44edf: Difference between revisions
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{{Infobox ET}} | {{todo|add examples|text=add examples of how music can be made with this tuning, stuff like instruments tuned to it, 4 to 12 note scales within it, etc.}}{{Infobox ET}} | ||
'''44EDF''' is the [[EDF|equal division of the just perfect fifth]] into 44 parts of 15.9535 [[ | '''44EDF''' is the [[EDF|equal division of the just perfect fifth]] into 44 parts of 15.9535 [[cents]] each, corresponding to 75.2185 [[edo]]. | ||
It is related to the [[regular temperament]] which [[tempers out]] |183 -51 -44> in the [[5-limit]], which is supported by {{EDOs|301, 376, 677, 1053, 1429, 1730, 2407, and 2783}} EDOs. | |||
==Related regular temperaments== | |||
===5-limit 677&1053=== | |||
Comma: |183 -51 -44> | |||
POTE generator: ~|-104 29 25> = 15.9540 | |||
Mapping: [<1 1 3|, <0 44 -51|] | |||
EDOs: {{EDOs|75, 301, 376, 677, 978, 1053, 1429, 1730, 2407, 2783, 3836}} | |||
===2.3.5.11 677&1053=== | |||
Commas: 184549376/184528125, 38084983750656/38060880859375 | |||
POTE generator: ~|-104 29 25> = 15.9535 | |||
Mapping: [<1 1 3 1|, <0 44 -51 185|] | |||
EDOs: {{EDOs|301, 376, 677, 978, 1053, 1429, 1730, 2407, 2783, 3084}} | |||
===13-limit 677&1053=== | |||
Commas: 6656/6655, 184549376/184528125, 1162261467/1161875000 | |||
POTE generator: ~|-104 29 25> = 15.9540 | |||
Mapping: [<1 1 3 1 -3|, <0 44 -51 185 504|] | |||
EDOs: {{EDOs|677, 1053, 1730, 2407, 3084, 4137}} | |||
==Harmonics== | |||
{{Harmonics in equal|44|3|2|intervals=prime}} | |||
==Intervals== | ==Intervals== | ||
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[[Category:Edf]] | [[Category:Edf]] | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
Revision as of 04:50, 18 December 2024
| ← 43edf | 44edf | 45edf → |
44EDF is the equal division of the just perfect fifth into 44 parts of 15.9535 cents each, corresponding to 75.2185 edo.
It is related to the regular temperament which tempers out |183 -51 -44> in the 5-limit, which is supported by 301, 376, 677, 1053, 1429, 1730, 2407, and 2783 EDOs.
Related regular temperaments
5-limit 677&1053
Comma: |183 -51 -44>
POTE generator: ~|-104 29 25> = 15.9540
Mapping: [<1 1 3|, <0 44 -51|]
EDOs: 75, 301, 376, 677, 978, 1053, 1429, 1730, 2407, 2783, 3836
2.3.5.11 677&1053
Commas: 184549376/184528125, 38084983750656/38060880859375
POTE generator: ~|-104 29 25> = 15.9535
Mapping: [<1 1 3 1|, <0 44 -51 185|]
EDOs: 301, 376, 677, 978, 1053, 1429, 1730, 2407, 2783, 3084
13-limit 677&1053
Commas: 6656/6655, 184549376/184528125, 1162261467/1161875000
POTE generator: ~|-104 29 25> = 15.9540
Mapping: [<1 1 3 1 -3|, <0 44 -51 185 504|]
