4edo: Difference between revisions

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{{interwiki

| de = ~~4edo~~

| de = 4-EDO

| en = 4edo

| es =

| ja =

| ja = 4平均律

}}

~~'''4 equal divisions of the octave''' ('''4EDO''') is the [[tuning system]] derived by dividing the [[octave]] into 4 equal steps of 300 [[cent]]s each.~~

== Theory ==

Like [[3edo~~|3EDO~~]], ~~4EDO~~ is already familiar as a chord of ~~12EDO~~. Not only that, but ~~4EDO~~ establishes tonality in much the same ways that ~~3EDO does — with~~ only two notes at a time as opposed to three aside from octave reduplications of the tonic, though the Tonic-Antitonic contrast from ~~2EDO~~ also works. Also like with 3edo, it has a theoretical interest in that it preserves a kind of outline, or skeleton, of melodic movement while erasing key distinctions concerning harmony. The 7-limit [[mapping]], or [[~~Vals and_Tuning Space|~~val]], for ~~4EDO~~ goes {{val|4 6 9 11}}, all of which are distinct modulo 4. It therefore goes with tetradic harmony in much the same way that ~~3EDO~~ goes with triadic harmony, mapping the [[7-limit]] [[consistent]]ly, and sending 15/14, 21/20, 25/24, and 36/35 to the unison. Somewhat confusingly, the patent mapping of 4edo sees 9/8 mapped to the unison also, leading to [[Very low accuracy temperaments #Antitonic|antitonic]], though this can be traced to both 3/2 and 4/3 being mapped to 2\4.

Like [[3edo]], 4edo is already familiar as a chord of [[12edo]]. Not only that, but 4edo establishes tonality in much the same ways that 3edo does—with only two notes at a time as opposed to three aside from octave reduplications of the tonic, though the Tonic-Antitonic contrast from [[2edo]] also works. Also like with 3edo, it has a theoretical interest in that it preserves a kind of outline, or skeleton, of melodic movement while erasing key distinctions concerning harmony. The 7-limit [[mapping]], or [[val]], for 4edo goes {{val| 4 6 9 11 }}, all of which are distinct modulo 4. It therefore goes with tetradic harmony in much the same way that 3edo goes with triadic harmony, mapping the [[7-limit]] [[consistent]]ly, and sending [[15/14]], [[21/20]], [[25/24]], and [[36/35]] to the unison. Somewhat confusingly, the patent mapping of 4edo sees [[9/8]] mapped to the unison also, leading to [[Very low accuracy temperaments #Antitonic|antitonic]], though this can be traced to both [[3/2]] and [[4/3]] being mapped to 2\4.

By putting together the triples of integers which uniquely represent 7-limit tetrads in the [[~~The_Seven_Limit_Symmetrical_Lattices~~|7-limit cubic lattice of tetrads]] with the number of ~~4EDO~~ steps returned by the {{val|4 6 9 11}} we obtain a representation of the 7-limit in terms of four integers, which differs from the usual (monzo) representation in that the triple representing the chord can be swapped for another such triple, resulting in a similar note tuned to a different chord. It is even possible under some circumstances to create a sort of recombinant merging of two pieces of music by using the chords of one with the ~~4EDO~~ skeletons of another.

By putting together the triples of integers which uniquely represent 7-limit tetrads in the [[The Seven Limit Symmetrical Lattices|7-limit cubic lattice of tetrads]] with the number of 4edo steps returned by the {{val| 4 6 9 11 }} we obtain a representation of the 7-limit in terms of four integers, which differs from the usual (monzo) representation in that the triple representing the chord can be swapped for another such triple, resulting in a similar note tuned to a different chord. It is even possible under some circumstances to create a sort of recombinant merging of two pieces of music by using the chords of one with the 4edo skeletons of another.

We can also add more kinds of chords, for instance the subminor (1-7/~~6-3~~/~~2-5~~/3) and supermajor (~~1-9~~/~~7-3~~/~~2-9~~/5) to the mix, and by encoding which kind of tetrad a note reconstitute a version of 9-odd-limit tetradic harmony, again changing the harmonic content of a note without changing its ~~4EDO~~ skeletal position.

