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&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&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;" | | |||
|} | |||
Revision as of 17:27, 29 June 2020
The 64 equal division or 64-EDO 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&64 temperament, which would perhaps be of more interest if it was lower in badness.
Intervals
| Degree | Cents |
|---|---|
| 0 | 0.0000 |
| 1 | 18.75 |
| 2 | 37.5 |
| 3 | 56.25 |
| 4 | 75 |
| 5 | 93.75 |
| 6 | 112.5 |
| 7 | 131.25 |
| 8 | 150 |
| 9 | 168.75 |
| 10 | 187.5 |
| 11 | 206.25 |
| 12 | 225 |
| 13 | 243.75 |
| 14 | 262.5 |
| 15 | 281.25 |
| 16 | 300 |
| 17 | 318.75 |
| 18 | 337.5 |
| 19 | 356.25 |
| 20 | 375 |
| 21 | 393.75 |
| 22 | 412.5 |
| 23 | 431.25 |
| 24 | 450 |
| 25 | 468.75 |
| 26 | 487.5 |
| 27 | 506.25 |
| 28 | 525 |
| 29 | 543.75 |
| 30 | 562.5 |
| 31 | 581.25 |
| 32 | 600 |
| 33 | 618.75 |
| 34 | 637.5 |
| 35 | 656.25 |
| 36 | 675 |
| 37 | 693.75 |
| 38 | 712.5 |
| 39 | 731.25 |
| 40 | 750 |
| 41 | 768.75 |
| 42 | 787.5 |
| 43 | 806.25 |
| 44 | 825 |
| 45 | 843.75 |
| 46 | 862.5 |
| 47 | 881.25 |
| 48 | 900 |
| 49 | 918.75 |
| 50 | 937.5 |
| 51 | 956.25 |
| 52 | 975 |
| 53 | 993.75 |
| 54 | 1012.5 |
| 55 | 1031.25 |
| 56 | 1050 |
| 57 | 1068.75 |
| 58 | 1087.5 |
| 59 | 1106.25 |
| 60 | 1125 |
| 61 | 1143.75 |
| 62 | 1162.5 |
| 63 | 1181.25 |
| 64 | 1200 |