Xenharmonic Wiki

22edt: Difference between revisions

← Older edit
VisualWikitext
No edit summary
Fredg999 category edits (talk | contribs)
autopatrolled, Bots, emailconfirmed
4,330 edits
m Removing from Category:Edt using Cat-a-lot
 
(16 intermediate revisions by 3 users not shown)
Line 1: Line 1:
{{Infobox ET}}
{{Infobox ET}}
{{ED intro}}
{{ED intro}} It supports [[mintaka]] temperament.


22edt has good approximations of the 7th, 11th, 19th and 20th harmonics, being better for its size in the 3.7.11 subgroup than even [[13edt]] is in 3.5.7. In this subgroup, it tempers out the commas [[1331/1323]] and [[387420489/386683451]], with the former comma allowing a hard [[5L 2s (3/1-equivalent)|5L 2s]] (macrodiatonic) scale generated by [[11/7]], two of which are equated to [[27/11]] and three of which are equated to [[9/7]] up a tritave. This [[9/7]] can also serve as the generator for a [[4L 5s (3/1-equivalent)|4L 5s]] (BPS Lambda) scale, supporting [[Bohlen-Pierce-Stearns]] harmony by tempering out [[245/243]], although its representation of the 3.5.7 subgroup is less accurate than that of 13edt.
Like [[11edt]], both the [[octave]] and [[small whole tone]] ([[10/9]]) are about 10c off (sharp and flat respectively) dissonant but recognizable. Akin to [[16edt]] with [[Blackwood]], admitting the octave induces an interpretation into a tritave-based version of [[Whitewood]] temperament, therefore allowing the system to function as an octave stretch of [[14edo]]. However, it can just as well be treated as a pure no-twos system, which is the main interpretation used in the below article.


Like [[11edt]], both the [[octave]] and [[small whole tone]] ([[10/9]]) are about 10c off (sharp and flat respectively) dissonant but recognizable. Akin to [[16edt]] with [[Blackwood]], admitting the octave induces an interpretation into a tritave-based version of [[Whitewood]] temperament.
22edt has good approximations of the 7th, 11th, 19th and 20th harmonics, being better for its size in the 3.7.11 subgroup than even [[13edt]] is in 3.5.7. In this subgroup, it tempers out the commas [[1331/1323]] and [[387420489/386683451]], with the former comma allowing a hard [[5L 2s (3/1-equivalent)|5L 2s]] (macrodiatonic) scale generated by [[11/7]], two of which are equated to [[27/11]] and three of which are equated to [[9/7]] up a tritave. This [[9/7]] can also serve as the generator for a [[4L 5s (3/1-equivalent)|4L 5s]] (BPS Lambda) scale, supporting [[Bohlen-Pierce-Stearns]] harmony by tempering out [[245/243]], although its representation of the 3.5.7 subgroup is less accurate than that of 13edt, and tempered in the wrong direction relative to 13edt for ideal BPS.


{{Harmonics in equal|22|3|1|intervals=prime|columns=15}}  
{{Harmonics in equal|22|3|1|intervals=prime|columns=15}}  


== Intervals ==
== Intervals ==
The notation schemes below are based on the BPS-Lambda enneatonic scale presented in the symmetric (sLsLsLsLs, Cassiopeian) mode in J, and the Mintaka macrodiatonic scale presented in the macro-Phrygian (sLLLsLL) mode in E.


