24edf: Difference between revisions

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Created page with "'''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 abo..."
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Lookalikes: [[41edo]], [[65edt]], [[95ed5]]
Lookalikes: [[41edo]], [[65edt]], [[95ed5]]


== Intervals ==
{| class="wikitable"
|-
! |
! |Cents Value
! |Approximate Ratios in the [[11-limit]]
|-
| style="text-align:center;" |0
| style="text-align:center;" |0.00
| |[[1/1]]
|-
| style="text-align:center;" |1
| style="text-align:center;" |29.2481
| |[[81/80]]
|-
| style="text-align:center;" |2
| style="text-align:center;" |58.49625
| |[[25/24]], [[28/27]], [[33/32]]
|-
| style="text-align:center;" |3
| style="text-align:center;" |87.7444
| |[[21/20]], [[22/21]]
|-
| style="text-align:center;" |4
| style="text-align:center;" |116.9925
| |[[16/15]], [[15/14]]
|-
| style="text-align:center;" |5
| style="text-align:center;" |146.2406
| |[[12/11]]
|-
| style="text-align:center;" |6
| style="text-align:center;" |175.48875
| |[[10/9]], [[11/10]]
|-
| style="text-align:center;" |7
| style="text-align:center;" |204.7369
| |[[9/8]]
|-
| style="text-align:center;" |8
| style="text-align:center;" |233.985
| |[[8/7]]
|-
| style="text-align:center;" |9
| style="text-align:center;" |263.2331
| |[[7/6]], [[32/25]]
|-
| style="text-align:center;" |10
| style="text-align:center;" |292.48125
| |[[32/27]]
|-
| style="text-align:center;" |11
| style="text-align:center;" |321.7293
| |[[6/5]]
|-
| style="text-align:center;" |12
| style="text-align:center;" |350.9775
| |[[11/9]],[[27/22]]
|-
| style="text-align:center;" |13
| style="text-align:center;" |380.2256
| |[[5/4]]
|-
| style="text-align:center;" |14
| style="text-align:center;" |409.47375
| |[[14/11]], [[81/64]]
|-
| style="text-align:center;" |15
| style="text-align:center;" |438.7219
| |[[9/7]]
|-
| style="text-align:center;" |16
| style="text-align:center;" |467.97
| |[[21/16]]
|-
| style="text-align:center;" |17
| style="text-align:center;" |497.2181
| |[[4/3]]
|-
| style="text-align:center;" |18
| style="text-align:center;" |526.46625
| |[[15/11]], [[27/20]]
|-
| style="text-align:center;" |19
| style="text-align:center;" |556.7144
| |[[11/8]]
|-
| style="text-align:center;" |20
| style="text-align:center;" |584.9625
| |[[7/5]]
|-
| style="text-align:center;" |21
| style="text-align:center;" |614.2106
| |[[10/7]]
|-
| style="text-align:center;" |22
| style="text-align:center;" |643.45875
| |[[16/11]]
|-
| style="text-align:center;" |23
| style="text-align:center;" |671.7069
| |[[22/15]], [[40/27]]
|-
| style="text-align:center;" |24
| style="text-align:center;" |701.955
| |[[3/2]]
|-
| style="text-align:center;" |25
| style="text-align:center;" |731.2031
| |[[32/21]]
|-
| style="text-align:center;" |26
| style="text-align:center;" |760.45125
| |[[14/9]], [[25/16]]
|-
| style="text-align:center;" |27
| style="text-align:center;" |789.6994
| |[[11/7]], [[128/81]]
|-
| style="text-align:center;" |28
| style="text-align:center;" |818.9475
| |[[8/5]]
|-
| style="text-align:center;" |29
| style="text-align:center;" |848.1956
| |[[18/11]], [[44/27]]
|-
| style="text-align:center;" |30
| style="text-align:center;" |877.44375
| |[[5/3]]
|-
| style="text-align:center;" |31
| style="text-align:center;" |906.6919
| |[[27/16]]
|-
| style="text-align:center;" |32
| style="text-align:center;" |935.94
| |[[12/7]]
|-
| style="text-align:center;" |33
| style="text-align:center;" |965.1881
| |[[7/4]]
|-
| style="text-align:center;" |34
| style="text-align:center;" |994.43625
| |[[16/9]]
|-
| style="text-align:center;" |35
| style="text-align:center;" |1023.6844
| |[[9/5]], [[20/11]]
|-
| style="text-align:center;" |36
| style="text-align:center;" |1052.9325
| |[[11/6]]
|-
| style="text-align:center;" |37
| style="text-align:center;" |1082.1806
| |[[15/8]]
|-
| style="text-align:center;" |38
| style="text-align:center;" |1111.42875
| |[[40/21]], [[21/11]]
|-
| style="text-align:center;" |39
| style="text-align:center;" |1140.6769
| |[[48/25]], [[27/14]], [[64/33]]
|-
| style="text-align:center;" |40
| style="text-align:center;" |1169.925
| |[[160/81]]
|-
| style="text-align:center;" |41
| style="text-align:center;" |1199.1731
| |2/1
|}
[[Category:Edf]]
[[Category:Edf]]
[[Category:Edonoi]]
[[Category:Edonoi]]

Revision as of 23:11, 20 February 2019

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

Intervals

Cents Value Approximate Ratios in the 11-limit
0 0.00 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
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