EDOs: 677, 1053, 1730, 2407, 3084, 4137
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -3.49 | -3.49 | +5.55 | -2.63 | -3.40 | -5.45 | -7.22 | +7.61 | -4.08 | -6.54 | +5.63 |
| Relative (%) | -21.8 | -21.8 | +34.8 | -16.5 | -21.3 | -34.2 | -45.3 | +47.7 | -25.6 | -41.0 | +35.3 | |
| Steps (reduced) |
75 (31) |
119 (31) |
175 (43) |
211 (35) |
260 (40) |
278 (14) |
307 (43) |
320 (12) |
340 (32) |
365 (13) |
373 (21) | |
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | exact 1/1 | ||
| 1 | 15.9535 | ||
| 2 | 31.907 | ||
| 3 | 47.8606 | ||
| 4 | 63.8141 | ||
| 5 | 79.7676 | 22/21 | |
| 6 | 95.7211 | 37/35 | |
| 7 | 111.6747 | 16/15 | |
| 8 | 127.6282 | 14/13 | |
| 9 | 143.5817 | 25/23 | |
| 10 | 159.5352 | 34/31 | |
| 11 | 175.48875 | 31/28 | |
| 12 | 191.4423 | 19/17 | |
| 13 | 207.3958 | 62/55 | |
| 14 | 223.3493 | 33/29 | |
| 15 | 239.3028 | 31/27 | |
| 16 | 255.2564 | 51/44 | |
| 17 | 271.2099 | 62/53 | |
| 18 | 287.1634 | ||
| 19 | 303.1169 | 81/68 | |
| 20 | 319.0705 | 6/5 | |
| 21 | 335.024 | ||
| 22 | 350.9775 | 60/49, 49/40 | |
| 23 | 366.931 | ||
| 24 | 382.8845 | 5/4 | |
| 25 | 398.8381 | 34/27 | |
| 26 | 414.7916 | 14/11 | |
| 27 | 430.7451 | 9/7 | |
| 28 | 446.6986 | 22/17 | |
| 29 | 462.6522 | ||
| 30 | 478.6057 | ||
| 31 | 494.5592 | 4/3 | |
| 32 | 510.5127 | ||
| 33 | 526.46625 | 42/31, 27/20 | |
| 34 | 542.4198 | ||
| 35 | 558.3733 | ||
| 36 | 574.3268 | ||
| 37 | 590.2803 | 45/32 | |
| 38 | 606.2339 | ||
| 39 | 622.1874 | 63/44 | |
| 40 | 638.1409 | 81/56 | |
| 41 | 654.0944 | ||
| 42 | 670.048 | ||
| 43 | 686.0015 | 40/27 | |
| 44 | 701.955 | exact 3/2 | just perfect fifth |
| 45 | 717.8985 | 243/160 | |
| 46 | 733.862 | ||
| 47 | 749.8156 | ||
| 48 | 765.7691 | 14/9 | |
| 49 | 781.7226 | 11/7 | |
| 50 | 797.6761 | ||
| 51 | 813.6297 | 8/5 | |
| 52 | 829.5832 | ||
| 53 | 845.5367 | ||
| 54 | 861.4902 | ||
| 55 | 877.44375 | 5/3 | |
| 56 | 893.3973 | ||
| 57 | 909.3508 | 27/16 | |
| 58 | 925.3043 | ||
| 59 | 941.2578 | ||
| 60 | 957.2184 | 153/88 | |
| 61 | 973.1649 | 7/4 | |
| 62 | 989.1184 | 99/56 | |
| 63 | 1005.0719 | 243/136 | |
| 64 | 1021.0255 | 9/5 | |
| 65 | 1036.979 | ||
| 66 | 1052.9325 | ||
| 67 | 1068.886 | 13/7 | |
| 68 | 1084.89355 | 15/8 | |
| 69 | 1100.7931 | ||
| 70 | 1116.7466 | ||
| 71 | 1132.7001 | ||
| 72 | 1148.6536 | ||
| 73 | 1164.9072 | ||
| 74 | 1180.5607 | 160/81 | |
| 75 | 1196.5142 | 2/1 | |
| 76 | 1212.4677 | ||
| 77 | 1228.42125 | ||
| 78 | 1244.3748 | ||
| 79 | 1260.3283 | ||
| 80 | 1276.2818 | ||
| 81 | 1292.2353 | ||
| 82 | 1308.1889 | ||
| 83 | 1324.1424 | ||
| 84 | 1340.0959 | ||
| 85 | 1356.0494 | ||
| 86 | 1372.003 | ||
| 87 | 1387.9565 | 20/9 | |
| 88 | 1403.91 | exact 9/4 | |