22edo: Difference between revisions
Wikispaces>JosephRuhf **Imported revision 597414674 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 597515888 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-10- | : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-30 21:06:58 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>597515888</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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==Intervals by degree (Superpyth/Porcupine)== | ==Intervals by degree (Superpyth/Porcupine)== | ||
|| Degree || Name and Abbreviation || Cents ||= Approximate | || Degree || Name and Abbreviation || Cents coarse/fine ||= Approximate | ||
Ratios* || | Ratios* || | ||
|| 0 || Natural Unison, 1 || 0 ||= 1/1 || | || 0 || Natural Unison, 1 || 0 ||= 1/1 || | ||
|| 1 || s-minor second, sm2 || 54. | || 1 || s-minor second, sm2 || 54.545, 65.455 ||= 33/32, 34/33, 32/31 || | ||
|| 2 || p-diminished second, pd2 || 109.09 ||= 18/17, 17/16, 16/15, 15/14 || | || 2 || p-diminished second, pd2 || 109.09, 130.90 ||= 18/17, 17/16, 16/15, 15/14 || | ||
|| 3 || p-minor second, pm2 || 163.64 ||= 11/10, 10/9, 32/29 || | || 3 || p-minor second, pm2 || 163.64, 196.36 ||= 11/10, 10/9, 32/29 || | ||
|| 4 || (s/p) Major second, M2 || 218.18 ||= 9/8, 8/7, 17/15 || | || 4 || (s/p) Major second, M2 || 218.18, 261.82 ||= 9/8, 8/7, 17/15 || | ||
|| 5 || s-minor third, sm3 || 272.73 ||= [[7_6|7/6]], [[20_17|20/17]] || | || 5 || s-minor third, sm3 || 272.73, 327.27 ||= [[7_6|7/6]], [[20_17|20/17]] || | ||
|| 6 || p-minor third, pm3 || 327.27 ||= 6/5, 17/14, 11/9, 29/24 || | || 6 || p-minor third, pm3 || 327.27, 392.73 ||= 6/5, 17/14, 11/9, 29/24 || | ||
|| 7 || p-Major third, pM3 || 381.82 ||= 5/4 || | || 7 || p-Major third, pM3 || 381.82, 459.18 ||= 5/4 || | ||
|| 8 || s-Major third, sM3 || 436.36 ||= 9/7, 14/11, 22/17 || | || 8 || s-Major third, sM3 || 436.36, 524.64 ||= 9/7, 14/11, 22/17 || | ||
|| 9 || Natural Fourth, 4, N4 || 490.91 ||= 4/3 || | || 9 || Natural Fourth, 4, N4 || 490.91, 589.09 ||= 4/3 || | ||
|| 10 || p-Major Fourth, pM4 | || 10 || p-Major Fourth, pM4 | ||
s-dim fifth || 545. | s-dim fifth || 545.455, 654.545 ||= 11/8, 15/11 || | ||
|| 11 || Augmented Fourth, A4, | || 11 || Augmented Fourth, A4, | ||
Half-Octave, HO || 600 ||= 7/5, 10/7, 17/12, 24/17 || | Half-Octave, HO || 600, 720 ||= 7/5, 10/7, 17/12, 24/17 || | ||
|| 12 || p-minor Fifth, pm5 | || 12 || p-minor Fifth, pm5 | ||
s-aug fourth || 654. | s-aug fourth || 654.545, 785.455 ||= 16/11, 22/15 || | ||
|| 13 || Natural Fifth, 5, N5 || 709.09 ||= 3/2 || | || 13 || Natural Fifth, 5, N5 || 709.09, 850.90 ||= 3/2 || | ||
|| 14 || s-minor sixth, sm6 || 763.64 ||= 11/7, 14/9, 17/11 || | || 14 || s-minor sixth, sm6 || 763.64, 916.36 ||= 11/7, 14/9, 17/11 || | ||
|| 15 || p-minor sixth, pm6 || 818.18 ||= 8/5 || | || 15 || p-minor sixth, pm6 || 818.18, 981.82 ||= 8/5 || | ||
|| 16 || p-Major sixth, pM6 || 872.73 ||= 5/3, 18/11, 28/17 || | || 16 || p-Major sixth, pM6 || 872.73, 1047.27 ||= 5/3, 18/11, 28/17 || | ||
|| 17 || s-Major sixth, sM6 || 927.27 ||= [[12_7|12/7]], [[17_10|17/10]] || | || 17 || s-Major sixth, sM6 || 927.27, 1112.73 ||= [[12_7|12/7]], [[17_10|17/10]] || | ||
|| 18 || (s/p) minor seventh, m7 || 981.82 ||= 7/4, 16/9, 30/17 || | || 18 || (s/p) minor seventh, m7 || 981.82, 1179.18 ||= 7/4, 16/9, 30/17 || | ||
|| 19 || p-Major seventh, pM7 || 1036.36 ||= 20/11, 9/5, 29/16 || | || 19 || p-Major seventh, pM7 || 1036.36, 1244.64 ||= 20/11, 9/5, 29/16 || | ||
|| 20 || p-Augmented Seventh || 1090.91 ||= 15/8, 32/17, 17/9, 28/15 || | || 20 || p-Augmented Seventh || 1090.91, 1309.09 ||= 15/8, 32/17, 17/9, 28/15 || | ||
|| 21 || s-Major Seventh, sM7 || 1145. | || 21 || s-Major Seventh, sM7 || 1145.455, 1374.545 ||= 33/17, 64/33, 31/16 || | ||
|| 22 || Octave, 8 || 1200 ||= 2/1 || | || 22 || Octave, 8 || 1200, 1440 ||= 2/1 || | ||
22edo intervals can also be notated using [[Ups and Downs Notation|ups and downs]]: The keyboard runs C * * * D * * * E F * * * G * * * A * * * B C. | 22edo intervals can also be notated using [[Ups and Downs Notation|ups and downs]]: The keyboard runs C * * * D * * * E F * * * G * * * A * * * B C. | ||
==Intervals by degree (ups and downs)== | ==Intervals by degree (ups and downs)== | ||
||= Degree ||= Interval Name ||= Abbreviation ||= Cents ||= Example || | ||= Degree ||= Interval Name ||= Abbreviation ||= Cents coarse/fine ||= Example || | ||
||= 0 ||= perfect unison ||= P1 ||= 0 ||= C || | ||= 0 ||= perfect unison ||= P1 ||= 0 ||= C || | ||
||= 1 ||= minor second ||= m2 ||= | ||= 1 ||= minor second ||= m2 ||= 54.5, 65.5 ||= Db || | ||
||= 2 ||= upminor 2nd ||= ^m2 ||= 109 ||= Db^ || | ||= 2 ||= upminor 2nd ||= ^m2 ||= 109, 131 ||= Db^ || | ||
||= 3 ||= downmajor 2nd ||= vM2 ||= 164 ||= Dv || | ||= 3 ||= downmajor 2nd ||= vM2 ||= 164, 196 ||= Dv || | ||
||= 4 ||= major second ||= M2 ||= 218 ||= D || | ||= 4 ||= major second ||= M2 ||= 218, 262 ||= D || | ||
||= 5 ||= minor third ||= m3 ||= 273 ||= Eb || | ||= 5 ||= minor third ||= m3 ||= 273, 327 ||= Eb || | ||
||= 6 ||= upminor third ||= ^m3 ||= 327 ||= Eb^ || | ||= 6 ||= upminor third ||= ^m3 ||= 327, 393 ||= Eb^ || | ||
||= 7 ||= downmajor third ||= vM3 ||= 382 ||= Ev || | ||= 7 ||= downmajor third ||= vM3 ||= 382, 459 ||= Ev || | ||
||= 8 ||= major third ||= M3 ||= 436 ||= E || | ||= 8 ||= major third ||= M3 ||= 436, 525 ||= E || | ||
||= 9 ||= perfect fourth ||= P4 ||= 491 ||= F || | ||= 9 ||= perfect fourth ||= P4 ||= 491, 589 ||= F || | ||
||= 10 ||= up-fourth or dim fifth ||= ^4 or d5 ||= 545 ||= F^ or Gb || | ||= 10 ||= up-fourth or dim fifth ||= ^4 or d5 ||= 545.5, 654.5 ||= F^ or Gb || | ||
||= 11 ||= downaug fourth or updim fifth ||= vA4 or ^d5 ||= 600 ||= F#v or Gb^ || | ||= 11 ||= downaug fourth or updim fifth ||= vA4 or ^d5 ||= 600, 720 ||= F#v or Gb^ || | ||
||= 12 ||= aug fourth or down-fifth ||= A4 or v5 ||= | ||= 12 ||= aug fourth or down-fifth ||= A4 or v5 ||= 654.5, 785.5 ||= F# or Gv || | ||
||= 13 ||= perfect fifth ||= P5 ||= 709 ||= G || | ||= 13 ||= perfect fifth ||= P5 ||= 709, 851 ||= G || | ||
||= 14 ||= minor sixth ||= m6 ||= 764 ||= Ab || | ||= 14 ||= minor sixth ||= m6 ||= 764, 916 ||= Ab || | ||
||= 15 ||= upminor sixth ||= ^m6 ||= 818 ||= Ab^ || | ||= 15 ||= upminor sixth ||= ^m6 ||= 818, 982 ||= Ab^ || | ||
||= 16 ||= downmajor sixth ||= vM6 ||= 873 ||= Av || | ||= 16 ||= downmajor sixth ||= vM6 ||= 873, 1047 ||= Av || | ||
||= 17 ||= major sixth ||= M6 ||= 927 ||= A || | ||= 17 ||= major sixth ||= M6 ||= 927, 1113 ||= A || | ||
||= 18 ||= minor seventh ||= m7 ||= 982 ||= Bb || | ||= 18 ||= minor seventh ||= m7 ||= 982, 1179 ||= Bb || | ||
||= 19 ||= upminor seventh ||= ^m7 ||= 1036 ||= Bb^ || | ||= 19 ||= upminor seventh ||= ^m7 ||= 1036, 1245 ||= Bb^ || | ||
||= 20 ||= downmajor seventh ||= vM7 ||= 1091 ||= Bv || | ||= 20 ||= downmajor seventh ||= vM7 ||= 1091, 1309 ||= Bv || | ||
||= 21 ||= major seventh ||= M7 ||= 1145 ||= B || | ||= 21 ||= major seventh ||= M7 ||= 1145.5, 1374.5 ||= B || | ||
||= 22 ||= octave ||= P8 ||= 1200 ||= C || | ||= 22 ||= octave ||= P8 ||= 1200, 1440 ||= C || | ||
Another possible notation uses the porcupine generator to generate the notation as well. The 2nd and 7th are perfect, and the 4th and 5th are imperfect like the 3rd and 6th. The keyboard runs D * * E * * F * * G * * * A * * B * * C * * D. | Another possible notation uses the porcupine generator to generate the notation as well. The 2nd and 7th are perfect, and the 4th and 5th are imperfect like the 3rd and 6th. The keyboard runs D * * E * * F * * G * * * A * * B * * C * * D. | ||
==Intervals by degree (Porcupine)== | ==Intervals by degree (Porcupine)== | ||
||= Degree ||= Interval Name ||= Abbreviation ||= Cents ||= Example || | ||= Degree ||= Interval Name ||= Abbreviation ||= Cents coarse/fine ||= Example || | ||
||= 0 ||= perfect unison ||= P1 ||= 0 ||= D || | ||= 0 ||= perfect unison ||= P1 ||= 0 ||= D || | ||
||= 1 ||= aug unison ||= A1 ||= | ||= 1 ||= aug unison ||= A1 ||= 54.5, 65.5 ||= D# || | ||
||= 2 ||= dim second ||= d2 ||= 109 ||= Eb || | ||= 2 ||= dim second ||= d2 ||= 109, 131 ||= Eb || | ||
||= 3 ||= perfect second ||= P2 ||= 164 ||= E || | ||= 3 ||= perfect second ||= P2 ||= 164, 196 ||= E || | ||
||= 4 ||= aug second ||= A2 ||= 218 ||= E# || | ||= 4 ||= aug second ||= A2 ||= 218, 262 ||= E# || | ||
||= 5 ||= dim third ||= d3 ||= 273 ||= Fb || | ||= 5 ||= dim third ||= d3 ||= 273, 327 ||= Fb || | ||
||= 6 ||= minor third ||= m3 ||= 327 ||= F || | ||= 6 ||= minor third ||= m3 ||= 327, 393 ||= F || | ||
||= 7 ||= major third ||= M3 ||= 382 ||= F# || | ||= 7 ||= major third ||= M3 ||= 382, 459 ||= F# || | ||
||= 8 ||= aug third or dim fourth ||= A3 or d4 ||= 436 ||= Gb || | ||= 8 ||= aug third or dim fourth ||= A3 or d4 ||= 436, 525 ||= Gb || | ||
||= 9 ||= minor fourth ||= m4 ||= 491 ||= G || | ||= 9 ||= minor fourth ||= m4 ||= 491, 589 ||= G || | ||
||= 10 ||= major fourth ||= M4 ||= 545 ||= G# || | ||= 10 ||= major fourth ||= M4 ||= 545.5, 654.5 ||= G# || | ||
||= 11 ||= aug fourth or dim fifth ||= A4 or d5 ||= 600 ||= Gx or Abb || | ||= 11 ||= aug fourth or dim fifth ||= A4 or d5 ||= 600, 720 ||= Gx or Abb || | ||
||= 12 ||= minor fifth ||= m5 ||= | ||= 12 ||= minor fifth ||= m5 ||= 654.5, 785.5 ||= Ab || | ||
||= 13 ||= major fifth ||= M5 ||= 709 ||= A || | ||= 13 ||= major fifth ||= M5 ||= 709, 851 ||= A || | ||
||= 14 ||= aug fifth or dim sixth ||= A5 or d6 ||= 764 ||= A# || | ||= 14 ||= aug fifth or dim sixth ||= A5 or d6 ||= 764, 916 ||= A# || | ||
||= 15 ||= minor sixth ||= m6 ||= 818 ||= Bb || | ||= 15 ||= minor sixth ||= m6 ||= 818, 982 ||= Bb || | ||
||= 16 ||= major sixth ||= M6 ||= 873 ||= B || | ||= 16 ||= major sixth ||= M6 ||= 873, 1047 ||= B || | ||
||= 17 ||= aug sixth ||= A6 ||= 927 ||= B# || | ||= 17 ||= aug sixth ||= A6 ||= 927, 1113 ||= B# || | ||
||= 18 ||= dim seventh ||= d7 ||= 982 ||= Cb || | ||= 18 ||= dim seventh ||= d7 ||= 982, 1179 ||= Cb || | ||
||= 19 ||= perfect seventh ||= P7 ||= 1036 ||= C || | ||= 19 ||= perfect seventh ||= P7 ||= 1036, 1245 ||= C || | ||
||= 20 ||= aug seventh ||= A7 ||= 1091 ||= C# || | ||= 20 ||= aug seventh ||= A7 ||= 1091, 1309 ||= C# || | ||
||= 21 ||= dim octave ||= d8 ||= 1145 ||= Db || | ||= 21 ||= dim octave ||= d8 ||= 1145.5, 1374.5 ||= Db || | ||
||= 22 ||= octave ||= P8 ||= 1200 ||= D || | ||= 22 ||= octave ||= P8 ||= 1200, 1440 ||= D || | ||
