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| es =  
| es =  
| ja = 23平均律
| ja = 23平均律
}}__FORCETOC__
}}
-----


=Theory=
== Theory ==


<b>23-TET</b>, or <b>23-EDO</b>, is a tempered musical system which divides the [[Octave|octave]] into 23 equal parts of approximately 52.173913 cents, which is also called with the neologism Icositriphony ''(Icositrifonía)''. It has good approximations for [[5/3|5/3]], [[11/7|11/7]], 13 and 17, allowing it to represent the 2.5/3.11/7.13.17 [[just_intonation_subgroup|just intonation subgroup]]. If to this subgroup is added the commas of [[17-limit|17-limit]] [[46edo|46edo]], the larger 17-limit [[k*N_subgroups|2*23 subgroup]] 2.9.15.21.33.13.17 is obtained. This is the largest subgroup on which 23 has the same tuning and commas as does 17-limit·46edo, and may be regarded as a basis for analyzing the harmony of 23-EDO so far, as approximations to just intervals goes. 23edo is the 9th [[prime_numbers|prime]] edo, following [[19edo|19edo]] and coming before [[29edo|29edo]].
<b>23-TET</b>, or <b>23-EDO</b>, is a tempered musical system which divides the [[Octave|octave]] into 23 equal parts of approximately 52.173913 cents, which is also called with the neologism Icositriphony ''(Icositrifonía)''. It has good approximations for [[5/3]], [[11/7]], 13 and 17, allowing it to represent the 2.5/3.11/7.13.17 [[just intonation subgroup]]. If to this subgroup is added the commas of [[17-limit]] [[46edo]], the larger 17-limit [[k*N_subgroups|2*23 subgroup]] 2.9.15.21.33.13.17 is obtained. This is the largest subgroup on which 23 has the same tuning and commas as does 17-limit·46edo, and may be regarded as a basis for analyzing the harmony of 23-EDO so far, as approximations to just intervals goes. 23edo is the 9th [[prime numbers|prime]] edo, following [[19edo]] and coming before [[29edo]].


23-EDO was proposed by ethnomusicologist [http://en.wikipedia.org/wiki/Erich_von_Hornbostel Erich von Hornbostel] as the result of continuing a circle of "blown" fifths of ~678-cent fifths that (he argued) resulted from "overblowing" a bamboo pipe.
23-EDO was proposed by ethnomusicologist [http://en.wikipedia.org/wiki/Erich_von_Hornbostel Erich von Hornbostel] as the result of continuing a circle of "blown" fifths of ~678-cent fifths that (he argued) resulted from "overblowing" a bamboo pipe.


23-EDO is also significant in that it is the largest EDO that fails to approximate the 3rd, 5th, 7th, and 11th harmonics within 20 cents, which makes it well-suited for musicians seeking to explore harmonic territory that is unusual even for the average microtonalist. Oddly, despite the fact that it fails to approximate these harmonics, it approximates the intervals between them (5/3, 7/3, 11/3, 7/5, 11/7, and 11/5) very well. The lowest harmonics well-approximated by 23-EDO are 9, 13, 15, 17, 21, and 23. See [[Harmony_of_23edo|here]] for more details. Also note that some approximations can be improved by [[23edo_and_octave_stretching|octave stretching]].
23-EDO is also significant in that it is the largest EDO that fails to approximate the 3rd, 5th, 7th, and 11th harmonics within 20 cents, which makes it well-suited for musicians seeking to explore harmonic territory that is unusual even for the average microtonalist. Oddly, despite the fact that it fails to approximate these harmonics, it approximates the intervals between them (5/3, 7/3, 11/3, 7/5, 11/7, and 11/5) very well. The lowest harmonics well-approximated by 23-EDO are 9, 13, 15, 17, 21, and 23. See [[Harmony of 23edo|here]] for more details. Also note that some approximations can be improved by [[23edo and octave stretching|octave stretching]].


As with[[9edo| 9-EDO]], [[16edo|16-EDO]], and [[25edo|25-EDO]], one way to treat 23-EDO is as a Pelogic temperament, tempering out the "comma" of 135/128 and equating three 'acute [[4/3|4/3]]'s with 5/1 (related to the Armodue system). This means mapping '[[3/2|3/2]]' to 13 degrees of 23, and results in a 7 notes [[2L_5s|Anti-diatonic scale]] of 3 3 4 3 3 3 4 (in steps of 23-EDO), which extends to 9 notes [[7L_2s|Superdiatonic scale]] (3 3 3 1 3 3 3 3 1). One can notate 23-EDO using the Armodue system, but just like notating 17-EDO with familiar diatonic notation, flats will be lower in pitch than enharmonic sharps, because in 23-EDO, the "Armodue 6th" is sharper than it is in 16-EDO, just like the Diatonic 5th in 17-EDO is sharper than in 12-EDO. In other words, 2b is lower in pitch than 1#, just like how in 17-EDO, Eb is lower than D#.
As with[[9edo| 9-EDO]], [[16edo|16-EDO]], and [[25edo|25-EDO]], one way to treat 23-EDO is as a Pelogic temperament, tempering out the "comma" of 135/128 and equating three 'acute [[4/3]]'s with 5/1 (related to the Armodue system). This means mapping '[[3/2]]' to 13 degrees of 23, and results in a 7 notes [[2L 5s|Anti-diatonic scale]] of 3 3 4 3 3 3 4 (in steps of 23-EDO), which extends to 9 notes [[7L 2s|Superdiatonic scale]] (3 3 3 1 3 3 3 3 1). One can notate 23-EDO using the Armodue system, but just like notating 17-EDO with familiar diatonic notation, flats will be lower in pitch than enharmonic sharps, because in 23-EDO, the "Armodue 6th" is sharper than it is in 16-EDO, just like the Diatonic 5th in 17-EDO is sharper than in 12-EDO. In other words, 2b is lower in pitch than 1#, just like how in 17-EDO, Eb is lower than D#.