We can also add more kinds of chords, for instance the subminor ([[6:7:9:10|1–7/6–3/2–5/3]]) and supermajor ([[70:90:105:126|1–9/7–3/2–9/5]]) to the mix, and by encoding which kind of tetrad a note reconstitute a version of 9-odd-limit tetradic harmony, again changing the harmonic content of a note without changing its 4edo skeletal position.

~~When~~ viewed ~~from~~ a [[~~regular temperament~~]] ~~perspective~~, ~~4EDO can be seen as a tuning of~~ the [[~~Dimipent family #Dimipent|dimipent temperament~~]], ~~since it tempers~~ [[~~648/625~~]] (the major ~~diesis) by equating four minor thirds~~ ([[~~6/5~~]]) ~~to an octave~~. ~~Alternately, it can be viewed as a critically flat~~ [[~~hanson~~]] or [[~~myna~~]] ~~scale~~, ~~as both 6~~ and ~~10 generators reach~~ the ~~best approximation~~ to the 5th. This interpretation works best if you stretch the octaves, 4edo is the first edo that is [[The_Riemann_zeta_function_and_tuning#Zeta_EDO_lists|zeta peak but not zeta peak integer]], which means the point of ~~maximum harmonicity is somewhat further away from pure octaves than the previous two edos. If you compress the octaves instead, it can be interpreted as critically sharp~~ [[~~Chromatic_pairs#Gariberttet|Gariberttet~~]].

4edo can be viewed as a [[dual-fifth]] system (the smallest in fact, besides the trivial [[1edo]]), with the tritone and major sixth as the flat and sharp "fifths". The tritone represents 3/2 in the [[patent val]], while the major sixth represents 3/2 in the 4b val (using [[wart notation]]). The 4b val has one of the sharpest mappings of 3/2 of any [[octave]]-repeating equal temperaments, only outmatched by that of [[1edo]], and even falling outside of the 600- to 800-cent range of [[2L 1s]].

== ~~Music~~ ==

4edo can be seen as a trivial tuning of the [[diminished (temperament)|diminished]] temperament, since it tempers out [[648/625]] (the major diesis) by equating four minor thirds ([[6/5]]) to an octave. Alternately, it can be viewed as a critically flat [[hanson]] or [[myna]] tuning, as both 6 and 10 generators reach the best approximation to the 5th. This interpretation works best if you stretch the octaves; 4edo is the first edo that is [[The Riemann zeta function and tuning #Zeta edo lists|zeta peak but not zeta peak integer]], which means the point of maximum harmonicity is somewhat further away from pure octaves than the previous two edos. If you compress the octaves instead, it can be interpreted as a critically sharp [[subgroup temperaments #Gariberttet|gariberttet]] tuning.

{| class="wikitable ~~sortable~~"

!~~Title~~

=== Odd harmonics ===

!~~Composer~~

!~~Year~~

!~~Genre~~

=== Subsets and supersets ===

!~~Additional links~~

4edo is the first composite edo, containing [[2edo]] as the only nontrivial subset edo.

== Intervals ==

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Intervals of 4edo

|-

! rowspan="2" | [[Degree]]

! rowspan="2" | [[Cent]]s

! rowspan="2" | [[Interval region]]

! colspan="4" | Approximated [[JI]] intervals* ([[error]] in [[¢]])

! rowspan="2" | Audio

|-

! [[3-limit]]

! [[5-limit]]

! [[7-limit]]

