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'''[[Edt|Division of the third harmonic]] into 62 equal parts''' (62EDT) is related to [[39edo|39 edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 3.6090 cents compressed and the step size is about 30.6767 cents. It is consistent to the [[7-odd-limit|7-integer-limit]], but not to the 8-integer-limit. In comparison, 39edo is only consistent up to the [[5-odd-limit|6-integer-limit]].
{{Infobox ET}}
{{ED intro}}


{| class="wikitable"
== Theory ==
62edt is related to [[39edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 3.61 cents compressed and the step size is about 30.6767 cents. 62edt is [[consistent]] to the [[integer limit|7-integer-limit]], but not to the 8-integer-limit. In comparison, 39edo is only consistent up to the 6-integer-limit.
 
=== Harmonics ===
{{Harmonics in equal|62|3|1|columns=11}}
{{Harmonics in equal|62|3|1|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 62edt (continued)}}
 
=== Subsets and supersets ===
Since 62 factors into primes as {{nowrap| 2 × 31 }}, 62edt contains [[2edt]] and [[31edt]] as subset edts.
 
== Intervals ==
{| class="wikitable center-1 right-2 right-3"
|-
|-
! | degree
! #
! | cents value
! Cents
!hekts
! Hekts
! | corresponding <br>JI intervals
! Approximate ratios
! | comments
|-
|-
| | 0
| 0
| colspan="2"| 0
| 0.0
| | '''exact [[1/1]]'''
| 0.0
| |
| [[1/1]]
|-
|-
| | 1
| 1
| | 30.6767
| 30.7
|20.9677
| 21.0
| | 57/56, 56/55
| [[36/35]], [[50/49]], [[55/54]], [[56/55]], [[81/80]]
| |
|-
|-
| | 2
| 2
| | 61.3534
| 61.4
|41.9355
| 41.9
| | 57/55
| [[22/21]], [[28/27]], [[33/32]], [[45/44]], [[49/48]]
| |
|-
|-
| | 3
| 3
| | 92.0301
| 92.0
|62.9032
| 62.9
| | 96/91
| [[16/15]], [[19/18]], [[20/19]], [[21/20]], [[25/24]]
| |
|-
|-
| | 4
| 4
| | 122.7068
| 122.7
|83.871
| 83.9
| | 161/150, 189/176
| [[15/14]]
| |
|-
|-
| | 5
| 5
| | 153.3835
| 153.4
|104.8387
| 104.8
| | 12/11
| [[11/10]], [[12/11]]
| |
|-
|-
| | 6
| 6
| | 184.0602
| 184.1
|125.80645
| 125.8
| |10/9
| [[10/9]]
| |
|-
|-
| | 7
| 7
| | 214.7369
| 214.7
|146.7742
| 146.8
| |17/15
| [[8/7]], [[9/8]]
| |
|-
|-
| | 8
| 8
| | 245.4135
| 245.4
|167.7412
| 167.7
| | 121/105
| [[22/19]]
| |
|-
|-
| | 9
| 9
| | 276.0902
| 276.1
|188.7097
| 188.7
| | 20/17
| [[7/6]]
| |
|-
|-
| | 10
| 10
| | 306.7669
| 306.8
|209.6774
| 209.7
| | 6/5
| [[6/5]]
| |
|-
|-
| | 11
| 11
| | 337.4436
| 337.4