However, one can also map 3/2 to 14 degrees of 23-EDO without significantly increasing the error, taking us to a [[7-limit|7-limit]] temperament where two 'broad 3/2's equals 7/3, meaning 28/27 is tempered out, and six 4/3's octave-reduced equals 5/4, meaning 4096/3645 is tempered out. Both of these are very large commas, so this is not at all an accurate temperament, but it is related to [[13edo|13-EDO]] and [[18edo|18-EDO]] and produces [[MOSScales|MOS scales]] of 5 and 8 notes: 5 5 4 5 4 (the [[3L_2s|"anti-pentatonic"]]) and 4 1 4 1 4 4 1 4 (the "quarter-tone" version of the Blackwood/[http://en.wikipedia.org/wiki/Paul_Rapoport_%28music_critic%29 Rapoport]/Wilson 13-EDO "subminor" scale). Alternatively we can treat this temperament as a 2.9.21 subgroup, and instead of calling 9 degrees of 23-EDO a Sub-"4/3", we can call it 21/16. Here three 21/16's gets us to 9/4, meaning 1029/1024 is tempered out. This allows us to treat a triad of 0-4-9 degrees of 23-EDO as an approximation to 16:18:21, and 0-5-9 as 1/(16:18:21); both of these triads are abundant in the 8-note MOS scale.
However, one can also map 3/2 to 14 degrees of 23-EDO without significantly increasing the error, taking us to a [[7-limit]] temperament where two 'broad 3/2's equals 7/3, meaning 28/27 is tempered out, and six 4/3's octave-reduced equals 5/4, meaning 4096/3645 is tempered out. Both of these are very large commas, so this is not at all an accurate temperament, but it is related to [[13edo|13-EDO]] and [[18edo|18-EDO]] and produces [[MOSScales|MOS scales]] of 5 and 8 notes: 5 5 4 5 4 (the [[3L 2s|"anti-pentatonic"]]) and 4 1 4 1 4 4 1 4 (the "quarter-tone" version of the Blackwood/[http://en.wikipedia.org/wiki/Paul_Rapoport_%28music_critic%29 Rapoport]/Wilson 13-EDO "subminor" scale). Alternatively we can treat this temperament as a 2.9.21 subgroup, and instead of calling 9 degrees of 23-EDO a Sub-"4/3", we can call it 21/16. Here three 21/16's gets us to 9/4, meaning 1029/1024 is tempered out. This allows us to treat a triad of 0-4-9 degrees of 23-EDO as an approximation to 16:18:21, and 0-5-9 as 1/(16:18:21); both of these triads are abundant in the 8-note MOS scale.
 
== Notation ==


=Notation=
23edo can be notated with conventional notation, including the staff, note names, relative notation, etc. in two ways. The first preserves the <u>melodic</u> meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5.
23edo can be notated with conventional notation, including the staff, note names, relative notation, etc. in two ways. The first preserves the <u>melodic</u> meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5.


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Armodue notation is a nonatonic notation that uses the numbers 1-9 as note names.
Armodue notation is a nonatonic notation that uses the numbers 1-9 as note names.


{| class="wikitable"
{| class="wikitable center-all left-9"
|-
|-
| style="text-align:center;" | <span style="color: #660000;">[[Degree|Degree]]*</span>
! [[Degree]] <ref>The dots indicate which frets on a 23-edo guitar would have dots.</ref>
| style="text-align:center;" | [[cent|Cent]]s
! [[Cent]]s
| style="text-align:center;" | Approximate
! Approximate <br> Ratios <ref>Based on treating 23-EDO as a 2.9.15.21.33.13.17 subgroup temperament; other approaches are possible.</ref>
 
! colspan="2" | Major wider <br> than minor
Ratios **
! colspan="2" | Major narrower <br> than minor
| colspan="2" style="text-align:center;" | Major wider
! Armodue <br> Notation
 
