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'''29EDT''' is the [[Edt|equal division of the third harmonic]] into 29 parts of 65.5847 [[cent|cents]] each, corresponding to 18.2970 [[edo]]. It is related to the regular temperament supported by [[183edo]], [[311edo]], and [[494edo]].
{{Infobox ET}}
'''29EDT''' is the [[Edt|equal division of the third harmonic]] into 29 parts of 65.5847 [[cent|cents]] each, corresponding to 18.2970 [[edo]]. It is related to the [[Metric microtemperaments #Luminal|luminal temperament]].


{| class="wikitable"
While not possessing good approximations to most integer harmonics, it does have a few very good rational intervals: notably [[27/26]], [[17/10]], [[45/32]], and [[11/6]].
 
==Intervals==
{| class="wikitable right-2 right-3"
|-
|-
! | degree
! steps
! | cents value
! [[cent]]s
! | corresponding <br>JI intervals
! [[hekt]]s
! | comments
! corresponding <br>JI intervals
! comments
|-
|-
| | 0
! colspan="3" | 0
| | 0.0000
| [[1/1]]
| | '''exact [[1/1]]'''
|  
| |  
|-
|-
| | 1
| 1
| | 65.5847
| 65.5847
| | [[27/26]]
| 44.8276
| |  
| [[27/26]]
|  
|-
|-
| | 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
| | 64/51
| 268.9655
| |
| 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
| | [[45/32]]
| 403.4483
| |  
| [[45/32]]
|  
|-
|-
| | 10
| 10
| | 655.8466
| 655.8466
| |  
| 448.2759
| |  
| 16/11
|  
|-
|-
| | 11
| 11
| | 721.4312
| 721.4312
| |  
| 493.1034
| |
|  
| pseudo-[[3/2]]
|-
|-
| | 12
| 12
| | 787.0159
| 787.0159
| | 63/40, 52/33
| 537.9310
| |
| 63/40, 52/33
| pseudo-[[8/5]]
|-
|-
| | 13
| 13
| | 852.6005
| 852.6005
| | [[18/11]]
| 582.7586
| |
| [[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
| | [[11/6]]
| 717.2414
| |
| [[11/6]]
| sharp pseudo-[[9/5]]
|-
|-
| | 17
| 17
| | 1114.9391
| 1114.9391
| | 99/52, 40/21
| 772.0690
| |
| 99/52, 40/21
| pseudo-[[15/8]]
|-
|-
| | 18
| 18
| | 1180.5238
| 1180.5238
| |  
| 806.8966
| |
|  
| pseudooctave
|-
|-
| | 19
| 19
| | 1246.1084
| 1246.1084
| |  
| 851.7241
| |  
| 33/16
|  
|-
|-
| | 20
| 20
| | 1311.6931
| 1311.6931
| | [[16/15|32/15]]
| 896.5517
| |  
| [[16/15|32/15]]
|  
|-
|-
| | 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
| | 153/64
| 1031.0345
| |
| 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
| | [[13/9|26/9]]
| 1255.1724
| |  
| [[13/9|26/9]]
|  
|-
|-
| | 29
| 29
| | 1901.9550
| 1901.9550
| | '''exact [[3/1]]'''
| 1300.0000
| | [[3/2|just perfect fifth]] plus an octave
| [[3/1]]
| [[3/2|just perfect fifth]] plus an octave
|}
|}


==Related regular temperament==
==Harmonics==
===5-limit 183&amp;311===
{{Harmonics in equal
Comma: |145 -49 -29&gt;
| steps = 29
 
| num = 3
POTE generator: 65.585
| denom = 1
 
| intervals = integer
Map: [&lt;1 0 5|, &lt;0 29 -49|]
}}
 
{{Harmonics in equal
EDOs: 183, 311, 494, 677, 860, 1171, 1665, 1848, 2159, 2836, 3019, 4007
| steps = 29
 
| num = 3
Badness: 0.1949
| denom = 1
 
| start = 12
===7-limit 183&amp;311===
| collapsed = 1
Commas: 703125/702464, 26843545600/26795786661
| intervals = integer
 
}}
POTE generator: ~8505/8192 = 65.588
 
Map: [&lt;1 0 5 8|, &lt;0 29 -49 -95|]
 
EDOs: 128, 183, 311, 494, 677, 805, 1116, 1299
 
Badness: 0.1348
 
===11-limit 183&amp;311===
Commas: 3025/3024, 131072/130977, 703125/702464
 
POTE generator: ~5103/4840 = 65.588
 
Map: [&lt;1 0 5 8 1|, &lt;0 29 -49 -95 45|]
 
EDOs: 128, 183, 311, 494, 677, 805, 1299
 
===13-limit 183&amp;311===
Commas: 2080/2079, 3025/3024, 4096/4095, 31250/31213
 
POTE generator: ~1404/1331 = 65.588
 
Map: [&lt;1 0 5 8 1 -1|, &lt;0 29 -49 -95 45 86|]
 
EDOs: 128, 183, 311, 494, 677, 805, 1299
 
===17-limit 183&amp;311===
Commas: 1156/1155, 1275/1274, 2080/2079, 2431/2430, 4096/4095
 
POTE generator: ~1404/1331 = 65.588
 
Map: [&lt;1 0 5 8 1 -1 6|, &lt;0 29 -49 -95 45 86 -35|]
 
EDOs: 128, 183, 311, 494, 677, 805


[[Category:Edt]]
{{todo|expand}}
[[Category:Edonoi]]
Retrieved from "https://en.xen.wiki/w/29edt"