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64edo: Difference between revisions

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Added intervals table.
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The <b>64 equal division</b> or <b>64-EDO</b> divides the octave into 64 equal parts of exactly 18.75 cents each. The patent val tempers out 648/625 in the 5-limit and 64/63 and 225/224 in the 7-limit, plus 121/120 and 441/440 in the 11-limit and 144/143 in the 13-limit. It provides the optimal patent val in the 7-, 11- and 13-limits for the 16&amp;64 temperament, which would perhaps be of more interest if it was lower in badness.
The <b>64 equal division</b> or <b>64-EDO</b> divides the octave into 64 equal parts of exactly 18.75 cents each. The patent val tempers out 648/625 in the 5-limit and 64/63 and 225/224 in the 7-limit, plus 121/120 and 441/440 in the 11-limit and 144/143 in the 13-limit. It provides the optimal patent val in the 7-, 11- and 13-limits for the 16&amp;64 temperament, which would perhaps be of more interest if it was lower in badness.
=Intervals=
{| class="wikitable"
|-
![[Degree|Degree]]
![[cent|Cents]]
|-
| style="text-align:center;" |0
| style="text-align:right;" |0.0000
|-
| style="text-align:center;" |1
| style="text-align:right;" |18.75
|-
| style="text-align:center;" |2
| style="text-align:right;" |37.5
|-
| style="text-align:center;" |3
| style="text-align:right;" |56.25
|-
| style="text-align:center;" |4
| style="text-align:right;" |75
|-
| style="text-align:center;" |5
| style="text-align:right;" |93.75
|-
| style="text-align:center;" |6
| style="text-align:right;" |112.5
|-
| style="text-align:center;" |7
| style="text-align:right;" |131.25
|-
| style="text-align:center;" |8
| style="text-align:right;" |150
|-
| style="text-align:center;" |9
| style="text-align:right;" |168.75
|-
| style="text-align:center;" |10
| style="text-align:right;" |187.5
|-
| style="text-align:center;" |11
| style="text-align:right;" |206.25
|-
| style="text-align:center;" |12
| style="text-align:right;" |225
|-
| style="text-align:center;" |13
| style="text-align:right;" |243.75
|-
| style="text-align:center;" |14
| style="text-align:right;" |262.5
|-
| style="text-align:center;" |15
| style="text-align:right;" |281.25
|-
| style="text-align:center;" |16
| style="text-align:right;" |300
|-
| style="text-align:center;" |17
| style="text-align:right;" |318.75
|-
| style="text-align:center;" |18
| style="text-align:right;" |337.5
|-
| style="text-align:center;" |19
| style="text-align:right;" |356.25
|-
| style="text-align:center;" |20
| style="text-align:right;" |375
|-
| style="text-align:center;" |21
| style="text-align:right;" |393.75
|-
| style="text-align:center;" |22
| style="text-align:right;" |412.5
|-
| style="text-align:center;" |23
| style="text-align:right;" |431.25
|-
| style="text-align:center;" |24
| style="text-align:right;" |450
|-
| style="text-align:center;" |25
| style="text-align:right;" |468.75
|-
| style="text-align:center;" |26
| style="text-align:right;" |487.5
|-
| style="text-align:center;" |27
| style="text-align:right;" |506.25
|-
| style="text-align:center;" |28
| style="text-align:right;" |525
|-
| style="text-align:center;" |29
| style="text-align:right;" |543.75
|-
| style="text-align:center;" |30
| style="text-align:right;" |562.5
|-
| style="text-align:center;" |31
| style="text-align:right;" |581.25
|-
| style="text-align:center;" |32
| style="text-align:right;" |600
|-
| style="text-align:center;" |33
| style="text-align:right;" |618.75
|-
| style="text-align:center;" |34
| style="text-align:right;" |637.5
|-
| style="text-align:center;" |35
| style="text-align:right;" |656.25
|-
| style="text-align:center;" |36
| style="text-align:right;" |675
|-
| style="text-align:center;" |37
| style="text-align:right;" |693.75
|-
| style="text-align:center;" |38
| style="text-align:right;" |712.5
|-
| style="text-align:center;" |39
| style="text-align:right;" |731.25
|-
| style="text-align:center;" |40
| style="text-align:right;" |750
|-
| style="text-align:center;" |41
| style="text-align:right;" |768.75
|-
| style="text-align:center;" |42
| style="text-align:right;" |787.5
|-
| style="text-align:center;" |43
| style="text-align:right;" |806.25
|-
| style="text-align:center;" |44
| style="text-align:right;" |825
|-
| style="text-align:center;" |45
| style="text-align:right;" |843.75
|-
| style="text-align:center;" |46
| style="text-align:right;" |862.5
|-
| style="text-align:center;" |47
| style="text-align:right;" |881.25
|-
| style="text-align:center;" |48
| style="text-align:right;" |900
|-
| style="text-align:center;" |49
| style="text-align:right;" |918.75
|-
| style="text-align:center;" |50
| style="text-align:right;" |937.5
|-
| style="text-align:center;" |51
| style="text-align:right;" |956.25
|-
| style="text-align:center;" |52
| style="text-align:right;" |975
|-
| style="text-align:center;" |53
| style="text-align:right;" |993.75
|-
| style="text-align:center;" |54
| style="text-align:right;" |1012.5
|-
| style="text-align:center;" |55
| style="text-align:right;" |1031.25
|-
| style="text-align:center;" |56
| style="text-align:right;" |1050
|-
| style="text-align:center;" |57
| style="text-align:right;" |1068.75
|-
| style="text-align:center;" |58
| style="text-align:right;" |1087.5
|-
| style="text-align:center;" |59
| style="text-align:right;" |1106.25
|-
| style="text-align:center;" |60
| style="text-align:right;" |1125
|-
| style="text-align:center;" |61
| style="text-align:right;" |1143.75
|-
| style="text-align:center;" |62
| style="text-align:right;" |1162.5
|-
| style="text-align:center;" |63
| style="text-align:right;" |1181.25
|-
| style="text-align:center;" |64
| style="text-align:right;" |1200
|-
| style="text-align:center;" |
| style="text-align:right;" |
|}
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