Yet another notation is pentatonic. This is the only way to use a chain-of-fifths notation without additional accidentals. The pentatonic degrees are unison, subthird, fourthoid, fifthoid, subseventh and octoid. The keyboard runs D * * * E * * * * G * * * A * * * * C * * * D. | Yet another notation is pentatonic. This is the only way to use a chain-of-fifths notation without additional accidentals. The pentatonic degrees are unison, subthird, fourthoid, fifthoid, subseventh and octoid. The keyboard runs D * * * E * * * * G * * * A * * * * C * * * D. | ||
==Intervals by degree (pentatonic)== | ==Intervals by degree (pentatonic)== | ||
||= Degree ||= Interval Name ||= Abbreviation ||= Cents ||= Example || | ||= Degree ||= Interval Name ||= Abbreviation ||= Cents coarse/fine ||= Example || | ||
||= 0 ||= perfect unison ||= P1 ||= 0 ||= D || | ||= 0 ||= perfect unison ||= P1 ||= 0 ||= D || | ||
||= 1 ||= aug unison ||= A1 ||= | ||= 1 ||= aug unison ||= A1 ||= 54.5, 65.5 ||= D# || | ||
||= 2 ||= double-aug unison or | ||= 2 ||= double-aug unison or | ||
double-dim sub3rd ||= AA1 or dds3 ||= 109 ||= Dx or Ebb || | double-dim sub3rd ||= AA1 or dds3 ||= 109, 131 ||= Dx or Ebb || | ||
||= 3 ||= dim sub3rd ||= ds3 ||= 164 ||= Eb || | ||= 3 ||= dim sub3rd ||= ds3 ||= 164, 196 ||= Eb || | ||
||= 4 ||= minor sub3rd ||= ms3 ||= 218 ||= E || | ||= 4 ||= minor sub3rd ||= ms3 ||= 218, 262 ||= E || | ||
||= 5 ||= major sub3rd ||= Ms3 ||= 273 ||= E# || | ||= 5 ||= major sub3rd ||= Ms3 ||= 273, 327 ||= E# || | ||
||= 6 ||= aug sub3rd ||= As3 ||= 327 ||= Ex || | ||= 6 ||= aug sub3rd ||= As3 ||= 327, 393 ||= Ex || | ||
||= 7 ||= double-aug sub3rd or | ||= 7 ||= double-aug sub3rd or | ||
double-dim 4thoid ||= AAs3 or dd4d ||= 382 ||= Gbb || | double-dim 4thoid ||= AAs3 or dd4d ||= 382, 459 ||= Gbb || | ||
||= 8 ||= dim 4thoid ||= d4d ||= 436 ||= Gb || | ||= 8 ||= dim 4thoid ||= d4d ||= 436, 525 ||= Gb || | ||
||= 9 ||= perfect 4thoid ||= P4d ||= 491 ||= G || | ||= 9 ||= perfect 4thoid ||= P4d ||= 491, 589 ||= G || | ||
||= 10 ||= aug 4thoid ||= A4d ||= 545 ||= G# || | ||= 10 ||= aug 4thoid ||= A4d ||= 545.5, 654.5 ||= G# || | ||
||= 11 ||= double-aug 4thoid or | ||= 11 ||= double-aug 4thoid or | ||
double-dim 5thoid ||= AA4d or dd5d ||= 600 ||= Gx or Abb || | double-dim 5thoid ||= AA4d or dd5d ||= 600, 720 ||= Gx or Abb || | ||
||= 12 ||= dim 5thoid ||= d5d ||= | ||= 12 ||= dim 5thoid ||= d5d ||= 654.5, 785.5 ||= Ab || | ||
||= 13 ||= perfect 5thoid ||= P5d ||= 709 ||= A || | ||= 13 ||= perfect 5thoid ||= P5d ||= 709, 851 ||= A || | ||
||= 14 ||= aug 5thoid ||= A5d ||= 764 ||= A# || | ||= 14 ||= aug 5thoid ||= A5d ||= 764, 916 ||= A# || | ||
||= 15 ||= double-aug 5thoid or | ||= 15 ||= double-aug 5thoid or | ||
double-dim sub7th ||= AA5d or dds7 ||= 818 ||= Ax || | double-dim sub7th ||= AA5d or dds7 ||= 818, 982 ||= Ax || | ||
||= 16 ||= dim sub7th ||= ds7 ||= 873 ||= Cbb || | ||= 16 ||= dim sub7th ||= ds7 ||= 873, 1047 ||= Cbb || | ||
||= 17 ||= minor sub7th ||= ms7 ||= 927 ||= Cb || | ||= 17 ||= minor sub7th ||= ms7 ||= 927, 1047 ||= Cb || | ||
||= 18 ||= major sub7th ||= Ms7 ||= 982 ||= C || | ||= 18 ||= major sub7th ||= Ms7 ||= 982, 1113 ||= C || | ||
||= 19 ||= aug sub7th ||= As7 ||= 1036 ||= C# || | ||= 19 ||= aug sub7th ||= As7 ||= 1036, 1245 ||= C# || | ||
||= 20 ||= double-aug sub7th or | ||= 20 ||= double-aug sub7th or | ||
double-dim octoid ||= AAs7 or dd8d ||= 1091 ||= Cx or Dbb || | double-dim octoid ||= AAs7 or dd8d ||= 1091, 1309 ||= Cx or Dbb || | ||
||= 21 ||= dim octoid ||= d8d ||= 1145 ||= Db || | ||= 21 ||= dim octoid ||= d8d ||= 1145.5, 1374.5 ||= Db || | ||
||= 22 ||= octave ||= P8 ||= 1200 ||= D || | ||= 22 ||= octave ||= P8 ||= 1200, 1440 ||= D || | ||
==Selected just intervals by error== | ==Selected just intervals by error== | ||
The following table shows how [[Just-24|some prominent just intervals]] are represented in 22edo (ordered by absolute error). | The following table shows how [[Just-24|some prominent just intervals]] are represented in 22edo (ordered by absolute error). | ||
| Line 216: | Line 215: | ||
||= 3125/3072 ||< | -10 -1 5 > ||> 29.61 ||= Small Diesis ||= Magic Comma ||= || | ||= 3125/3072 ||< | -10 -1 5 > ||> 29.61 ||= Small Diesis ||= Magic Comma ||= || | ||
||= 2048/2025 ||< | 11 -4 -2 > ||> 19.55 ||= Diaschisma ||= ||= || | ||= 2048/2025 ||< | 11 -4 -2 > ||> 19.55 ||= Diaschisma ||= ||= || | ||
||= | ||= ||< | -21 3 7 > ||> 10.06 ||= Semicomma ||= Fokker Comma ||= || | ||
||= | ||= ||< | 32 -7 -9 > ||> 9.49 ||= Escapade Comma || ||= || | ||
||= | ||= ||< | -53 10 16 > ||> 0.57 ||= Kwazy ||= ||= || | ||
||= 50/49 ||< | 1 0 2 -2 > ||> 34.98 ||= Tritonic Diesis ||= Jubilisma ||= || | ||= 50/49 ||< | 1 0 2 -2 > ||> 34.98 ||= Tritonic Diesis ||= Jubilisma ||= || | ||
||= 64/63 ||< | 6 -2 0 -1 > ||> 27.26 ||= Septimal Comma ||= Archytas' Comma ||= Leipziger Komma || | ||= 64/63 ||< | 6 -2 0 -1 > ||> 27.26 ||= Septimal Comma ||= Archytas' Comma ||= Leipziger Komma || | ||
| Line 229: | Line 228: | ||
||= 6144/6125 ||< | 11 1 -3 -2 > ||> 5.36 ||= Porwell ||= ||= || | ||= 6144/6125 ||< | 11 1 -3 -2 > ||> 5.36 ||= Porwell ||= ||= || | ||
||= 65625/65536 ||< | -16 1 5 1 > ||> 2.35 ||= Horwell ||= ||= || | ||= 65625/65536 ||< | -16 1 5 1 > ||> 2.35 ||= Horwell ||= ||= || | ||
||= | ||= ||< | -6 -8 2 5 > ||> 1.12 ||= Wizma ||= ||= || | ||
||= 99/98 ||< | -1 2 0 -2 1 > ||> 17.58 ||= Mothwellsma ||= ||= || | ||= 99/98 ||< | -1 2 0 -2 1 > ||> 17.58 ||= Mothwellsma ||= ||= || | ||
||= 100/99 ||< | 2 -2 2 0 -1 > ||> 17.40 ||= Ptolemisma ||= ||= || | ||= 100/99 ||< | 2 -2 2 0 -1 > ||> 17.40 ||= Ptolemisma ||= ||= || | ||
| Line 325: | Line 324: | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>22edo</title></head><body><span style="display: block; text-align: right;"><a class="wiki_link" href="http://xenharmonie.wikispaces.com/22edo">Deutsch</a> - <a class="wiki_link" href="/22%E5%B9%B3%E5%9D%87%E5%BE%8B">日本語</a><br /> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>22edo</title></head><body><span style="display: block; text-align: right;"><a class="wiki_link" href="http://xenharmonie.wikispaces.com/22edo">Deutsch</a> - <a class="wiki_link" href="/22%E5%B9%B3%E5%9D%87%E5%BE%8B">日本語</a><br /> | ||
</span><br /> | </span><br /> | ||
<!-- ws:start:WikiTextTocRule: | <!-- ws:start:WikiTextTocRule:34:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --><div style="margin-left: 1em;"><a href="#Theory">Theory</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><div style="margin-left: 2em;"><a href="#Theory-Intervalic Naming Systems">Intervalic Naming Systems</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><div style="margin-left: 2em;"><a href="#Theory-Intervals by degree (Superpyth/Porcupine)">Intervals by degree (Superpyth/Porcupine)</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><div style="margin-left: 2em;"><a href="#Theory-Intervals by degree (ups and downs)">Intervals by degree (ups and downs)</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><div style="margin-left: 2em;"><a href="#Theory-Intervals by degree (Porcupine)">Intervals by degree (Porcupine)</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --><div style="margin-left: 2em;"><a href="#Theory-Intervals by degree (pentatonic)">Intervals by degree (pentatonic)</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><div style="margin-left: 2em;"><a href="#Theory-Selected just intervals by error">Selected just intervals by error</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --><div style="margin-left: 2em;"><a href="#Theory-Properties of 22 equal temperament">Properties of 22 equal temperament</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><div style="margin-left: 3em;"><a href="#Theory-Properties of 22 equal temperament-Rank Two Temperaments">Rank Two Temperaments</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --><div style="margin-left: 3em;"><a href="#Theory-Properties of 22 equal temperament-Commas">Commas</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --><div style="margin-left: 3em;"><a href="#Theory-Properties of 22 equal temperament-How to Notate 22edo in Sagittal">How to Notate 22edo in Sagittal</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --><div style="margin-left: 1em;"><a href="#The Decatonic System">The Decatonic System</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --><div style="margin-left: 2em;"><a href="#The Decatonic System-Decatonic Alphabet">Decatonic Alphabet</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --><div style="margin-left: 2em;"><a href="#The Decatonic System-External links">External links</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --><div style="margin-left: 2em;"><a href="#The Decatonic System-References">References</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --><div style="margin-left: 1em;"><a href="#Music">Music</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --></div> | ||
<!-- ws:end:WikiTextTocRule:51 --><hr /> | |||
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<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc0"><a name="Theory"></a><!-- ws:end:WikiTextHeadingRule:2 -->Theory</h1> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc0"><a name="Theory"></a><!-- ws:end:WikiTextHeadingRule:2 -->Theory</h1> | ||
<br /> | <br /> | ||
| Line 368: | Line 366: | ||
<td>Name and Abbreviation<br /> | <td>Name and Abbreviation<br /> | ||
</td> | </td> | ||
<td>Cents<br /> | <td>Cents coarse/fine<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Approximate<br /> | <td style="text-align: center;">Approximate<br /> | ||
| Line 389: | Line 387: | ||
<td>s-minor second, sm2<br /> | <td>s-minor second, sm2<br /> | ||
</td> | </td> | ||
<td>54. | <td>54.545, 65.455<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">33/32, 34/33, 32/31<br /> | <td style="text-align: center;">33/32, 34/33, 32/31<br /> | ||
| Line 399: | Line 397: | ||
<td>p-diminished second, pd2<br /> | <td>p-diminished second, pd2<br /> | ||
</td> | </td> | ||
<td>109.09<br /> | <td>109.09, 130.90<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">18/17, 17/16, 16/15, 15/14<br /> | <td style="text-align: center;">18/17, 17/16, 16/15, 15/14<br /> | ||
| Line 409: | Line 407: | ||
<td>p-minor second, pm2<br /> | <td>p-minor second, pm2<br /> | ||
</td> | </td> | ||
<td>163.64<br /> | <td>163.64, 196.36<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">11/10, 10/9, 32/29<br /> | <td style="text-align: center;">11/10, 10/9, 32/29<br /> | ||
| Line 419: | Line 417: | ||
