3edf: Difference between revisions
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| Line 12: | Line 12: | ||
! rowspan="2" |ed121/81 (~ed11\19) | ! rowspan="2" |ed121/81 (~ed11\19) | ||
! rowspan="2" |ed696¢ | ! rowspan="2" |ed696¢ | ||
! rowspan="2" |ed32\55 | |||
! rowspan="2" |ed700¢=''r¢'' | |||
! rowspan="2" |ed3/2 | ! rowspan="2" |ed3/2 | ||
! colspan="2" |Pyrite | ! colspan="2" |Pyrite | ||
| Line 27: | Line 29: | ||
|231.605 | |231.605 | ||
|232 | |232 | ||
|232.727 | |||
|''233.333'' | |||
|233.985 | |233.985 | ||
|234.545 | |234.545 | ||
| Line 40: | Line 44: | ||
|463.211 | |463.211 | ||
|464 | |464 | ||
|465.4545 | |||
|''466.667'' | |||
|467.97 | |467.97 | ||
|469.091 | |469.091 | ||
| Line 53: | Line 59: | ||
|694.816 | |694.816 | ||
|696 | |696 | ||
|698.182 | |||
|''700'' | |||
|701.995 | |701.995 | ||
|703.636 | |703.636 | ||
| Line 66: | Line 74: | ||
|926.421 | |926.421 | ||
|928 | |928 | ||
|930.909 | |||
|''933.333'' | |||
|935.94 | |935.94 | ||
|938.181 | |938.181 | ||
| Line 79: | Line 89: | ||
|1158.0265 | |1158.0265 | ||
|1160 | |1160 | ||
|1163.636 | |||
|''1166.667'' | |||
|1169.925 | |1169.925 | ||
|1172.727 | |1172.727 | ||
| Line 92: | Line 104: | ||
|1389.632 | |1389.632 | ||
|1392 | |1392 | ||
|1396.364 | |||
|''1400'' | |||
|1403.91 | |1403.91 | ||
|1407.272 | |1407.272 | ||
Revision as of 22:29, 19 August 2019
3EDF, if the attempt is made to use it as an actual scale, would divide the just perfect fifth into three equal parts, each of size 233.985 cents, which is to say (3/2)^(1/3) as a frequency ratio. It corresponds to 5.1285 edo. If we want to consider it to be a temperament, it tempers out 16/15, 21/20, 28/27, 81/80, and 256/243 as well as 5edo.
Factoids about 3EDF
3EDF is related to the gamelismic temperaments, which temper out 1029/1024 in the 7-limit.
Intervals
| ed233\420-5¢ | ed31\54 | ed121/81 (~ed11\19) | ed696¢ | ed32\55 | ed700¢=r¢ | ed3/2 | Pyrite | ed708¢ | ed122/81 (~ed13\22) | ed34\57 | ed37\60+5¢ | ||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| (~ed17\29) | (~ed10\17) | ||||||||||||
| 1 | 220.238-221.905 | 229.63 | 231.605 | 232 | 232.727 | 233.333 | 233.985 | 234.545 | 235.285 | 236 | 236.355 | 238.597 | 246.667-248.333 |
| 2 | 440.476-443.8095 | 259.259 | 463.211 | 464 | 465.4545 | 466.667 | 467.97 | 469.091 | 470.57 | 472 | 472.71 | 477.193 | 493.333-496.667 |
| 3 | 660.714-665.714 | 688.888 | 694.816 | 696 | 698.182 | 700 | 701.995 | 703.636 | 705.8885 | 708 | 709.065 | 715.7895 | 740-745 |
| 4 | 880.952-887.619 | 918.5185 | 926.421 | 928 | 930.909 | 933.333 | 935.94 | 938.181 | 941.141 | 944 | 945.42 | 954.386 | 986.667-993.333 |
| 5 | 1101.1905-1109.524 | 1148.148 | 1158.0265 | 1160 | 1163.636 | 1166.667 | 1169.925 | 1172.727 | 1176.426 | 1180 | 1181.775 | 1192.9825 | 1233.333-1241.667 |
| 6 | 1321.429-1331.429 | 1377.778 | 1389.632 | 1392 | 1396.364 | 1400 | 1403.91 | 1407.272 | 1411.711 | 1416 | 1418.13 | 1431.579 | 1480-1490 |