35edt: Difference between revisions

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Created page with "'''Division of the third harmonic into 35 equal parts''' (35edt) is related to 22 edo, but with the 3/1 rather than the 2/1 being just. The octave is about 4..."
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Line 5: Line 5:
! | degree
! | degree
! | cents value
! | cents value
!hekts
! | corresponding <br>JI intervals
! | corresponding <br>JI intervals
! | comments
! | comments
|-
|-
| | 0
| | 0
| | 0.0000
| colspan="2"| 0.0000
| | '''exact [[1/1]]'''
| | '''exact [[1/1]]'''
| |  
| |  
Line 15: Line 16:
| | 1
| | 1
| | 54.3416
| | 54.3416
|37.1429
| | [[33/32]], 32/31
| | [[33/32]], 32/31
| |  
| |  
Line 20: Line 22:
| | 2
| | 2
| | 108.6831
| | 108.6831
|74.2857
| | 33/31
| | 33/31
| |  
| |  
Line 25: Line 28:
| | 3
| | 3
| | 163.0247
| | 163.0247
| |  
|111.4286
| |11/10
| |  
| |  
|-
|-
| | 4
| | 4
| | 217.3663
| | 217.3663
|148.5714
| | [[17/15]]
| | [[17/15]]
| |  
| |  
Line 35: Line 40:
| | 5
| | 5
| | 271.7079
| | 271.7079
| |  
|185.7143
| |7/6
| |  
| |  
|-
|-
| | 6
| | 6
| | 326.0494
| | 326.0494
|222.8571
| |  
| |  
| |  
| |pseudo-[[6/5]]
|-
|-
| | 7
| | 7
| | 380.3910
| | 380.391
|260
| | 81/65
| | 81/65
| | pseudo-[[5/4]]
| | pseudo-[[5/4]]
Line 50: Line 58:
| | 8
| | 8
| | 434.7326
| | 434.7326
|297.1429
| | [[9/7]]
| | [[9/7]]
| |  
| |  
Line 55: Line 64:
| | 9
| | 9
| | 489.0741
| | 489.0741
|334.2857
| | 69/52
| | 69/52
| |  
| |  
Line 60: Line 70:
| | 10
| | 10
| | 543.4157
| | 543.4157
|371.4286
| | [[26/19]]
| | [[26/19]]
| |  
| |  
Line 65: Line 76:
| | 11
| | 11
| | 597.7573
| | 597.7573
|408.5714
| | [[24/17]]
| | [[24/17]]
| |  
| |  
Line 70: Line 82:
| | 12
| | 12
| | 652.0989
| | 652.0989
|445.7143
| | [[35/24]]
| | [[35/24]]
| |  
| |  
Line 75: Line 88:
| | 13
| | 13
| | 706.4404
| | 706.4404
|482.8571
| |  
| |  
| | pseudo-[[3/2]]
| | pseudo-[[3/2]]
|-
|-
| | 14
| | 14
| | 760.7820
| | 760.782
|520
| | 45/29
| | 45/29
| |  
| |  
Line 85: Line 100:
| | 15
| | 15
| | 815.1236
| | 815.1236
|557.1429
| | [[8/5]]
| | [[8/5]]
| |  
| |  
Line 90: Line 106:
| | 16
| | 16
| | 869.4651
| | 869.4651
|594.2857
| | 38/23, 81/49
| | 38/23, 81/49
| |  
| |  
Line 95: Line 112:
| | 17
| | 17
| | 923.8067
| | 923.8067
|631.4286
| | 46/27
| | 46/27
| |  
| |  
Line 100: Line 118:
| | 18
| | 18
| | 978.1483
| | 978.1483
|668.5714
| | 81/46
| | 81/46
| |  
| |  
Line 105: Line 124:
| | 19
| | 19
| | 1032.4899
| | 1032.4899
|705.7143
| | 49/27, 69/38
| | 49/27, 69/38
| |  
| |  
Line 110: Line 130:
| | 20
| | 20
| | 1086.8314
| | 1086.8314
|742.8571
| | [[15/8]]
| | [[15/8]]
| |  
| |  
|-
|-
| | 21
| | 21
| | 1141.1730
| | 1141.173
|780
| | 29/15
| | 29/15
| |  
| |  
Line 120: Line 142:
| | 22
| | 22
| | 1195.5146
| | 1195.5146
|817.1429
| |  
| |  
| | pseudo-[[octave]]
| | pseudo-[[octave]]
Line 125: Line 148:
| | 23
| | 23
| | 1249.8561
| | 1249.8561
|854.2857
| | [[36/35|72/35]]
| | [[36/35|72/35]]
| |  
| |  
Line 130: Line 154:
| | 24
| | 24
| | 1304.1977
| | 1304.1977
|891.4286
| | [[17/16|17/8]]
| | [[17/16|17/8]]
| |  
| |  
Line 135: Line 160:
| | 25
| | 25
| | 1358.5393
| | 1358.5393
|928.5714
| | 57/26
| | 57/26
| |  
| |  
Line 140: Line 166:
| | 26
| | 26
| | 1412.8809
| | 1412.8809
|965.7143
| | 52/23
| | 52/23
| |  
| |  
Line 145: Line 172:
| | 27
| | 27
| | 1467.2224
| | 1467.2224
|1002.8571
| | [[7/3]]
| | [[7/3]]
| |  
| |  
|-
|-
| | 28
| | 28
| | 1521.5640
| | 1521.564
|1040
| | 65/27
| | 65/27
| |  
| |pseudo-12/5
|-
|-
| | 29
| | 29
| | 1575.9056
| | 1575.9056
|1077.1429
| |  
| |  
| |  
| |pseudo-5/2
|-
|-
| | 30
| | 30
| | 1630.2471
| | 1630.2471
| |  
|1114.2857
| |18/7
| |  
| |  
|-
|-
| | 31
| | 31
| | 1684.5887
| | 1684.5887
|1151.4286
| | 45/17
| | 45/17
| |  
| |  
Line 170: Line 202:
| | 32
| | 32
| | 1738.9303
| | 1738.9303
| |  
|1188.5714
| |03/11
| |  
| |  
|-
|-
| | 33
| | 33
| | 1793.2719
| | 1793.2719
|1225.7143
| | 31/11
| | 31/11
| |  
| |  
Line 180: Line 214:
| | 34
| | 34
| | 1847.6134
| | 1847.6134
| | [[16/11|32/11]]
|1262.8571
| | [[16/11|32/11]], 93/32
| |  
| |  
|-
|-
| | 35
| | 35
| | 1901.9550
| | 1901.955
|1300
| | '''exact [[3/1]]'''
| | '''exact [[3/1]]'''
| | [[3/2|just perfect fifth]] plus an octave
| | [[3/2|just perfect fifth]] plus an octave