<td>(s/p) Major second, M2<br /> | <td>(s/p) Major second, M2<br /> | ||
</td> | </td> | ||
<td>218.18<br /> | <td>218.18, 261.82<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">9/8, 8/7, 17/15<br /> | <td style="text-align: center;">9/8, 8/7, 17/15<br /> | ||
| Line 429: | Line 427: | ||
<td>s-minor third, sm3<br /> | <td>s-minor third, sm3<br /> | ||
</td> | </td> | ||
<td>272.73<br /> | <td>272.73, 327.27<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/7_6">7/6</a>, <a class="wiki_link" href="/20_17">20/17</a><br /> | <td style="text-align: center;"><a class="wiki_link" href="/7_6">7/6</a>, <a class="wiki_link" href="/20_17">20/17</a><br /> | ||
| Line 439: | Line 437: | ||
<td>p-minor third, pm3<br /> | <td>p-minor third, pm3<br /> | ||
</td> | </td> | ||
<td>327.27<br /> | <td>327.27, 392.73<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">6/5, 17/14, 11/9, 29/24<br /> | <td style="text-align: center;">6/5, 17/14, 11/9, 29/24<br /> | ||
| Line 449: | Line 447: | ||
<td>p-Major third, pM3<br /> | <td>p-Major third, pM3<br /> | ||
</td> | </td> | ||
<td>381.82<br /> | <td>381.82, 459.18<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">5/4<br /> | <td style="text-align: center;">5/4<br /> | ||
| Line 459: | Line 457: | ||
<td>s-Major third, sM3<br /> | <td>s-Major third, sM3<br /> | ||
</td> | </td> | ||
<td>436.36<br /> | <td>436.36, 524.64<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">9/7, 14/11, 22/17<br /> | <td style="text-align: center;">9/7, 14/11, 22/17<br /> | ||
| Line 469: | Line 467: | ||
<td>Natural Fourth, 4, N4<br /> | <td>Natural Fourth, 4, N4<br /> | ||
</td> | </td> | ||
<td>490.91<br /> | <td>490.91, 589.09<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">4/3<br /> | <td style="text-align: center;">4/3<br /> | ||
| Line 480: | Line 478: | ||
s-dim fifth<br /> | s-dim fifth<br /> | ||
</td> | </td> | ||
<td>545. | <td>545.455, 654.545<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">11/8, 15/11<br /> | <td style="text-align: center;">11/8, 15/11<br /> | ||
| Line 491: | Line 489: | ||
Half-Octave, HO<br /> | Half-Octave, HO<br /> | ||
</td> | </td> | ||
<td>600<br /> | <td>600, 720<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">7/5, 10/7, 17/12, 24/17<br /> | <td style="text-align: center;">7/5, 10/7, 17/12, 24/17<br /> | ||
| Line 502: | Line 500: | ||
s-aug fourth<br /> | s-aug fourth<br /> | ||
</td> | </td> | ||
<td>654. | <td>654.545, 785.455<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">16/11, 22/15<br /> | <td style="text-align: center;">16/11, 22/15<br /> | ||
| Line 512: | Line 510: | ||
<td>Natural Fifth, 5, N5<br /> | <td>Natural Fifth, 5, N5<br /> | ||
</td> | </td> | ||
<td>709.09<br /> | <td>709.09, 850.90<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">3/2<br /> | <td style="text-align: center;">3/2<br /> | ||
| Line 522: | Line 520: | ||
<td>s-minor sixth, sm6<br /> | <td>s-minor sixth, sm6<br /> | ||
</td> | </td> | ||
<td>763.64<br /> | <td>763.64, 916.36<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">11/7, 14/9, 17/11<br /> | <td style="text-align: center;">11/7, 14/9, 17/11<br /> | ||
| Line 532: | Line 530: | ||
<td>p-minor sixth, pm6<br /> | <td>p-minor sixth, pm6<br /> | ||
</td> | </td> | ||
<td>818.18<br /> | <td>818.18, 981.82<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">8/5<br /> | <td style="text-align: center;">8/5<br /> | ||
| Line 542: | Line 540: | ||
<td>p-Major sixth, pM6<br /> | <td>p-Major sixth, pM6<br /> | ||
</td> | </td> | ||
<td>872.73<br /> | <td>872.73, 1047.27<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">5/3, 18/11, 28/17<br /> | <td style="text-align: center;">5/3, 18/11, 28/17<br /> | ||
| Line 552: | Line 550: | ||
<td>s-Major sixth, sM6<br /> | <td>s-Major sixth, sM6<br /> | ||
</td> | </td> | ||
<td>927.27<br /> | <td>927.27, 1112.73<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/12_7">12/7</a>, <a class="wiki_link" href="/17_10">17/10</a><br /> | <td style="text-align: center;"><a class="wiki_link" href="/12_7">12/7</a>, <a class="wiki_link" href="/17_10">17/10</a><br /> | ||
| Line 562: | Line 560: | ||
<td>(s/p) minor seventh, m7<br /> | <td>(s/p) minor seventh, m7<br /> | ||
</td> | </td> | ||
<td>981.82<br /> | <td>981.82, 1179.18<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">7/4, 16/9, 30/17<br /> | <td style="text-align: center;">7/4, 16/9, 30/17<br /> | ||
| Line 572: | Line 570: | ||
<td>p-Major seventh, pM7<br /> | <td>p-Major seventh, pM7<br /> | ||
</td> | </td> | ||
<td>1036.36<br /> | <td>1036.36, 1244.64<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">20/11, 9/5, 29/16<br /> | <td style="text-align: center;">20/11, 9/5, 29/16<br /> | ||
| Line 582: | Line 580: | ||
<td>p-Augmented Seventh<br /> | <td>p-Augmented Seventh<br /> | ||
</td> | </td> | ||
<td>1090.91<br /> | <td>1090.91, 1309.09<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">15/8, 32/17, 17/9, 28/15<br /> | <td style="text-align: center;">15/8, 32/17, 17/9, 28/15<br /> | ||
| Line 592: | Line 590: | ||
<td>s-Major Seventh, sM7<br /> | <td>s-Major Seventh, sM7<br /> | ||
</td> | </td> | ||
<td>1145. | <td>1145.455, 1374.545<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">33/17, 64/33, 31/16<br /> | <td style="text-align: center;">33/17, 64/33, 31/16<br /> | ||
| Line 602: | Line 600: | ||
<td>Octave, 8<br /> | <td>Octave, 8<br /> | ||
</td> | </td> | ||
<td>1200<br /> | <td>1200, 1440<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">2/1<br /> | <td style="text-align: center;">2/1<br /> | ||
| Line 622: | Line 620: | ||
<td style="text-align: center;">Abbreviation<br /> | <td style="text-align: center;">Abbreviation<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Cents<br /> | <td style="text-align: center;">Cents coarse/fine<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Example<br /> | <td style="text-align: center;">Example<br /> | ||
| Line 646: | Line 644: | ||
<td style="text-align: center;">m2<br /> | <td style="text-align: center;">m2<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">54.5, 65.5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Db<br /> | <td style="text-align: center;">Db<br /> | ||
| Line 658: | Line 656: | ||
<td style="text-align: center;">^m2<br /> | <td style="text-align: center;">^m2<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">109<br /> | <td style="text-align: center;">109, 131<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Db^<br /> | <td style="text-align: center;">Db^<br /> | ||
| Line 670: | Line 668: | ||
<td style="text-align: center;">vM2<br /> | <td style="text-align: center;">vM2<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">164<br /> | <td style="text-align: center;">164, 196<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Dv<br /> | <td style="text-align: center;">Dv<br /> | ||
| Line 682: | Line 680: | ||
<td style="text-align: center;">M2<br /> | <td style="text-align: center;">M2<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">218<br /> | <td style="text-align: center;">218, 262<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">D<br /> | <td style="text-align: center;">D<br /> | ||
| Line 694: | Line 692: | ||
<td style="text-align: center;">m3<br /> | <td style="text-align: center;">m3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">273<br /> | <td style="text-align: center;">273, 327<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Eb<br /> | <td style="text-align: center;">Eb<br /> | ||
| Line 706: | Line 704: | ||
<td style="text-align: center;">^m3<br /> | <td style="text-align: center;">^m3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">327<br /> | <td style="text-align: center;">327, 393<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Eb^<br /> | <td style="text-align: center;">Eb^<br /> | ||
| Line 718: | Line 716: | ||
<td style="text-align: center;">vM3<br /> | <td style="text-align: center;">vM3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">382<br /> | <td style="text-align: center;">382, 459<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Ev<br /> | <td style="text-align: center;">Ev<br /> | ||
| Line 730: | Line 728: | ||
<td style="text-align: center;">M3<br /> | <td style="text-align: center;">M3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">436<br /> | <td style="text-align: center;">436, 525<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">E<br /> | <td style="text-align: center;">E<br /> | ||
| Line 742: | Line 740: | ||
<td style="text-align: center;">P4<br /> | <td style="text-align: center;">P4<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">491<br /> | <td style="text-align: center;">491, 589<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">F<br /> | <td style="text-align: center;">F<br /> | ||
| Line 754: | Line 752: | ||
<td style="text-align: center;">^4 or d5<br /> | <td style="text-align: center;">^4 or d5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">545<br /> | <td style="text-align: center;">545.5, 654.5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">F^ or Gb<br /> | <td style="text-align: center;">F^ or Gb<br /> | ||
| Line 766: | Line 764: | ||
<td style="text-align: center;">vA4 or ^d5<br /> | <td style="text-align: center;">vA4 or ^d5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">600<br /> | <td style="text-align: center;">600, 720<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">F#v or Gb^<br /> | <td style="text-align: center;">F#v or Gb^<br /> | ||
| Line 778: | Line 776: | ||
<td style="text-align: center;">A4 or v5<br /> | <td style="text-align: center;">A4 or v5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">654.5, 785.5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">F# or Gv<br /> | <td style="text-align: center;">F# or Gv<br /> | ||
| Line 790: | Line 788: | ||
<td style="text-align: center;">P5<br /> | <td style="text-align: center;">P5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">709<br /> | <td style="text-align: center;">709, 851<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">G<br /> | <td style="text-align: center;">G<br /> | ||
| Line 802: | Line 800: | ||
<td style="text-align: center;">m6<br /> | <td style="text-align: center;">m6<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">764<br /> | <td style="text-align: center;">764, 916<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Ab<br /> | <td style="text-align: center;">Ab<br /> | ||
