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'''[[Ed7|Division of the 7th harmonic]] into 87 equal parts''' (87ed7) is related to [[31edo|31 edo]], but with the 7/1 rather than the 2/1 being just. The octave is slightly stretched (about 0.3862 cents) and the step size is about 38.7221 cents.
{{Infobox ET}}
{{ED intro}}


{| class="wikitable"
== Theory ==
|-
87ed7 is related to [[31edo]], but with the 7/1 rather than the [[2/1]] being just. The octave is slightly stretched (about 0.3862{{c}}). Like 31edo, 87ed7 is [[consistent]] through the [[integer limit|12-integer-limit]].  
! | degree
! | cents value
! | corresponding <br>JI intervals
! | comments
|-
| | 0
| | 0.0000
| | '''exact [[1/1]]'''
| |
|-
| | 1
| | 38.7221
| |
| |
|-
| | 2
| | 77.4443
| |
| |
|-
| | 3
| | 116.1664
| | 77/72, [[15/14]]
| |
|-
| | 4
| | 154.8885
| |
| |
|-
| | 5
| | 193.6107
| |
| |
|-
| | 6
| | 232.3328
| | [[8/7]]
| |
|-
| | 7
| | 271.0550
| |
| |
|-
| | 8
| | 309.7771
| |
| |
|-
| | 9
| | 348.4992
| | [[11/9]], [[49/40]]
| |
|-
| | 10
| | 387.2214
| |
| |
|-
| | 11
| | 425.9435
| |
| |
|-
| | 12
| | 464.6656
| | 98/75
| |
|-
| | 13
| | 503.3878
| |
| |
|-
| | 14
| | 542.1099
| |
| |
|-
| | 15
| | 580.8321
| | [[7/5]]
| |
|-
| | 16
| | 619.5542
| |
| |
|-
| | 17
| | 658.2763
| |
| |
|-
| | 18
| | 696.9985
| | 112/75, 121/81, 136/91, 187/125
| |
|-
| | 19
| | 735.7206
| |
| |
|-
| | 20
| | 774.4427
| |
| |
|-
| | 21
| | 813.1649
| | [[8/5]]
| |
|-
| | 22
| | 851.8870
| |
| |
|-
| | 23
| | 890.6091
| |
| |
|-
| | 24
| | 929.3313
| | 65/38
| |
|-
| | 25
| | 968.0534
| |
| |
|-
| | 26
| | 1006.7756
| |
| |
|-
| | 27
| | 1045.4977
| | 64/35
| |
|-
| | 28
| | 1084.2198
| |
| |
|-
| | 29
| | 1122.9420
| |
| |
|-
| | 30
| | 1161.6641
| | 88/45, 96/49, 49/25
| |
|-
| | 31
| | 1200.3862
| |
| |
|-
| | 32
| | 1239.1084
| |
| |
|-
| | 33
| | 1277.8305
| | [[22/21|44/21]]
| |
|-
| | 34
| | 1316.5527
| |
| |
|-
| | 35
| | 1355.2748
| |
| |
|-
| | 36
| | 1393.9969
| | [[19/17|38/17]], 85/38
| |
|-
| | 37
| | 1432.7191
| |
| |
|-
| | 38
| | 1471.4412
| |
| |
|-
| | 39
| | 1510.1633
| |
| |
|-
| | 40
| | 1548.8855
| |
| |
|-
| | 41
| | 1587.6076
| |
| |
|-
| | 42
| | 1626.3297
| | [[32/25|64/25]]
| |
|-
| | 43
| | 1665.0519
| |
| |
|-
| | 44
| | 1703.7740
| |
| |
|-
| | 45
| | 1742.4962
| | [[26/19|52/19]]
| |
|-
| | 46
| |
| |
| |
|-
| | 47
| |
| |
| |
|-
| | 48
| | 1858.6626
| | [[19/13|38/13]]
| |
|-
| | 49
| |
| |
| |
|-
| | 50
| |
| |
| |
|-
| | 51
| | 1974.8290
| | [[25/16|25/8]]
| |
|-
| | 52
| |
| |
| |
|-
| | 53
| |
| |
| |
|-
| | 54
| | 2090.9954
| |
| |
|-
| | 55
| |
| |
| |
|-
| | 56
| |
| |
| |
|-
| | 57
| | 2207.1618
| | [[34/19|68/19]]
| |
|-
| | 58
| |
| |
| |
|-
| | 59
| |
| |
| |
|-
| | 60
| | 2323.3282
| | 65/17
| |
|-
| | 61
| |
| |
| |
|-
| | 62
| |
| |
| |
|-
| | 63
| | 2439.4946
| | [[45/44|45/11]]
| |
|-
| | 64
| |
| |
| |
|-
| | 65
| |
| |
| |
|-
| | 66
| | 2555.6610
| | 35/8
| |
|-
| | 67
| |
| |
| |
|-
| | 68
| |
| |
| |
|-
| | 69
| | 2671.8274
| |
| |
|-
| | 70
| |
| |
| |
|-
| | 71
| |
| |
| |
|-
| | 72
| | 2787.9939
| | [[5/1]]
| |
|-
| | 73
| |
| |
| |
|-
| | 74
| |
| |
| |
|-
| | 75
| | 2904.1603
| | 75/14
| |
|-
| | 76
| |
| |
| |
|-
| | 77
| |
| |
| |
|-
| | 78
| | 3020.3267
| | [[10/7|40/7]], 63/11
| |
|-
| | 79
| |
| |
| |
|-
| | 80
| |
| |
| |
|-
| | 81
| | 3136.4931
| | [[49/32|49/8]]
| |
|-
| | 82
| |
| |
| |
|-
| | 83
| |
| |
| |
|-
| | 84
| | 3252.6595
| | 98/15, [[18/11|72/11]]
| |
|-
| | 85
| |
| |
| |
|-
| | 86
| |
| |
| |
|-
| | 87
| | 3368.8259
| | '''exact [[7/1]]'''
| | [[7/4|harmonic seventh]] plus two octaves
|}


[[Category:Ed7]]
=== Harmonics ===
[[Category:Edonoi]]
{{Harmonics in equal|87|7|1|intervals=integer|columns=11}}
{{Harmonics in equal|87|7|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 87ed7 (continued)}}
 
=== Subsets and supersets ===
Since 87 factors into primes as {{nowrap| 3 × 29 }}, 87ed7 contains [[3ed7]] and [[29ed7]] as subset ed7's.
 
== Intervals ==
{{Interval table}}
 
== See also ==
* [[18edf]] – relative edf
* [[31edo]] – relative edo
* [[49edt]] – relative edt
* [[72ed5]] – relative ed5
* [[80ed6]] – relative ed6
* [[107ed11]] – relative ed11
* [[111ed12]] – relative ed12
* [[138ed22]] – relative ed22
* [[204ed96]] – close to the zeta-optimized tuning for 31edo
* [[39cET]]
 
[[Category:31edo]]
Retrieved from "https://en.xen.wiki/w/87ed7"