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| de = 23edo
| de = 23edo
| en = 23edo
| en = 23edo
| es =  
| es = 23 EDO
| ja = 23平均律
| ja = 23平均律
}}
}}
{{Infobox ET}}
{{Infobox ET}}
'''23 equal divisions of the octave''' ('''23edo''') is a musical system which divides the [[octave]] into 23 [[equal]] parts of approximately 52.2 [[cent]]s.
{{Wikipedia|23 equal temperament}}
{{ED intro}}


== Theory ==
== Theory ==
{{Harmonics in equal|23}}
23edo is significant in that it is the last edo that has no [[5L 2s|diatonic]] perfect fifths and not even [[5edo]] or [[7edo]] fifths. It is also the last edo that fails to approximate the [[3/1|3rd]], [[5/1|5th]], [[7/1|7th]], and [[11/1|11th]] [[harmonic]]s 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]], [[11/5]], [[11/7]]) and combinations of them ([[15/8]], [[21/16]], [[33/32]], [[35/32]], [[55/32]], [[77/64]]) very well. The lowest harmonics well-approximated by 23edo are [[9/1|9]], [[13/1|13]], [[15/1|15]], [[17/1|17]], [[21/1|21]], [[23/1|23]], [[31/1|31]], [[33/1|33]] and [[35/1|35]].
 
=== Mapping ===
As with [[9edo]], [[16edo]], and [[25edo]], one way to treat 23edo is as a tuning of the [[mavila]] 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-note [[2L 5s|antidiatonic]] scale of 3–3–4–3–3–3–4 (in steps of 23edo), which extends to a 9-note [[7L 2s|superdiatonic]] scale (3–3–3–1–3–3–3–3–1). One can notate 23edo using the [[Armodue]] system, but just like notating 17edo with familiar diatonic notation, flats will be lower in pitch than enharmonic sharps, because in 23edo, the "Armodue 6th" is sharper than it is in 16edo, just like the diatonic 5th in 17edo is sharper than in 12edo. In other words, 2b is lower in pitch than 1#, just like how in 17edo Eb is lower than D#.
 
However, one can also map 3/2 to 14 degrees of 23edo 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]] and [[18edo]] and produces [[mos scale]]s of 5 and 8 notes: 5–5–4–5–4 ([[3L 2s|antipentic]]) and 4–1–4–1–4–4–1–4 (the "quartertone" version of the [[Easley Blackwood Jr.|Blackwood]]/[[Paul Rapoport|Rapoport]]/[[Erv Wilson|Wilson]] 13edo "subminor" scale). Alternatively we can treat this temperament as a 2.9.21 subgroup, and instead of calling 9 degrees of 23edo 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 23edo 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.
 
23edo has good approximations for [[5/3]], [[11/7]], 13 and 17, among many others, allowing it to represent the 2.5/3.11/7.13.17 [[just intonation subgroup]]. If to this subgroup is added the commas of no-19's [[23-limit]] [[46edo]], the larger no-19's 23-limit [[k*N subgroups|2*23 subgroup]] 2.9.15.21.33.13.17.23 is obtained. This is the largest subgroup on which 23 has the same tuning and commas as does no-19's 23-limit 46edo, and may be regarded as a basis for analyzing the harmony of 23edo so far, as approximations to just intervals goes. If one dares to take advantage of this harmony by using 23edo as a period, you get [[icositritonic]], a [[23rd-octave temperaments|23rd-octave temperament]], so that the harmony of 23edo is adequately explained by what harmonies you can achieve using only periods and zero generators.


23edo 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 23edo so far, as approximations to just intervals goes. 23edo is the 9th [[prime edo]], following [[19edo]] and coming before [[29edo]].
See ''[[Harmony of 23edo]]'' for more details.  


23edo was proposed by ethnomusicologist [[Wikipedia: 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.
=== Odd harmonics ===
{{Harmonics in equal|23}}


23edo 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]], [[11/5]], [[11/7]]) and combinations of them ([[15/8]], [[21/16]], [[33/32]], [[35/32]], [[55/32]], [[77/64]]) very well. The lowest harmonics well-approximated by 23edo are 9, 13, 15, 17, 21, and 23. See ''[[Harmony of 23edo]]'' for more details. Also note that some approximations can be improved by [[23edo and octave stretching|octave stretching]].
=== Octave stretch ===
Some approximations can be improved by octave stretching. See ''[[23edo and octave stretching]]'' for more details.