| Line 814: | Line 812: | ||
<td style="text-align: center;">^m6<br /> | <td style="text-align: center;">^m6<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">818<br /> | <td style="text-align: center;">818, 982<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Ab^<br /> | <td style="text-align: center;">Ab^<br /> | ||
| Line 826: | Line 824: | ||
<td style="text-align: center;">vM6<br /> | <td style="text-align: center;">vM6<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">873<br /> | <td style="text-align: center;">873, 1047<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Av<br /> | <td style="text-align: center;">Av<br /> | ||
| Line 838: | Line 836: | ||
<td style="text-align: center;">M6<br /> | <td style="text-align: center;">M6<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">927<br /> | <td style="text-align: center;">927, 1113<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">A<br /> | <td style="text-align: center;">A<br /> | ||
| Line 850: | Line 848: | ||
<td style="text-align: center;">m7<br /> | <td style="text-align: center;">m7<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">982<br /> | <td style="text-align: center;">982, 1179<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Bb<br /> | <td style="text-align: center;">Bb<br /> | ||
| Line 862: | Line 860: | ||
<td style="text-align: center;">^m7<br /> | <td style="text-align: center;">^m7<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">1036<br /> | <td style="text-align: center;">1036, 1245<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Bb^<br /> | <td style="text-align: center;">Bb^<br /> | ||
| Line 874: | Line 872: | ||
<td style="text-align: center;">vM7<br /> | <td style="text-align: center;">vM7<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">1091<br /> | <td style="text-align: center;">1091, 1309<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Bv<br /> | <td style="text-align: center;">Bv<br /> | ||
| Line 886: | Line 884: | ||
<td style="text-align: center;">M7<br /> | <td style="text-align: center;">M7<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">1145<br /> | <td style="text-align: center;">1145.5, 1374.5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">B<br /> | <td style="text-align: center;">B<br /> | ||
| Line 898: | Line 896: | ||
<td style="text-align: center;">P8<br /> | <td style="text-align: center;">P8<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">1200<br /> | <td style="text-align: center;">1200, 1440<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">C<br /> | <td style="text-align: center;">C<br /> | ||
| Line 918: | Line 916: | ||
<td style="text-align: center;">Abbreviation<br /> | <td style="text-align: center;">Abbreviation<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Cents<br /> | <td style="text-align: center;">Cents coarse/fine<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Example<br /> | <td style="text-align: center;">Example<br /> | ||
| Line 942: | Line 940: | ||
<td style="text-align: center;">A1<br /> | <td style="text-align: center;">A1<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">54.5, 65.5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">D#<br /> | <td style="text-align: center;">D#<br /> | ||
| Line 954: | Line 952: | ||
<td style="text-align: center;">d2<br /> | <td style="text-align: center;">d2<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">109<br /> | <td style="text-align: center;">109, 131<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Eb<br /> | <td style="text-align: center;">Eb<br /> | ||
| Line 966: | Line 964: | ||
<td style="text-align: center;">P2<br /> | <td style="text-align: center;">P2<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">164<br /> | <td style="text-align: center;">164, 196<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">E<br /> | <td style="text-align: center;">E<br /> | ||
| Line 978: | Line 976: | ||
<td style="text-align: center;">A2<br /> | <td style="text-align: center;">A2<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">218<br /> | <td style="text-align: center;">218, 262<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">E#<br /> | <td style="text-align: center;">E#<br /> | ||
| Line 990: | Line 988: | ||
<td style="text-align: center;">d3<br /> | <td style="text-align: center;">d3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">273<br /> | <td style="text-align: center;">273, 327<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Fb<br /> | <td style="text-align: center;">Fb<br /> | ||
| Line 1,002: | Line 1,000: | ||
<td style="text-align: center;">m3<br /> | <td style="text-align: center;">m3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">327<br /> | <td style="text-align: center;">327, 393<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">F<br /> | <td style="text-align: center;">F<br /> | ||
| Line 1,014: | Line 1,012: | ||
<td style="text-align: center;">M3<br /> | <td style="text-align: center;">M3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">382<br /> | <td style="text-align: center;">382, 459<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">F#<br /> | <td style="text-align: center;">F#<br /> | ||
| Line 1,026: | Line 1,024: | ||
<td style="text-align: center;">A3 or d4<br /> | <td style="text-align: center;">A3 or d4<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">436<br /> | <td style="text-align: center;">436, 525<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Gb<br /> | <td style="text-align: center;">Gb<br /> | ||
| Line 1,038: | Line 1,036: | ||
<td style="text-align: center;">m4<br /> | <td style="text-align: center;">m4<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">491<br /> | <td style="text-align: center;">491, 589<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">G<br /> | <td style="text-align: center;">G<br /> | ||
| Line 1,050: | Line 1,048: | ||
<td style="text-align: center;">M4<br /> | <td style="text-align: center;">M4<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">545<br /> | <td style="text-align: center;">545.5, 654.5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">G#<br /> | <td style="text-align: center;">G#<br /> | ||
| Line 1,062: | Line 1,060: | ||
<td style="text-align: center;">A4 or d5<br /> | <td style="text-align: center;">A4 or d5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">600<br /> | <td style="text-align: center;">600, 720<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Gx or Abb<br /> | <td style="text-align: center;">Gx or Abb<br /> | ||
| Line 1,074: | Line 1,072: | ||
<td style="text-align: center;">m5<br /> | <td style="text-align: center;">m5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">654.5, 785.5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Ab<br /> | <td style="text-align: center;">Ab<br /> | ||
| Line 1,086: | Line 1,084: | ||
<td style="text-align: center;">M5<br /> | <td style="text-align: center;">M5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">709<br /> | <td style="text-align: center;">709, 851<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">A<br /> | <td style="text-align: center;">A<br /> | ||
| Line 1,098: | Line 1,096: | ||
<td style="text-align: center;">A5 or d6<br /> | <td style="text-align: center;">A5 or d6<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">764<br /> | <td style="text-align: center;">764, 916<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">A#<br /> | <td style="text-align: center;">A#<br /> | ||
| Line 1,110: | Line 1,108: | ||
<td style="text-align: center;">m6<br /> | <td style="text-align: center;">m6<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">818<br /> | <td style="text-align: center;">818, 982<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Bb<br /> | <td style="text-align: center;">Bb<br /> | ||
| Line 1,122: | Line 1,120: | ||
<td style="text-align: center;">M6<br /> | <td style="text-align: center;">M6<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">873<br /> | <td style="text-align: center;">873, 1047<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">B<br /> | <td style="text-align: center;">B<br /> | ||
| Line 1,134: | Line 1,132: | ||
<td style="text-align: center;">A6<br /> | <td style="text-align: center;">A6<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">927<br /> | <td style="text-align: center;">927, 1113<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">B#<br /> | <td style="text-align: center;">B#<br /> | ||
| Line 1,146: | Line 1,144: | ||
<td style="text-align: center;">d7<br /> | <td style="text-align: center;">d7<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">982<br /> | <td style="text-align: center;">982, 1179<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Cb<br /> | <td style="text-align: center;">Cb<br /> | ||
| Line 1,158: | Line 1,156: | ||
<td style="text-align: center;">P7<br /> | <td style="text-align: center;">P7<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">1036<br /> | <td style="text-align: center;">1036, 1245<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">C<br /> | <td style="text-align: center;">C<br /> | ||
| Line 1,170: | Line 1,168: | ||
<td style="text-align: center;">A7<br /> | <td style="text-align: center;">A7<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">1091<br /> | <td style="text-align: center;">1091, 1309<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">C#<br /> | <td style="text-align: center;">C#<br /> | ||
| Line 1,182: | Line 1,180: | ||
<td style="text-align: center;">d8<br /> | <td style="text-align: center;">d8<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">1145<br /> | <td style="text-align: center;">1145.5, 1374.5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Db<br /> | <td style="text-align: center;">Db<br /> | ||
| Line 1,194: | Line 1,192: | ||
<td style="text-align: center;">P8<br /> | <td style="text-align: center;">P8<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">1200<br /> | <td style="text-align: center;">1200, 1440<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">D<br /> | <td style="text-align: center;">D<br /> | ||
| Line 1,213: | Line 1,211: | ||
<td style="text-align: center;">Abbreviation<br /> | <td style="text-align: center;">Abbreviation<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Cents<br /> | <td style="text-align: center;">Cents coarse/fine<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Example<br /> | <td style="text-align: center;">Example<br /> | ||