|230.6452
| 230.6
| | 243/200
| [[11/9]]
| |
|-
|-
| | 12
| 12
| | 368.1203
| 368.1
|251.6129
| 251.6
| | 16/13
| [[27/22]]
| |
|-
|-
| | 13
| 13
| | 398.797
| 398.8
|272.58065
| 272.6
| | 34/27
| [[5/4]]
| |
|-
|-
| | 14
| 14
| | 429.4737
| 429.5
|293.5484
| 293.5
| | 9/7
| [[9/7]], [[14/11]]
| |
|-
|-
| | 15
| 15
| | 460.1504
| 460.2
|314.5161
| 314.5
| |21/16
| [[35/27]], [[57/44]]
| |
|-
|-
| | 16
| 16
| | 490.8271
| 490.8
|335.4839
| 335.5
| | [[4/3]]
| [[4/3]]
| |
|-
|-
| | 17
| 17
| | 521.5038
| 521.5
|356.4516
| 356.5
| | 77/57
| [[19/14]], [[27/20]]
| |
|-
|-
| | 18
| 18
| | 552.1805
| 552.2
|377.49135
| 377.5
| | [[11/8]]
| [[11/8]], [[15/11]]
| |
|-
|-
| | 19
| 19
| | 582.8572
| 582.9
|398.3871
| 398.4
| | [[7/5]]
| [[7/5]]
| |
|-
|-
| | 20
| 20
| | 613.5339
| 613.5
|419.3548
| 419.4
| | 57/40
| [[10/7]]
| |
|-
|-
| | 21
| 21
| | 644.2106
| 644.2
|440.3226
| 440.3
| |16/11
| [[16/11]], [[22/15]]
| |
|-
|-
| | 22
| 22
| | 674.8873
| 674.9
|461.2903
| 461.3
| | 96/65
| [[28/19]], [[35/24]]
| |
|-
|-
| | 23
| 23
| | 705.564
| 705.6
|482.2851
| 482.3
| |[[3/2]]
| [[3/2]]
| |
|-
|-
| | 24
| 24
| | 736.2406
| 736.2
|503.2258
| 503.2
| | 153/100
| [[54/35]], [[88/57]]
| |
|-
|-
| | 25
| 25
| | 766.9173
| 766.9
|524.19355
| 524.2
| | 81/52
| [[11/7]], [[14/9]]
| |
|-
|-
| | 26
| 26
| | 797.594
| 797.6
|545.1613
| 545.2
| |27/17
| [[8/5]], [[19/12]]
| |
|-
|-
| | 27
| 27
| | 828.2707
| 828.3
|566.129
| 566.1
| |13/8
| [[44/27]]
| |
|-
|-
| | 28
| 28
| | 858.9474
| 858.9
|587.0968
| 587.1
| | 69/42
| [[18/11]]
| |
|-
|-
| | 29
| 29
| | 889.6241
| 889.6
|608.0645
| 608.1
| | 117/70
| [[5/3]]
| | pseudo-[[5/3]]
|-
|-
| | 30
| 30
| | 920.3008
| 920.3
|629.0323
| 629.0
| | 17/10
| [[12/7]]
| |
|-
|-
| | 31
| 31
| | 950.9775
| 951.0
|650
| 650.0
| | 26/15
| [[19/11]]
| |
|-
|-
| | 32
| 32
| | 981.6542
| 981.7
|670.9677
| 671.0
| | 30/17
| [[7/4]], [[16/9]]
| |
|-
|-
| | 33
| 33
| | 1012.3309
| 1012.3
|691.9355
| 691.9
| | 70/39
| [[9/5]]
| | pseudo-[[9/5]]
|-
|-
| | 34
| 34
| | 1043.0076
| 1043.0
|712.9032
| 712.9
| | 42/23
| [[11/6]], [[20/11]]
| |
|-
|-
| | 35
| 35
| | 1073.6843
| 1073.7
|733.871
| 733.9
| | 119/64
| [[28/15]]
| |
|-
|-
| | 36
| 36
| | 1104.361
| 1104.4
|754.8387
| 754.8
| |17/9
| [[15/8]], [[19/10]]
| |
|-
|-
| | 37
| 37
| | 1135.0377
| 1135.0
|775.80645
| 775.8
| | 52/27
| [[21/11]], [[27/14]]
| |
|-
|-
| | 38
| 38
| | 1165.7144
