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| {{Infobox ET}} | | {{Infobox ET}} |
| '''102edo''' is the [[Equal_division_of_the_octave|equal division of the octave]] into 102 steps of size 11.765 [[cent]]s each. In the [[5-limit|5-limit]] it [[tempering_out|tempers out]] the same [[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.
| | {{ED intro}} |
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| == Harmonics == | | == 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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| | === Odd harmonics === |
| {{Harmonics in equal|102}} | | {{Harmonics in equal|102}} |
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| {{Interval table}} | | {{Interval table}} |
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| == 13-limit Echidnic ==
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| {| class="wikitable"
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| !Degree
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| !Cents
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| !Difference from 46edo
| |
| |-
| |
| | |2
| |
| | |23.529
| |
| | -2.5575¢
| |
| |-
| |
| | |4
| |
| | |47.059
| |
| | -5.115¢
| |
| |-
| |
| | | 7
| |
| | |82.353
| |
| |4.092¢
| |
| |-
| |
| | |9
| |
| | |105.882
| |
| |1.5345¢
| |
| |-
| |
| | |11
| |
| | |129.412
| |
| | -1.023¢
| |
| |-
| |
| | |13
| |
| | |152.941
| |
| |8.184¢
| |
| |-
| |
| | |16
| |
| | |188.235
| |
| |5.627¢
| |
| |-
| |
| | | 18
| |
| | |211.765
| |
| |3.069¢
| |
| |-
| |
| | |20
| |
| | |235.294
| |
| |0.511¢
| |
| |-
| |
| | |22
| |
| | |258.824
| |
| | -2.046¢
| |
| |-
| |
| | | 24
| |
| | |282.353
| |
| | -4.604¢
| |
| |-
| |
| | |27
| |
| | |317.647
| |
| |4.604¢
| |
| |-
| |
| | |29
| |
| | |341.176
| |
| |2.046¢
| |
| |-
| |
| | |31
| |
| | |364.706
| |
| | -0.5115¢
| |
| |-
| |
| | |33
| |
| | |388.235
| |
| | -3.069¢
| |
| |-
| |
| | |35
| |
| | |411.765
| |
| | -5.627¢
| |
| |-
| |
| | |38
| |
| | |447.059
| |
| | 3.581¢
| |
| |-
| |
| | |40
| |
| | |470.588
| |
| |1.023¢
| |
| |-
| |
| | |42
| |
| | |494.117
| |
| | -1.5345¢
| |
| |-
| |
| | |44
| |
| | |517.647
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| | -4.092¢
| |
| |-
| |
| | |47
| |
| | |552.941
| |
| |5.115¢
| |
| |-
| |
| | |49
| |
| | |576.471
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| |2.5575¢
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| |}
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| [[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
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| [[Category:Echidnic]] | | [[Category:Echidnic]] |