| Line 1,237: | Line 1,235: | ||
<td style="text-align: center;">A1<br /> | <td style="text-align: center;">A1<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">54.5, 65.5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">D#<br /> | <td style="text-align: center;">D#<br /> | ||
| Line 1,250: | Line 1,248: | ||
<td style="text-align: center;">AA1 or dds3<br /> | <td style="text-align: center;">AA1 or dds3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">109<br /> | <td style="text-align: center;">109, 131<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Dx or Ebb<br /> | <td style="text-align: center;">Dx or Ebb<br /> | ||
| Line 1,262: | Line 1,260: | ||
<td style="text-align: center;">ds3<br /> | <td style="text-align: center;">ds3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">164<br /> | <td style="text-align: center;">164, 196<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Eb<br /> | <td style="text-align: center;">Eb<br /> | ||
| Line 1,274: | Line 1,272: | ||
<td style="text-align: center;">ms3<br /> | <td style="text-align: center;">ms3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">218<br /> | <td style="text-align: center;">218, 262<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">E<br /> | <td style="text-align: center;">E<br /> | ||
| Line 1,286: | Line 1,284: | ||
<td style="text-align: center;">Ms3<br /> | <td style="text-align: center;">Ms3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">273<br /> | <td style="text-align: center;">273, 327<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">E#<br /> | <td style="text-align: center;">E#<br /> | ||
| Line 1,298: | Line 1,296: | ||
<td style="text-align: center;">As3<br /> | <td style="text-align: center;">As3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">327<br /> | <td style="text-align: center;">327, 393<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Ex<br /> | <td style="text-align: center;">Ex<br /> | ||
| Line 1,311: | Line 1,309: | ||
<td style="text-align: center;">AAs3 or dd4d<br /> | <td style="text-align: center;">AAs3 or dd4d<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">382<br /> | <td style="text-align: center;">382, 459<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Gbb<br /> | <td style="text-align: center;">Gbb<br /> | ||
| Line 1,323: | Line 1,321: | ||
<td style="text-align: center;">d4d<br /> | <td style="text-align: center;">d4d<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">436<br /> | <td style="text-align: center;">436, 525<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Gb<br /> | <td style="text-align: center;">Gb<br /> | ||
| Line 1,335: | Line 1,333: | ||
<td style="text-align: center;">P4d<br /> | <td style="text-align: center;">P4d<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">491<br /> | <td style="text-align: center;">491, 589<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">G<br /> | <td style="text-align: center;">G<br /> | ||
| Line 1,347: | Line 1,345: | ||
<td style="text-align: center;">A4d<br /> | <td style="text-align: center;">A4d<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">545<br /> | <td style="text-align: center;">545.5, 654.5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">G#<br /> | <td style="text-align: center;">G#<br /> | ||
| Line 1,360: | Line 1,358: | ||
<td style="text-align: center;">AA4d or dd5d<br /> | <td style="text-align: center;">AA4d or dd5d<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">600<br /> | <td style="text-align: center;">600, 720<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Gx or Abb<br /> | <td style="text-align: center;">Gx or Abb<br /> | ||
| Line 1,372: | Line 1,370: | ||
<td style="text-align: center;">d5d<br /> | <td style="text-align: center;">d5d<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">654.5, 785.5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Ab<br /> | <td style="text-align: center;">Ab<br /> | ||
| Line 1,384: | Line 1,382: | ||
<td style="text-align: center;">P5d<br /> | <td style="text-align: center;">P5d<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">709<br /> | <td style="text-align: center;">709, 851<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">A<br /> | <td style="text-align: center;">A<br /> | ||
| Line 1,396: | Line 1,394: | ||
<td style="text-align: center;">A5d<br /> | <td style="text-align: center;">A5d<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">764<br /> | <td style="text-align: center;">764, 916<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">A#<br /> | <td style="text-align: center;">A#<br /> | ||
| Line 1,409: | Line 1,407: | ||
<td style="text-align: center;">AA5d or dds7<br /> | <td style="text-align: center;">AA5d or dds7<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">818<br /> | <td style="text-align: center;">818, 982<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Ax<br /> | <td style="text-align: center;">Ax<br /> | ||
| Line 1,421: | Line 1,419: | ||
<td style="text-align: center;">ds7<br /> | <td style="text-align: center;">ds7<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">873<br /> | <td style="text-align: center;">873, 1047<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Cbb<br /> | <td style="text-align: center;">Cbb<br /> | ||
| Line 1,433: | Line 1,431: | ||
<td style="text-align: center;">ms7<br /> | <td style="text-align: center;">ms7<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">927<br /> | <td style="text-align: center;">927, 1047<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Cb<br /> | <td style="text-align: center;">Cb<br /> | ||
| Line 1,445: | Line 1,443: | ||
<td style="text-align: center;">Ms7<br /> | <td style="text-align: center;">Ms7<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">982<br /> | <td style="text-align: center;">982, 1113<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">C<br /> | <td style="text-align: center;">C<br /> | ||
| Line 1,457: | Line 1,455: | ||
<td style="text-align: center;">As7<br /> | <td style="text-align: center;">As7<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">1036<br /> | <td style="text-align: center;">1036, 1245<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">C#<br /> | <td style="text-align: center;">C#<br /> | ||
| Line 1,470: | Line 1,468: | ||
<td style="text-align: center;">AAs7 or dd8d<br /> | <td style="text-align: center;">AAs7 or dd8d<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">1091<br /> | <td style="text-align: center;">1091, 1309<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Cx or Dbb<br /> | <td style="text-align: center;">Cx or Dbb<br /> | ||
| Line 1,482: | Line 1,480: | ||
<td style="text-align: center;">d8d<br /> | <td style="text-align: center;">d8d<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">1145<br /> | <td style="text-align: center;">1145.5, 1374.5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Db<br /> | <td style="text-align: center;">Db<br /> | ||
| Line 1,494: | Line 1,492: | ||
<td style="text-align: center;">P8<br /> | <td style="text-align: center;">P8<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">1200<br /> | <td style="text-align: center;">1200, 1440<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">D<br /> | <td style="text-align: center;">D<br /> | ||
| Line 1,502: | Line 1,500: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc6 | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc6"><a name="Theory-Selected just intervals by error"></a><!-- ws:end:WikiTextHeadingRule:14 -->Selected just intervals by error</h2> | ||
The following table shows how <a class="wiki_link" href="/Just-24">some prominent just intervals</a> are represented in 22edo (ordered by absolute error).<br /> | The following table shows how <a class="wiki_link" href="/Just-24">some prominent just intervals</a> are represented in 22edo (ordered by absolute error).<br /> | ||
| Line 1,663: | Line 1,660: | ||
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See also: <a class="wiki_link" href="/22edo%20Solfege">22edo Solfege</a>, <a class="wiki_link" href="/22edo%20Tetrachords">22edo Tetrachords</a>, <a class="wiki_link" href="/22%20EDO%20Chords">22 EDO Chords</a>, <a class="wiki_link" href="/22edo%20Modes">22edo Modes</a><br /> | See also: <a class="wiki_link" href="/22edo%20Solfege">22edo Solfege</a>, <a class="wiki_link" href="/22edo%20Tetrachords">22edo Tetrachords</a>, <a class="wiki_link" href="/22%20EDO%20Chords">22 EDO Chords</a>, <a class="wiki_link" href="/22edo%20Modes">22edo Modes</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc7"><a name="Theory-Properties of 22 equal temperament"></a><!-- ws:end:WikiTextHeadingRule:16 -->Properties of 22 equal temperament</h2> | ||
<br /> | <br /> | ||
Possibly the most striking characteristic of 22-et to those not used to it is that it does <strong>not</strong> &quot;temper out&quot; the syntonic comma of 81/80, and therefore is not a system of <a class="wiki_link" href="/Regular%20Temperaments#meantone">meantone</a> temperament. This means that 22 distinguishes a number of Pythagorean and 5-limit intervals that 12-EDO, 19-EDO, 31-EDO, ... do not distinguish, such as the two whole tones 9/8 and 10/9. Indeed, these distinctions are exaggerated in comparison to 5-limit JI and many more accurate temperaments such as <a class="wiki_link" href="/34edo">34edo</a>, <a class="wiki_link" href="/41edo">41edo</a> and <a class="wiki_link" href="/53edo">53edo</a>.<br /> | Possibly the most striking characteristic of 22-et to those not used to it is that it does <strong>not</strong> &quot;temper out&quot; the syntonic comma of 81/80, and therefore is not a system of <a class="wiki_link" href="/Regular%20Temperaments#meantone">meantone</a> temperament. This means that 22 distinguishes a number of Pythagorean and 5-limit intervals that 12-EDO, 19-EDO, 31-EDO, ... do not distinguish, such as the two whole tones 9/8 and 10/9. Indeed, these distinctions are exaggerated in comparison to 5-limit JI and many more accurate temperaments such as <a class="wiki_link" href="/34edo">34edo</a>, <a class="wiki_link" href="/41edo">41edo</a> and <a class="wiki_link" href="/53edo">53edo</a>.<br /> | ||
| Line 1,685: | Line 1,682: | ||