As with [[9edo]], [[16edo]], and [[25edo]], one way to treat 23edo is as a tuning of the [[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|antidiatonic scale]] of 3 3 4 3 3 3 4 (in steps of 23edo), which extends to 9 notes [[7L 2s|superdiatonic scale]] (3 3 3 1 3 3 3 3 1). One can notate 23edo using the [[Armodue]] system, but just like notating 17edo with familiar diatonic notation, flats will be lower in pitch than enharmonic sharps, because in 23edo, the "Armodue 6th" is sharper than it is in 16edo, just like the diatonic 5th in 17edo is sharper than in 12edo. In other words, 2b is lower in pitch than 1#, just like how in 17edo Eb is lower than D#.
=== Subsets and supersets ===
23edo is the 9th [[prime edo]], following [[19edo]] and coming before [[29edo]], so it does not contain any nontrivial subset edos, though it contains [[23ed4]]. 46edo, which doubles it, considerably improves most of its approximations of lower harmonics.  


However, one can also map 3/2 to 14 degrees of 23edo 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]] and [[18edo]] and produces [[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/[[Wikipedia: Paul Rapoport %28music critic%29|Rapoport]]/Wilson 13edo "subminor" scale). Alternatively we can treat this temperament as a 2.9.21 subgroup, and instead of calling 9 degrees of 23edo 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 23edo 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.
=== Miscellany ===
23edo was proposed by ethnomusicologist {{w|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.


== Selected just intervals ==
== Selected just intervals ==
{| class="wikitable center-all"
{{Q-odd-limit intervals|23}}
|+Direct mapping (even if inconsistent)
|-
! Interval, complement
! Error (abs, [[Cent|¢]])
|-
| [[14/11]], [[11/7]]
| 0.117
|-
| [[6/5]], [[5/3]]
| 2.598
|-
| [[9/8]], [[16/9]]
| 4.786
|-
| '''[[16/13]], [[13/8]]'''
| '''5.745'''
|-
| [[12/11]], [[11/6]]
| 5.885
|-
| [[7/6]], [[12/7]]
| 6.001
|-
| [[16/15]], [[15/8]]
| 7.383
|-
| [[11/10]], [[20/11]]
| 8.482
|-
| [[7/5]], [[10/7]]
| 8.599
|-
| [[18/13]], [[13/9]]
| 10.531
|-
| [[15/13]], [[26/15]]
| 12.958
|}


== Notation ==
== Notation ==
===Conventional notation ===
{{Mavila}}


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 is not E. Chord names are different because C - E - G is not P1 - M3 - P5.
===Sagittal notation===
====Best fifth notation====
This notation uses the same sagittal sequence as EDOs [[28edo#Sagittal notation|28]] and [[33edo#Sagittal notation|33]].


The second approach preserves the <u>harmonic</u> meaning of sharp/flat, major/minor and aug/dim, in that the former is always further fifthwards on the chain of fifths than the latter. Sharp is lower in pitch than flat, and major/aug is narrower than minor/dim. While this approach may seem bizarre at first, interval arithmetic and chord names work as usual. Furthermore, conventional 12edo music can be directly translated to 23edo "on the fly".
<imagemap>
File:23-EDO_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 367 0 527 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 367 106 [[Fractional_3-limit_notation#Bad-fifths_limma-fraction_notation | limma-fraction notation]]
default [[File:23-EDO_Sagittal.svg]]
</imagemap>


====Second-best fifth notation====
This notation uses the same sagittal sequence as EDOs [[30edo#Sagittal notation|30]], [[37edo#Sagittal notation|37]], and [[44edo#Sagittal notation|44]].
<imagemap>
File:23b_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 375 0 535 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 375 106 [[Fractional_3-limit_notation#Bad-fifths_apotome-fraction_notation | apotome-fraction notation]]
default [[File:23b_Sagittal.svg]]
</imagemap>
=== Armodue notation  ===
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.