! Notes
than minor
| colspan="2" style="text-align:center;" | Major narrower
 
than minor
| style="text-align:center;" | Armodue
 
Notation
| | Notes
|-
|-
| style="text-align:center;" | 0
| 0
| style="text-align:center;" | 0.000
| 0.000
| style="text-align:center;" | 1/1
| 1/1
| style="text-align:center;" | P1
| P1
| style="text-align:center;" | D
| D
| style="text-align:center;" | P1
| P1
| style="text-align:center;" | D
| D
| style="text-align:center;" | 1
| 1
| |
|
|-
|-
| style="text-align:center;" | 1
| 1
| style="text-align:center;" | 52.174
| 52.174
| style="text-align:center;" | 33/32, 34/33
| 33/32, 34/33
| style="text-align:center;" | A1
| A1
| style="text-align:center;" | D#
| D#
| style="text-align:center;" | d1
| d1
| style="text-align:center;" | Db
| Db
| style="text-align:center;" | 2b
| 2b
| |
|
|-
|-
| style="text-align:center;" | 2
| 2
| style="text-align:center;" | 104.348
| 104.348
| style="text-align:center;" | 17/16, 16/15, 18/17
| 17/16, 16/15, 18/17
| style="text-align:center;" | d2
| d2
| style="text-align:center;" | Eb
| Eb
| style="text-align:center;" | A2
| A2
| style="text-align:center;" | E#
| E#
| style="text-align:center;" | 1#
| 1#
| | Less than 1 cent off 17/16
| Less than 1 cent off 17/16
|-
|-
| style="text-align:center;" | 3
| 3
| style="text-align:center;" | 156.522
| 156.522
| style="text-align:center;" | 11/10, 12/11, 35/32
| 11/10, 12/11, 35/32
| style="text-align:center;" | m2
| m2
| style="text-align:center;" | E
| E
| style="text-align:center;" | M2
| M2
| style="text-align:center;" | E
| E
| style="text-align:center;" | 2
| 2
| |
|
|-
|-
| style="text-align:center;" | 4·
| 4·
| style="text-align:center;" | 208.696
| 208.696
| style="text-align:center;" | 9/8, 44/39
| 9/8, 44/39
| style="text-align:center;" | M2
| M2
| style="text-align:center;" | E#
| E#
| style="text-align:center;" | m2
| m2
| style="text-align:center;" | Eb
| Eb
| style="text-align:center;" | 3b
| 3b
| |
|
|-
|-
| style="text-align:center;" | 5
| 5
| style="text-align:center;" | 260.87
| 260.87
| style="text-align:center;" | 7/6, 15/13, 29/25
| 7/6, 15/13, 29/25
| style="text-align:center;" | A2, d3
| A2, d3
| style="text-align:center;" | Ex, Fbb
| Ex, Fbb
| style="text-align:center;" | d2, A3
| d2, A3
| style="text-align:center;" | Ebb, Fx
| Ebb, Fx
| style="text-align:center;" | 2#
| 2#
| |
|
|-
|-
| style="text-align:center;" | 6
| 6
| style="text-align:center;" | 313.0435
| 313.0435
| style="text-align:center;" | 6/5
| 6/5
| style="text-align:center;" | m3
| m3
| style="text-align:center;" | Fb
| Fb
| style="text-align:center;" | M3
| M3
| style="text-align:center;" | F#
| F#
| style="text-align:center;" | 3
| 3
| | Much better 6/5 than 12-edo
| Much better 6/5 than 12-edo
|-
|-
| style="text-align:center;" | 7·
| 7·
| style="text-align:center;" | 365.217
| 365.217
| style="text-align:center;" | 16/13, 21/17, 26/21
| 16/13, 21/17, 26/21
| style="text-align:center;" | M3
| M3
| style="text-align:center;" | F
| F
| style="text-align:center;" | m3
| m3
| style="text-align:center;" | F
| F
| style="text-align:center;" | 4b
| 4b
| |
|
|-
|-
| style="text-align:center;" | 8
| 8
| style="text-align:center;" | 417.391
| 417.391
| style="text-align:center;" | 14/11, 33/26
| 14/11, 33/26
| style="text-align:center;" | A3
| A3
| style="text-align:center;" | F#
| F#
| style="text-align:center;" | d3
| d3
| style="text-align:center;" | Fb
| Fb
| style="text-align:center;" | 3#
| 3#
| | Practically just 14/11
| Practically just 14/11
|-
|-
| style="text-align:center;" | 9
| 9
| style="text-align:center;" | 469.565
| 469.565
| style="text-align:center;" | 21/16, 17/13
| 21/16, 17/13
| style="text-align:center;" | d4
| d4
| style="text-align:center;" | Gb
| Gb
| style="text-align:center;" | A4
| A4
| style="text-align:center;" | G#
| G#
| style="text-align:center;" | 4
| 4
| |
|
|-
|-
| style="text-align:center;" | 10·
| 10·
| style="text-align:center;" | 521.739
| 521.739
| style="text-align:center;" | 23/17, 88/65, 256/189
| 23/17, 88/65, 256/189
| style="text-align:center;" | P4
| P4
| style="text-align:center;" | G
| G
| style="text-align:center;" | P4
| P4
| style="text-align:center;" | G
| G
| style="text-align:center;" | 5
| 5
| |
|
|-
|-
| style="text-align:center;" | 11
| 11
| style="text-align:center;" | 573.913
| 573.913
| style="text-align:center;" | 7/5, 32/23, 46/33
| 7/5, 32/23, 46/33
| style="text-align:center;" | A4
| A4
| style="text-align:center;" | G#
| G#
| style="text-align:center;" | d4
| d4
| style="text-align:center;" | Gb
| Gb
| style="text-align:center;" | 6b
| 6b
| |
|
|-
|-
| style="text-align:center;" | 12
| 12
| style="text-align:center;" | 626.087
| 626.087
| style="text-align:center;" | 10/7, 23/16, 33/23
| 10/7, 23/16, 33/23
| style="text-align:center;" | d5
| d5
| style="text-align:center;" | Ab
| Ab
| style="text-align:center;" | A5
| A5
| style="text-align:center;" | A#
| A#
| style="text-align:center;" | 5#
| 5#
| |
|
|-
|-
| style="text-align:center;" | 13·
| 13·
| style="text-align:center;" | 678.261
| 678.261
| style="text-align:center;" | 34/23, 65/44, 189/128
| 34/23, 65/44, 189/128
| style="text-align:center;" | P5
| P5
| style="text-align:center;" | A
| A
| style="text-align:center;" | P5
| P5
| style="text-align:center;" | A
| A
| style="text-align:center;" | 6
| 6
| | Great Hornbostel generator
| Great Hornbostel generator
|-
|-
| style="text-align:center;" | 14
| 14
| style="text-align:center;" | 730.435
| 730.435
| style="text-align:center;" | 32/21, 26/17
| 32/21, 26/17
| style="text-align:center;" | A5
| A5
| style="text-align:center;" | A#
| A#
| style="text-align:center;" | d5
| d5
| style="text-align:center;" | Ab
| Ab
| style="text-align:center;" | 7b
| 7b
| |
|
|-
|-
| style="text-align:center;" | 15
| 15
| style="text-align:center;" | 782.609
| 782.609
| style="text-align:center;" | 11/7, 52/33
| 11/7, 52/33
| style="text-align:center;" | d6
| d6
| style="text-align:center;" | Bb
| Bb
| style="text-align:center;" | A6
| A6
| style="text-align:center;" | B#
| B#
| style="text-align:center;" | 6#
| 6#
| |
|
|-
|-
| style="text-align:center;" | 16·
| 16·
| style="text-align:center;" | 834.783
| 834.783
| style="text-align:center;" | 13/8, 34/21, 21/13
| 13/8, 34/21, 21/13
| style="text-align:center;" | m6
| m6
| style="text-align:center;" | B
| B
| style="text-align:center;" | M6
| M6
| style="text-align:center;" | B
| B
| style="text-align:center;" | 7
| 7
| |
|
|-
|-
| style="text-align:center;" | 17
| 17
| style="text-align:center;" | 886.9565
| 886.9565
| style="text-align:center;" | 5/3
| 5/3
| style="text-align:center;" | M6
| M6
| style="text-align:center;" | B#
| B#
| style="text-align:center;" | m6
| m6
| style="text-align:center;" | Bb
| Bb
| style="text-align:center;" | 8b
| 8b
| |
|
|-
|-
| style="text-align:center;" | 18
| 18
| style="text-align:center;" | 939.13
| 939.13
| style="text-align:center;" | 12/7, 26/15, 50/29
| 12/7, 26/15, 50/29
| style="text-align:center;" | A6, d7
| A6, d7
| style="text-align:center;" | Bx, Cbb
| Bx, Cbb
| style="text-align:center;" | d6, A7
| d6, A7
| style="text-align:center;" | Bbb, Cx
| Bbb, Cx
| style="text-align:center;" | 7#
| 7#
| |
|
|-
|-
| style="text-align:center;" | 19·
| 19·
| style="text-align:center;" | 991.304
| 991.304
| style="text-align:center;" | 16/9, 39/22
| 16/9, 39/22
| style="text-align:center;" | m7
| m7
| style="text-align:center;" | Cb
| Cb
| style="text-align:center;" | M7
| M7
| style="text-align:center;" | C#
| C#
| style="text-align:center;" | 8
| 8
| |
|
|-
|-
| style="text-align:center;" | 20
| 20
| style="text-align:center;" | 1043.478
| 1043.478
| style="text-align:center;" | 11/6, 20/11, 64/35
| 11/6, 20/11, 64/35
| style="text-align:center;" | M7
| M7
| style="text-align:center;" | C
| C
| style="text-align:center;" | m7
| m7
| style="text-align:center;" | C
| C
| style="text-align:center;" | 9b
| 9b
| |
|
|-
|-
| style="text-align:center;" | 21
| 21
| style="text-align:center;" | 1095.652
| 1095.652
| style="text-align:center;" | 15/8, 17/9, 32/17
| 15/8, 17/9, 32/17
| style="text-align:center;" | A7
| A7
| style="text-align:center;" | C#
| C#
| style="text-align:center;" | d7
| d7
| style="text-align:center;" | Cb
| Cb
| style="text-align:center;" | 8#
| 8#
| |
|
|-
|-
| style="text-align:center;" | 22
| 22
| style="text-align:center;" | 1147.826
| 1147.826
| style="text-align:center;" | 33/17, 64/33
| 33/17, 64/33
| style="text-align:center;" | d8
| d8
| style="text-align:center;" | Db
| Db
| style="text-align:center;" | A8
| A8
| style="text-align:center;" | D#
| D#
| style="text-align:center;" | 9
| 9
| |
|
|-
|-
| style="text-align:center;" | 23··
| 23··
| style="text-align:center;" | 1200
| 1200
| style="text-align:center;" | 2/1
| 2/1
| style="text-align:center;" | P8
| P8
| style="text-align:center;" | D
| D
| style="text-align:center;" | P8
| P8
| style="text-align:center;" | D
| D
| style="text-align:center;" | 1
| 1
| |
|
|}
|}
<ul><li>The dots indicate which frets on a 23-edo guitar would have dots.<ul><li>Based on treating 23-EDO as a 2.9.15.21.33.13.17 subgroup temperament; other approaches are possible.</li></ul></li></ul>


