42edf: Difference between revisions
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Created page with "'''Division of the just perfect fifth into 42 equal parts''' (42EDF) is related to 72 edo, but with the 3/2 rather than the 2/1 being just. The octave is abo..." Tags: Mobile edit Mobile web edit |
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Lookalikes: [[72edo]], [[114edt]] | Lookalikes: [[72edo]], [[114edt]] | ||
{| class="wikitable" | |||
|- | |||
| |degrees | |||
| |cents value | |||
| |approximate ratios (11-limit) | |||
|- | |||
| |0 | |||
| |0 | |||
| |1/1 | |||
|- | |||
| |1 | |||
| |16.7132 | |||
| |81/80 | |||
|- | |||
| |2 | |||
| |33.4264 | |||
| |45/44 | |||
|- | |||
| |3 | |||
| |50.1396 | |||
| |33/32 | |||
|- | |||
| |4 | |||
| |66.8529 | |||
| |25/24 | |||
|- | |||
| |5 | |||
| |83.5661 | |||
| |21/20 | |||
|- | |||
| |6 | |||
| |100.2793 | |||
| |35/33 | |||
|- | |||
| |7 | |||
| |116.9925 | |||
| |15/14 | |||
|- | |||
| |8 | |||
| |133.7057 | |||
| |27/25 | |||
|- | |||
| |9 | |||
| |150.4189 | |||
| |12/11 | |||
|- | |||
| |10 | |||
| |167.1321 | |||
| |11/10 | |||
|- | |||
| |11 | |||
| |183.8454 | |||
| |10/9 | |||
|- | |||
| |12 | |||
| |200.5586 | |||
| |9/8 | |||
|- | |||
| |13 | |||
| |217.2717 | |||
| |25/22 | |||
|- | |||
| |14 | |||
| |233.985 | |||
| |8/7 | |||
|- | |||
| |15 | |||
| |250.6982 | |||
| |81/70 | |||
|- | |||
| |16 | |||
| |267.4114 | |||
| |7/6 | |||
|- | |||
| |17 | |||
| |284.1246 | |||
| |33/28 | |||
|- | |||
| |18 | |||
| |300.8379 | |||
| |25/21 | |||
|- | |||
| |19 | |||
| |317.5511 | |||
| |6/5 | |||
|- | |||
| |20 | |||
| |334.2643 | |||
| |40/33 | |||
|- | |||
| |21 | |||
| |350.9775 | |||
| |11/9 | |||
|- | |||
| |22 | |||
| |367.6907 | |||
| |99/80 | |||
|- | |||
| |23 | |||
| |384.4039 | |||
| |5/4 | |||
|- | |||
| |24 | |||
| |401.1171 | |||
| |44/35 | |||
|- | |||
| |25 | |||
| |417.8304 | |||
| |14/11 | |||
|- | |||
| |26 | |||
| |434.5436 | |||
| |9/7 | |||
|- | |||
| |27 | |||
| |451.2568 | |||
| |35/27 | |||
|- | |||
| |28 | |||
| |467.97 | |||
| |21/16 | |||
|- | |||
| |29 | |||
| |484.6832 | |||
| |33/25 | |||
|- | |||
| |30 | |||
| |501.3964 | |||
| |4/3 | |||
|- | |||
| |31 | |||
| |518.1096 | |||
| |27/20 | |||
|- | |||
| |32 | |||
| |534.8229 | |||
| |15/11 | |||
|- | |||
| |33 | |||
| |551.536 | |||
| |11/8 | |||
|- | |||
| |34 | |||
| |568.2493 | |||
| |25/18 | |||
|- | |||
| |35 | |||
| |584.9625 | |||
| |7/5 | |||
|- | |||
| |36 | |||
| |601.6757 | |||
| |99/70 | |||
|- | |||
| |37 | |||
| |618.3889 | |||
| |10/7 | |||
|- | |||
| |38 | |||
| |635.1021 | |||
| |36/25 | |||
|- | |||
| |39 | |||
| |651.8154 | |||
| |16/11 | |||
|- | |||
| |40 | |||
| |668.5286 | |||
| |22/15 | |||
|- | |||
| |41 | |||
| |685.2418 | |||
| |40/27 | |||
|- | |||
| |42 | |||
| |701.955 | |||
| |3/2 | |||
|- | |||
| |43 | |||
| |718.6682 | |||
| |50/33 | |||
|- | |||
| |44 | |||
| |735.3814 | |||
| |32/21 | |||
|- | |||
| |45 | |||
| |752.0946 | |||
| |54/35 | |||
|- | |||
| |46 | |||
| |768.8079 | |||
| |14/9 | |||
|- | |||
| |47 | |||
| |785.5211 | |||
| |11/7 | |||
|- | |||
| |48 | |||
| |802.2343 | |||
| |35/22 | |||
|- | |||
| |49 | |||
| |818.9475 | |||
| |8/5 | |||
|- | |||
| |50 | |||
| |835.6607 | |||
| |81/50 | |||
|- | |||
| |51 | |||
| |852.3739 | |||
| |18/11 | |||
|- | |||
| |52 | |||
| |869.0871 | |||
| |33/20 | |||
|- | |||
| |53 | |||
| |885.8004 | |||
| |5/3 | |||
|- | |||
| |54 | |||
| |902.5136 | |||