| 1165.7
|796.7742
| 796.8
| | 100/51
| [[35/18]], [[49/25]], [[55/28]]
| |
|-
|-
| | 39
| 39
| | 1196.391
| 1196.4
|817.7419
| 817.7
| | 2/1
| [[2/1]]
| | pseudo-[[octave]]
|-
|-
| | 40
| 40
| | 1227.0677
| 1227.1
|838.7097
| 838.7
| | 65/32
| [[55/27]], [[81/40]]
| |
|-
|-
| | 41
| 41
| | 1257.7444
| 1257.7
|859.6774
| 859.7
| |114/55
| [[33/16]], [[45/22]], [[49/24]]
| |
|-
|-
| | 42
| 42
| | 1288.4211
| 1288.4
|880.6452
| 880.6
| | [[20/19|40/19]]
| [[19/9]], [[21/10]], [[25/12]]
| |
|-
|-
| | 43
| 43
| | 1319.0978
| 1319.1
|901.6129
| 901.6
| | [[15/7]]
| [[15/7]]
| |
|-
|-
| | 44
| 44
| | 1349.7745
| 1349.8
|922.58065
| 922.6
| | [[12/11|24/11]]
| [[11/5]]
| |
|-
|-
| | 45
| 45
| | 1380.4512
| 1380.5
|943.5484
| 943.5
| | 20/9
| [[20/9]]
| |
|-
|-
| | 46
| 46
| | 1411.1279
| 1411.1
|964.5161
| 964.5
| | 9/4
| [[9/4]]
| |
|-
|-
| | 47
| 47
| | 1441.8046
| 1441.8
|985.4839
| 985.5
| | 23/10
| [[44/19]]
| |
|-
|-
| | 48
| 48
| | 1472.4813
| 1472.5
|1006.4516
| 1006.5
| | 7/3
| [[7/3]]
| |
|-
|-
| | 49
| 49
| | 1503.158
| 1503.2
|1027.4194
| 1027.4
| | 81/34
| [[12/5]], [[19/8]]
| |
|-
|-
| | 50
| 50
| | 1533.8347
| 1533.8
|1048.3871
| 1048.4
| | 39/16
| [[22/9]]
| |
|-
|-
| | 51
| 51
| | 1564.5114
| 1564.5
|1069.3548
| 1069.4
| | 200/81
| [[27/11]]
| |
|-
|-
| | 52
| 52
| | 1595.1881
| 1595.2
|1090.3226
| 1090.3
| | 98/39
| [[5/2]]
| |
|-
|-
| | 53
| 53
| | 1625.8648
| 1625.9
|1111.2903
| 1111.3
| | 51/20
| [[18/7]], [[28/11]]
| |
|-
|-
| | 54
| 54
| | 1656.5415
| 1656.5
|1132.2581
| 1132.3
| | 192/65
| [[57/22]], [[70/27]]
| |
|-
|-
| | 55
| 55
| | 1687.2181
| 1687.2
|1153.2258
| 1153.2
| | 8/3
| [[8/3]]
| |
|-
|-
| | 56
| 56
| | 1717.8948
| 1717.9
|1174.19355
| 1174.2
| |27/10
| [[19/7]], [[27/10]]
| |
|-
|-
| | 57
| 57
| | 1748.5715
| 1748.6
|1195.1613
| 1195.2
| |11/4
| [[11/4]]
| |
|-
|-
| | 58
| 58
| | 1779.2482
| 1779.2
|1216.129
| 1216.1
| | 176/63
| [[14/5]]
| |
|-
|-
| | 59
| 59
| | 1809.9249
| 1809.9
|1237.0968
| 1237.1
| | 91/32
| [[20/7]]
| |
|-
|-
| | 60
| 60
| | 1840.6016
| 1840.6
|1258.0645
| 1258.1
| | 55/19
| [[32/11]]
| |
|-
|-
| | 61
| 61
| | 1871.2783
| 1871.3
|1279.0323
| 1279.0
| | 56/19
| [[35/12]]
| |
|-
|-
| | 62
| 62
| | 1901.955
| 1902.0
|1300
| 1300.0
| | '''exact [[3/1]]'''
| [[3/1]]
| | [[3/2|just perfect fifth]] plus an octave
|}
|}
[[Category:Edt]]
[[Category:Edonoi]]
Retrieved from "https://en.xen.wiki/w/62edt"