=== Armodue Notation ===
<references/>
 
=== Armodue Notation ===
 
[[File:Ciclo_Icositrifonía.png|alt=Ciclo Icositrifonía.png|491x490px|link=Harmony_of_23edo]]
[[File:Ciclo_Icositrifonía.png|alt=Ciclo Icositrifonía.png|491x490px|link=Harmony_of_23edo]]


=Commas=
== Commas ==
23 EDO tempers out the following [[commas]]. (Note: This assumes the val &lt; 23 36 53 65 80 85 |.) Also note the discussion above, where there are some commas mentioned that are not in the standard comma list (e.g., 28/27).
23 EDO tempers out the following [[commas]]. (Note: This assumes the val &lt; 23 36 53 65 80 85 |.) Also note the discussion above, where there are some commas mentioned that are not in the standard comma list (e.g., 28/27).


{| class="wikitable"
{| class="wikitable center-all left-2 right-3"
|-
|-
! | [[Ratio]]
! [[Ratio]]
! | [[Monzo]]
! [[Monzo]]
! | [[Cents]]
! [[Cents]]
![[Color notation/Temperament Names|Color Name]]
! [[Color notation/Temperament Names|Color Name]]
! | Name 1
! Name 1
! | Name 2
! Name 2
! | Name 3
! Name 3
|-
|-
| style="text-align:center;" | 135/128
| 135/128
| |<nowiki> | -7 3 1 </nowiki>&gt;
| {{Monzo| -7 3 1 }}
| style="text-align:right;" | 92.18
| 92.18
| style="text-align:center;" |Layobi
| Layobi
| style="text-align:center;" | Major Chroma
| Major Chroma
| style="text-align:center;" | Major Limma
| Major Limma
| style="text-align:center;" | Pelogic Comma
| Pelogic Comma
|-
|-
| style="text-align:center;" | 15625/15552
| 15625/15552
| |<nowiki> | -6 -5 6 </nowiki>&gt;
| {{Monzo| -6 -5 6 }}
| style="text-align:right;" | 8.11
| 8.11
| style="text-align:center;" |Tribiyo
| Tribiyo
| style="text-align:center;" | Kleisma
| Kleisma
| style="text-align:center;" | Semicomma Majeur
| Semicomma Majeur
| style="text-align:center;" |
|  
|-
|-
| style="text-align:center;" | 36/35
| 36/35
| |<nowiki> | 2 2 -1 -1 </nowiki>&gt;
| {{Monzo| 2 2 -1 -1 }}
| style="text-align:right;" | 48.77
| 48.77
| style="text-align:center;" |Rugu
| Rugu
| style="text-align:center;" | Septimal Quarter Tone
| Septimal Quarter Tone
| style="text-align:center;" |
|  
| style="text-align:center;" |
|  
|-
|-
| style="text-align:center;" | 525/512
| 525/512
| |<nowiki> | -9 1 2 1 </nowiki>&gt;
| {{Monzo| -9 1 2 1 }}
| style="text-align:right;" | 43.41
| 43.41
| style="text-align:center;" |Lazoyoyo
| Lazoyoyo
| style="text-align:center;" | Avicennma
| Avicennma
| style="text-align:center;" | Avicenna's Enharmonic Diesis
| Avicenna's Enharmonic Diesis
| style="text-align:center;" |
|  
|-
|-
| style="text-align:center;" | 4000/3969
| 4000/3969
| |<nowiki> | 5 -4 3 -2 </nowiki>&gt;
| {{Monzo| 5 -4 3 -2 }}
| style="text-align:right;" | 13.47
| 13.47
| style="text-align:center;" |Rurutriyo
| Rurutriyo
| style="text-align:center;" | Octagar
| Octagar
| style="text-align:center;" |
|  
| style="text-align:center;" |
|  
|-
|-
| style="text-align:center;" | 6144/6125
| 6144/6125
| |<nowiki> | 11 1 -3 -2 </nowiki>&gt;
| {{Monzo| 11 1 -3 -2 }}
| style="text-align:right;" | 5.36
| 5.36
| style="text-align:center;" |Sarurutrigu
| Sarurutrigu
| style="text-align:center;" | Porwell
| Porwell
| style="text-align:center;" |
|  
| style="text-align:center;" |
|  
|-
|-
| style="text-align:center;" | 100/99
| 100/99
| |<nowiki> | 2 -2 2 0 -1 </nowiki>&gt;
| {{Monzo| 2 -2 2 0 -1 }}
| style="text-align:right;" | 17.40
| 17.40
| style="text-align:center;" |Luyoyo
| Luyoyo
| style="text-align:center;" | Ptolemisma
| Ptolemisma
| style="text-align:center;" |
|  
| style="text-align:center;" |
|  
|-
|-
| style="text-align:center;" | 441/440
| 441/440
| |<nowiki> | -3 2 -1 2 -1 </nowiki>&gt;
| {{Monzo| -3 2 -1 2 -1 }}
| style="text-align:right;" | 3.93
| 3.93
| style="text-align:center;" |Luzozogu
| Luzozogu
| style="text-align:center;" | Werckisma
| Werckisma
| style="text-align:center;" |
|  
| style="text-align:center;" |
|  
|}
|}