| |27/16 | |||
|- | |||
| |55 | |||
| |919.2268 | |||
| |56/33 | |||
|- | |||
| |56 | |||
| |935.94 | |||
| |12/7 | |||
|- | |||
| |57 | |||
| |952.6532 | |||
| |121/70 | |||
|- | |||
| |58 | |||
| |969.3664 | |||
| |7/4 | |||
|- | |||
| |59 | |||
| |986.0796 | |||
| |44/25 | |||
|- | |||
| |60 | |||
| |1002.7929 | |||
| |16/9 | |||
|- | |||
| |61 | |||
| |1019.506 | |||
| |9/5 | |||
|- | |||
| |62 | |||
| |1036.2193 | |||
| |20/11 | |||
|- | |||
| |63 | |||
| |1052.9235 | |||
| |11/6 | |||
|- | |||
| |64 | |||
| |1069.6457 | |||
| |50/27 | |||
|- | |||
| |65 | |||
| |1086.3589 | |||
| |15/8 | |||
|- | |||
| |66 | |||
| |1103.0721 | |||
| |66/35 | |||
|- | |||
| |67 | |||
| |1119.7854 | |||
| |21/11 | |||
|- | |||
| |68 | |||
| |1136.4986 | |||
| |27/14 | |||
|- | |||
| |69 | |||
| |1153.2118 | |||
| |35/18 | |||
|- | |||
| |70 | |||
| |1169.925 | |||
| |49/25 | |||
|- | |||
| |71 | |||
| |1186.6382 | |||
| |99/50 | |||
|- | |||
| |72 | |||
| |1203.3514 | |||
| |2/1 | |||
|} | |||
[[Category:Edf]] | [[Category:Edf]] | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
Revision as of 20:37, 23 February 2019
Division of the just perfect fifth into 42 equal parts (42EDF) is related to 72 edo, but with the 3/2 rather than the 2/1 being just. The octave is about 3.3514 cents stretched and the step size is about 16.7132 cents (corresponding to 71.7995 edo, practically identical to every fifth step of 359edo). Unlike 72edo, it is only consistent up to the 7-integer-limit, with discrepancy for the 8th harmonic (three octaves).
| degrees | cents value | approximate ratios (11-limit) |
| 0 | 0 | 1/1 |
| 1 | 16.7132 | 81/80 |
| 2 | 33.4264 | 45/44 |
| 3 | 50.1396 | 33/32 |
| 4 | 66.8529 | 25/24 |
| 5 | 83.5661 | 21/20 |
| 6 | 100.2793 | 35/33 |
| 7 | 116.9925 | 15/14 |
| 8 | 133.7057 | 27/25 |
| 9 | 150.4189 | 12/11 |
| 10 | 167.1321 | 11/10 |
| 11 | 183.8454 | 10/9 |
| 12 | 200.5586 | 9/8 |
| 13 | 217.2717 | 25/22 |
| 14 | 233.985 | 8/7 |
| 15 | 250.6982 | 81/70 |
| 16 | 267.4114 | 7/6 |
| 17 | 284.1246 | 33/28 |
| 18 | 300.8379 | 25/21 |
| 19 | 317.5511 | 6/5 |
| 20 | 334.2643 | 40/33 |
| 21 | 350.9775 | 11/9 |
| 22 | 367.6907 | 99/80 |
| 23 | 384.4039 | 5/4 |
| 24 | 401.1171 | 44/35 |
| 25 | 417.8304 | 14/11 |
| 26 | 434.5436 | 9/7 |
| 27 | 451.2568 | 35/27 |
| 28 | 467.97 | 21/16 |
| 29 | 484.6832 | 33/25 |
| 30 | 501.3964 | 4/3 |
| 31 | 518.1096 | 27/20 |
| 32 | 534.8229 | 15/11 |
| 33 | 551.536 | 11/8 |
| 34 | 568.2493 | 25/18 |
| 35 | 584.9625 | 7/5 |
| 36 | 601.6757 | 99/70 |
| 37 | 618.3889 | 10/7 |
| 38 | 635.1021 | 36/25 |
| 39 | 651.8154 | 16/11 |
| 40 | 668.5286 | 22/15 |
| 41 | 685.2418 | 40/27 |
| 42 | 701.955 | 3/2 |
| 43 | 718.6682 | 50/33 |
| 44 | 735.3814 | 32/21 |
| 45 | 752.0946 | 54/35 |
| 46 | 768.8079 | 14/9 |
| 47 | 785.5211 | 11/7 |
| 48 | 802.2343 | 35/22 |
| 49 | 818.9475 | 8/5 |
| 50 | 835.6607 | 81/50 |
| 51 | 852.3739 | 18/11 |
| 52 | 869.0871 | 33/20 |
| 53 | 885.8004 | 5/3 |
| 54 | 902.5136 | 27/16 |
| 55 | 919.2268 | 56/33 |
| 56 | 935.94 | 12/7 |
| 57 | 952.6532 | 121/70 |
| 58 | 969.3664 | 7/4 |
| 59 | 986.0796 | 44/25 |
| 60 | 1002.7929 | 16/9 |
| 61 | 1019.506 | 9/5 |
| 62 | 1036.2193 | 20/11 |
| 63 | 1052.9235 | 11/6 |
| 64 | 1069.6457 | 50/27 |
| 65 | 1086.3589 | 15/8 |
| 66 | 1103.0721 | 66/35 |
| 67 | 1119.7854 | 21/11 |
| 68 | 1136.4986 | 27/14 |
| 69 | 1153.2118 | 35/18 |
| 70 | 1169.925 | 49/25 |
| 71 | 1186.6382 | 99/50 |
| 72 | 1203.3514 | 2/1 |