Revision as of 20:33, 20 April 2019

Division of the third harmonic into 35 equal parts (35edt) is related to 22 edo, but with the 3/1 rather than the 2/1 being just. The octave is about 4.4854 cents compressed and the step size is about 54.3416 cents. It is consistent to the 12-integer-limit.

degree cents value hekts corresponding
JI intervals 		comments
0 0.0000 exact 1/1
1 54.3416 37.1429 33/32, 32/31
2 108.6831 74.2857 33/31
3 163.0247 111.4286 11/10
4 217.3663 148.5714 17/15
5 271.7079 185.7143 7/6
6 326.0494 222.8571 pseudo-6/5
7 380.391 260 81/65 pseudo-5/4
8 434.7326 297.1429 9/7
9 489.0741 334.2857 69/52
10 543.4157 371.4286 26/19
11 597.7573 408.5714 24/17
12 652.0989 445.7143 35/24
13 706.4404 482.8571 pseudo-3/2
14 760.782 520 45/29
15 815.1236 557.1429 8/5
16 869.4651 594.2857 38/23, 81/49
17 923.8067 631.4286 46/27
18 978.1483 668.5714 81/46
19 1032.4899 705.7143 49/27, 69/38
20 1086.8314 742.8571 15/8
21 1141.173 780 29/15
22 1195.5146 817.1429 pseudo-octave
23 1249.8561 854.2857 72/35
24 1304.1977 891.4286 17/8
25 1358.5393 928.5714 57/26
26 1412.8809 965.7143 52/23
27 1467.2224 1002.8571 7/3
28 1521.564 1040 65/27 pseudo-12/5
29 1575.9056 1077.1429 pseudo-5/2
30 1630.2471 1114.2857 18/7
31 1684.5887 1151.4286 45/17
32 1738.9303 1188.5714 03/11
33 1793.2719 1225.7143 31/11
34 1847.6134 1262.8571 32/11, 93/32
35 1901.955 1300 exact 3/1 just perfect fifth plus an octave
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