24edf: Difference between revisions
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'''[[EDF|Division of the just perfect fifth]] into 24 equal parts''' (24EDF) is related to [[41edo|41 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 0.8269 cents compressed and the step size is about 29.2481 cents. It is consistent to the [[ | '''[[EDF|Division of the just perfect fifth]] into 24 equal parts''' (24EDF) is related to [[41edo|41 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 0.8269 cents compressed and the step size is about 29.2481 cents. It is [[consistent]] to the 16-[[integer-limit]]. | ||
Lookalikes: [[41edo]], [[65edt]], [[95ed5]] | Lookalikes: [[41edo]], [[65edt]], [[95ed5]] | ||
== Harmonics == | |||
{{Harmonics in equal|24|3|2|intervals=prime}} | |||
{{Harmonics in equal|24|3|2|start=12|collapsed=1|intervals=prime}} | |||
== Intervals == | == Intervals == | ||
{| class="wikitable" | {| class="wikitable mw-collapsible" | ||
|+ Intervals of 24edf | |||
|- | |- | ||
! | | ! | | ||
| Line 206: | Line 211: | ||
|9/4 | |9/4 | ||
|} | |} | ||
{{stub}} | |||
[[Category:Edf]] | [[Category:Edf]] | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
Revision as of 06:21, 19 December 2024
| ← 23edf | 24edf | 25edf → |
(convergent)
(convergent)
Division of the just perfect fifth into 24 equal parts (24EDF) is related to 41 edo, but with the 3/2 rather than the 2/1 being just. The octave is about 0.8269 cents compressed and the step size is about 29.2481 cents. It is consistent to the 16-integer-limit.
Lookalikes: 41edo, 65edt, 95ed5
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.8 | -0.8 | -7.7 | -5.3 | +1.9 | +5.2 | +8.7 | -8.3 | +11.9 | -9.2 | -7.7 |
| Relative (%) | -2.8 | -2.8 | -26.5 | -18.1 | +6.6 | +17.7 | +29.8 | -28.5 | +40.6 | -31.5 | -26.2 | |
| Steps (reduced) |
41 (17) |
65 (17) |
95 (23) |
115 (19) |
142 (22) |
152 (8) |
168 (0) |
174 (6) |
186 (18) |
199 (7) |
203 (11) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +7.8 | +5.5 | +10.8 | +3.1 | -0.2 | -10.4 | -9.6 | +3.5 | -9.2 | +1.2 | +10.7 |
| Relative (%) | +26.5 | +18.9 | +37.0 | +10.5 | -0.7 | -35.5 | -32.8 | +11.9 | -31.3 | +4.2 | +36.7 | |
| Steps (reduced) |
214 (22) |
220 (4) |
223 (7) |
228 (12) |
235 (19) |
241 (1) |
243 (3) |
249 (9) |
252 (12) |
254 (14) |
259 (19) | |
Intervals
| Cents Value | Approximate Ratios in the 11-limit | |
|---|---|---|
| 0 | 1/1 | |
| 1 | 29.2481 | 81/80 |
| 2 | 58.49625 | 25/24, 28/27, 33/32 |
| 3 | 87.7444 | 21/20, 22/21 |
| 4 | 116.9925 | 16/15, 15/14 |
| 5 | 146.2406 | 12/11 |
| 6 | 175.48875 | 10/9, 11/10 |
| 7 | 204.7369 | 9/8 |
| 8 | 233.985 | 8/7 |
| 9 | 263.2331 | 7/6, 32/25 |
| 10 | 292.48125 | 32/27 |
| 11 | 321.7293 | 6/5 |
| 12 | 350.9775 | 11/9,27/22 |
| 13 | 380.2256 | 5/4 |
| 14 | 409.47375 | 14/11, 81/64 |
| 15 | 438.7219 | 9/7 |
| 16 | 467.97 | 21/16 |
| 17 | 497.2181 | 4/3 |
| 18 | 526.46625 | 15/11, 27/20 |
| 19 | 556.7144 | 11/8 |
| 20 | 584.9625 | 7/5 |
| 21 | 614.2106 | 10/7 |
| 22 | 643.45875 | 16/11 |
| 23 | 671.7069 | 22/15, 40/27 |
| 24 | 701.955 | 3/2 |
| 25 | 731.2031 | 32/21 |
| 26 | 760.45125 | 14/9, 25/16 |
| 27 | 789.6994 | 11/7, 128/81 |
| 28 | 818.9475 | 8/5 |
| 29 | 848.1956 | 18/11, 44/27 |
| 30 | 877.44375 | 5/3 |
| 31 | 906.6919 | 27/16 |
| 32 | 935.94 | 12/7 |
| 33 | 965.1881 | 7/4 |
| 34 | 994.43625 | 16/9 |
| 35 | 1023.6844 | 9/5, 20/11 |
| 36 | 1052.9325 | 11/6 |
| 37 | 1082.1806 | 15/8 |
| 38 | 1111.42875 | 40/21, 21/11 |
| 39 | 1140.6769 | 48/25, 27/14, 64/33 |
| 40 | 1169.925 | 160/81 |
| 41 | 1199.1731 | 2/1 |
| 42 | 1228.42125 | 81/40 |
| 43 | 1257.6694 | 25/12, 56/27, 33/16 |
| 44 | 1286.9175 | 21/10, 44/21 |
| 45 | 1316.1656 | 32/15, 15/7 |
| 46 | 1345.41375 | 24/11 |
| 47 | 1374.6619 | 20/9, 11/5 |
| 48 | 1403.91 | 9/4 |
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