22edt: Difference between revisions

(11 intermediate revisions by 4 users not shown)

Line 1:

{{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~~.

== Harmonics ==

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.

== 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.

Line 186:

[[File:22ed3-1.mp3]]

short composition by Wensik, based on the 7:9:11 chord and its inversion, 63:77:99.

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)

; [[Merct]]

* [https://soundcloud.com/merct/dysfunctional?in=merct/sets/breathe ''dysfunctional'' from the album ''breathe''] (2025)

; [[Ray Perlner]]

* [https://www.youtube.com/watch?v=EWy0y_WsVNk ''<nowiki>Fugue in 22EDT Mintaka[7] sLLLsLL "Macro-Phrygian"</nowiki>''] (2025)

* [https://www.youtube.com/watch?v=edyA0QN-Zmc ''<nowiki>7/8 Fugue in 22EDT Mintaka[7] LLsLLLs "Macro-Ionian"</nowiki>''] (2026)

~~== Compositions ==~~

; [[Chris Vaisvil]]

* http://www.archive.org/details/TuneIn22Edt by [[~~Peter Kosmorsky~~]]

* [http://micro.soonlabel.com/22-edt/daily20111206-22edt-improv.mp3 ''22 edt piano improvisation''] {{dead link}}

* [http://micro.soonlabel.com/22-edt/daily20111206-22edt-improv.mp3 22 edt piano improvisation] ~~by [[Chris Vaisvil]]~~

~~[[Category:Edt]]~~

[[Category:Nonoctave]]

[[Category:Listen]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{ED intro}}
+{{ED intro}} It supports [[mintaka]] temperament.
-edt 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.
+== Harmonics ==
+edt 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}}
 == 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.
@@ Line 186: / Line 186: @@
 [[File:22ed3-1.mp3]]
-short composition by Wensik, based on the 7:9:11 chord and its inversion, 63:77:99.
+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)
+; [[Merct]]
+* [https://soundcloud.com/merct/dysfunctional?in=merct/sets/breathe ''dysfunctional'' from the album ''breathe''] (2025)
+; [[Ray Perlner]]
+* [https://www.youtube.com/watch?v=EWy0y_WsVNk ''<nowiki>Fugue in 22EDT Mintaka[7] sLLLsLL "Macro-Phrygian"</nowiki>''] (2025)
+* [https://www.youtube.com/watch?v=edyA0QN-Zmc ''<nowiki>7/8 Fugue in 22EDT Mintaka[7] LLsLLLs "Macro-Ionian"</nowiki>''] (2026)
-== Compositions ==
+; [[Chris Vaisvil]]
-* http://www.archive.org/details/TuneIn22Edt by [[Peter Kosmorsky]]
+* [http://micro.soonlabel.com/22-edt/daily20111206-22edt-improv.mp3 ''22 edt piano improvisation''] {{dead link}}
-* [http://micro.soonlabel.com/22-edt/daily20111206-22edt-improv.mp3 22 edt piano improvisation] by [[Chris Vaisvil]]
-[[Category:Edt]]
 [[Category:Nonoctave]]
 [[Category:Listen]]