=MOS Scales=
== MOS Scales ==


The chart below shows some of the [[MOSScales|Moment of Symmetry (MOS)]] modes of [[Mavila|Mavila]] available in 23edo, mainly Pentatonic(5-note), anti-diatonic(7-note), 9- and 16-note MOSs. Here the outer ring represents individual step of 23edo itself, while the rings moving inward represent 16, 9, 7 and 5 note MOSs:
The chart below shows some of the [[MOSScales|Moment of Symmetry (MOS)]] modes of [[Mavila]] available in 23edo, mainly Pentatonic(5-note), anti-diatonic(7-note), 9- and 16-note MOSs. Here the outer ring represents individual step of 23edo itself, while the rings moving inward represent 16, 9, 7 and 5 note MOSs:


[[File:23edoMavilaMOS.jpg|alt=23edoMavilaMOS.jpg|23edoMavilaMOS.jpg]]
[[File:23edoMavilaMOS.jpg|alt=23edoMavilaMOS.jpg|23edoMavilaMOS.jpg]]


==23 tone [[MOS scale|MOS Scales]]:==
=== 23 tone MOS scales ===


{| class="wikitable"
{| class="wikitable"
! [[MOS scale]]
! Name
|-
|-
| | 10 10 3
| 10 10 3
| |
|
|-
|-
| | 9 9 5
| 9 9 5
| |
|
|-
|-
| | 8 8 7
| 8 8 7
| |
|
|-
|-
| | 7 7 7 2
| 7 7 7 2
| |
|
|-
|-
| | 7 2 7 7
| 7 2 7 7
| |
|
|-
|-
| | 6 6 6 5
| 6 6 6 5
| |
|
|-
|-
| | 6 5 6 6
| 6 5 6 6
| |
|
|-
|-
| | 5 4 5 5 4
| 5 4 5 5 4
| | [[3L_2s|3L 2s (father)]]
| [[3L 2s|3L 2s (father)]]
|-
|-
| | 5 4 5 4 5
| 5 4 5 4 5
| |
|
|-
|-
| | 7 1 7 7 1
| 7 1 7 7 1
| |
|
|-
|-
| | 7 1 7 1 7
| 7 1 7 1 7
| |
|
|-
|-
| | 5 5 5 5 3
| 5 5 5 5 3
| | [[4L_1s|4L 1s (bug)]]
| [[4L 1s|4L 1s (bug)]]
|-
|-
| | 5 3 5 5 5
| 5 3 5 5 5
| |
|
|-
|-
| | 4 4 4 4 4 3
| 4 4 4 4 4 3
| | [[5L_1s|5L 1s (Grumpy hexatonic)]]
| [[5L 1s|5L 1s (Grumpy hexatonic)]]
|-
|-
| | 4 3 4 4 4 4
| 4 3 4 4 4 4
| |
|
|-
|-
| | 5 1 5 1 5 1 5
| 5 1 5 1 5 1 5
| | [[4L_3s|4L 3s (mish)]]
| [[4L 3s|4L 3s (mish)]]
|-
|-
| | 3 3 3 5 3 3 3
| 3 3 3 5 3 3 3
| | [[1L_6s|1L 6s (Happy heptatonic)]]
| [[1L 6s|1L 6s (Happy heptatonic)]]
|-
|-
| | 4 3 3 3 3 3 4
| 4 3 3 3 3 3 4
| | [[2L_5s|2L 5s (mavila, anti-diatonic)]]
| [[2L 5s|2L 5s (mavila, anti-diatonic)]]
|-
|-
| | 3 4 3 3 4 3 3
| 3 4 3 3 4 3 3
| |
|
|-
|-
| | 3 3 4 3 3 3 4
| 3 3 4 3 3 3 4
| |
|
|-
|-
| | 3 3 3 4 3 3 4
| 3 3 3 4 3 3 4
| |
|
|-
|-
| | 3 3 3 4 3 4 3
| 3 3 3 4 3 4 3
| |
|
|-
|-
| | 2 5 2 5 2 5 2
| 2 5 2 5 2 5 2
| | [[3L_4s|3L 4s (mosh)]]
| [[3L 4s|3L 4s (mosh)]]
|-
|-
| | 4 1 4 4 1 4 4 1
| 4 1 4 4 1 4 4 1
| | [[5L_3s|5L 3s (unfair father)]]
| [[5L 3s|5L 3s (unfair father)]]
|-
|-
| | 3 3 3 3 3 3 3 2
| 3 3 3 3 3 3 3 2
| | [[7L_1s|7L 1s (Grumpy octatonic)]]
| [[7L 1s|7L 1s (Grumpy octatonic)]]
|-
|-
| | 3 2 3 3 3 3 3 3
| 3 2 3 3 3 3 3 3
| |
|
|-
|-
| | '''3 3 3 1 3 3 3 3 1'''
| '''3 3 3 1 3 3 3 3 1'''
| | [[7L_2s|7L 2s (mavila superdiatonic)]]
| [[7L 2s|7L 2s (mavila superdiatonic)]]
|-
|-
| | 3 3 1 3 3 3 1 3 3
| 3 3 1 3 3 3 1 3 3
| |
|
|-
|-
| | 3 2 3 2 3 2 3 2 3
| 3 2 3 2 3 2 3 2 3
| | [[5L_4s|5L 4s (unfair bug)]]
| [[5L 4s|5L 4s (unfair bug)]]
|-
|-
| | 2 2 2 3 2 2 3 2 2 3
| 2 2 2 3 2 2 3 2 2 3
| | Mode Keter
| Mode Keter
|-
|-
| | 2 2 3 2 2 3 2 2 3 2
| 2 2 3 2 2 3 2 2 3 2
| | Chesed
| Chesed
|-
|-
| | 2 3 2 2 3 2 2 3 2 2
| 2 3 2 2 3 2 2 3 2 2
| | Netzach
| Netzach
|-
|-
| | 3 2 2 3 2 2 3 2 2 2
| 3 2 2 3 2 2 3 2 2 2
| | Malkuth
| Malkuth
|-
|-
| | 2 2 3 2 2 3 2 2 2 3
| 2 2 3 2 2 3 2 2 2 3
| | Binah
| Binah
|-
|-
| | 2 3 2 2 3 2 2 2 3 2
| 2 3 2 2 3 2 2 2 3 2
| | Tiferet
| Tiferet
|-
|-
| | 3 2 2 3 2 2 2 3 2 2
| 3 2 2 3 2 2 2 3 2 2
| | Yesod
| Yesod
|-
|-
| | 2 2 3 2 2 2 3 2 2 3
| 2 2 3 2 2 2 3 2 2 3
| | Chokmah
| Chokmah
|-
|-
| | 2 3 2 2 2 3 2 2 3 2
| 2 3 2 2 2 3 2 2 3 2
| | Gevurah
| Gevurah
|-
|-
| | 3 2 2 2 3 2 2 3 2 2
| 3 2 2 2 3 2 2 3 2 2
| | Hod
| Hod
|-
|-
| | '''3 1 3 1 3 1 3 1 3 1 3'''
| '''3 1 3 1 3 1 3 1 3 1 3'''
| | Palestine 11
| Palestine 11
|-
|-
| | 2 <span style="font-size: 12.8000001907349px;">2 2 2 1 2 2 2 1 2 2 2 1</span>