! Other

|-

| 0

| Unison (prime)

| [[1/1]] (just)

|

| [[File:piano_0_1edo.mp3]]

|-

| 1

| 300

| Minor third

| [[32/27]] (+5.865)

| [[6/5]] (-15.641)

| [[7/6]] (+33.129) [[25/21]] (-1.847)

| [[19/16]] (+2.487)

| [[File:piano_1_4edo.mp3]]

|-

| 2

| 600

| [[Tritone]]

|

| [[7/5]] (+17.488) [[10/7]] (-17.488)

| [[24/17]] (+3.000) [[99/70]] (-0.088) [[17/12]] (-3.000)

| [[File:piano_1_2edo.mp3]]

|-

| 3

| 900

| Major sixth

| [[27/16]] (-5.865)

| [[5/3]] (+15.641)

| [[42/25]] (+1.847) [[12/7]] (-33.129)

| [[32/19]] (-2.487)

| [[File:piano_3_4edo.mp3]]

|-

| 4

| 1200

| Octave

| [[2/1]] (just)

|

| [[File:piano_1_1edo.mp3]]

|}

<nowiki />* Based on treating 4edo as a subset of [[12edo]], itself treated as a 2.3.5.7.17.19 subgroup temperament; other approaches are possible.

== Notation ==

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Notation of 4edo

|-

! rowspan="2" | [[Degree]]

! rowspan="2" | [[Cent]]s

! colspan="2" | [[12edo]] [[subset notation]]

|-

! [[5L 2s|Diatonic]] interval names

! Note names (on D)

|-

| 0

| '''Perfect unison (P1)'''

| '''D'''

|-

| 1

| 300

| Augmented second (A2) '''Minor third (m3)'''

| E# '''F'''

|-

| 2

| 600

| Augmented fourth (A4) Diminished fifth (d5)

| G# Ab

|-

| 3

| 900

| '''Major sixth (M6)''' Diminished seventh (d7)

| '''B''' Cb

|-

| 4

| 1200

| '''Perfect octave (P8)'''

| '''D'''

|}

In 4edo:

* [[ups and downs notation]] is identical to standard notation;

* Mixed [[sagittal notation]] is identical to standard notation, but pure sagittal notation exchanges sharps (#) and flats (b) for sagittal sharp ([[File:Sagittal sharp.png]]) and sagittal flat ([[File:Sagittal flat.png]]) respectively.

== Solfege ==

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Solfege of 4edo

|-

! [[Degree]]

! [[Cents]]

! 12edo subset standard [[solfege]] (movable do)

! 12edo subset [[Uniform solfege]] (2-3 vowels)

|-

| 0

| Do (P1)

| Da (P1)

|-

|~~''Nothing of any importance''~~

| 1

|~~[[Rozencrantz|Rozencrantz the Sane]]~~

| 300

|~~2006~~

| Ri (A2) Me (m3)

|(?)

| Ru (A2) Na (m3)

~~|His contribution to the [[MMMday06|MMM day 2006]]~~

|-

|~~[http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/fouredo.mp3 ''A simple 4EDO piece'']~~

| 2

|~~[[Gene Ward Smith]]~~

| 600

|~~2011~~ (?)

| Fi (A4) Se (d5)

|~~Classical~~

| Pa (A4) Sha (d5)

~~|Explanation: [[Composing_with_tablets|Composing with tablets]]~~

|-

|~~data-sort-value="Entering (from Edolian)"|[https://www.youtube.com/watch?v=rCfWHwrEaA0 "Entering"] (from [https://www.youtube.com/playlist?list=PLg1YtcJbLxnwTJkG4m0BWZWxIHj7ScdNn ''Edolian''])~~

| 3

|~~NullPointerException Music~~

| 900

|~~2020~~

| La (M6)

~~|Classical~~

| La (M6) Tho (d7)

|

|-

|~~data-sort-value="Neainaz Antithetica, Variation II (from STAFFcirc vol. 7)"|"[https://soundcloud.com/sexytoadsandfrogsfriendcircle/~~4~~-stc-s1003-neainaz Neainaz Antithetica, Variation II]" (from [https://soundcloud.com/sexytoadsandfrogsfriendcircle/sets/staffcirc-vol-7-terra-octava ''STAFFcirc vol. 7''])~~

| 4

|~~STC_1003~~

| 1200

|~~2021~~

| Do (P8)

~~|Electronic~~

| Da (P8)

|~~[https://sexytoadsandfrogsfriendcircle.bandcamp.com/album/staffcirc-vol-7-terra-octava Album~~ (~~Bandcamp~~)]

|}

== Music ==

; [[Aeterna]]

