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| '''102edo''' is the [[Equal_division_of_the_octave|equal division of the octave]] into 102 steps of size 11.765 [[cent|cent]]s each. In the [[5-limit|5-limit]] it [[tempering_out|tempers out]] the same [[Comma|comma]]s (2048/2025, 15625/15552, 20000/19683) as [[34edo|34edo]]. In the [[7-limit|7-limit]] it tempers out 686/675 and 1029/1024; in the [[11-limit|11-limit]] 385/384, 441/440 and 4000/3993; in the [[13-limit|13-limit]] 91/90 and 169/168; in the [[17-limit|17-limit]] 136/135 and 154/153; and in the [[19-limit|19-limit]] 133/132 and 190/189. It is the [[Optimal_patent_val|optimal patent val]] for 13-limit [[Diaschismic_family#Echidnic|echidnic temperament]], and the rank five temperament tempering out 91/90.
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| | {{ED intro}} |
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| ===13-limit Echidnic=== | | == Theory == |
| | 102edo is [[enfactoring|enfactored]] in the [[5-limit]], where it [[tempering out|tempers out]] the same [[comma]]s ([[2048/2025]], [[15625/15552]], [[20000/19683]]) as [[34edo]]. In the [[7-limit]] it tempers out [[686/675]] and [[1029/1024]]; in the [[11-limit]] [[385/384]], [[441/440]] and [[4000/3993]]; in the [[13-limit]] [[91/90]] and [[169/168]]; in the [[17-limit]] [[136/135]] and [[154/153]]; and in the [[19-limit]] [[133/132]] and [[190/189]]. It is the [[optimal patent val]] for 13-limit [[Diaschismic family #Echidnic|echidnic]] temperament, and the rank-5 temperament tempering out 91/90. |
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| {| class="wikitable"
| | === Odd harmonics === |
| |- | | {{Harmonics in equal|102}} |
| | | 2
| | |
| | | 23.529
| | == Intervals == |
| |-
| | {{Interval table}} |
| | | 4
| | |
| | | 47.059
| | [[Category:Echidnic]] |
| |-
| |
| | | 7
| |
| | | 82.353
| |
| |-
| |
| | | 9
| |
| | | 105.882
| |
| |-
| |
| | | 11
| |
| | | 129.412
| |
| |-
| |
| | | 13
| |
| | | 152.941
| |
| |-
| |
| | | 16
| |
| | | 188.235
| |
| |-
| |
| | | 18
| |
| | | 211.765
| |
| |-
| |
| | | 20
| |
| | | 235.294
| |
| |-
| |
| | | 22
| |
| | | 258.824
| |
| |-
| |
| | | 24
| |
| | | 282.353
| |
| |-
| |
| | | 27
| |
| | | 317.647
| |
| |-
| |
| | | 29
| |
| | | 341.176
| |
| |-
| |
| | | 31
| |
| | | 364.706
| |
| |-
| |
| | | 33
| |
| | | 388.235
| |
| |-
| |
| | | 35
| |
| | | 411.765
| |
| |-
| |
| | | 38
| |
| | | 447.059
| |
| |-
| |
| | | 40
| |
| | | 470.588
| |
| |-
| |
| | | 42
| |
| | | 494.117
| |
| |-
| |
| | | 44
| |
| | | 517.647
| |
| |-
| |
| | | 47
| |
| | | 552.941
| |
| |-
| |
| | | 49
| |
| | | 576.471
| |
| |}
| |
| [[Category:echidnic]]
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| [[Category:Equal divisions of the octave]] | |