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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.
'''64 equal divisions of the octave''' ('''64edo''') is the tuning system that divides the octave into 64 equal parts of exactly 18.75{{cent}} each.
{{harmonics in equal|64}}
 
=Intervals=
== Theory ==
{| class="wikitable"
{{Harmonics in equal|64}}
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 center-all right-2"
|-
|-
![[Degree|Degree]]
![[Degree|#]]
![[cent|Cents]]
![[Cent]]s
|-
|-
| style="text-align:center;" |0
| 0
| style="text-align:right;" |0.0000
| 0.00
|-
|-
| style="text-align:center;" |1
| 1
| style="text-align:right;" |18.75
| 18.75
|-
|-
| style="text-align:center;" |2
| 2
| style="text-align:right;" |37.5
| 37.50
|-
|-
| style="text-align:center;" |3
| 3
| style="text-align:right;" |56.25
| 56.25
|-
|-
| style="text-align:center;" |4
| 4
| style="text-align:right;" |75
| 75.00
|-
|-
| style="text-align:center;" |5
| 5
| style="text-align:right;" |93.75
| 93.75
|-
|-
| style="text-align:center;" |6
| 6
| style="text-align:right;" |112.5
| 112.50
|-
|-
| style="text-align:center;" |7
| 7
| style="text-align:right;" |131.25
| 131.25
|-
|-
| style="text-align:center;" |8
| 8
| style="text-align:right;" |150
| 150.00
|-
|-
| style="text-align:center;" |9
| 9
| style="text-align:right;" |168.75
| 168.75
|-
|-
| style="text-align:center;" |10
| 10
| style="text-align:right;" |187.5
| 187.50
|-
|-
| style="text-align:center;" |11
| 11
| style="text-align:right;" |206.25
| 206.25
|-
|-
| style="text-align:center;" |12
| 12
| style="text-align:right;" |225
| 225.00
|-
|-
| style="text-align:center;" |13
| 13
| style="text-align:right;" |243.75
| 243.75
|-
|-
| style="text-align:center;" |14
| 14
| style="text-align:right;" |262.5
| 262.50
|-
|-
| style="text-align:center;" |15
| 15
| style="text-align:right;" |281.25
| 281.25
|-
|-
| style="text-align:center;" |16
| 16
| style="text-align:right;" |300
| 300.00
|-
|-
| style="text-align:center;" |17
| 17
| style="text-align:right;" |318.75
| 318.75
|-
|-
| style="text-align:center;" |18
| 18
| style="text-align:right;" |337.5
| 337.50
|-
|-
| style="text-align:center;" |19
| 19
| style="text-align:right;" |356.25
| 356.25
|-
|-
| style="text-align:center;" |20
| 20
| style="text-align:right;" |375
| 375.00
|-
|-
| style="text-align:center;" |21
| 21
| style="text-align:right;" |393.75
| 393.75
|-
|-
| style="text-align:center;" |22
| 22
| style="text-align:right;" |412.5
| 412.50
|-
|-
| style="text-align:center;" |23
| 23
| style="text-align:right;" |431.25
| 431.25
|-
|-
| style="text-align:center;" |24
| 24
| style="text-align:right;" |450
| 450.00
|-
|-
| style="text-align:center;" |25
| 25
| style="text-align:right;" |468.75
| 468.75
|-
|-
| style="text-align:center;" |26
| 26
| style="text-align:right;" |487.5
| 487.50
|-
|-
| style="text-align:center;" |27
| 27
| style="text-align:right;" |506.25
| 506.25
|-
|-
| style="text-align:center;" |28
| 28
| style="text-align:right;" |525
| 525.00
|-
|-
| style="text-align:center;" |29
| 29
| style="text-align:right;" |543.75
| 543.75
|-
|-
| style="text-align:center;" |30
| 30
