29edt: Difference between revisions

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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
| | '''exact [[1/1]]'''
| | '''exact [[1/1]]'''
| |  
| |  
Line 15: Line 16:
| | 1
| | 1
| | 65.5847
| | 65.5847
|44.8276
| | [[27/26]]
| | [[27/26]]
| |  
| |  
Line 20: Line 22:
| | 2
| | 2
| | 131.1693
| | 131.1693
| |  
|89.6552
| |14/13, 27/25, 55/51
| |  
| |  
|-
|-
| | 3
| | 3
| | 196.7540
| | 196.7540
| | [[28/25]]
|134.4828
| |  
| | 9/8, [[28/25]]
| |pseudo-[[10/9]]
|-
|-
| | 4
| | 4
| | 262.3386
| | 262.3386
| |  
|179.3103
| |7/6
| |  
| |  
|-
|-
| | 5
| | 5
| | 327.9233
| | 327.9233
|224.1379
| |  
| |  
| |  
| |pseudo-[[6/5]]
|-
|-
| | 6
| | 6
| | 393.5079
| | 393.5079
|268.9655
| | 64/51
| | 64/51
| |  
| |pseudo-[[5/4]]
|-
|-
| | 7
| | 7
| | 459.0926
| | 459.0926
| |  
|313.7931
| |13/10
| |  
| |  
|-
|-
| | 8
| | 8
| | 524.6772
| | 524.6772
| | 65/48
|358.6206
| | 65/48, 27/20
| |  
| |  
|-
|-
| | 9
| | 9
| | 590.2619
| | 590.2619
|403.4483
| | [[45/32]]
| | [[45/32]]
| |  
| |  
Line 60: Line 70:
| | 10
| | 10
| | 655.8466
| | 655.8466
| |  
|448.2759
| |16/11
| |  
| |  
|-
|-
| | 11
| | 11
| | 721.4312
| | 721.4312
|493.10345
| |  
| |  
| |  
| |pseudo-[[3/2]]
|-
|-
| | 12
| | 12
| | 787.0159
| | 787.0159
|537.931
| | 63/40, 52/33
| | 63/40, 52/33
| |  
| |pseudo-[[8/5]]
|-
|-
| | 13
| | 13
| | 852.6005
| | 852.6005
|582.7586
| | [[18/11]]
| | [[18/11]]
| |  
| |flat pseudo-[[5/3]]
|-
|-
| | 14
| | 14
| | 918.1852
| | 918.1852
| |  
|627.5862
| |  
| |17/10
| |sharp pseudo-[[5/3]]
|-
|-
| | 15
| | 15
| | 983.7698
| | 983.7698
| |  
|672.4138
| |  
| |30/17
| |flat pseudo-[[9/5]]
|-
|-
| | 16
| | 16
| | 1049.3545
| | 1049.3545
|717.2414
| | [[11/6]]
| | [[11/6]]
| |  
| |sharp pseudo-[[9/5]]
|-
|-
| | 17
| | 17
| | 1114.9391
| | 1114.9391
|772.069
| | 99/52, 40/21
| | 99/52, 40/21
| |  
| |pseudo-[[15/8]]
|-
|-
| | 18
| | 18
| | 1180.5238
| | 1180.5238
|806.89655
| |  
| |  
| |  
| |pseudooctave
|-
|-
| | 19
| | 19
| | 1246.1084
| | 1246.1084
| |  
|851.7241
| |33/16
| |  
| |  
|-
|-
| | 20
| | 20
| | 1311.6931
| | 1311.6931
|896.5517
| | [[16/15|32/15]]
| | [[16/15|32/15]]
| |  
| |  
Line 115: Line 136:
| | 21
| | 21
| | 1377.2778
| | 1377.2778
| | 144/65
|941.3794
| | 144/65, 20/9
| |  
| |  
|-
|-
| | 22
| | 22
| | 1442.8624
| | 1442.8624
| |  
|986.2069
| |  
| |30/13
| |pseudo-7/3 (7/6 plus pseudooctave)
|-
|-
| | 23
| | 23
| | 1508.4471
| | 1508.4471
|1031.0345
| | 153/64
| | 153/64
| |  
| |pseudo-12/5
|-
|-
| | 24
| | 24
| | 1574.0317
| | 1574.0317
|1075.8621
| |  
| |  
| |  
| |pseudo-5/2
|-
|-
| | 25
| | 25
| | 1639.6164
| | 1639.6164
| |  
|1120.6897
| |18/7
| |  
| |  
|-
|-
| | 26
| | 26
| | 1705.2010
| | 1705.2010
| | 75/28
|1165.5172
| |  
| | 8/3, 75/28
| |pseudo-27/10
|-
|-
| | 27
| | 27
| | 1770.7857
| | 1770.7857
| |  
|1210.3448
| |39/14, 25/9, 153/55
| |  
| |  
|-
|-
| | 28
| | 28
| | 1836.3703
| | 1836.3703
|1255.1724
| | [[13/9|26/9]]
| | [[13/9|26/9]]
| |  
| |  
Line 155: Line 184:
| | 29
| | 29
| | 1901.9550
| | 1901.9550
|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 19:56, 15 April 2019

