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'''[[Edt|Division of the third harmonic]] into 54 equal parts''' (54edt) is related to [[34edo|34 edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 2.4728 cents compressed and the step size is about 35.2214 cents. It is consistent to the [[7-odd-limit|7-integer-limit]], but not to the 8-integer-limit. In comparison, 34edo is only consistent up to the [[5-odd-limit|6-integer-limit]].
{{Infobox ET}}
'''[[Edt|Division of the third harmonic]] into 54 equal parts''' (54EDT) is related to [[34edo|34 edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 2.4728 cents compressed and the step size is about 35.2214 cents. It is consistent to the [[7-odd-limit|7-integer-limit]], but not to the 8-integer-limit. In comparison, 34edo is only consistent up to the [[5-odd-limit|6-integer-limit]].


== Commas ==
This tuning tempers out [[50/49]] and [[64/63]] in the [[7-limit]] and [[78/77]] in the [[13-limit]].
== Intervals ==
{| class="wikitable"
{| class="wikitable"
|-
|-
! | degree
! | degree
! | cents value
! | cents value
!hekts
! | corresponding <br>JI intervals
! | corresponding <br>JI intervals
! | comments
! | comments
|-
|-
| | 0
! colspan="3" | 0
| | 0.0000
| | '''exact [[1/1]]'''
| | '''exact [[1/1]]'''
| |  
| |  
Line 15: Line 20:
| | 1
| | 1
| | 35.2214
| | 35.2214
|24.0741
| | [[50/49]], [[49/48]]
| | [[50/49]], [[49/48]]
| |  
| |  
Line 20: Line 26:
| | 2
| | 2
| | 70.4428
| | 70.4428
|48.14815
| | [[25/24]]
| | [[25/24]]
| |  
| |  
Line 25: Line 32:
| | 3
| | 3
| | 105.6642
| | 105.6642
|72.2222
| | [[17/16]]
| | [[17/16]]
| |  
| |  
Line 30: Line 38:
| | 4
| | 4
| | 140.8856
| | 140.8856
| |  
|96.2963
| | [[13/12]]
| |  
| |  
|-
|-
| | 5
| | 5
| | 176.1069
| | 176.1069
| |  
|120.3704
| | [[10/9]]
| |  
| |  
|-
|-
| | 6
| | 6
| | 211.3283
| | 211.3283
|144.4444
| | 26/23
| | 26/23
| |  
| |  
Line 45: Line 56:
| | 7
| | 7
| | 246.5497
| | 246.5497
|168.5185
| | [[15/13]]
| | [[15/13]]
| |  
| |  
Line 50: Line 62:
| | 8
| | 8
| | 281.7711
| | 281.7711
|192.5926
| | [[20/17]]
| | [[20/17]]
| |  
| |  
Line 55: Line 68:
| | 9
| | 9
| | 316.9925
| | 316.9925
|216.6667
| |[[6/5]]
| |  
| |  
| | pseudo-[[6/5]]
|-
|-
| | 10
| | 10
| | 352.2139
| | 352.2139
| |  
|240.7407
| |[[11/9]]
| |  
| |  
|-
|-
| | 11
| | 11
| | 387.4353
| | 387.4353
|264.8148
| | [[5/4]]
| | [[5/4]]
| |  
| |  
Line 70: Line 86:
| | 12
| | 12
| | 422.6567
| | 422.6567
| | 60/47
|288.8889
| |23/18
| |  
| |  
|-
|-
| | 13
| | 13
| | 457.8781
| | 457.8781
| | 99/76
|312.963
| |[[13/10]]
| |  
| |  
|-
|-
| | 14
| | 14
| | 493.0994
| | 493.0994
| | 117/88
|337.037
| | pseudo-[[4/3]]
| |[[4/3]]
| |
|-
|-
| | 15
| | 15
| | 528.3208
| | 528.3208
|361.1111
| | [[19/14]]
| | [[19/14]]
| |  
| |  
Line 90: Line 110:
| | 16
| | 16
| | 563.5422
| | 563.5422
|385.1852
| | [[18/13]]
| | [[18/13]]
| |  
| |  
Line 95: Line 116:
| | 17
| | 17
| | 598.7636
| | 598.7636
|409.2593
| | 41/29, 140/99
| | 41/29, 140/99
| |  
| |  
|-
|-
| | 18
| | 18
| | 633.9850
| | 633.985
| |  
|433.3333
| | [[13/9]]
| |  
| |  
|-
|-
| | 19
| | 19
| | 669.2064
| | 669.2064
| |  
|457.4074
| |[[28/19]]
| |  
| |  
|-
|-
| | 20
| | 20
| | 704.4278
| | 704.4278
| |
|481.4815
| | pseudo-[[3/2]]
| | [[3/2]]
| |
|-
|-
| | 21
| | 21
| | 739.6492
| | 739.6492
| |  
|505.5559
| |20/13
| |  
| |  
|-
|-
| | 22
| | 22
| | 774.8706
| | 774.8706
|529.6296
| | 36/23
| | 36/23
| |  
