24edf: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
'''[[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 [[15-odd-limit|16-integer-limit]].
'''[[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 →
Prime factorization 23 × 3
Step size 29.2481 ¢ 
Octave 41\24edf (1199.17 ¢)
(convergent)
Twelfth 65\24edf (1901.13 ¢)
(convergent)
Consistency limit 16
Distinct consistency limit 10
Special properties

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

Approximation of prime harmonics in 24edf
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)
Approximation of prime harmonics in 24edf
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

Intervals of 24edf
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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