| 2 2 2 2 1 2 2 2 1 2 2 2 1
| | <span style="background-color: #ffffff; font-size: 12.8000001907349px;">Mode Tishrei</span>
| Mode Tishrei
|-
|-
| | 2 <span style="font-size: 12.8000001907349px;">2 2 1 2 2 2 1 2 2 2 1 2</span>
| 2 2 2 1 2 2 2 1 2 2 2 1 2
| | <span style="background-color: #ffffff; font-size: 12.8000001907349px;">Cheshvan</span>
| Cheshvan
|-
|-
| | 2 <span style="font-size: 12.8000001907349px;">2 1 2 2 2 1 2 2 2 1 2 2</span>
| 2 2 1 2 2 2 1 2 2 2 1 2 2
| | <span style="background-color: #ffffff; font-size: 12.8000001907349px;">Kislev</span>
| Kislev
|-
|-
| | 2 <span style="font-size: 12.8000001907349px;">1 2 2 2 1 2 2 2 1 2 2 2</span>
| 2 1 2 2 2 1 2 2 2 1 2 2 2
| | <span style="background-color: #ffffff; font-size: 12.8000001907349px;">Tevet</span>
| Tevet
|-
|-
| | 1 <span style="font-size: 12.8000001907349px;">2 2 2 1 2 2 2 1 2 2 2 2</span>
| 1 2 2 2 1 2 2 2 1 2 2 2 2
| | <span style="background-color: #ffffff; font-size: 12.8000001907349px;">Shvat</span>
| Shvat
|-
|-
| | 2 2 2 1 2 2 2 1 2 2 2 2 1
| 2 2 2 1 2 2 2 1 2 2 2 2 1
| | <span style="background-color: #ffffff; font-size: 12.8000001907349px;">Adar minor</span>
| Adar minor
|-
|-
| | <span style="font-size: 12.8000001907349px;">2 2 1 2 2 2 1 2 2 2 2 1 2</span>
| 2 2 1 2 2 2 1 2 2 2 2 1 2
| | <span style="background-color: #ffffff; font-size: 12.8000001907349px;">Adar major</span>
| Adar major
|-
|-
| | <span style="font-size: 12.8000001907349px;">2 1 2 2 2 1 2 2 2 2 1 2 2</span>
| 2 1 2 2 2 1 2 2 2 2 1 2 2
| | <span style="background-color: #ffffff; font-size: 12.8000001907349px;">Nisan</span>
| Nisan
|-
|-
| | <span style="font-size: 12.8000001907349px;">1 2 2 2 1 2 2 2 2 1 2 2 2</span>
| 1 2 2 2 1 2 2 2 2 1 2 2 2
| | <span style="background-color: #ffffff; font-size: 12.8000001907349px;">Iyar</span>
| Iyar
|-
|-
| | <span style="font-size: 12.8000001907349px;">2 2 2 1 2 2 2 2 1 2 2 2 1</span>
| 2 2 2 1 2 2 2 2 1 2 2 2 1
| | <span style="background-color: #ffffff; font-size: 12.8000001907349px;">Sivan</span>
| Sivan
|-
|-
| | <span style="font-size: 12.8000001907349px;">2 2 1 2 2 2 2 1 2 2 2 1 2</span>
| 2 2 1 2 2 2 2 1 2 2 2 1 2
| | <span style="background-color: #ffffff; font-size: 12.8000001907349px;">Tammuz</span>
| Tammuz
|-
|-
| | <span style="font-size: 12.8000001907349px;">2 1 2 2 2 2 1 2 2 2 1 2 2</span>
| 2 1 2 2 2 2 1 2 2 2 1 2 2
| | <span style="background-color: #ffffff; font-size: 12.8000001907349px;">Av</span>
| Av
|-
|-
| | <span style="font-size: 12.8000001907349px;">1 2 2 2 2 1 2 2 2 1 2 2 1</span>
| 1 2 2 2 2 1 2 2 2 1 2 2 1
| | <span style="background-color: #ffffff; font-size: 12.8000001907349px;">Elul</span>
| Elul
|-
|-
| | 2 2 1 2 2 1 2 2 1 2 2 1 2 1
| 2 2 1 2 2 1 2 2 1 2 2 1 2 1
| |
|
|-
|-
| | '''2 1 2 2 1 2 2 1 2 2 1 2 2 1'''
| '''2 1 2 2 1 2 2 1 2 2 1 2 2 1'''
| | Palestine 14
| Palestine 14
|-
|-
| | 1 1 1 4 1 1 1 1 4 1 1 1 1 4
| 1 1 1 4 1 1 1 1 4 1 1 1 1 4
| |
|
|-
|-
| | 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
| 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
| |
|
|-
|-
| | '''2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1'''
| '''2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1'''
| | Palestine 17
| Palestine 17
|-
|-
| | 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1
| 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1
| |
|
|}
|}


==Kosmorsky's Sephiroth modes==
=== Kosmorsky's Sephiroth modes ===
I would argue that the most significant modes of 23 edo are those of the 2 2 2 3 2 2 3 2 2 3 scale ([[3L_7s|3L 7s fair mosh]]); This is derived from extending the ~1/3 comma tempered 13th Harmonic, two of which add up to the 21st harmonic and three add up to the 17th harmonic almost perfectly. Interestingly, the chord 8:13:21:34 is a fragment of the fibonacci sequence.
 
