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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}}
'''[[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]].


== 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 17:
| | 1
| | 1
| | 30.6767
| | 30.6767
|20.9677
| | 57/56, 56/55
| | 57/56, 56/55
| |  
| |  
Line 20: Line 23:
| | 2
| | 2
| | 61.3534
| | 61.3534
|41.9355
| | 57/55
| | 57/55
| |  
| |  
Line 25: Line 29:
| | 3
| | 3
| | 92.0301
| | 92.0301
|62.9032
| | 96/91
| | 96/91
| |  
| |  
Line 30: Line 35:
| | 4
| | 4
| | 122.7068
| | 122.7068
| |  
|83.871
| | 161/150, 189/176
| |  
| |  
|-
|-
| | 5
| | 5
| | 153.3835
| | 153.3835
| |  
|104.8387
| | 12/11
| |  
| |  
|-
|-
| | 6
| | 6
| | 184.0602
| | 184.0602
| | 208/187
|125.80645
| |10/9
| |  
| |  
|-
|-
| | 7
| | 7
| | 214.7369
| | 214.7369
| |  
|146.7742
| |17/15
| |  
| |  
|-
|-
| | 8
| | 8
| | 245.4135
| | 245.4135
|167.7412
| | 121/105
| | 121/105
| |  
| |  
Line 55: Line 65:
| | 9
| | 9
| | 276.0902
| | 276.0902
| |  
|188.7097
| | 20/17
| |  
| |  
|-
|-
| | 10
| | 10
| | 306.7669
| | 306.7669
| |  
|209.6774
| | 6/5
| |  
| |  
|-
|-
| | 11
| | 11
| | 337.4436
| | 337.4436
|230.6452
| | 243/200
| | 243/200
| |  
| |  
Line 70: Line 83:
| | 12
| | 12
| | 368.1203
| | 368.1203
| |  
|251.6129
| | 16/13
| |  
| |  
|-
|-
| | 13
| | 13
| | 398.7970
| | 398.797
|272.58065
| | 34/27
| | 34/27
| |  
| |  
Line 80: Line 95:
| | 14
| | 14
| | 429.4737
| | 429.4737
| |  
|293.5484
| | 9/7
| |  
| |  
|-
|-
| | 15
| | 15
| | 460.1504
| | 460.1504
| |  
|314.5161
| |21/16
| |  
| |  
|-
|-
| | 16
| | 16
| | 490.8271
| | 490.8271
| |  
|335.4839
| | [[4/3]]
| |  
| |  
|-
|-
| | 17
| | 17
| | 521.5038
| | 521.5038
|356.4516
| | 77/57
| | 77/57
| |  
| |  
Line 100: Line 119:
| | 18
| | 18
| | 552.1805
| | 552.1805
|377.49135
| | [[11/8]]
| | [[11/8]]
| |  
| |  
Line 105: Line 125:
| | 19
| | 19
| | 582.8572
| | 582.8572
|398.3871
| | [[7/5]]
| | [[7/5]]
| |  
| |  
Line 110: Line 131:
| | 20
| | 20
| | 613.5339
| | 613.5339
|419.3548
| | 57/40
| | 57/40
| |  
| |  
Line 115: Line 137:
| | 21
| | 21
| | 644.2106
| | 644.2106
| |  
|440.3226
| |16/11
| |  
| |  
|-
|-
| | 22
| | 22
| | 674.8873
| | 674.8873
|461.2903
| | 96/65
| | 96/65
| |  
| |  
|-
|-
| | 23
| | 23
| | 705.5640
| | 705.564
| |  
|482.2851
| |  
| |[[3/2]]
| |
|-
|-
| | 24
| | 24
| | 736.2406
| | 736.2406
|503.2258
| | 153/100
| | 153/100
| |  
| |  
Line 135: Line 161:
| | 25
| | 25
| | 766.9173
| | 766.9173
|524.19355
| | 81/52
| | 81/52
| |  
| |  
|-
|-
| | 26
| | 26
| | 797.5940
| | 797.594
| |  
|545.1613
| |27/17
| |  
| |  
|-
|-
| | 27
| | 27
| | 828.2707
| | 828.2707
| |  
|566.129
| |13/8
| |  
| |  
|-
|-
| | 28
| | 28
| | 858.9474
| | 858.9474
|587.0968
| | 69/42
| | 69/42
| |  
| |  
Line 155: Line 185:
| | 29
| | 29
| | 889.6241
| | 889.6241
|608.0645
| | 117/70
| | 117/70
| |  
| | pseudo-[[5/3]]
|-
|-
| | 30
| | 30
| | 920.3008
| | 920.3008
| |  
|629.0323
| | 17/10
| |  
| |  
|-
|-
| | 31
| | 31
| | 950.9775
| | 950.9775
| |  
|650
| | 26/15
| |  
| |  
|-
|-
| | 32
| | 32
| | 981.6542
| | 981.6542
| |  
|670.9677
| | 30/17
| |  
| |  
|-
|-
| | 33