| style="text-align:right;" |562.5
| 562.50
|-
|-
| style="text-align:center;" |31
| 31
| style="text-align:right;" |581.25
| 581.25
|-
|-
| style="text-align:center;" |32
| 32
| style="text-align:right;" |600
| 600.00
|-
|-
| style="text-align:center;" |33
| 33
| style="text-align:right;" |618.75
| 618.75
|-
|-
| style="text-align:center;" |34
| 34
| style="text-align:right;" |637.5
| 637.50
|-
|-
| style="text-align:center;" |35
| 35
| style="text-align:right;" |656.25
| 656.25
|-
|-
| style="text-align:center;" |36
| 36
| style="text-align:right;" |675
| 675.00
|-
|-
| style="text-align:center;" |37
| 37
| style="text-align:right;" |693.75
| 693.75
|-
|-
| style="text-align:center;" |38
| 38
| style="text-align:right;" |712.5
| 712.50
|-
|-
| style="text-align:center;" |39
| 39
| style="text-align:right;" |731.25
| 731.25
|-
|-
| style="text-align:center;" |40
| 40
| style="text-align:right;" |750
| 750.00
|-
|-
| style="text-align:center;" |41
| 41
| style="text-align:right;" |768.75
| 768.75
|-
|-
| style="text-align:center;" |42
| 42
| style="text-align:right;" |787.5
| 787.50
|-
|-
| style="text-align:center;" |43
| 43
| style="text-align:right;" |806.25
| 806.25
|-
|-
| style="text-align:center;" |44
| 44
| style="text-align:right;" |825
| 825.00
|-
|-
| style="text-align:center;" |45
| 45
| style="text-align:right;" |843.75
| 843.75
|-
|-
| style="text-align:center;" |46
| 46
| style="text-align:right;" |862.5
| 862.50
|-
|-
| style="text-align:center;" |47
| 47
| style="text-align:right;" |881.25
| 881.25
|-
|-
| style="text-align:center;" |48
| 48
| style="text-align:right;" |900
| 900.00
|-
|-
| style="text-align:center;" |49
| 49
| style="text-align:right;" |918.75
| 918.75
|-
|-
| style="text-align:center;" |50
| 50
| style="text-align:right;" |937.5
| 937.50
|-
|-
| style="text-align:center;" |51
| 51
| style="text-align:right;" |956.25
| 956.25
|-
|-
| style="text-align:center;" |52
| 52
| style="text-align:right;" |975
| 975.00
|-
|-
| style="text-align:center;" |53
| 53
| style="text-align:right;" |993.75
| 993.75
|-
|-
| style="text-align:center;" |54
| 54
| style="text-align:right;" |1012.5
| 1012.50
|-
|-
| style="text-align:center;" |55
| 55
| style="text-align:right;" |1031.25
| 1031.25
|-
|-
| style="text-align:center;" |56
| 56
| style="text-align:right;" |1050
| 1050.00
|-
|-
| style="text-align:center;" |57
| 57
| style="text-align:right;" |1068.75
| 1068.75
|-
|-
| style="text-align:center;" |58
| 58
| style="text-align:right;" |1087.5
| 1087.50
|-
|-
| style="text-align:center;" |59
| 59
| style="text-align:right;" |1106.25
| 1106.25
|-
|-
| style="text-align:center;" |60
| 60
| style="text-align:right;" |1125
| 1125.00
|-
|-
| style="text-align:center;" |61
| 61
| style="text-align:right;" |1143.75
| 1143.75
|-
|-
| style="text-align:center;" |62
| 62
| style="text-align:right;" |1162.5
| 1162.50
|-
|-
| style="text-align:center;" |63
| 63
| style="text-align:right;" |1181.25
| 1181.25
|-
|-
| style="text-align:center;" |64
| 64
| style="text-align:right;" |1200
| 1200.00
|}
|}
[[Category:Equal divisions of the octave|##]] <!-- 2-digit number -->
Retrieved from "https://en.xen.wiki/w/64edo"