | 23
| | 745.95
| | 745.95
|790.7
|954.81 (3BA.D<sub>16</sub>)
| | 20/13
| | 20/13
| |  
| |  
Line 269: Line 318:
| | 24
| | 24
| | 778.38
| | 778.38
|825.08
|996.32 (3E4.53<sub>16</sub>)
| | 11/7
| | 11/7
| |  
| |  
Line 277: Line 328:
| | 25
| | 25
| | 810.81
| | 810.81
|859.46
|1037.84 (40D.D68<sub>16</sub>)
| | 8/5
| | 8/5
| |  
| |  
Line 285: Line 338:
| | 26
| | 26
| | 843.24
| | 843.24
|893.84
|1079.35 (437.56<sub>16</sub>)
| | 13/8, 44/27
| | 13/8, 44/27
| |  
| |  
Line 293: Line 348:
| | 27
| | 27
| | 875.68
| | 875.68
|928.22
|1120.865 (460.DE<sub>16</sub>)
| |  
| |  
| | 5/3
| | 5/3
Line 301: Line 358:
| | 28
| | 28
| | 908.11
| | 908.11
|962.595
|1162.38 (48A.61<sub>16</sub>)
| | 22/13, 27/16
| | 22/13, 27/16
| |  
| |  
Line 309: Line 368:
| | 29
| | 29
| | 940.54
| | 940.54
|996.97
|1203.89 (4B3.E4<sub>16</sub>)
| |  
| |  
| | 12/7
| | 12/7
Line 317: Line 378:
| | 30
| | 30
| | 972.97
| | 972.97
|1031.35
|1245.405 (4DD.68<sub>16</sub>)
| | 7/4
| | 7/4
| |  
| |  
Line 324: Line 387:
|-
|-
| | 31
| | 31
| | 1005.41
| | 1005.405
|1065.73
|1286.92 (506.EB<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 333: Line 398:
| | 32
| | 32
| | 1037.84
| | 1037.84
| | 20/11
|1100.11
|1328.43 (530.6F<sub>16</sub>)
| | 11/6
| | 11/6
| | 24/13
| | 24/13
| |  
| |  
| | 9/5
| | 9/5
|
|-
|-
| | 33
| | 33
| | 1070.27
| | 1070.27
|1134.49
|1369.95 (559.F2<sub>16</sub>)
| | 13/7
| | 13/7
| | 24/13
| | 24/13
Line 348: Line 417:
|-
|-
| | 34
| | 34
| | 1102.70
| | 1102.7
|1168.865
|1411.46 (583.76<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 356: Line 427:
|-
|-
| | 35
| | 35
| | 1135.14
| | 1135.135
|1203.24
|1452.97 (5AC.F9<sub>16</sub>)
| | 27/14, 52/27
| | 27/14, 52/27
| |  
| |  
Line 365: Line 438:
| | 36
| | 36
| | 1167.57
| | 1167.57
|1237.62
|1494.49 (5D6.7D<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 370: Line 445:
| |  
| |  
| |  
| |  
|-
|3
|1200
|1272
|1536 (600<sub>16</sub>)
|2/
|
|
|
|
|}
|}


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