* [https://www.youtube.com/watch?v=catncLv5oSk "Mimetism"], from [https://youtube.com/playlist?list=OLAK5uy_meMItS3Zalh3jNeQ-4XVwEp0JUPO3A9rQ ''Tribute to Armodue''] (2008)

; [[No Clue Music]]

* [https://www.youtube.com/watch?v=JBGqDbbZ0Fw ''Dimpulse''] (2024)

; [[NullPointerException Music]]

* [https://www.youtube.com/watch?v=rCfWHwrEaA0 "Entering"], from [https://www.youtube.com/playlist?list=PLg1YtcJbLxnwTJkG4m0BWZWxIHj7ScdNn ''Edolian''] (2020)

; [[User:Phanomium|Phanomium]]

* [https://www.youtube.com/watch?v=T0J1D_E94L4 ''Diminished''] (2024)

; [[Rozencrantz|Rozencrantz the Sane]]

* ''Nothing of any importance'' (2006) – his contribution to the [[MMMday06|MMM day 2006]][''where?'']

; [[Gene Ward Smith]]

* [https://web.archive.org/web/20201127012143/http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/fouredo.mp3 ''A simple 4EDO piece''] (2011?) – see also [[Composing with tablets]]

; [[STC_1003]]

* "Neainaz Antithetica, Variation II", from [https://soundcloud.com/sexytoadsandfrogsfriendcircle/sets/staffcirc-vol-7-terra-octava ''STAFFcirc vol. 7''] (2021) – [https://soundcloud.com/sexytoadsandfrogsfriendcircle/4-stc-s1003-neainaz SoundCloud] | [https://sexytoadsandfrogsfriendcircle.bandcamp.com/track/4-neainaz-antithetica-variation-ii Bandcamp]

[[Category:7-limit]]

[[Category:~~Equal divisions of the octave]]~~

[[Category:Listen]]

~~[[Category:macrotonal~~]]