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<references/>
<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]]


== Acoustic π and ϕ ==
== Approximation to irrational intervals ==
23edo has a very close approximation of [[11/7#Proximity with π/2|acoustic π/2]] on 15\23 and a very close approximation of [[acoustic phi]] on the step just above (16\23).
23edo has good approximations of [[acoustic phi]] on 16\23, and [[pi]] on 38\23. Not until [[72edo|72]] do we find a better edo in terms of absolute error, and not until [[749edo|749]] do we find one in terms of relative error.


{| class="wikitable center-all"
{| class="wikitable center-all"
|+Direct mapping
|+Direct approximation
|-
|-
! Interval
! Interval
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|}
|}


Not until [[72edo|72]] do we find a better EDO in terms of absolute error, and not until [[749edo|749]] do we find one in terms of relative error.
== Regular temperament properties ==
=== Uniform maps ===
{{Uniform map|edo=23}}


== Commas ==
=== Commas ===
23edo [[tempers out]] the following [[comma]]s. (Note: This assumes the [[val]] {{val| 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).
23et [[tempering out|tempers out]] the following [[comma]]s. This assumes the [[val]] {{val| 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="commatable wikitable center-all left-3 right-4 left-6"
{| class="commatable wikitable center-all left-3 right-4 left-6"
|-
|-
! [[Harmonic limit|Prime<br>Limit]]
! [[Harmonic limit|Prime<br>limit]]
! [[Ratio]]
! [[Ratio]]
! [[Monzo]]
! [[Monzo]]
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| 92.18
| 92.18
| Layobi
| Layobi
| Major Chroma, Major Limma, Pelogic Comma
| Mavila comma, major chroma
|-
|-
| 5
| 5
Line 324: Line 323:
| 8.11
| 8.11
| Tribiyo
| Tribiyo
| Kleisma, Semicomma Majeur
| Kleisma, semicomma majeur
|-
|-
| 7
| 7
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| 48.77
| 48.77
| Rugu
| Rugu
| Septimal Quarter Tone
| Mint comma, septimal quartertone
|-
|-
| 7
| 7
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| 43.41
| 43.41
| Lazoyoyo
| Lazoyoyo
| Avicennma, Avicenna's Enharmonic Diesis
| Avicennma, Avicenna's enharmonic diesis
|-
|-
| 7
| 7
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| 13.47
| 13.47
| Rurutriyo
| Rurutriyo
| Octagar
| Octagar comma
|-
|-
| 7
| 7
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| 5.36
| 5.36
| Sarurutrigu
| Sarurutrigu
| Porwell
| Porwell comma
|-
|-
| 11
| 11
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Important [[mos]]ses include:
Important [[mos]]ses include:


* mavila 2L5s 4334333 (13\23, 1\1)
* Mavila 2L5s 4334333 (13\23, 1\1)
* mavila 7L2s 133313333 (13\23, 1\1)
* Mavila 7L2s 133313333 (13\23, 1\1)
* sephiroth 3L4s 2525252 (7\23, 1\1)
* Sephiroth 3L4s 2525252 (7\23, 1\1)
* [[semiquartal]] 5L4s 332323232 (5\23, 1\1)
* [[Semiquartal]] 5L4s 332323232 (5\23, 1\1)


