Xenharmonic Wiki

25edt: Difference between revisions

← Older edit
VisualWikitext
No edit summary
+subsets and supersets; +see also
 
(8 intermediate revisions by 4 users not shown)
Line 1: Line 1:
{{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}}


{{Harmonics in equal|17|3|1|intervals=prime|columns=15}}  
== Theory ==
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:
* 6th = 1065.095{{c}}
* squared = 2130.19{{c}} → 228.235{{c}}
* cubed = 1293.33{{c}}
* fourth power = 2358.425{{c}} → 456.47{{c}}


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:
It can be used as a tuning for [[mavila]] and has an antidiatonic ([[2L 5s]]) scale which approximates [[Pelog]] tunings in Indonesian gamelan music.
* 6th = 1065.095 cents
* squared = 2130.19 cents = 228.235 cents
* cubed = 1293.33 cents
* fourth power = 2358.425 cents = 456.47 cents


{| class="wikitable"
=== 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 ==
{| class="wikitable center-1 right-2 right-3"
|-
|-
! | Degree
! #
! | cents
! [[Cent]]s
!hekts
! [[Hekt]]s
! | Armodue name
! Armodue name
|-
|-
| | 1
| 0
| | 76.08
| 0.0
|52
| 0.0
| | 1#/2bb
| 1
|-
|-
| | 2
| 1
| | 152.16
| 76.1
|104
| 52.0
| | 1x/2b
| 1#/2bb
|-
|-
| | 3
| 2
| | 228.235
| 152.2
|156
| 104.0
| | 2
| 1x/2b
|-
|-
| | 4
| 3
| | 304.31
| 228.2
|208
| 156.0
| | 2#/3bb
| 2
|-
|-
| | 5
| 4
| | 380.39
| 304.3
|260
| 208.0
| | 2x/3b
| 2#/3bb
|-
|-
| | 6
| 5
| | 456.47
| 380.4
|312
| 260.0
| | 3
| 2x/3b
|-
|-
| | 7
| 6
| | 532.55
| 456.5
|364
| 312.0
| | 3#/4b
| 3
|-
|-
| | 8
| 7
| | 608.625
| 532.5
|416
| 364.0
| | 4
| 3#/4b
|-
|-
| | 9
| 8
| | 684.70
| 608.6
|468
| 416.0
| | 4#/5bb
| 4
|-
|-
| | 10
| 9
| | 760.78
| 684.7
|520
| 468.0
| | 4x/5b
| 4#/5bb
|-
|-
| | 11
| 10
| | 836.86
| 760.8
|572
| 520.0
| | 5
| 4x/5b
|-
|-
| | 12
| 11
| | 912.94
| 836.9
|624
| 572.0
| | 5#/6bb
| 5
|-
|-
| | 13
| 12
| | 989.02
| 912.9
|676
| 624.0
| | 5x/6b
| 5#/6bb
|-
|-
| | 14
| 13
| | 1065.095
| 989.0
|728
| 676.0
| | 6
| 5x/6b
|-
|-
| | 15
| 14
| | 1141.17
| 1065.1
|780
| 728.0
| | 6#/7bb
| 6
|-
|-
| | 16
| 15
| | 1217.25
| 1141.2
|832
| 780.0
| | 6x/7b
| 6#/7bb
|-
|-
| | 17
| 16
| | 1293.33
| 1217.3
|884
| 832.0
| | 7
| 6x/7b
|-
|-
| | 18
| 17
| | 1369.41
| 1293.3
|936
| 884.0
| | 7#/8b
| 7
|-
|-
| | 19
| 18
| | 1445.485
| 1369.4
|988
| 936.0
| | 8
| 7#/8b
|-
|-
| | 20
| 19
| | 1521.56
| 1445.5
|1040
| 988.0
| | 8#/9bb
| 8
|-
|-
| | 21
| 20
| | 1597.64
| 1521.6
|1092
| 1040.0
| | 8x/9b
| 8#/9bb
|-
|-
| | 22
| 21
| | 1673.72
| 1597.6
|1144
| 1092.0
| | 9
| 8x/9b
|-
|-
| | 23
| 22
| | 1749.80
| 1673.7
|1196
| 1144.0
| | 9#/1bb
| 9
|-
|-
| | 24
| 23
| | 1825.88
| 1749.8
|1248
| 1196.0
| | 9x/1b
| 9#/1bb
|-
|-
| | 25
| 24
| | 1901.955
| 1825.9
|1300
| 1248.0
| | 1
| 9x/1b
|-
| 25
| 1902.0
| 1300.0
| 1
|}
|}
== See also ==
* [[16edo]] – relative edo
* [[41ed6]] – relative ed6
* [[57ed12]] – relative ed12
{{Todo|expand}}
[[Category:Armodue]]
[[Category:Armodue]]
[[Category:Edt]]
[[Category:Edonoi]]
Retrieved from "https://en.xen.wiki/w/25edt"