@@ Line 1: / Line 1: @@
 {{interwiki
-| de = 4edo
+| de = 4-EDO
 | en = 4edo
 | es =
-| ja =
+| ja = 4平均律
 }}
-'''4 equal divisions of the octave''' ('''4EDO''') is the [[tuning system]] derived by dividing the [[octave]] into 4 equal steps of 300 [[cent]]s each.
+{{Infobox ET}}
+{{ED intro}}
 == Theory ==
-Like [[3edo|3EDO]], 4EDO is already familiar as a chord of 12EDO.  Not only that, but 4EDO establishes tonality in much the same ways that 3EDO does — with only two notes at a time as opposed to three aside from octave reduplications of the tonic, though the Tonic-Antitonic contrast from 2EDO also works.  Also like with 3edo, it has a theoretical interest in that it preserves a kind of outline, or skeleton, of melodic movement while erasing key distinctions concerning harmony. The 7-limit [[mapping]], or [[Vals and_Tuning Space|val]], for 4EDO goes {{val|4 6 9 11}}, all of which are distinct modulo 4. It therefore goes with tetradic harmony in much the same way that 3EDO goes with triadic harmony, mapping the [[7-limit]] [[consistent]]ly, and sending 15/14, 21/20, 25/24, and 36/35 to the unison. Somewhat confusingly, the patent mapping of 4edo sees 9/8 mapped to the unison also, leading to [[Very low accuracy temperaments #Antitonic|antitonic]], though this can be traced to both 3/2 and 4/3 being mapped to 2\4.
+Like [[3edo]], 4edo is already familiar as a chord of [[12edo]]. Not only that, but 4edo establishes tonality in much the same ways that 3edo does—with only two notes at a time as opposed to three aside from octave reduplications of the tonic, though the Tonic-Antitonic contrast from [[2edo]] also works.  Also like with 3edo, it has a theoretical interest in that it preserves a kind of outline, or skeleton, of melodic movement while erasing key distinctions concerning harmony. The 7-limit [[mapping]], or [[val]], for 4edo goes {{val| 4 6 9 11 }}, all of which are distinct modulo 4. It therefore goes with tetradic harmony in much the same way that 3edo goes with triadic harmony, mapping the [[7-limit]] [[consistent]]ly, and sending [[15/14]], [[21/20]], [[25/24]], and [[36/35]] to the unison. Somewhat confusingly, the patent mapping of 4edo sees [[9/8]] mapped to the unison also, leading to [[Very low accuracy temperaments #Antitonic|antitonic]], though this can be traced to both [[3/2]] and [[4/3]] being mapped to 2\4.
-By putting together the triples of integers which uniquely represent 7-limit tetrads in the [[The_Seven_Limit_Symmetrical_Lattices|7-limit cubic lattice of tetrads]] with the number of 4EDO steps returned by the {{val|4 6 9 11}} we obtain a representation of the 7-limit in terms of four integers, which differs from the usual (monzo) representation in that the triple representing the chord can be swapped for another such triple, resulting in a similar note tuned to a different chord. It is even possible under some circumstances to create a sort of recombinant merging of two pieces of music by using the chords of one with the 4EDO skeletons of another.
+By putting together the triples of integers which uniquely represent 7-limit tetrads in the [[The Seven Limit Symmetrical Lattices|7-limit cubic lattice of tetrads]] with the number of 4edo steps returned by the {{val| 4 6 9 11 }} we obtain a representation of the 7-limit in terms of four integers, which differs from the usual (monzo) representation in that the triple representing the chord can be swapped for another such triple, resulting in a similar note tuned to a different chord. It is even possible under some circumstances to create a sort of recombinant merging of two pieces of music by using the chords of one with the 4edo skeletons of another.
-We can also add more kinds of chords, for instance the subminor (1-7/6-3/2-5/3) and supermajor (1-9/7-3/2-9/5) to the mix, and by encoding which kind of tetrad a note reconstitute a version of 9-odd-limit tetradic harmony, again changing the harmonic content of a note without changing its 4EDO skeletal position.