The chart below shows some of the mos modes of [[mavila]] available in 23edo, mainly Pentatonic (5-note), antidiatonic (7-note), 9- and 16-note mosses. Here the outer ring represents individual step of 23edo itself, while the rings moving inward represent 16, 9, 7 and 5 note mosses:
The chart below shows some of the mos modes of [[mavila]] available in 23edo, mainly Pentatonic (5-note), antidiatonic (7-note), 9- and 16-note mosses. Here the outer ring represents individual step of 23edo itself, while the rings moving inward represent 16, 9, 7 and 5 note mosses:
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|-
|-
| 3 3 4 3 3 3 4
| 3 3 4 3 3 3 4
|[[2L 5s|2L 5s (mavila, anti-diatonic)]]
| [[2L 5s|2L 5s (mavila, anti-diatonic)]]
|-
|-
| 4 3 3 3 3 4 3
| 4 3 3 3 3 4 3
Line 454: Line 453:
| [[3L 7s|3L 7s (sephiroid)]]
| [[3L 7s|3L 7s (sephiroid)]]
|-
|-
|4 1 1 4 1 1 4 1 1 4 1
| 4 1 1 4 1 1 4 1 1 4 1
|[[4L 7s|4L 7s (kleistonic)]]
| [[4L 7s|4L 7s (kleistonic)]]
|-
|-
| 3 1 3 1 3 1 3 1 3 1 3
| 3 1 3 1 3 1 3 1 3 1 3
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|-
|-
| 3 1 1 3 1 3 1 1 3 1 3 1 1
| 3 1 1 3 1 3 1 1 3 1 3 1 1
|[[5L 8s|5L 8s (ateamtonic)]]
| [[5L 8s|5L 8s (ateamtonic)]]
|-
|-
|2 2 2 2 1 2 2 2 1 2 2 2 1
| 2 2 2 2 1 2 2 2 1 2 2 2 1
|[[10L 3s|10L 3s (luachoid)]]
| [[10L 3s|10L 3s (luachoid)]]
|-
|-
| 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
|[[9L 5s]] (Brittle [[Titanium]])
| [[9L 5s]] (Brittle [[Titanium]])
|-
|-
|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
|[[3L 11s]]
| [[3L 11s]]
|-
|-
| 3 1 1 1 3 1 1 1 3 1 1 1 3 1 1
| 3 1 1 1 3 1 1 1 3 1 1 1 3 1 1
|[[4L 11s|4L 11s (mynoid)]]
| [[4L 11s|4L 11s (mynoid)]]
|-
|-
| 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
|[[8L 7s]]
| [[8L 7s]]
|-
|-
|2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 1
| 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 1
|[[7L 9s|7L 9s (mavila chromatic)]]
| [[7L 9s|7L 9s (mavila chromatic)]]
|-
|-
|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 2 1 1 2 1 1 1 2 1 1 2 1 1 1
| 2 1 1 1 2 1 1 2 1 1 1 2 1 1 2 1 1 1
| Pathological 5L 13s (ateamtonic[18])
| [[5L 13s]]
|-
|-
| 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
|Pathological [[4L 15s|<nowiki>4L 15s (mynoid[19]]</nowiki>]]
| [[4L 15s]]
|}
|}
While [[35edo]] is the largest edo without a nondegenerate [[5L 2s]] scale, it has both degenerate cases (the equalised 7edo and the collapsed 5edo).
23edo is the largest edo without any form of 5L 2s, including the degenerate cases.


=== Kosmorsky's Sephiroth modes ===
=== Kosmorsky's Sephiroth modes ===
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=== Miscellaneous ===
=== Miscellaneous ===
5 5 1 2 5 5 - [[Antipental blues]]
5 5 1 2 5 5 - [[Antipental blues]] (approximated from [[Dwarf17marv]])
 
7 2 4 6 4 - Arcade (approximated from [[32afdo]])
 
6 4 1 2 2 6 2 - [[Blackened skies]] (approximated from [[Compton]] in [[72edo]])


2 3 8 2 8 - [[Pelog]] lima
5 5 3 7 3 - Geode (approximated from [[6afdo]])


== Further reading ==
5 4 2 2 4 2 4 - Lost phantom (approximated from [[Mavila]] in [[30edo]])
[[File:Libro_Icositrifónico.PNG|alt=Libro_Icositrifónico.PNG|302x365px|Libro_Icositrifónico.PNG|thumb|''Icosikaitriphonic Scales for Guitar'' cover art.]]
 
