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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 [[15-odd-limit|16-integer-limit]].
{{Infobox ET}}
{{ED intro}}


Lookalikes: [[41edo]], [[65edt]], [[95ed5]]
== Theory ==
24edf is related to [[41edo]], but with the 3/2 rather than the [[2/1]] being just. The octave is about 0.8269 cents compressed. Like 41edo, 24edf is [[consistent]] to the [[integer limit|16-integer-limit]].
 
=== Harmonics ===
{{Harmonics in equal|24|3|2|intervals=integer}}
{{Harmonics in equal|24|3|2|intervals=integer|columns=12|start=12|collapsed=true|Approximation of harmonics in 65edt (continued)}}
 
=== Subsets and supersets ===
24edt is the 6th [[highly composite equal division|highly composite edt]]. Its nontrivial subsets are {{EDs|equave=t| 2, 3, 4, 6, 8, and 12 }}.


== Intervals ==
== Intervals ==
{| class="wikitable"
{| class="wikitable center-1 right-2"
|+ Intervals of 24edf
|-
|-
! |
! #
! |Cents Value
! Cents
! |Approximate Ratios in the [[11-limit]]
! Approximate ratios
|-
|-
| style="text-align:center;" |0
| 0
| style="text-align:center;" |0.00
| 0.0
| |[[1/1]]
| [[1/1]]
|-
|-
| style="text-align:center;" |1
| 1
| style="text-align:center;" |29.2481
| 29.2
| |[[81/80]]
| [[49/48]], [[50/49]], [[64/63]], [[81/80]]
|-
|-
| style="text-align:center;" |2
| 2
| style="text-align:center;" |58.49625
| 58.5
| |[[25/24]], [[28/27]], [[33/32]]
| [[25/24]], [[28/27]], [[33/32]], [[36/35]]
|-
|-
| style="text-align:center;" |3
| 3
| style="text-align:center;" |87.7444
| 87.7
| |[[21/20]], [[22/21]]
| [[19/18]], [[20/19]], [[21/20]], [[22/21]]
|-
|-
| style="text-align:center;" |4
| 4
| style="text-align:center;" |116.9925
| 117.0
| |[[16/15]], [[15/14]]
| [[14/13]], [[15/14]], [[16/15]]
|-
|-
| style="text-align:center;" |5
| 5
| style="text-align:center;" |146.2406
| 146.2
| |[[12/11]]
| [[12/11]], [[13/12]]
|-
|-
| style="text-align:center;" |6
| 6
| style="text-align:center;" |175.48875
| 175.5
| |[[10/9]], [[11/10]]
| [[10/9]], [[11/10]], [[21/19]]
|-
|-
| style="text-align:center;" |7
| 7
| style="text-align:center;" |204.7369
| 204.7
| |[[9/8]]
| [[9/8]]
|-
|-
| style="text-align:center;" |8
| 8
| style="text-align:center;" |233.985
| 234.0
| |[[8/7]]
| [[8/7]], [[15/13]]
|-
|-
| style="text-align:center;" |9
| 9
| style="text-align:center;" |263.2331
| 263.2
| |[[7/6]], [[32/25]]
| [[7/6]], [[22/19]]
|-
|-
| style="text-align:center;" |10
| 10
| style="text-align:center;" |292.48125
| 292.5
| |[[32/27]]
| [[13/11]], [[19/16]], [[32/27]]
|-
|-
| style="text-align:center;" |11
| 11
| style="text-align:center;" |321.7293
| 321.7
| |[[6/5]]
| [[6/5]]
|-
|-
| style="text-align:center;" |12
| 12
| style="text-align:center;" |350.9775
| 351.0
| |[[11/9]],[[27/22]]
| [[11/9]], [[16/13]]
|-
|-
| style="text-align:center;" |13
| 13
| style="text-align:center;" |380.2256
| 380.2
| |[[5/4]]
| [[5/4]], [[26/21]]
|-
|-
| style="text-align:center;" |14
| 14
| style="text-align:center;" |409.47375
| 409.5
| |[[14/11]], [[81/64]]
| [[14/11]], [[19/15]], [[24/19]]
|-
|-
| style="text-align:center;" |15
| 15
| style="text-align:center;" |438.7219
| 438.7
| |[[9/7]]
| [[9/7]], [[32/25]]
|-
|-
| style="text-align:center;" |16
| 16
| style="text-align:center;" |467.97
| 468.0
| |[[21/16]]
| [[21/16]], [[13/10]]
|-
|-
| style="text-align:center;" |17
| 17
| style="text-align:center;" |497.2181
| 497.2
| |[[4/3]]
| [[4/3]]
|-
|-
| style="text-align:center;" |18
| 18
| style="text-align:center;" |526.46625
| 526.5
| |[[15/11]], [[27/20]]
| [[15/11]], [[19/14]], [[27/20]]
|-
|-
| style="text-align:center;" |19
| 19
| style="text-align:center;" |556.7144
| 556.7