+We can also add more kinds of chords, for instance the subminor ([[6:7:9:10|1–7/6–3/2–5/3]]) and supermajor ([[70:90:105:126|1–9/7–3/2–9/5]]) to the mix, and by encoding which kind of tetrad a note reconstitute a version of 9-odd-limit tetradic harmony, again changing the harmonic content of a note without changing its 4edo skeletal position.
-When viewed from a [[regular temperament]] perspective, 4EDO can be seen as a tuning of the [[Dimipent family #Dimipent|dimipent temperament]], since it tempers [[648/625]] (the major diesis) by equating four minor thirds ([[6/5]]) to an octave. Alternately, it can be viewed as a critically flat [[hanson]] or [[myna]] scale, as both 6 and 10 generators reach the best approximation to the 5th. This interpretation works best if you stretch the octaves, 4edo is the first edo that is [[The_Riemann_zeta_function_and_tuning#Zeta_EDO_lists|zeta peak but not zeta peak integer]], which means the point of maximum harmonicity is somewhat further away from pure octaves than the previous two edos. If you compress the octaves instead, it can be interpreted as critically sharp [[Chromatic_pairs#Gariberttet|Gariberttet]].
+edo can be viewed as a [[dual-fifth]] system (the smallest in fact, besides the trivial [[1edo]]), with the tritone and major sixth as the flat and sharp "fifths". The tritone represents 3/2 in the [[patent val]], while the major sixth represents 3/2 in the 4b val (using [[wart notation]]). The 4b val has one of the sharpest mappings of 3/2 of any [[octave]]-repeating equal temperaments, only outmatched by that of [[1edo]], and even falling outside of the 600- to 800-cent range of [[2L 1s]].
-== Music ==
+edo can be seen as a trivial tuning of the [[diminished (temperament)|diminished]] temperament, since it tempers out [[648/625]] (the major diesis) by equating four minor thirds ([[6/5]]) to an octave. Alternately, it can be viewed as a critically flat [[hanson]] or [[myna]] tuning, as both 6 and 10 generators reach the best approximation to the 5th. This interpretation works best if you stretch the octaves; 4edo is the first edo that is [[The Riemann zeta function and tuning #Zeta edo lists|zeta peak but not zeta peak integer]], which means the point of maximum harmonicity is somewhat further away from pure octaves than the previous two edos. If you compress the octaves instead, it can be interpreted as a critically sharp [[subgroup temperaments #Gariberttet|gariberttet]] tuning.
-{| class="wikitable sortable"
-!Title
+=== Odd harmonics ===
-!Composer
+{{Harmonics in equal|4}}
-!Year
-!Genre
+=== Subsets and supersets ===
-!Additional links
+edo is the first composite edo, containing [[2edo]] as the only nontrivial subset edo.
+== Intervals ==
+{| class="wikitable center-all"
+|+ style="font-size: 105%;" | Intervals of 4edo
+|-
+! rowspan="2" | [[Degree]]
+! rowspan="2" | [[Cent]]s
+! rowspan="2" | [[Interval region]]
+! colspan="4" | Approximated [[JI]] intervals* ([[error]] in [[¢]])
+! rowspan="2" | Audio
+|-
+! [[3-limit]]
+! [[5-limit]]
+! [[7-limit]]
+! Other
+|-
+| 0
+| 0
+| Unison (prime)
+| [[1/1]] (just)
+|
+|
+|
+| [[File:piano_0_1edo.mp3]]
+|-
+| 1
+| 300
+| Minor third
+| [[32/27]] (+5.865)
+| [[6/5]] (-15.641)
+| [[7/6]] (+33.129)<br>[[25/21]] (-1.847)
+| [[19/16]] (+2.487)
+| [[File:piano_1_4edo.mp3]]
+|-
+| 2
+| 600
+| [[Tritone]]
+|
+|
+| [[7/5]] (+17.488)<br>[[10/7]] (-17.488)
+| [[24/17]] (+3.000)<br>[[99/70]] (-0.088)<br>[[17/12]] (-3.000)
+| [[File:piano_1_2edo.mp3]]
+|-
+| 3
+| 900
+| Major sixth
+| [[27/16]] (-5.865)
+| [[5/3]] (+15.641)
+| [[42/25]] (+1.847)<br>[[12/7]] (-33.129)
+| [[32/19]] (-2.487)
+| [[File:piano_3_4edo.mp3]]
+|-
+| 4
+| 1200
+| Octave
+| [[2/1]] (just)
+|
+|
+|
+| [[File:piano_1_1edo.mp3]]
+|}
+<nowiki />* Based on treating 4edo as a subset of [[12edo]], itself treated as a 2.3.5.7.17.19 subgroup temperament; other approaches are possible.