I would argue that the most significant modes of 23 edo are those of the 2 2 2 3 2 2 3 2 2 3 scale ([[3L 7s|3L 7s fair mosh]]); This is derived from extending the ~1/3 comma tempered 13th Harmonic, two of which add up to the 21st harmonic and three add up to the 17th harmonic almost perfectly. Interestingly, the chord 8:13:21:34 is a fragment of the fibonacci sequence.


Notated in ascending (standard) form. I have named these 10 modes according to the Sephiroth as follows:
Notated in ascending (standard) form. I have named these 10 modes according to the Sephiroth as follows:
Line 580: Line 577:
3 2 2 2 3 2 2 3 2 2 - Hod
3 2 2 2 3 2 2 3 2 2 - Hod


=Books=
== Books ==
 
[[File:Libro_Icositrifónico.PNG|alt=Libro_Icositrifónico.PNG|302x365px|Libro_Icositrifónico.PNG]]
[[File:Libro_Icositrifónico.PNG|alt=Libro_Icositrifónico.PNG|302x365px|Libro_Icositrifónico.PNG]]


=Instruments=
== Instruments ==


[[File:Icositriphonic_Guitar.PNG|alt=Icositriphonic_Guitar.PNG|601x305px|Icositriphonic_Guitar.PNG]]
[[File:Icositriphonic_Guitar.PNG|alt=Icositriphonic_Guitar.PNG|601x305px|Icositriphonic_Guitar.PNG]]
Line 615: Line 613:
This movie is a series of still shots Chris took during the process of making a 23 edo guitar in a stick like form. At the end the guitar is played without effects etc. and the open string tuning is sounded - which starts with a normal E and then adjusted to the 9th / 7th fret unison, like a typical 12edo guitar fashion.
This movie is a series of still shots Chris took during the process of making a 23 edo guitar in a stick like form. At the end the guitar is played without effects etc. and the open string tuning is sounded - which starts with a normal E and then adjusted to the 9th / 7th fret unison, like a typical 12edo guitar fashion.


=Music=
<youtube>K4iO7k152og</youtube>
[https://www.youtube.com/watch?v=lYb4iK4Lt5Q Promethean Elegies], by [http://benfuhrman.com/ Ben Fuhrman]
 
== Music ==
[https://soundcloud.com/overtoneshock/curiosity-finds-a-frown-23-edo Curiosity Finds a Frown, by Stephen Weigel]
 
[http://soonlabel.com/xenharmonic/archives/2460 Chromatic canon, by Claudi Meneghin]
 
<span style=""><span style="">''[http://home.vicnet.net.au/%7Eepoetry/family.mp3 The Family Supper]''</span></span> by [[Warren_Burt|Warren Burt]]
 
<span style=""><span style="">''[http://www.youtube.com/watch?v=Hqst8MaRiYM Icositriphonic Heptatonic MOS]''</span></span> by [[Igliashon_Jones|Igliashon Jones]]
 
<span style=""><span style="">''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%20His%20Wandering%20Kinship%20with%20Ashes.mp3 His Wandering Kinship with Ashes]''</span></span> by Igliashon Jones
 
<span style=""><span style="">''[http://www.nonoctave.com/tunes/CosmicChamber.mp3 Cosmic Chamber]''</span></span> by [[X._J._Scott|X. J. Scott]]
 
<span style=""><span style="">''[http://www.nonoctave.com/tunes/Daisies.mp3 Daisies on the Beach]''</span></span> by X. J. Scott
 
<span style="background-position: 100% 50%; cursor: pointer; padding-right: 10px;"><span style=""><span style="">''[http://www.akjmusic.com/audio/boogie_pie.mp3 Boogie Pie]''</span></span></span>by [[Aaron_Krister_Johnson|Aaron Krister Johnson]]
 
<span style=""><span style="">''[http://clones.soonlabel.com/public/micro/23edo/daily20110619_23edo_23_chilled.mp3 23 Chilled]''</span></span> by [[Chris_Vaisvil|Chris Vaisvil]]
 
<span style=""><span style="">''[http://www.seraph.it/dep/det/DesertWinds.mp3 Desert Winds]''</span></span> by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/926007c7483e4abc5a48d582c0667947-105.html blog entry])
 
<span style=""><span style="">''[http://www.seraph.it/dep/det/23Laments.mp3 23 Laments]''</span></span> by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/b2bf6f252efd467ee36ecc332a4872ac-106.html blog entry])
 
<span style="">''[http://www.seraph.it/dep/det/Doomsday23.mp3 Doomsday 23]''</span> by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/add481fdf4ae8c3afe56a0d2cb6dd672-164.html blog entry])
 
<span style="">''[http://www.seraph.it/dep/int/Adagio23ForStrings.mp3 Barber’s Adagio For Strings in 23ED2]''</span> by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/9e630d3f8ba93ab8264a3862dac950ce-192.html blog entry])
 
<span style="">''[http://www.seraph.it/dep/det/Nubian%20Dance.mp3 Nubian Dance]''</span> by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/694f0a26d29cd2a215f37754dd8428c3-237.html blog entry])
 
<span style="">''[http://www.seraph.it/dep/det/AroundTheBonfire.mp3 Around the bonfire]''</span> by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/9c6c54c593bc4720c8bd775fd5e244f4-261.html blog entry])
 
''Allegro Moderato'' by Easley Blackwood
 
[http://andrewheathwaite.bandcamp.com/track/pentaswing Pentaswing] [[Technical_Notes_for_Newbeams#Track notes:-Pentaswing|Notes]] by [[Andrew_Heathwaite|Andrew Heathwaite]]
 
<span style="">''[http://micro.soonlabel.com/MOS/20120418-9mos-mindaugas.mp3 Mindaugas Rex Lithuaniae]''</span> by [http://chrisvaisvil.com/?p=2267 Chris Vaisvil] (in Superpelog-9 tuning)
 
''[http://micro.soonlabel.com/23edo/Tutim_Dennsuul/T%fatim%20Dennsuul%20-%20Indigorange.mp3 Indigorange]'' by Tutim Dennsuul
 