As 22 is divisible by 11, a 22edo instrument can play any music in <a class="wiki_link" href="/11edo">11edo</a>, in the same way that 12edo can play 6edo (the whole tone scale). 11-equal is interesting for sounding melodically very similar to 12-equal (whole steps, half steps and minor thirds in the familiar 1:2:3 ratio), but harmonically very different, in particular because it lacks perfect fifths/fourths and 5-limit major thirds/minor sixths. Similarly, 22edo is melodically similar to 24edo as both contain quarter-tones and minor, neutral, and major seconds; but 22edo offers much better all-around harmonies than 24. In <a class="wiki_link" href="/Sagittal">Sagittal</a>, 11 can be notated as every other note of 22.<br /> | As 22 is divisible by 11, a 22edo instrument can play any music in <a class="wiki_link" href="/11edo">11edo</a>, in the same way that 12edo can play 6edo (the whole tone scale). 11-equal is interesting for sounding melodically very similar to 12-equal (whole steps, half steps and minor thirds in the familiar 1:2:3 ratio), but harmonically very different, in particular because it lacks perfect fifths/fourths and 5-limit major thirds/minor sixths. Similarly, 22edo is melodically similar to 24edo as both contain quarter-tones and minor, neutral, and major seconds; but 22edo offers much better all-around harmonies than 24. In <a class="wiki_link" href="/Sagittal">Sagittal</a>, 11 can be notated as every other note of 22.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h3&gt; --><h3 id="toc8"><a name="Theory-Properties of 22 equal temperament-Rank Two Temperaments"></a><!-- ws:end:WikiTextHeadingRule:18 -->Rank Two Temperaments</h3> | ||
<a class="wiki_link" href="/List%20of%2022et%20rank%20two%20temperaments%20by%20badness">List of 22et rank two temperaments by badness</a><br /> | <a class="wiki_link" href="/List%20of%2022et%20rank%20two%20temperaments%20by%20badness">List of 22et rank two temperaments by badness</a><br /> | ||
<a class="wiki_link" href="/List%20of%2022et%20rank%20two%20temperaments%20by%20complexity">List of 22et rank two temperaments by complexity</a><br /> | <a class="wiki_link" href="/List%20of%2022et%20rank%20two%20temperaments%20by%20complexity">List of 22et rank two temperaments by complexity</a><br /> | ||
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</table> | </table> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h3&gt; --><h3 id="toc9"><a name="Theory-Properties of 22 equal temperament-Commas"></a><!-- ws:end:WikiTextHeadingRule:20 -->Commas</h3> | ||
22 EDO tempers out the following commas. (Note: This assumes the val &lt; <a class="wiki_link" href="http://tel.wikispaces.com/22%2035%2051%2062%2076%2081">22 35 51 62 76 81</a> |.)<br /> | 22 EDO tempers out the following commas. (Note: This assumes the val &lt; <a class="wiki_link" href="http://tel.wikispaces.com/22%2035%2051%2062%2076%2081">22 35 51 62 76 81</a> |.)<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">| -21 3 7 &gt;<br /> | <td style="text-align: left;">| -21 3 7 &gt;<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">| 32 -7 -9 &gt;<br /> | <td style="text-align: left;">| 32 -7 -9 &gt;<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">| -53 10 16 &gt;<br /> | <td style="text-align: left;">| -53 10 16 &gt;<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">| -6 -8 2 5 &gt;<br /> | <td style="text-align: left;">| -6 -8 2 5 &gt;<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h3&gt; --><h3 id="toc10"><a name="Theory-Properties of 22 equal temperament-How to Notate 22edo in Sagittal"></a><!-- ws:end:WikiTextHeadingRule:22 -->How to Notate 22edo in Sagittal</h3> | ||
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When 22edo is treated as generated by a cycle of its fifths, the naturals F C G D A E B represent a chain of those 13\22 fifths; consequently, the whole tone comes out to four degrees and the apotome (pythagorean sharp/flat) comes out to three degrees. Three pairs of sagittal symbols, dividing that apotome into three parts, are all that is necessary, and offer plenty of enharmonic equivalents:<br /> | When 22edo is treated as generated by a cycle of its fifths, the naturals F C G D A E B represent a chain of those 13\22 fifths; consequently, the whole tone comes out to four degrees and the apotome (pythagorean sharp/flat) comes out to three degrees. Three pairs of sagittal symbols, dividing that apotome into three parts, are all that is necessary, and offer plenty of enharmonic equivalents:<br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:1931:&lt;img src=&quot;/file/view/22edo.png/269078624/22edo.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/22edo.png/269078624/22edo.png" alt="22edo.png" title="22edo.png" /><!-- ws:end:WikiTextLocalImageRule:1931 --><br /> | ||
This notation is consistent with Sagittal's notation of 5-limit JI harmony: &quot;major&quot; 3rds and 6ths appear as (super)pythagorean intervals flattened by a syntonic comma.<br /> | This notation is consistent with Sagittal's notation of 5-limit JI harmony: &quot;major&quot; 3rds and 6ths appear as (super)pythagorean intervals flattened by a syntonic comma.<br /> | ||
<br /> | <br /> | ||
The division of the apotome into three syntonic commas also indicates 22's tempering out of the <a class="wiki_link" href="/250_243">porcupine comma</a> (which is equivalent to three syntonic commas minus a Pythagorean apotome).<br /> | The division of the apotome into three syntonic commas also indicates 22's tempering out of the <a class="wiki_link" href="/250_243">porcupine comma</a> (which is equivalent to three syntonic commas minus a Pythagorean apotome).<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc11"><a name="The Decatonic System"></a><!-- ws:end:WikiTextHeadingRule:24 -->The Decatonic System</h1> | ||
<span style="background-color: #ffffff; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;">The decatonic system is an approach of notation based on Paul Erlich's decatonic scales. Unlike typical notation, the decatonic system bases music into a 10 tone scale rather than 7. </span><br /> | <span style="background-color: #ffffff; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;">The decatonic system is an approach of notation based on Paul Erlich's decatonic scales. Unlike typical notation, the decatonic system bases music into a 10 tone scale rather than 7. </span><br /> | ||
<span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;">This approach requires an entire re-learning of chords, intervals, and notation but the advantage is that it allows 22 EDO to be notated using only one pair of accidentals, as well as</span><span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;">gives the opportunity to escape a heptatonic thinking pattern.</span><br /> | <span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;">This approach requires an entire re-learning of chords, intervals, and notation but the advantage is that it allows 22 EDO to be notated using only one pair of accidentals, as well as</span><span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;">gives the opportunity to escape a heptatonic thinking pattern.</span><br /> | ||
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<span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;"><br /> | <span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;"><br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:26:&lt;h2&gt; --><h2 id="toc12"><a name="The Decatonic System-Decatonic Alphabet"></a><!-- ws:end:WikiTextHeadingRule:26 --><!-- ws:start:WikiTextAnchorRule:52:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@TOC-Decatonic-Alphabet&quot; title=&quot;Anchor: TOC-Decatonic-Alphabet&quot;/&gt; --><a name="TOC-Decatonic-Alphabet"></a><!-- ws:end:WikiTextAnchorRule:52 -->Decatonic Alphabet</h2> | ||
</span><span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;">The system is based on two chains of fifths. One represented by latin letters, the other greek. The two chains can be looked at as two juxtaposed pentatonic scales.</span><br /> | </span><span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;">The system is based on two chains of fifths. One represented by latin letters, the other greek. The two chains can be looked at as two juxtaposed pentatonic scales.</span><br /> | ||
<br /> | <br /> | ||
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</span><span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;"><span style="font-family: helvetica,arial,sans-serif; font-size: 12px;">In this alphabet, a chain of fifths is preserved because equivalent greek letters also represent fifths if they are the same as their latin counter parts. For example G D is a fifth as well as </span><span style="color: #141823; font-family: helvetica,arial,sans-serif; font-size: 14px;">γ δ.</span></span><span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;"><br /> | </span><span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;"><span style="font-family: helvetica,arial,sans-serif; font-size: 12px;">In this alphabet, a chain of fifths is preserved because equivalent greek letters also represent fifths if they are the same as their latin counter parts. For example G D is a fifth as well as </span><span style="color: #141823; font-family: helvetica,arial,sans-serif; font-size: 14px;">γ δ.</span></span><span style="background-color: #ffffff; display: block; font-family: Arial,Verdana,sans-serif; font-size: 13.33px;"><br /> | ||
</span><br /> | </span><br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc13"><a name="The Decatonic System-External links"></a><!-- ws:end:WikiTextHeadingRule:28 -->External links</h2> | ||
<br /> | <br /> | ||
<a class="wiki_link_ext" href="http://lumma.org/tuning/erlich/erlich-decatonic.pdf" rel="nofollow">Erlich, Paul, ''Tuning, Tonality, and Twenty-Two Tone Temperament''</a><br /> | <a class="wiki_link_ext" href="http://lumma.org/tuning/erlich/erlich-decatonic.pdf" rel="nofollow">Erlich, Paul, ''Tuning, Tonality, and Twenty-Two Tone Temperament''</a><br /> | ||
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<a class="wiki_link_ext" href="http://porcupinemusic.weebly.com/" rel="nofollow">&quot;Porcupine Music&quot; - Website Focused on the Development of 22 EDO music </a><br /> | <a class="wiki_link_ext" href="http://porcupinemusic.weebly.com/" rel="nofollow">&quot;Porcupine Music&quot; - Website Focused on the Development of 22 EDO music </a><br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:30:&lt;h2&gt; --><h2 id="toc14"><a name="The Decatonic System-References"></a><!-- ws:end:WikiTextHeadingRule:30 -->References</h2> | ||