+== Notation ==
+{| class="wikitable center-all"
+|+ style="font-size: 105%;" | Notation of 4edo
+|-
+! rowspan="2" | [[Degree]]
+! rowspan="2" | [[Cent]]s
+! colspan="2" | [[12edo]] [[subset notation]]
+|-
+! [[5L 2s|Diatonic]] interval names
+! Note names (on D)
+|-
+| 0
+| 0
+| '''Perfect unison (P1)'''
+| '''D'''
+|-
+| 1
+| 300
+| Augmented second (A2)<br>'''Minor third (m3)'''
+| E#<br>'''F'''
+|-
+| 2
+| 600
+| Augmented fourth (A4)<br>Diminished fifth (d5)
+| G#<br>Ab
+|-
+| 3
+| 900
+| '''Major sixth (M6)'''<br>Diminished seventh (d7)
+| '''B'''<br>Cb
+|-
+| 4
+| 1200
+| '''Perfect octave (P8)'''
+| '''D'''
+|}
+In 4edo:
+* [[ups and downs notation]] is identical to standard notation;
+* Mixed [[sagittal notation]] is identical to standard notation, but pure sagittal notation exchanges sharps (#) and flats (b) for sagittal sharp ([[File:Sagittal sharp.png]]) and sagittal flat ([[File:Sagittal flat.png]]) respectively.
+== Solfege ==
+{| class="wikitable center-all"
+|+ style="font-size: 105%;" | Solfege of 4edo
+|-
+! [[Degree]]
+! [[Cents]]
+! 12edo subset<br>standard [[solfege]]<br>(movable do)
+! 12edo subset<br>[[Uniform solfege]]<br>(2-3 vowels)
+|-
+| 0
+| 0
+| Do (P1)
+| Da (P1)
 |-
-|''Nothing of any importance''
+| 1
-|[[Rozencrantz|Rozencrantz the Sane]]
+| 300
-|2006
+| Ri (A2)<br>Me (m3)
-|(?)
+| Ru (A2)<br>Na (m3)
-|His contribution to the [[MMMday06|MMM day 2006]]
 |-
-|[http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/fouredo.mp3 ''A simple 4EDO piece'']
+| 2
-|[[Gene Ward Smith]]
+| 600
-|2011 (?)
+| Fi (A4)<br>Se (d5)
-|Classical
+| Pa (A4)<br>Sha (d5)
-|Explanation: [[Composing_with_tablets|Composing with tablets]]
 |-
-|data-sort-value="Entering (from Edolian)"|[https://www.youtube.com/watch?v=rCfWHwrEaA0 "Entering"] (from [https://www.youtube.com/playlist?list=PLg1YtcJbLxnwTJkG4m0BWZWxIHj7ScdNn ''Edolian''])
+| 3
-|NullPointerException Music
+| 900
-|2020
+| La (M6)
-|Classical
+| La (M6)<br>Tho (d7)
-|
 |-
-|data-sort-value="Neainaz Antithetica, Variation II (from STAFFcirc vol. 7)"|"[https://soundcloud.com/sexytoadsandfrogsfriendcircle/4-stc-s1003-neainaz Neainaz Antithetica, Variation II]" (from [https://soundcloud.com/sexytoadsandfrogsfriendcircle/sets/staffcirc-vol-7-terra-octava ''STAFFcirc vol. 7''])
+| 4
-|STC_1003
+| 1200
-|2021
+| Do (P8)
-|Electronic
+| Da (P8)
-|[https://sexytoadsandfrogsfriendcircle.bandcamp.com/album/staffcirc-vol-7-terra-octava Album (Bandcamp)]
 |}
+== Music ==
+; [[Aeterna]]
+* [https://www.youtube.com/watch?v=catncLv5oSk "Mimetism"], from [https://youtube.com/playlist?list=OLAK5uy_meMItS3Zalh3jNeQ-4XVwEp0JUPO3A9rQ ''Tribute to Armodue''] (2008)
+; [[No Clue Music]]
+* [https://www.youtube.com/watch?v=JBGqDbbZ0Fw ''Dimpulse''] (2024)
+; [[NullPointerException Music]]
+* [https://www.youtube.com/watch?v=rCfWHwrEaA0 "Entering"], from [https://www.youtube.com/playlist?list=PLg1YtcJbLxnwTJkG4m0BWZWxIHj7ScdNn ''Edolian''] (2020)
+; [[User:Phanomium|Phanomium]]
+* [https://www.youtube.com/watch?v=T0J1D_E94L4 ''Diminished''] (2024)
+; [[Rozencrantz|Rozencrantz the Sane]]
+* ''Nothing of any importance'' (2006) – his contribution to the [[MMMday06|MMM day 2006]]<sup>[''where?'']</sup>
+; [[Gene Ward Smith]]
+* [https://web.archive.org/web/20201127012143/http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/fouredo.mp3 ''A simple 4EDO piece''] (2011?) – see also [[Composing with tablets]]
+; [[STC_1003]]
+* "Neainaz Antithetica, Variation II", from [https://soundcloud.com/sexytoadsandfrogsfriendcircle/sets/staffcirc-vol-7-terra-octava ''STAFFcirc vol. 7''] (2021) – [https://soundcloud.com/sexytoadsandfrogsfriendcircle/4-stc-s1003-neainaz SoundCloud] | [https://sexytoadsandfrogsfriendcircle.bandcamp.com/track/4-neainaz-antithetica-variation-ii Bandcamp]
 [[Category:7-limit]]
-[[Category:Equal divisions of the octave]]
+[[Category:Listen]]
-[[Category:macrotonal]]