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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]].


[[Category:Edf]]
=== Harmonics ===
[[Category:Edonoi]]
{{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 ==
{| class="wikitable center-1 right-2"
|+ Intervals of 24edf
|-
! #
! Cents
! Approximate ratios
|-
| 0
| 0.0
| [[1/1]]
|-
| 1
| 29.2
| [[49/48]], [[50/49]], [[64/63]], [[81/80]]
|-
| 2
| 58.5
| [[25/24]], [[28/27]], [[33/32]], [[36/35]]
|-
| 3
| 87.7
| [[19/18]], [[20/19]], [[21/20]], [[22/21]]
|-
| 4
| 117.0
| [[14/13]], [[15/14]], [[16/15]]
|-
| 5
| 146.2
| [[12/11]], [[13/12]]
|-
| 6
| 175.5
| [[10/9]], [[11/10]], [[21/19]]
|-
| 7
| 204.7
| [[9/8]]
|-
| 8
| 234.0
| [[8/7]], [[15/13]]
|-
| 9
| 263.2
| [[7/6]], [[22/19]]
|-
| 10
| 292.5
| [[13/11]], [[19/16]], [[32/27]]
|-
| 11
| 321.7
| [[6/5]]
|-
| 12
| 351.0
| [[11/9]], [[16/13]]
|-
| 13
| 380.2
| [[5/4]], [[26/21]]
|-
| 14
| 409.5
| [[14/11]], [[19/15]], [[24/19]]
|-
| 15
| 438.7
| [[9/7]], [[32/25]]
|-
| 16
| 468.0
| [[21/16]], [[13/10]]
|-
| 17
| 497.2
| [[4/3]]
|-
| 18
| 526.5
| [[15/11]], [[19/14]], [[27/20]]
|-
| 19
| 556.7
| [[11/8]], [[18/13]], [[26/19]]
|-
| 20
| 585.0
| [[7/5]], [[45/32]]
|-
| 21
| 614.2
| [[10/7]], [[64/45]]
|-
| 22
| 643.5
| [[13/9]], [[16/11]], [[19/13]]
|-
| 23
| 671.7
| [[22/15]], [[28/19]], [[40/27]]
|-
| 24
| 702.0
| [[3/2]]
|-
| 25
| 731.2
| [[20/13]], [[32/21]]
|-
| 26
| 760.5
| [[14/9]], [[25/16]]
|-
| 27
| 789.7
| [[11/7]], [[19/12]], [[30/19]]
|-
| 28
| 818.9
| [[8/5]]
|-
| 29
| 848.2
| [[13/8]], [[18/11]]
|-
| 30
| 877.4
| [[5/3]]
|-
| 31
| 906.7
| [[22/13]], [[27/16]], [[32/19]]
|-
| 32
| 935.9
| [[12/7]], [[19/11]]
|-
| 33
| 965.2
| [[7/4]], [[26/15]]
|-
| 34
| 994.4
| [[16/9]]
|-
| 35
| 1023.7
| [[9/5]]
|-
| 36
| 1052.9
| [[11/6]]
|-
| 37
| 1082.2
| [[13/7]], [[15/8]]
|-
| 38
| 1111.4
| [[19/10]], [[21/11]]
|-
| 39
| 1140.7
| [[27/14]], [[35/18]]
|-
| 40
| 1169.9
| [[49/25]], [[56/28]], [[63/32]]
|-
| 41
| 1199.2
| 2/1
|-
| 42
| 1228.4
| [[45/22]], [[49/24]], [[55/27]], [[81/40]]
|-
| 43
| 1257.7
| [[25/12]], [[33/16]]
|-
| 44
| 1286.9
| [[19/9]], [[21/10]]
|-
| 45
| 1316.2
| [[15/7]]
|-
| 46
| 1345.4
| [[13/6]]
|-
| 47
| 1374.7
| [[11/5]]
|-
| 48
| 1403.9
| [[9/4]]
|}
 
== 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]]
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