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{{Infobox ET}}
{{Infobox ET}}
'''25EDT''' is the [[Edt|equal division of the third harmonic]] into 25 parts of 76.0782 [[cent|cents]] each, corresponding to 15.7732 [[edo]] (stretched version of [[16edo]]).
{{ED intro}}


This scale coincidentally turns out to be 16 equal divisions of a stretched octave (1217.25 cents) and a tritave twin of the Armodue/Hornbostel flat third-tone system:
== Theory ==
* 6th = 1065.095 cents
25edt corresponds to 15.7732…[[edo]], or 16 equal divisions of a stretched octave (1217.25{{c}}) and a tritave twin of the Armodue/Hornbostel flat third-tone system:
* squared = 2130.19 cents = 228.235 cents
* 6th = 1065.095{{c}}
* cubed = 1293.33 cents
* squared = 2130.19{{c}} → 228.235{{c}}
* fourth power = 2358.425 cents = 456.47 cents
* cubed = 1293.33{{c}}
* fourth power = 2358.425{{c}} → 456.47{{c}}
 
It can be used as a tuning for [[mavila]] and has an antidiatonic ([[2L 5s]]) scale which approximates [[Pelog]] tunings in Indonesian gamelan music.
 
=== Harmonics ===
{{Harmonics in equal|25|3|1|intervals=integer|columns=11}}
{{Harmonics in equal|25|3|1|intervals=integer|columns=11|start=12|collapsed=true|title=Approximation of harmonics in 25edt (continued)}}
 
=== Subsets and supersets ===
Since 25 factors into primes as 5<sup>2</sup>, 25edt contains [[5edt]] as its only nontrivial subset edt.


== Intervals ==
== Intervals ==
{| class="wikitable"
{| class="wikitable center-1 right-2 right-3"
|-
|-
! Degree
! #
! Cents
! [[Cent]]s
! Hekts
! [[Hekt]]s
! Armodue name
! Armodue name
|-
| 0
| 0.0
| 0.0
| 1
|-
|-
| 1
| 1
| 76.08
| 76.1
| 52
| 52.0
| 1#/2bb
| 1#/2bb
|-
|-
| 2
| 2
| 152.16
| 152.2
| 104
| 104.0
| 1x/2b
| 1x/2b
|-
|-
| 3
| 3
| 228.235
| 228.2
| 156
| 156.0
| 2
| 2
|-
|-
| 4
| 4
| 304.31
| 304.3
| 208
| 208.0
| 2#/3bb
| 2#/3bb
|-
|-
| 5
| 5
| 380.39
| 380.4
| 260
| 260.0
| 2x/3b
| 2x/3b
|-
|-
| 6
| 6
| 456.47
| 456.5
| 312
| 312.0
| 3
| 3
|-
|-
| 7
| 7
| 532.55
| 532.5
| 364
| 364.0
| 3#/4b
| 3#/4b
|-
|-
| 8
| 8
| 608.625
| 608.6
| 416
| 416.0
| 4
| 4
|-
|-
| 9
| 9
| 684.70
| 684.7
| 468
| 468.0
| 4#/5bb
| 4#/5bb
|-
|-
| 10
| 10
| 760.78
| 760.8
| 520
| 520.0
| 4x/5b
| 4x/5b
|-
|-
| 11
| 11
| 836.86
| 836.9
| 572
| 572.0
| 5
| 5
|-
|-
| 12
| 12
| 912.94
| 912.9
| 624
| 624.0
| 5#/6bb
| 5#/6bb
|-
|-
| 13
| 13
| 989.02
| 989.0
| 676
| 676.0
| 5x/6b
| 5x/6b
|-
|-
| 14
| 14
| 1065.095
| 1065.1
| 728
| 728.0
| 6
| 6
|-
|-
| 15
| 15
| 1141.17
| 1141.2
| 780
| 780.0
| 6#/7bb
| 6#/7bb
|-
|-
| 16
| 16
| 1217.25
| 1217.3
| 832
| 832.0
| 6x/7b
| 6x/7b
|-
|-
| 17
| 17
| 1293.33
| 1293.3
| 884
| 884.0
| 7
| 7
|-
|-
| 18
| 18
| 1369.41
| 1369.4
| 936
| 936.0
| 7#/8b
| 7#/8b
|-
|-
| 19
| 19
| 1445.485
| 1445.5
| 988
| 988.0
| 8
| 8
|-
|-
| 20
| 20
| 1521.56
| 1521.6
| 1040
| 1040.0
| 8#/9bb
| 8#/9bb
|-
|-
| 21
| 21
| 1597.64
| 1597.6
| 1092
| 1092.0
| 8x/9b
| 8x/9b
|-
|-
| 22
| 22
| 1673.72
| 1673.7
| 1144
| 1144.0
| 9
| 9
|-
|-
| 23
| 23
| 1749.80
| 1749.8
| 1196
| 1196.0
| 9#/1bb
| 9#/1bb
|-
|-
| 24
| 24
| 1825.88
| 1825.9
| 1248
| 1248.0
| 9x/1b
| 9x/1b
|-
|-
| 25
| 25
| 1901.955
| 1902.0
| 1300
| 1300.0
| 1
| 1
|}
|}


== Harmonics ==
== See also ==
{{Harmonics in equal
* [[16edo]] – relative edo
| steps = 25
* [[41ed6]] – relative ed6
| num = 3
* [[57ed12]] – relative ed12
| denom = 1
| intervals = prime
}}
{{Harmonics in equal
| steps = 25
| num = 3
| denom = 1
| start = 12
| collapsed = 1
| intervals = prime
}}


{{Todo|expand}}
[[Category:Armodue]]
[[Category:Armodue]]
[[Category:Edt]]
[[Category:Edonoi]]
Retrieved from "https://en.xen.wiki/w/25edt"