| | 33
| | 1012.3309
| | 1012.3309
|691.9355
| | 70/39
| | 70/39
| |  
| | pseudo-[[9/5]]
|-
|-
| | 34
| | 34
| | 1043.0076
| | 1043.0076
|712.9032
| | 42/23
| | 42/23
| |  
| |  
Line 185: Line 221:
| | 35
| | 35
| | 1073.6843
| | 1073.6843
|733.871
| | 119/64
| | 119/64
| |  
| |  
|-
|-
| | 36
| | 36
| | 1104.3610
| | 1104.361
| |  
|754.8387
| |17/9
| |  
| |  
|-
|-
| | 37
| | 37
| | 1135.0377
| | 1135.0377
|775.80645
| | 52/27
| | 52/27
| |  
| |  
Line 200: Line 239:
| | 38
| | 38
| | 1165.7144
| | 1165.7144
|796.7742
| | 100/51
| | 100/51
| |  
| |  
|-
|-
| | 39
| | 39
| | 1196.3910
| | 1196.391
| |  
|817.7419
| |  
| | 2/1
| | pseudo-[[octave]]
|-
|-
| | 40
| | 40
| | 1227.0677
| | 1227.0677
|838.7097
| | 65/32
| | 65/32
| |  
| |  
Line 215: Line 257:
| | 41
| | 41
| | 1257.7444
| | 1257.7444
| |  
|859.6774
| |114/55
| |  
| |  
|-
|-
| | 42
| | 42
| | 1288.4211
| | 1288.4211
|880.6452
| | [[20/19|40/19]]
| | [[20/19|40/19]]
| |  
| |  
Line 225: Line 269:
| | 43
| | 43
| | 1319.0978
| | 1319.0978
|901.6129
| | [[15/7]]
| | [[15/7]]
| |  
| |  
Line 230: Line 275:
| | 44
| | 44
| | 1349.7745
| | 1349.7745
|922.58065
| | [[12/11|24/11]]
| | [[12/11|24/11]]
| |  
| |  
Line 235: Line 281:
| | 45
| | 45
| | 1380.4512
| | 1380.4512
| |  
|943.5484
| | 20/9
| |  
| |  
|-
|-
| | 46
| | 46
| | 1411.1279
| | 1411.1279
| |  
|964.5161
| | 9/4
| |  
| |  
|-
|-
| | 47
| | 47
| | 1441.8046
| | 1441.8046
|985.4839
| | 23/10
| | 23/10
| |  
| |  
Line 250: Line 299:
| | 48
| | 48
| | 1472.4813
| | 1472.4813
| |  
|1006.4516
| | 7/3
| |  
| |  
|-
|-
| | 49
| | 49
| | 1503.1580
| | 1503.158
|1027.4194
| | 81/34
| | 81/34
| |  
| |  
Line 260: Line 311:
| | 50
| | 50
| | 1533.8347
| | 1533.8347
| |  
|1048.3871
| | 39/16
| |  
| |  
|-
|-
| | 51
| | 51
| | 1564.5114
| | 1564.5114
|1069.3548
| | 200/81
| | 200/81
| |  
| |  
Line 270: Line 323:
| | 52
| | 52
| | 1595.1881
| | 1595.1881
|1090.3226
| | 98/39
| | 98/39
| |  
| |  
Line 275: Line 329:
| | 53
| | 53
| | 1625.8648
| | 1625.8648
| |  
|1111.2903
| | 51/20
| |  
| |  
|-
|-
| | 54
| | 54
| | 1656.5415
| | 1656.5415
| |  
|1132.2581
| | 192/65
| |  
| |  
|-
|-
| | 55
| | 55
| | 1687.2181
| | 1687.2181
| |  
|1153.2258
| | 8/3
| |  
| |  
|-
|-
| | 56
| | 56
| | 1717.8948
| | 1717.8948
| |  
|1174.19355
| |27/10
| |  
| |  
|-
|-
| | 57
| | 57
| | 1748.5715
| | 1748.5715
| |  
|1195.1613
| |11/4
| |  
| |  
|-
|-
| | 58
| | 58
| | 1779.2482
| | 1779.2482
| |  
|1216.129
| | 176/63
| |  
| |  
|-
|-
| | 59
| | 59
| | 1809.9249
| | 1809.9249
|1237.0968
| | 91/32
| | 91/32
| |  
| |  
Line 310: Line 371:
| | 60
| | 60
| | 1840.6016
| | 1840.6016
|1258.0645
| | 55/19
| | 55/19
| |  
| |  
Line 315: Line 377:
| | 61
| | 61
| | 1871.2783
| | 1871.2783
|1279.0323
| | 56/19
| | 56/19
| |  
| |  
|-
|-
| | 62
| | 62
| | 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
|}
|}


[[Category:Edt]]
== Harmonics ==
[[Category:Edonoi]]
{{Harmonics in equal
| steps = 62
| num = 3
| denom = 1
| intervals = integer
}}
{{Harmonics in equal
| steps = 62
| num = 3
| denom = 1
| start = 12
| collapsed = 1
| intervals = integer
}}
Retrieved from "https://en.xen.wiki/w/62edt"