''[http://micro.soonlabel.com/23edo/Tutim_Dennsuul/T%fatim%20Dennsuul%20-%20Wignud.mp3 Wignud]'' by Tutim Dennsuul
 
''[http://micro.soonlabel.com/23edo/Tutim_Dennsuul/Tutim%20Dennsuul%20-%20%20Harid.mp3 Harid]'' by Tutim Dennsuul
 
''[https://soundcloud.com/nanovibrationalrelations/a-rest-in-the-desert-23edo A Rest In The Desert]'' [http://micro.soonlabel.com/gene_ward_smith/Others/Mcandrew/A%20Rest%20In%20The%20Desert%20(23edo).mp3 play] by Gary Mcandrew
 
''[http://spectropolrecords.bandcamp.com/track/jacky-ligon-numenoctagon Numenoctagon]'' by Jacky Ligon (on spectropolrecords)


[http://www.dubbhism.com/2014/02/out-now-ligon-sevish-dubshot-23.html#more 23 (album)] by Jacky Ligon, Sevish &amp; Tony Dubshot ([https://soundcloud.com/ism-studio/sets/ligon-sevish-dubshot-23 soundcloud])
* [https://www.youtube.com/watch?v=lYb4iK4Lt5Q Promethean Elegies], by [http://benfuhrman.com/ Ben Fuhrman]
* [https://soundcloud.com/overtoneshock/curiosity-finds-a-frown-23-edo Curiosity Finds a Frown, by Stephen Weigel]
* [http://soonlabel.com/xenharmonic/archives/2460 Chromatic canon, by Claudi Meneghin]
* [http://home.vicnet.net.au/%7Eepoetry/family.mp3 The Family Supper] by [[Warren Burt]]
* [http://www.youtube.com/watch?v=Hqst8MaRiYM Icositriphonic Heptatonic MOS] by [[Igliashon Jones]]
* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%20His%20Wandering%20Kinship%20with%20Ashes.mp3 His Wandering Kinship with Ashes] by Igliashon Jones
* [http://www.nonoctave.com/tunes/CosmicChamber.mp3 Cosmic Chamber] by [[X. J. Scott]]
* [http://www.nonoctave.com/tunes/Daisies.mp3 Daisies on the Beach] by X. J. Scott
* [http://www.akjmusic.com/audio/boogie_pie.mp3 Boogie Pie] by [[Aaron Krister Johnson]]
* [http://clones.soonlabel.com/public/micro/23edo/daily20110619_23edo_23_chilled.mp3 23 Chilled] by [[Chris Vaisvil]]
* [http://www.seraph.it/dep/det/DesertWinds.mp3 Desert Winds] by [[Carlo Serafini]]  ([http://www.seraph.it/blog_files/926007c7483e4abc5a48d582c0667947-105.html blog entry])
* [http://www.seraph.it/dep/det/23Laments.mp3 23 Laments] by Carlo Serafini ([http://www.seraph.it/blog_files/b2bf6f252efd467ee36ecc332a4872ac-106.html blog entry])
* [http://www.seraph.it/dep/det/Doomsday23.mp3 Doomsday 23] by Carlo Serafini ([http://www.seraph.it/blog_files/add481fdf4ae8c3afe56a0d2cb6dd672-164.html blog entry])
* [http://www.seraph.it/dep/int/Adagio23ForStrings.mp3 Barber’s Adagio For Strings in 23ED2] by Carlo Serafini ([http://www.seraph.it/blog_files/9e630d3f8ba93ab8264a3862dac950ce-192.html blog entry])
* [http://www.seraph.it/dep/det/Nubian%20Dance.mp3 Nubian Dance] by Carlo Serafini ([http://www.seraph.it/blog_files/694f0a26d29cd2a215f37754dd8428c3-237.html blog entry])
* [http://www.seraph.it/dep/det/AroundTheBonfire.mp3 Around the bonfire] by Carlo Serafini ([http://www.seraph.it/blog_files/9c6c54c593bc4720c8bd775fd5e244f4-261.html blog entry])
* ''Allegro Moderato'' by Easley Blackwood
* [http://andrewheathwaite.bandcamp.com/track/pentaswing Pentaswing] [[Technical Notes for Newbeams#Track notes:-Pentaswing|Notes]] by [[Andrew Heathwaite]]
* [http://micro.soonlabel.com/MOS/20120418-9mos-mindaugas.mp3 Mindaugas Rex Lithuaniae] by [http://chrisvaisvil.com/?p=2267 Chris Vaisvil] (in Superpelog-9 tuning)
* [http://micro.soonlabel.com/23edo/Tutim_Dennsuul/T%fatim%20Dennsuul%20-%20Indigorange.mp3 Indigorange] by [[Tutim Dennsuul]]
* [http://micro.soonlabel.com/23edo/Tutim_Dennsuul/T%fatim%20Dennsuul%20-%20Wignud.mp3 Wignud] by Tutim Dennsuul
* [http://micro.soonlabel.com/23edo/Tutim_Dennsuul/Tutim%20Dennsuul%20-%20%20Harid.mp3 Harid] by Tutim Dennsuul
* [https://soundcloud.com/nanovibrationalrelations/a-rest-in-the-desert-23edo A Rest In The Desert] [http://micro.soonlabel.com/gene_ward_smith/Others/Mcandrew/A%20Rest%20In%20The%20Desert%20(23edo).mp3 play] by [[Gary Mcandrew]]
* [http://spectropolrecords.bandcamp.com/track/jacky-ligon-numenoctagon Numenoctagon] by [[Jacky Ligon]] (on spectropolrecords)
* [http://www.dubbhism.com/2014/02/out-now-ligon-sevish-dubshot-23.html#more 23 (album)] by Jacky Ligon, Sevish &amp; Tony Dubshot ([https://soundcloud.com/ism-studio/sets/ligon-sevish-dubshot-23 soundcloud])
* [https://soundcloud.com/shunya-kiyokawa/23edo-klavier8 23EDO Klavier8] by [[Shunya Kiyokawa]]


[https://soundcloud.com/shunya-kiyokawa/23edo-klavier8 23EDO Klavier8] by [[Shunya_Kiyokawa|Shunya Kiyokawa]]<youtube>K4iO7k152og</youtube>
[[Category:11/7]]
[[Category:11/7]]
[[Category:23-tone]]
[[Category:23-tone]]
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[[Category:Twentuning]]
[[Category:Twentuning]]


[[Category:todo:unify_precision]]
[[Category:Todo:unify precision]]
[[Category:Todo:improve synopsis]]
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