29EDT is the equal division of the third harmonic into 29 parts of 65.5847 cents each, corresponding to 18.2970 edo. It is related to the regular temperament supported by 183edo, 311edo, and 494edo.

degree cents value hekts corresponding
JI intervals 		comments
0 0 exact 1/1
1 65.5847 44.8276 27/26
2 131.1693 89.6552 14/13, 27/25, 55/51
3 196.7540 134.4828 9/8, 28/25 pseudo-10/9
4 262.3386 179.3103 7/6
5 327.9233 224.1379 pseudo-6/5
6 393.5079 268.9655 64/51 pseudo-5/4
7 459.0926 313.7931 13/10
8 524.6772 358.6206 65/48, 27/20
9 590.2619 403.4483 45/32
10 655.8466 448.2759 16/11
11 721.4312 493.10345 pseudo-3/2
12 787.0159 537.931 63/40, 52/33 pseudo-8/5
13 852.6005 582.7586 18/11 flat pseudo-5/3
14 918.1852 627.5862 17/10 sharp pseudo-5/3
15 983.7698 672.4138 30/17 flat pseudo-9/5
16 1049.3545 717.2414 11/6 sharp pseudo-9/5
17 1114.9391 772.069 99/52, 40/21 pseudo-15/8
18 1180.5238 806.89655 pseudooctave
19 1246.1084 851.7241 33/16
20 1311.6931 896.5517 32/15
21 1377.2778 941.3794 144/65, 20/9
22 1442.8624 986.2069 30/13 pseudo-7/3 (7/6 plus pseudooctave)
23 1508.4471 1031.0345 153/64 pseudo-12/5
24 1574.0317 1075.8621 pseudo-5/2
25 1639.6164 1120.6897 18/7
26 1705.2010 1165.5172 8/3, 75/28 pseudo-27/10
27 1770.7857 1210.3448 39/14, 25/9, 153/55
28 1836.3703 1255.1724 26/9
29 1901.9550 1300 exact 3/1 just perfect fifth plus an octave

Related regular temperament

5-limit 183&311

Comma: |145 -49 -29>

POTE generator: 65.585

Map: [<1 0 5|, <0 29 -49|]

EDOs: 183, 311, 494, 677, 860, 1171, 1665, 1848, 2159, 2836, 3019, 4007

Badness: 0.1949

7-limit 183&311

Commas: 703125/702464, 26843545600/26795786661

POTE generator: ~8505/8192 = 65.588

Map: [<1 0 5 8|, <0 29 -49 -95|]

EDOs: 128, 183, 311, 494, 677, 805, 1116, 1299

Badness: 0.1348

11-limit 183&311

Commas: 3025/3024, 131072/130977, 703125/702464

POTE generator: ~80/77 = 65.588

Map: [<1 0 5 8 1|, <0 29 -49 -95 45|]

EDOs: 128, 183, 311, 494, 677, 805, 1299

Badness: 0.0328

13-limit 183&311

Commas: 2080/2079, 3025/3024, 4096/4095, 31250/31213

POTE generator: ~27/26 = 65.588

Map: [<1 0 5 8 1 -1|, <0 29 -49 -95 45 86|]

EDOs: 128, 183, 311, 494, 677, 805, 1299

Badness: 0.0168

17-limit 183&311

Commas: 1156/1155, 1275/1274, 2080/2079, 2431/2430, 4096/4095

POTE generator: ~27/26 = 65.588

Map: [<1 0 5 8 1 -1 6|, <0 29 -49 -95 45 86 -35|]

EDOs: 128, 183, 311, 494, 677, 805

Badness: 0.0147

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