| |  
Line 125: Line 152:
| | 23
| | 23
| | 810.0919
| | 810.0919
| |
|553.7037
| | pseudo-[[8/5]]
| |[[8/5]]
| |
|-
|-
| | 24
| | 24
| | 845.3133
| | 845.3133
|577.7778
| | 44/27
| | 44/27
| |  
| |  
Line 135: Line 164:
| | 25
| | 25
| | 880.5347
| | 880.5347
| |
|601.85185
| | pseudo-[[5/3]]
| |[[5/3]]
| |
|-
|-
| | 26
| | 26
| | 915.7561
| | 915.7561
| |  
|625.9259
| | 17/10
| |  
| |  
|-
|-
| | 27
| | 27
| | 950.9775
| | 950.9775
| |  
|650
| | 26/15
| |  
| |  
|-
|-
| | 28
| | 28
| | 986.1989
| | 986.1989
| |  
|674.074
| |23/13
| |  
| |  
|-
|-
| | 29
| | 29
| | 1021.4203
| | 1021.4203
| |
|698.14815
| | pseudo-[[9/5]]
| |[[9/5]]
| |
|-
|-
| | 30
| | 30
| | 1056.6417
| | 1056.6417
|722.2222
| | 81/44
| | 81/44
| |  
| |  
Line 165: Line 200:
| | 31
| | 31
| | 1091.8631
| | 1091.8631
| |  
|746.2963
| | [[15/8]]
| |  
| |  
|-
|-
| | 32
| | 32
| | 1127.0844
| | 1127.0844
|770.3704
| | 23/12
| | 23/12
| |  
| |  
Line 175: Line 212:
| | 33
| | 33
| | 1162.3058
| | 1162.3058
| |  
|794.4444
| | 49/25, 96/49
| |  
| |  
|-
|-
| | 34
| | 34
| | 1197.5272
| | 1197.5272
| |
|818.5185
| | pseudo-[[2/1]]
| |[[2/1]]
| |
|-
|-
| | 35
| | 35
| | 1232.7486
| | 1232.7486
| |  
|842.5926
| | 100/49, 49/24
| |  
| |  
|-
|-
| | 36
| | 36
| | 1267.9700
| | 1267.97
| |  
|866.6667
| | 25/12
| |  
| |  
|-
|-
| | 37
| | 37
| | 1303.1914
| | 1303.1914
| |  
|890.7407
| | 17/8
| |  
| |  
|-
|-
| | 38
| | 38
| | 1338.4128
| | 1338.4128
|914.8148
| | [[13/6]]
| | [[13/6]]
| |  
| |  
Line 205: Line 248:
| | 39
| | 39
| | 1373.6342
| | 1373.6342
| | [[21/19|42/19]]
|938.8889
| | 20/9, [[21/19|42/19]]
| |  
| |  
|-
|-
| | 40
| | 40
| | 1408.8556
| | 1408.8556
|962.963
| | 88/39
| | 88/39
| |  
| |  
Line 215: Line 260:
| | 41
| | 41
| | 1444.0769
| | 1444.0769
|987.037
| | 76/33
| | 76/33
| |  
| |  
Line 220: Line 266:
| | 42
| | 42
| | 1479.2983
| | 1479.2983
|1011.1111
| | 47/20
| | 47/20
| |  
| |  
Line 225: Line 272:
| | 43
| | 43
| | 1514.5197
| | 1514.5197
|1035.1852
| | [[12/5]]
| | [[12/5]]
| |  
| |  
Line 230: Line 278:
| | 44
| | 44
| | 1549.7411
| | 1549.7411
| |  
|1059.2593
| | 27/11
| |  
| |  
|-
|-
| | 45
| | 45
| | 1584.9625
| | 1584.9625
| |
|1083.3333
| | pseudo-[[5/2]]
| |[[5/2]]
| |
|-
|-
| | 46
| | 46
| | 1620.1839
| | 1620.1839
|1107.4074
| | 51/20
| | 51/20
| |  
| |  
Line 245: Line 296:
| | 47
| | 47
| | 1655.4053
| | 1655.4053
|1131.4815
| | [[13/5]]
| | [[13/5]]
| |  
| |  
Line 250: Line 302:
| | 48
| | 48
| | 1690.6267
| | 1690.6267
| | 69/26
|1155.5556
| |8/3
| |  
| |  
|-
|-
| | 49
| | 49
| | 1725.8481
| | 1725.8481
| |  
|1179.6297
| |19/7
| |  
| |  
|-
|-
| | 50
| | 50
| | 1761.0694
| | 1761.0694
| |  
|1203.7037
| | 36/13
| |  
| |  
|-
|-
| | 51
| | 51
| | 1796.2908
| | 1796.2908
|1227.7778
| | [[24/17|48/17]]
| | [[24/17|48/17]]
| |  
| |  
Line 270: Line 326:
| | 52
| | 52
| | 1831.5122
| | 1831.5122
|1251.85185
| | [[36/25|72/25]]
| | [[36/25|72/25]]
| |  
| |  
Line 275: Line 332:
| | 53
| | 53
| | 1866.7336
| | 1866.7336
|1275.5926
| | 50/17
| | 50/17
| |  
| |  
Line 280: Line 338:
| | 54
| | 54
| | 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
|}
|}


[[Category:Edt]]
== Harmonics ==
[[Category:Edonoi]]
{{Harmonics in equal
| steps = 54
| num = 3
| denom = 1
| intervals = integer
}}
{{Harmonics in equal
| steps = 54
| num = 3
| denom = 1
| start = 12
| collapsed = 1
| intervals = integer
}}
Retrieved from "https://en.xen.wiki/w/54edt"