| |[[11/8]]
| [[11/8]], [[18/13]], [[26/19]]
|-
|-
| style="text-align:center;" |20
| 20
| style="text-align:center;" |584.9625
| 585.0
| |[[7/5]]
| [[7/5]], [[45/32]]
|-
|-
| style="text-align:center;" |21
| 21
| style="text-align:center;" |614.2106
| 614.2
| |[[10/7]]
| [[10/7]], [[64/45]]
|-
|-
| style="text-align:center;" |22
| 22
| style="text-align:center;" |643.45875
| 643.5
| |[[16/11]]
| [[13/9]], [[16/11]], [[19/13]]
|-
|-
| style="text-align:center;" |23
| 23
| style="text-align:center;" |671.7069
| 671.7
| |[[22/15]], [[40/27]]
| [[22/15]], [[28/19]], [[40/27]]
|-
|-
| style="text-align:center;" |24
| 24
| style="text-align:center;" |701.955
| 702.0
| |[[3/2]]
| [[3/2]]
|-
|-
| style="text-align:center;" |25
| 25
| style="text-align:center;" |731.2031
| 731.2
| |[[32/21]]
| [[20/13]], [[32/21]]
|-
|-
| style="text-align:center;" |26
| 26
| style="text-align:center;" |760.45125
| 760.5
| |[[14/9]], [[25/16]]
| [[14/9]], [[25/16]]
|-
|-
| style="text-align:center;" |27
| 27
| style="text-align:center;" |789.6994
| 789.7
| |[[11/7]], [[128/81]]
| [[11/7]], [[19/12]], [[30/19]]
|-
|-
| style="text-align:center;" |28
| 28
| style="text-align:center;" |818.9475
| 818.9
| |[[8/5]]
| [[8/5]]
|-
|-
| style="text-align:center;" |29
| 29
| style="text-align:center;" |848.1956
| 848.2
| |[[18/11]], [[44/27]]
| [[13/8]], [[18/11]]
|-
|-
| style="text-align:center;" |30
| 30
| style="text-align:center;" |877.44375
| 877.4
| |[[5/3]]
| [[5/3]]
|-
|-
| style="text-align:center;" |31
| 31
| style="text-align:center;" |906.6919
| 906.7
| |[[27/16]]
| [[22/13]], [[27/16]], [[32/19]]
|-
|-
| style="text-align:center;" |32
| 32
| style="text-align:center;" |935.94
| 935.9
| |[[12/7]]
| [[12/7]], [[19/11]]
|-
|-
| style="text-align:center;" |33
| 33
| style="text-align:center;" |965.1881
| 965.2
| |[[7/4]]
| [[7/4]], [[26/15]]
|-
|-
| style="text-align:center;" |34
| 34
| style="text-align:center;" |994.43625
| 994.4
| |[[16/9]]
| [[16/9]]
|-
|-
| style="text-align:center;" |35
| 35
| style="text-align:center;" |1023.6844
| 1023.7
| |[[9/5]], [[20/11]]
| [[9/5]]
|-
|-
| style="text-align:center;" |36
| 36
| style="text-align:center;" |1052.9325
| 1052.9
| |[[11/6]]
| [[11/6]]
|-
|-
| style="text-align:center;" |37
| 37
| style="text-align:center;" |1082.1806
| 1082.2
| |[[15/8]]
| [[13/7]], [[15/8]]
|-
|-
| style="text-align:center;" |38
| 38
| style="text-align:center;" |1111.42875
| 1111.4
| |[[40/21]], [[21/11]]
| [[19/10]], [[21/11]]
|-
|-
| style="text-align:center;" |39
| 39
| style="text-align:center;" |1140.6769
| 1140.7
| |[[48/25]], [[27/14]], [[64/33]]
| [[27/14]], [[35/18]]
|-
|-
| style="text-align:center;" |40
| 40
| style="text-align:center;" |1169.925
| 1169.9
| |[[160/81]]
| [[49/25]], [[56/28]], [[63/32]]
|-
|-
| style="text-align:center;" |41
| 41
| style="text-align:center;" |1199.1731
| 1199.2
| |2/1
| 2/1
|-
|-
|42
| 42
|1228.42125
| 1228.4
|81/40
| [[45/22]], [[49/24]], [[55/27]], [[81/40]]
|-
|-
|43
| 43
|1257.6694
| 1257.7
|25/12, 56/27, 33/16
| [[25/12]], [[33/16]]
|-
|-
|44
| 44
|1286.9175
| 1286.9
|21/10, 44/21
| [[19/9]], [[21/10]]
|-
|-
|45
| 45
|1316.1656
| 1316.2
|32/15, 15/7
| [[15/7]]
|-
|-
|46
| 46
|1345.41375
| 1345.4
|24/11
| [[13/6]]
|-
|-
|47
| 47
|1374.6619
| 1374.7
|20/9, 11/5
| [[11/5]]
|-
|-
|48
| 48
|1403.91
| 1403.9
|9/4
| [[9/4]]
|}
|}
[[Category:Edf]]
 
[[Category:Edonoi]]
== See also ==
* [[41edo]] – relative edo
* [[65edt]] – relative edt
* [[95ed5]] – relative ed5
* [[106ed6]] – relative ed6
* [[147ed12]] – relative ed12
* [[361ed448]] – close to the zeta-optimized tuning for 41edo
 
[[Category:41edo]]
Retrieved from "https://en.xen.wiki/w/24edf"