<br /> | <br /> | ||
Barbour, James Murray, ''Tuning and temperament, a historical survey'', East Lansing, Michigan State College Press, 1953 [c1951]<br /> | Barbour, James Murray, ''Tuning and temperament, a historical survey'', East Lansing, Michigan State College Press, 1953 [c1951]<br /> | ||
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<hr /> | <hr /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:32:&lt;h1&gt; --><h1 id="toc15"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:32 -->Music</h1> | ||
<br /> | <br /> | ||
<ul><li><a class="wiki_link_ext" href="https://soundcloud.com/overtoneshock/dose-of-familiarityode-to-microtonality-22-edo-studio-version" rel="nofollow" target="_blank">Stephen Weigel · Dose Of Familiarity/Ode to Microtonality</a></li><li><a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/archives/1145" rel="nofollow" target="_blank">Canon 2 in 1 upon a ground (22edo)</a> by Claudi Meneghin</li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://music.columbia.edu/%7Echris/sounds/TIBIA.mp3" rel="nofollow">Tibia</a></span></span> by <a class="wiki_link" href="/Paul%20Erlich">Paul Erlich</a><ul><li>Sagittal score of Tibia, <a href="http://xenharmonic.wikispaces.com/file/view/TIBIA.pdf/313029038/TIBIA.pdf" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/TIBIA.pdf/313029038/TIBIA.pdf');">in F||\</a> or <a href="http://xenharmonic.wikispaces.com/file/view/tibia%20in%20g.pdf/313029040/tibia%20in%20g.pdf" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/tibia%20in%20g.pdf/313029040/tibia%20in%20g.pdf');">in G</a></li></ul></li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.myspace.com/paulerlich/music/songs/glassic-in-22-tone-equal-temperament-45202095" rel="nofollow">Glassic</a></span></span> by Paul Erlich and <a class="wiki_link" href="/Ara%20Sarkissian">Ara Sarkissian</a></li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://lumma.org/tuning/erlich/decatonic-swing.mp3" rel="nofollow">Decatonic Swing</a></span></span> by Paul Erlich and Ara Sarkissian (jazz)</li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12-22hexachordal%20Dirge.mp3" rel="nofollow">12-22hexachordal Dirge</a> by <a class="wiki_link" href="/Joel%20Grant%20Taylor">Joel Grant Taylor</a></li><li><a class="wiki_link_ext" href="https://soundcloud.com/jdfreivald/chord-sequence-in-paul-erlichs" rel="nofollow" target="_blank">Chord sequence in Paul Erlich's 22 EDO decatonic major</a> by <a class="wiki_link" href="/Jake%20Freivald">Jake Freivald</a></li><li><a class="wiki_link_ext" href="https://soundcloud.com/jdfreivald/porcupine-comma-pump" rel="nofollow">Porcupine Comma Pump</a> by <a class="wiki_link" href="/Jake%20Freivald">Jake Freivald</a></li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%20Dragged%20By%20a%20Storm%20Across%20the%20Desert%20Years.mp3" rel="nofollow">Dragged by a Storm Across the Desert Years</a></span></span> by * <a class="wiki_link" href="/IgliashonJones">Igliashon Jones</a> (synth with electric guitar)</li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2022-Numerology.mp3" rel="nofollow">Numerology</a></span></span> by Iglashion Jones (progressive metal)</li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2022-Revenge%20of%20the%20Inorganic%20Compounds.mp3" rel="nofollow">Revenge of the inorganic compounds</a></span></span> by Iglashion Jones (progressive metal)</li><li><a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=267" rel="nofollow">My Crazy Aunt Sophie</a> <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/22edo-piano-my-crazy-aunt-sophie.mp3" rel="nofollow">play</a></span></span> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a>. Blatantly xenharmonic piano.</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839058" rel="nofollow">where words are said to mean</a> <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+wherewordsaresaidtomean.mp3" rel="nofollow">play</a></span></span> by <a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a>, a setting of a text by Herbert Brün to a 22-tone row, thrice repeated. This &amp; the following pieces by Andrew are for 22-tone guitar &amp; voice.</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=9101704" rel="nofollow">I've come with a bucket of roses</a> <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+ivecomewithabucketofroses.mp3" rel="nofollow">play</a></span></span> by Andrew Heathwaite (orwell-9: 3 2 3 2 3 2 3 2 2).</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=9101705" rel="nofollow">one drop of rain</a> <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+onedropofrain.mp3" rel="nofollow">play</a></span></span> by Andrew Heathwaite (orwell-9).</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839060" rel="nofollow">being a</a> <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+beinga.mp3" rel="nofollow">play</a></span></span> by Andrew Heathwaite (porcupine-8: 3 1 3 3 3 3 3).</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839071" rel="nofollow">my own house</a> <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+myownhouse.mp3" rel="nofollow">play</a></span></span> by Andrew Heathwaite (a pelog-flavored subset of orwell-9: 3 2 7 3 7).</li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/17%20-%2017.%2022%20octave.mp3" rel="nofollow">Comets Over Flatland 17</a></span></span> by <a class="wiki_link" href="/Randy%20Winchester">Randy Winchester</a></li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3" rel="nofollow">Night on Porcupine Mountain</a></span></span> Mussorgsky-Smith</li><li><span class="ywp-page-play-pause ywp-page-video ywp-link-hover"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=lO5xSjIHyMg" rel="nofollow">Paul Erlich 22-Equal Guitar Improvisation Shredfest Insanity</a></span></span> - youtube</li><li><span class="ywp-page-play-pause ywp-page-video ywp-link-hover"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=WMtp9Wk0tO0" rel="nofollow">Improvisation in 22-equal temperament</a></span></span>, Mike Battaglia - youtube</li><li>Boxwood Forest, Dream Tone, The Eternal Sleep, Sunday Pipes, Twisted Clowns - <a class="wiki_link_ext" href="http://www.angelfire.com/mo/oljare/midicomp.html" rel="nofollow">MIDI files</a> by Mats Öljare<ul><li><a href="http://xenharmonic.wikispaces.com/file/view/sunday3.pdf/269076436/sunday3.pdf" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/sunday3.pdf/269076436/sunday3.pdf');">Sagittal score of Sunday Pipes</a></li></ul></li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3" rel="nofollow">Phobos Light</a></span> by Chris Vaisvil in Hedgehog[14] <a class="wiki_link" href="/hedgehog14">tuned</a> to 22edo.</li><li><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/20120716_theorbo_22edo.mp3" rel="nofollow">The Capture and Release of the Fairy</a></em> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a> =&gt; <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=2494" rel="nofollow">blog post presentation</a></li><li><em><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=oNJr1YOOqF8" rel="nofollow">Yak Butter</a></em> by The Stern Brocot Band, 1L6s MOS, compressed period/generator</li><li><a class="wiki_link_ext" href="http://www.archive.org/download/Sevish_-_Golden_Hour/Sevish_-_03_-_Dirty_Drummer_vbr.mp3" rel="nofollow">Dirty Drummer</a>, Sevish</li><li><a class="wiki_link_ext" href="http://www.archive.org/download/Sevish_-_Golden_Hour/Sevish_-_12_-_Ganymede_vbr.mp3" rel="nofollow">Ganymede</a>, Sevish (doesn't sound that xen, but it's in 22-edo)</li><li><a class="wiki_link_ext" href="http://www.archive.org/download/HumanAstronomy/03Sevish-Ambrosia.mp3" rel="nofollow">Ambrosia</a>, Sevish</li><li><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/20120726-from-the-sky-islands-they-came.mp3" rel="nofollow">From the Sky Islands They Came</a></em> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a> =&gt; <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=2523" rel="nofollow">blog post presentation</a></li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/20120616-12-22h.scl-smoke-filled-bar.mp3" rel="nofollow">Smoke Filled Bar</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a> =&gt; <a class="wiki_link_ext" href="http://chrisvaisvil.com/smoke-filled-bar/" rel="nofollow" target="_blank">blog presentation</a></li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Sultan/__Recurring_Mimosa_by_Redrick_Sultan.mp3" rel="nofollow">Recurring Mimosa</a> by <a class="wiki_link_ext" href="https://soundcloud.com/redrick-sultan/recurring-mimosa" rel="nofollow">Redrick Sultan</a></li><li>The Saharan Pump by Chris Vaisvil <a class="wiki_link_ext" href="http://chrisvaisvil.com/the-saharan-pump-22-edo-rock/" rel="nofollow">blog post</a></li><li><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=qHHv3mwJTlg" rel="nofollow" target="_blank">Short piece and demonstration</a> (video) by <a class="wiki_link_ext" href="http://brendanbyrnes.com/" rel="nofollow" target="_blank">Brendan Byrnes</a> (electric guitar)</li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Byrnes/Brendan%20Byrnes%20-%2022%20EDO%20Guitar%20Etude.mp3" rel="nofollow">22 EDO Guitar Etude</a> by <a class="wiki_link_ext" href="http://brendanbyrnes.bandcamp.com/" rel="nofollow">Brendan Byrnes</a></li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Byrnes/Brendan%20Byrnes%20-%20Llurion.mp3" rel="nofollow">Llurion</a> by <a class="wiki_link_ext" href="http://brendanbyrnes.bandcamp.com/track/llurion" rel="nofollow">Brendan Byrnes</a></li><li><a class="wiki_link_ext" href="https://youtu.be/0VLJXecjYK4" rel="nofollow" target="_blank">Imzadi</a> by <a class="wiki_link_ext" href="http://omega9.github.io/" rel="nofollow" target="_blank">Omega9</a></li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/20150910_22edo.mp3" rel="nofollow">22 edo electric guitar duet</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></li><li><a class="wiki_link_ext" href="https://soundcloud.com/gareth-hearne/mass-in-22edo-sanctus" rel="nofollow">Mass in 22edo - Sanctus</a> by <a class="wiki_link" href="/Gareth%20Hearne">Gareth Hearne</a></li><li><a class="wiki_link_ext" href="https://soundcloud.com/gareth-hearne/mass-in-22edo-agnus-dei" rel="nofollow">Mass in 22edo - Agnus Dei</a> by Gareth Hearne</li><li><a class="wiki_link_ext" href="http://chrisvaisvil.com/for-the-sunset/" rel="nofollow" target="_blank">For the