{| class="wikitable"
{| class="wikitable"
|-
|-
! | Degree
! | Degree
! | Note (BPS-Lambda notation)
! | Note ([[4L 5s (3/1-equivalent)#Notation|BPS-Lambda notation]])
! | Note (Macrodiatonic notation)
! | Note (Macrodiatonic notation)
! | Approximate 3.7.11 subgroup interval
! | Approximate 3.7.11 subgroup interval
Line 20: Line 22:
|-
|-
| | 0
| | 0
| | E
| | J
| | E
| | E
| | 1/1
| | 1/1
Line 27: Line 29:
|-
|-
| | 1
| | 1
| | E# = Fb
| | J# = Kb
| | F
| | F
| | 81/77, 363/343
| | 81/77, 363/343
Line 34: Line 36:
|-
|-
| | 2
| | 2
| | F
| | K
| | Gb = Dx
| | Gb = Dx
| | 2673/2401, 6561/5929
| | 2673/2401, 6561/5929
Line 41: Line 43:
|-
|-
| | 3
| | 3
| | F#
| | K#
| | E# = Abb
| | E# = Abb
| | 343/297, 847/729
| | 343/297, 847/729
Line 48: Line 50:
|-
|-
| | 4
| | 4
| | Gb
| | Lb
| | F#
| | F#
| | 11/9, 147/121
| | 11/9, 147/121
Line 55: Line 57:
|-
|-
| | 5
| | 5
| | G
| | L
| | G
| | G
| | 9/7
| | 9/7
Line 62: Line 64:
|-
|-
| | 6
| | 6
| | G# = Hb
| | L# = Mb
| | Ab = Ex
| | Ab = Ex
| | 729/539
| | 729/539
Line 69: Line 71:
|-
|-
| | 7
| | 7
| | H
| | M
| | Fx = Bbb
| | Fx = Bbb
| | 343/243
| | 343/243
Line 76: Line 78:
|-
|-
| | 8
| | 8
| | H#
| | M#
| | G#
| | G#
| | 49/33, 121/81
| | 49/33, 121/81
Line 83: Line 85:
|-
|-
| | 9
| | 9
| | Jb
| | Nb
| | A
| | A
| | 11/7
| | 11/7
Line 90: Line 92:
|-
|-
| | 10
| | 10
| | J
| | N
| | Bb
| | Bb
| | 81/49
| | 81/49
Line 97: Line 99:
|-
|-
| | 11
| | 11
| | J# = Ab
| | N# = Ob
| | Cb = Gx
| | Cb = Gx
| | 3773/2187, 6561/3773
| | 3773/2187, 6561/3773
Line 104: Line 106:
|-
|-
| | 12
| | 12
| | A
| | O
| | A# = Dbb
| | A# = Dbb
| | 49/27
| | 49/27
Line 111: Line 113:
|-
|-
| | 13
| | 13
| | A#
| | O#
| | B
| | B
| | 21/11
| | 21/11
Line 118: Line 120:
|-
|-
| | 14
| | 14
| | Bb
| | Pb
| | C
| | C
| | 99/49, 243/121
| | 99/49, 243/121
Line 125: Line 127:
|-
|-
| | 15
| | 15
| | B
| | P
| | Db = Ax
| | Db = Ax
| | 729/343
| | 729/343
Line 132: Line 134:
|-
|-
| | 16
| | 16
| | B# = Cb
| | P# = Qb
| | B# = Ebb
| | B# = Ebb
| | 539/243
| | 539/243
Line 139: Line 141:
|-
|-
| | 17
| | 17
| | C
| | Q
| | C#
| | C#
| | 7/3
| | 7/3
Line 146: Line 148:
|-
|-
| | 18
| | 18
| | C#
| | Q#
| | D
| | D
| | 27/11, 121/49
| | 27/11, 121/49
Line 153: Line 155:
|-
|-
| | 19
| | 19
| | Db
| | Rb
| | Eb
| | Eb
| | 891/343, 2187/847
| | 891/343, 2187/847
Line 160: Line 162:
|-
|-
| | 20
| | 20
| | D
| | R
| | Fb = Cx
| | Fb = Cx
| | 2401/891, 5929/2187
| | 2401/891, 5929/2187
Line 167: Line 169:
|-
|-
| | 21
| | 21
| | D# = Eb
| | R# = Jb
| | D# = Gbb
| | D# = Gbb
| | 77/27, 343/121
| | 77/27, 343/121
Line 174: Line 176:
|-
|-
| | 22
| | 22
| | E
| | J
| | E
| | E
| | 3/1
| | 3/1
Line 181: Line 183:
|}
|}


== Compositions ==
== Audio examples ==
* http://www.archive.org/details/TuneIn22Edt by [[Peter Kosmorsky]]
[[File:22ed3-1.mp3]]
* [http://micro.soonlabel.com/22-edt/daily20111206-22edt-improv.mp3 22 edt piano improvisation] by [[Chris Vaisvil]]
 
A short composition by [[Wensik]], based on the 7:9:11 chord and its inversion, 63:77:99.
 
== Music ==
; [[Peter Kosmorsky]]
* [http://www.archive.org/details/TuneIn22Edt Tune in 22edt] (2011)
 
; [[Ray Perlner]]
* [https://www.youtube.com/watch?v=EWy0y_WsVNk ''Fugue in 22EDT Mintaka[7] sLLLsLL "Macro-Phrygian"''] (2025)
 
; [[Chris Vaisvil]]
* [http://micro.soonlabel.com/22-edt/daily20111206-22edt-improv.mp3 22 edt piano improvisation] {{dead link}}


[[Category:Edt]]
[[Category:Nonoctave]]
[[Category:Nonoctave]]
[[Category:Listen]]
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/22edt"