22edt: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ED intro}} | {{ED intro}} It supports [[mintaka]] temperament. | ||
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. | |||
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}} | ||
| Line 22: | Line 22: | ||
|- | |- | ||
| | 0 | | | 0 | ||
| | | | | J | ||
| | E | | | E | ||
| | 1/1 | | | 1/1 | ||
| Line 29: | Line 29: | ||
|- | |- | ||
| | 1 | | | 1 | ||
| | | | | J# = Kb | ||
| | F | | | F | ||
| | 81/77, 363/343 | | | 81/77, 363/343 | ||
| Line 36: | Line 36: | ||
|- | |- | ||
| | 2 | | | 2 | ||
| | | | | K | ||
| | Gb = Dx | | | Gb = Dx | ||
| | 2673/2401, 6561/5929 | | | 2673/2401, 6561/5929 | ||
| Line 43: | Line 43: | ||
|- | |- | ||
| | 3 | | | 3 | ||
| | | | | K# | ||
| | E# = Abb | | | E# = Abb | ||
| | 343/297, 847/729 | | | 343/297, 847/729 | ||
| Line 50: | Line 50: | ||
|- | |- | ||
| | 4 | | | 4 | ||
| | | | | Lb | ||
| | F# | | | F# | ||
| | 11/9, 147/121 | | | 11/9, 147/121 | ||
| Line 57: | Line 57: | ||
|- | |- | ||
| | 5 | | | 5 | ||
| | | | | L | ||
| | G | | | G | ||
| | 9/7 | | | 9/7 | ||
| Line 64: | Line 64: | ||
|- | |- | ||
| | 6 | | | 6 | ||
| | | | | L# = Mb | ||
| | Ab = Ex | | | Ab = Ex | ||
| | 729/539 | | | 729/539 | ||
| Line 71: | Line 71: | ||
|- | |- | ||
| | 7 | | | 7 | ||
| | | | | M | ||
| | Fx = Bbb | | | Fx = Bbb | ||
| | 343/243 | | | 343/243 | ||
| Line 78: | Line 78: | ||
|- | |- | ||
| | 8 | | | 8 | ||
| | | | | M# | ||
| | G# | | | G# | ||
| | 49/33, 121/81 | | | 49/33, 121/81 | ||
| Line 85: | Line 85: | ||
|- | |- | ||
| | 9 | | | 9 | ||
| | | | | Nb | ||
| | A | | | A | ||
| | 11/7 | | | 11/7 | ||
| Line 92: | Line 92: | ||
|- | |- | ||
| | 10 | | | 10 | ||
| | | | | N | ||
| | Bb | | | Bb | ||
| | 81/49 | | | 81/49 | ||
| Line 99: | Line 99: | ||
|- | |- | ||
| | 11 | | | 11 | ||
| | | | | N# = Ob | ||
| | Cb = Gx | | | Cb = Gx | ||
| | 3773/2187, 6561/3773 | | | 3773/2187, 6561/3773 | ||
| Line 106: | Line 106: | ||
|- | |- | ||
| | 12 | | | 12 | ||
| | | | | O | ||
| | A# = Dbb | | | A# = Dbb | ||
| | 49/27 | | | 49/27 | ||
| Line 113: | Line 113: | ||
|- | |- | ||
| | 13 | | | 13 | ||
| | | | | O# | ||
| | B | | | B | ||
| | 21/11 | | | 21/11 | ||
| Line 120: | Line 120: | ||
|- | |- | ||
| | 14 | | | 14 | ||
| | | | | Pb | ||
| | C | | | C | ||
| | 99/49, 243/121 | | | 99/49, 243/121 | ||
| Line 127: | Line 127: | ||
|- | |- | ||
| | 15 | | | 15 | ||
| | | | | P | ||
| | Db = Ax | | | Db = Ax | ||
| | 729/343 | | | 729/343 | ||
| Line 134: | Line 134: | ||
|- | |- | ||
| | 16 | | | 16 | ||
| | | | | P# = Qb | ||
| | B# = Ebb | | | B# = Ebb | ||
| | 539/243 | | | 539/243 | ||
| Line 141: | Line 141: | ||
|- | |- | ||
| | 17 | | | 17 | ||
| | | | | Q | ||
| | C# | | | C# | ||
| | 7/3 | | | 7/3 | ||
| Line 148: | Line 148: | ||
|- | |- | ||
| | 18 | | | 18 | ||
| | | | | Q# | ||
| | D | | | D | ||
| | 27/11, 121/49 | | | 27/11, 121/49 | ||
| Line 155: | Line 155: | ||
|- | |- | ||
| | 19 | | | 19 | ||
| | | | | Rb | ||
| | Eb | | | Eb | ||
| | 891/343, 2187/847 | | | 891/343, 2187/847 | ||
| Line 162: | Line 162: | ||
|- | |- | ||
| | 20 | | | 20 | ||
| | | | | R | ||
| | Fb = Cx | | | Fb = Cx | ||
| | 2401/891, 5929/2187 | | | 2401/891, 5929/2187 | ||
| Line 169: | Line 169: | ||
|- | |- | ||
| | 21 | | | 21 | ||
| | | | | R# = Jb | ||
| | D# = Gbb | | | D# = Gbb | ||
| | 77/27, 343/121 | | | 77/27, 343/121 | ||
| Line 176: | Line 176: | ||
|- | |- | ||
| | 22 | | | 22 | ||
| | | | | J | ||
| | E | | | E | ||
| | 3/1 | | | 3/1 | ||
| Line 186: | Line 186: | ||
[[File:22ed3-1.mp3]] | [[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) | |||
; [[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}} | |||
* [http://micro.soonlabel.com/22-edt/daily20111206-22edt-improv.mp3 22 edt piano improvisation] | |||
[[Category:Nonoctave]] | [[Category:Nonoctave]] | ||
[[Category:Listen]] | [[Category:Listen]] | ||