Sunset</a> - 22 edo rock ensemble by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></li><li><a class="wiki_link_ext" href="https://soundcloud.com/ilevens/tracks" rel="nofollow">tracks of ILEVENS</a> - all their tracks on SoundCloud are tagged with 22edo</li></ul><br /> | <ul><li><a class="wiki_link_ext" href="https://soundcloud.com/overtoneshock/dose-of-familiarityode-to-microtonality-22-edo-studio-version" rel="nofollow" target="_blank">Stephen Weigel · Dose Of Familiarity/Ode to Microtonality</a></li><li><a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/archives/1145" rel="nofollow" target="_blank">Canon 2 in 1 upon a ground (22edo)</a> by Claudi Meneghin</li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://music.columbia.edu/%7Echris/sounds/TIBIA.mp3" rel="nofollow">Tibia</a></span></span> by <a class="wiki_link" href="/Paul%20Erlich">Paul Erlich</a><ul><li>Sagittal score of Tibia, <a href="http://xenharmonic.wikispaces.com/file/view/TIBIA.pdf/313029038/TIBIA.pdf" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/TIBIA.pdf/313029038/TIBIA.pdf');">in F||\</a> or <a href="http://xenharmonic.wikispaces.com/file/view/tibia%20in%20g.pdf/313029040/tibia%20in%20g.pdf" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/tibia%20in%20g.pdf/313029040/tibia%20in%20g.pdf');">in G</a></li></ul></li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.myspace.com/paulerlich/music/songs/glassic-in-22-tone-equal-temperament-45202095" rel="nofollow">Glassic</a></span></span> by Paul Erlich and <a class="wiki_link" href="/Ara%20Sarkissian">Ara Sarkissian</a></li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://lumma.org/tuning/erlich/decatonic-swing.mp3" rel="nofollow">Decatonic Swing</a></span></span> by Paul Erlich and Ara Sarkissian (jazz)</li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12-22hexachordal%20Dirge.mp3" rel="nofollow">12-22hexachordal Dirge</a> by <a class="wiki_link" href="/Joel%20Grant%20Taylor">Joel Grant Taylor</a></li><li><a class="wiki_link_ext" href="https://soundcloud.com/jdfreivald/chord-sequence-in-paul-erlichs" rel="nofollow" target="_blank">Chord sequence in Paul Erlich's 22 EDO decatonic major</a> by <a class="wiki_link" href="/Jake%20Freivald">Jake Freivald</a></li><li><a class="wiki_link_ext" href="https://soundcloud.com/jdfreivald/porcupine-comma-pump" rel="nofollow">Porcupine Comma Pump</a> by <a class="wiki_link" href="/Jake%20Freivald">Jake Freivald</a></li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%20Dragged%20By%20a%20Storm%20Across%20the%20Desert%20Years.mp3" rel="nofollow">Dragged by a Storm Across the Desert Years</a></span></span> by * <a class="wiki_link" href="/IgliashonJones">Igliashon Jones</a> (synth with electric guitar)</li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2022-Numerology.mp3" rel="nofollow">Numerology</a></span></span> by Iglashion Jones (progressive metal)</li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2022-Revenge%20of%20the%20Inorganic%20Compounds.mp3" rel="nofollow">Revenge of the inorganic compounds</a></span></span> by Iglashion Jones (progressive metal)</li><li><a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=267" rel="nofollow">My Crazy Aunt Sophie</a> <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/22edo-piano-my-crazy-aunt-sophie.mp3" rel="nofollow">play</a></span></span> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a>. Blatantly xenharmonic piano.</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839058" rel="nofollow">where words are said to mean</a> <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+wherewordsaresaidtomean.mp3" rel="nofollow">play</a></span></span> by <a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a>, a setting of a text by Herbert Brün to a 22-tone row, thrice repeated. This &amp; the following pieces by Andrew are for 22-tone guitar &amp; voice.</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=9101704" rel="nofollow">I've come with a bucket of roses</a> <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+ivecomewithabucketofroses.mp3" rel="nofollow">play</a></span></span> by Andrew Heathwaite (orwell-9: 3 2 3 2 3 2 3 2 2).</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=9101705" rel="nofollow">one drop of rain</a> <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+onedropofrain.mp3" rel="nofollow">play</a></span></span> by Andrew Heathwaite (orwell-9).</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839060" rel="nofollow">being a</a> <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+beinga.mp3" rel="nofollow">play</a></span></span> by Andrew Heathwaite (porcupine-8: 3 1 3 3 3 3 3).</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839071" rel="nofollow">my own house</a> <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+myownhouse.mp3" rel="nofollow">play</a></span></span> by Andrew Heathwaite (a pelog-flavored subset of orwell-9: 3 2 7 3 7).</li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/17%20-%2017.%2022%20octave.mp3" rel="nofollow">Comets Over Flatland 17</a></span></span> by <a class="wiki_link" href="/Randy%20Winchester">Randy Winchester</a></li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3" rel="nofollow">Night on Porcupine Mountain</a></span></span> Mussorgsky-Smith</li><li><span class="ywp-page-play-pause ywp-page-video ywp-link-hover"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=lO5xSjIHyMg" rel="nofollow">Paul Erlich 22-Equal Guitar Improvisation Shredfest Insanity</a></span></span> - youtube</li><li><span class="ywp-page-play-pause ywp-page-video ywp-link-hover"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=WMtp9Wk0tO0" rel="nofollow">Improvisation in 22-equal temperament</a></span></span>, Mike Battaglia - youtube</li><li>Boxwood Forest, Dream Tone, The Eternal Sleep, Sunday Pipes, Twisted Clowns - <a class="wiki_link_ext" href="http://www.angelfire.com/mo/oljare/midicomp.html" rel="nofollow">MIDI files</a> by Mats Öljare<ul><li><a href="http://xenharmonic.wikispaces.com/file/view/sunday3.pdf/269076436/sunday3.pdf" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/sunday3.pdf/269076436/sunday3.pdf');">Sagittal score of Sunday Pipes</a></li></ul></li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3" rel="nofollow">Phobos Light</a></span> by Chris Vaisvil in Hedgehog[14] <a class="wiki_link" href="/hedgehog14">tuned</a> to 22edo.</li><li><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/20120716_theorbo_22edo.mp3" rel="nofollow">The Capture and Release of the Fairy</a></em> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a> =&gt; <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=2494" rel="nofollow">blog post presentation</a></li><li><em><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=oNJr1YOOqF8" rel="nofollow">Yak Butter</a></em> by The Stern Brocot Band, 1L6s MOS, compressed period/generator</li><li><a class="wiki_link_ext" href="http://www.archive.org/download/Sevish_-_Golden_Hour/Sevish_-_03_-_Dirty_Drummer_vbr.mp3" rel="nofollow">Dirty Drummer</a>, Sevish</li><li><a class="wiki_link_ext" href="http://www.archive.org/download/Sevish_-_Golden_Hour/Sevish_-_12_-_Ganymede_vbr.mp3" rel="nofollow">Ganymede</a>, Sevish (doesn't sound that xen, but it's in 22-edo)</li><li><a class="wiki_link_ext" href="http://www.archive.org/download/HumanAstronomy/03Sevish-Ambrosia.mp3" rel="nofollow">Ambrosia</a>, Sevish</li><li><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/20120726-from-the-sky-islands-they-came.mp3" rel="nofollow">From the Sky Islands They Came</a></em> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a> =&gt; <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=2523" rel="nofollow">blog post presentation</a></li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/20120616-12-22h.scl-smoke-filled-bar.mp3" rel="nofollow">Smoke Filled Bar</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a> =&gt; <a class="wiki_link_ext" href="http://chrisvaisvil.com/smoke-filled-bar/" rel="nofollow" target="_blank">blog presentation</a></li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Sultan/__Recurring_Mimosa_by_Redrick_Sultan.mp3" rel="nofollow">Recurring Mimosa</a> by <a class="wiki_link_ext" href="https://soundcloud.com/redrick-sultan/recurring-mimosa" rel="nofollow">Redrick Sultan</a></li><li>The Saharan Pump by Chris Vaisvil <a class="wiki_link_ext" href="http://chrisvaisvil.com/the-saharan-pump-22-edo-rock/" rel="nofollow">blog post</a></li><li><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=qHHv3mwJTlg" rel="nofollow" target="_blank">Short piece and demonstration</a> (video) by <a class="wiki_link_ext" href="http://brendanbyrnes.com/" rel="nofollow" target="_blank">Brendan Byrnes</a> (electric guitar)</li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Byrnes/Brendan%20Byrnes%20-%2022%20EDO%20Guitar%20Etude.mp3" rel="nofollow">22 EDO Guitar Etude</a> by <a class="wiki_link_ext" href="http://brendanbyrnes.bandcamp.com/" rel="nofollow">Brendan Byrnes</a></li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Byrnes/Brendan%20Byrnes%20-%20Llurion.mp3" rel="nofollow">Llurion</a> by <a class="wiki_link_ext" href="http://brendanbyrnes.bandcamp.com/track/llurion" rel="nofollow">Brendan Byrnes</a></li><li><a class="wiki_link_ext" href="https://youtu.be/0VLJXecjYK4" rel="nofollow" target="_blank">Imzadi</a> by <a class="wiki_link_ext" href="http://omega9.github.io/" rel="nofollow" target="_blank">Omega9</a></li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/20150910_22edo.mp3" rel="nofollow">22 edo electric guitar duet</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></li><li><a class="wiki_link_ext" href="https://soundcloud.com/gareth-hearne/mass-in-22edo-sanctus" rel="nofollow">Mass in 22edo - Sanctus</a> by <a class="wiki_link" href="/Gareth%20Hearne">Gareth Hearne</a></li><li><a class="wiki_link_ext" href="https://soundcloud.com/gareth-hearne/mass-in-22edo-agnus-dei" rel="nofollow">Mass in 22edo - Agnus Dei</a> by Gareth Hearne</li><li><a class="wiki_link_ext" href="http://chrisvaisvil.com/for-the-sunset/" rel="nofollow" target="_blank">For the Sunset</a> - 22 edo rock ensemble by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></li><li><a class="wiki_link_ext" href="https://soundcloud.com/ilevens/tracks" rel="nofollow">tracks of ILEVENS</a> - all their tracks on SoundCloud are tagged with 22edo</li></ul><br /> | ||
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