* [[Sword, Ron]]. ''[http://www.metatonalmusic.com/books.html Icosikaitriphonic Scales for Guitar: A Repository of Theory, Reference Materials, and Scale Charts for Xentonal Families]''. 2010.
6 4 2 1 5 1 4 - [[Lost spirit]] (approximated from [[Meantone]] in [[31edo]])
 
5 2 6 6 4 - Mechanical (approximated from [[31afdo]])
 
5 4 4 2 8 - Mushroom (approximated from [[30afdo]])
 
6 4 3 7 3 - Nightdrive (approximated from [[Mavila]] in [[30edo]])
 
6 4 1 2 6 4 - Pelagic (approximated from [[Mavila]] in [[30edo]])
 
2 3 8 2 8 - Approximation of [[Pelog]] lima
 
4 3 6 6 4 - Springwater (approximated from [[8afdo]])
 
2 5 2 4 6 4 - Starship (approximated from [[68ifdo]])
 
2 4 6 1 10 - Tightrope (this is the original/default tuning)
 
6 7 4 2 4 - Underpass (approximated from [[10afdo]])
 
2 5 6 6 4 - Volcanic (approximated from [[16afdo]])


== Instruments ==
== Instruments ==
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<youtube>K4iO7k152og</youtube>
<youtube>K4iO7k152og</youtube>
 
=== Lumatone ===
See: [[Lumatone mapping for 23edo]]
 
== Music ==
== Music ==
{{Main|23edo/Music}}
{{Catrel|23edo tracks}}
{{Catrel|23edo tracks}}


; [[Mike Battaglia]]
== Further reading ==
* [https://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments The Mavila Experiments &#45; 23&#45;EDO Version &#124; SoundCloud] (6 remapped classic pieces)
[[File:Libro_Icositrifónico.PNG|alt=Libro_Icositrifónico.PNG|302x365px|Libro_Icositrifónico.PNG|thumb|''Icosikaitriphonic Scales for Guitar'' cover art.]]
 
* [[Sword, Ron]]. ''[http://www.metatonalmusic.com/books.html Icosikaitriphonic Scales for Guitar: A Repository of Theory, Reference Materials, and Scale Charts for Xentonal Families]''. 2010.
; [[Easley Blackwood]]
*''Allegro Moderato'': [https://www.youtube.com/watch?v=enKFi8te8nY Easley Blackwood &#45; 23 NOTES (MIDI realization) &#45; YouTube]
 
; [[Warren Burt]]
* [http://home.vicnet.net.au/%7Eepoetry/family.mp3 The Family Supper]
 
; [[City of the Asleep]]
* [https://cityoftheasleep.bandcamp.com/track/permethrin-suite-23edo Permethrin Suite (23edo)]
 
; [[Cryptic Ruse]]
* [https://cryptic-ruse.bandcamp.com/album/unfertile UNFERTILE] (album)
 
; [[Tutim Dennsuul]]
* [http://micro.soonlabel.com/23edo/Tutim_Dennsuul/T%fatim%20Dennsuul%20-%20Indigorange.mp3 Indigorange]
* [http://micro.soonlabel.com/23edo/Tutim_Dennsuul/T%fatim%20Dennsuul%20-%20Wignud.mp3 Wignud]
* [http://micro.soonlabel.com/23edo/Tutim_Dennsuul/Tutim%20Dennsuul%20-%20%20Harid.mp3 Harid]
 
; [[E8 Heterotic]]
* [https://www.youtube.com/watch?v=1fopTqKjBZY Grand Theft Octave (23 EDO)]
 
; [[User:Francium|Francium]]
* [https://www.youtube.com/watch?v=PnyWCbQXn74 Elise Ain't Right]
* [https://www.youtube.com/watch?v=rXn02XuD5P8 Moonlight Party]
 
; [http://benfuhrman.com/ Ben Fuhrman]
* [https://www.youtube.com/watch?v=lYb4iK4Lt5Q Promethean Elegies]


; [[Andrew Heathwaite]]
* [http://andrewheathwaite.bandcamp.com/track/pentaswing Pentaswing] [[Technical Notes for Newbeams#Track notes:-Pentaswing|Notes]]
; [[Igliashon Jones]]
* [https://www.youtube.com/watch?v=Hqst8MaRiYM Icositriphonic Heptatonic MOS] {{dead link}}
* [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]
; [[Shunya Kiyokawa]]
* [https://soundcloud.com/shunya-kiyokawa/23edo-klavier8 23EDO Klavier8]
; [[Aaron Krister Johnson]]
* [http://www.akjmusic.com/audio/boogie_pie.mp3 Boogie Pie]
; [[Jacky Ligon]]
* [http://spectropolrecords.bandcamp.com/track/jacky-ligon-numenoctagon Numenoctagon] (on spectropolrecords)
; [[Jacky Ligon]], [[Sevish]] & [[Tony Dubshot]]
* [https://soundcloud.com/ism-studio/sets/ligon-sevish-dubshot-23 Ligon / Sevish / Dubshot ~ 23] (album)
; [[Gary Mcandrew]]
* [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]
; [[Claudi Meneghin]]
* [http://soonlabel.com/xenharmonic/archives/2460 Chromatic canon]
* [https://www.youtube.com/watch?v=bzy8ML6E3uc Two Mirror Canons in 23edo, for Oboe & Recorder]
* [https://www.youtube.com/watch?v=Pqg-N44bjgA Mavila Fugue]
* [https://www.youtube.com/watch?v=RbgNfV3gHR8 Fugue from the Dragnet, in Mavila (23edo), for baroque ensemble]
; [[müesk]]
* [https://soundcloud.com/muesk/doomsday-clock Doomsday Clock (23 edo, remastered) &#124; SoundCloud]
; [[NanoHarmony]]
* [https://soundcloud.com/nanoharmony/sun-ice-23edo-guitar Sun ice (23edo guitar) &#124; SoundCloud]
; [[Carlo Serafini]]
* [http://www.seraph.it/dep/det/DesertWinds.mp3 Desert Winds] ([http://www.seraph.it/blog_files/926007c7483e4abc5a48d582c0667947-105.html blog entry])
* [http://www.seraph.it/dep/det/23Laments.mp3 23 Laments] ([http://www.seraph.it/blog_files/b2bf6f252efd467ee36ecc332a4872ac-106.html blog entry])
* [http://www.seraph.it/dep/det/Doomsday23.mp3 Doomsday 23] ([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] ([http://www.seraph.it/blog_files/9e630d3f8ba93ab8264a3862dac950ce-192.html blog entry])
* [http://www.seraph.it/dep/det/Nubian%20Dance.mp3 Nubian Dance] ([http://www.seraph.it/blog_files/694f0a26d29cd2a215f37754dd8428c3-237.html blog entry])
* [http://www.seraph.it/dep/det/AroundTheBonfire.mp3 Around the bonfire] ([http://www.seraph.it/blog_files/9c6c54c593bc4720c8bd775fd5e244f4-261.html blog entry])
; [[X. J. Scott]]
* [http://www.nonoctave.com/tunes/CosmicChamber.mp3 Cosmic Chamber]
* [http://www.nonoctave.com/tunes/Daisies.mp3 Daisies on the Beach]
; [[Chris Vaisvil]]
* [http://clones.soonlabel.com/public/micro/23edo/daily20110619_23edo_23_chilled.mp3 23 Chilled]
* [http://micro.soonlabel.com/MOS/20120418-9mos-mindaugas.mp3 Mindaugas Rex Lithuaniae] (in Superpelog-9 tuning)
; [[Stephen Weigel]]
* [https://soundcloud.com/overtoneshock/curiosity-finds-a-frown-23-edo Curiosity Finds a Frown]
; [[Xotla]]
* [https://www.youtube.com/watch?v=COuE9uFlZ7A Warping]
[[Category:23edo| ]] <!-- main article -->
[[Category:Equal divisions of the octave|##]] <!-- 2-digit number -->
[[Category:23-tone scales]]
[[Category:23-tone scales]]
[[Category:Guitar]]
[[Category:Guitar]]
[[Category:Keyboard]]
[[Category:Listen]]
[[Category:Mavila]]
[[Category:Mavila]]
[[Category:Modes]]
[[Category:Modes]]
[[Category:Prime EDO]]
[[Category:Subgroup]]
[[Category:Twentuning]]
[[Category:Twentuning]]
[[Category:Todo:improve synopsis]]
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