45edo: Difference between revisions

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m Added EDO info box, changed interval names to match the note spelling, corrected 25\45 just cents value from 66.258 to 666.258
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{{Infobox ET
{{Infobox ET}}
| Prime factorization = 3<sup>2</sup> x 5
{{ED intro}}
| Step size = 26.667¢
| Fifth = 26\45 = 693.333¢
| Major 2nd = 7\45 = 186.667¢
| Minor 2nd = 5\45 = 133.333¢
| Augmented 1sn = 2\45 = 53.333¢
}}


'''45edo''' divides the octave into 45 equal parts of 26.667 [[cent]]s. It has two major thirds, each almost equally far from Just, but as the flat one is slightly closer, it qualifies as a meantone temperament, forming a good approximation to 2/5 comma meantone. It is the [[optimal patent val]] for [[flattone]] temperament, the [[7-limit]] 525/512 planar [[Avicennmic_temperaments|avicennmic]] temperament, the 11-limit [[calliope]] temperament tempering out [[45/44]] and [[81/80]], and the rank four temperament tempering out 45/44. It tempers out 81/80, 3125/3087, 525/512, 875/864 and 45/44. It is a flat-tending system in the 7-limit, with 3, 5 and 7 all flat, but the 11 is sharp. Also supports messed-up [[ennealimmal]], if you want. Since 45 is a multiple of 5 and 9, it can be used to model [[Indonesian]] music in both [[wikipedia:Slendro|Slendro]] (~ 5edo) and [[wikipedia:Pelog|Pelog]] (~ modes of 9edo) tunings.
== Theory ==
45edo effectively has two approximate [[5/4]] major thirds, each almost equally far from just, but the flat one is slightly closer. Combined with a [[3/2|perfect fifth]] 8.6 cents flat of just, it can be used as a [[meantone]] tuning, forming a good approximation to [[2/5-comma meantone]] (in fact falling into the [[flattone]] range). It is a flat-tending system in the [[7-limit]], with harmonics [[3/1|3]], [[5/1|5]], and [[7/1|7]] all flat. However, harmonics [[11/1|11]] and [[13/1|13]] are sharp, but this can be fixed with the 45ef val.


[[Category:Equal divisions of the octave]]
=== Odd harmonics ===
[[Category:Theory]]
{{Harmonics in equal|45}}


{| class="wikitable center-all"
=== As a tuning of other temperaments ===
It tempers out [[81/80]], [[525/512]], [[875/864]], and [[3125/3087]] in the 7-limit, and [[45/44]] in the [[11-limit]]. It provides the [[optimal patent val]] for 7- and 11-limit flattone temperament, and the 45f val is an excellent tuning for [[13-limit]] flattone. It also provides the optimal patent val for the 7-limit rank-3 [[avicennmic]] temperament, [[tempering out]] [[525/512]], the 11-limit [[calliope]] temperament, tempering out [[45/44]] and [[81/80]], and the rank-4 temperament tempering out 45/44. It is also the unique equal temperament tuning whose [[patent val]] tempers out both the syntonic comma and the [[ennealimma]].
 
45edo tempers out the [[quartisma]] and provides an excellent tuning for the 2.7/3.33-subgroup [[The Quartercache #Direct quartismic|direct quartismic]] temperament, in which it approximates the [[33/32]] quartertone with 2 steps and [[7/6]] with 10 steps. A bit more broadly, it maps the 2.27.25.63.33.65.17 subgroup to great precision; this is the part of the [[17-limit]] shared with [[270edo]].
 
Otherwise, it can be treated as a 2.5/3.7/3-subgroup system (borrowing 5/3 from [[15edo]] and 7/3 from [[9edo]]) and is a good tuning for [[gariberttet]], defined by tempering out [[3125/3087]] in this subgroup, approximating 2/5-comma gariberttet.
 
=== Subsets and supersets ===
Since 45 factors into primes as {{nowrap| 3<sup>2</sup> × 5 }}, 45edo has subset edos {{EDOs| 3, 5, 9, and 15 }}. [[135edo]], which triples it, corrects its primes 3, 7, and 11 to near-just qualities, and 270edo offers even more.
 
== Intervals ==
{| class="wikitable center-1 right-2 center-5 center-6"
|-
! #
! Cents
! Approximate ratios*
! colspan="4" | [[Ups and downs notation]]
|-
| 0
| 0.0
| [[1/1]]
| Perfect Unison
| P1
| D
|-
| 1
| 26.7
| [[49/48]], [[50/49]]
| Up unison
| ^1
| ^D
|-
| 2
| 53.3
| [[36/35]], ''[[25/24]]'', ''[[64/63]]''
| Augmented Unison
| A1
| D#
|-
| 3
| 80.0
| [[21/20]]
| Diminished 2nd
| d2
| Ebb
|-
| 4
| 106.7
| [[15/14]]
| Downminor 2nd
| vm2
| vEb
|-
| 5
| 133.3
| [[13/12]], [[14/13]], [[27/25]], ''[[16/15]]''
| Minor 2nd
| m2
| Eb
|-
| 6
| 160.0
| [[54/49]]
| Mid 2nd
| ~2
| vE
|-
| 7
| 186.7
| [[10/9]], ''[[9/8]]''
| Major 2nd
| M2
| E
|-
| 8
| 213.3
|
| Upmajor 2nd
| ^M2
| ^E
|-
| 9
| 240.0
| [[8/7]], [[15/13]]
| Augmented 2nd
| A2
| E#
|-
| 10
| 266.7
| [[7/6]]
| Diminished 3rd
| d3
| Fb
|-
| 11
| 293.3
| [[25/21]]
| Downminor 3rd
| vm3
| vF
|-
| 12
| 320.0
| [[6/5]]
| Minor 3rd
| m3
| F
|-
| 13
| 346.7
| [[49/40]], [[60/49]]
| Mid 3rd
| ~3
| ^F
|-
| 14
| 373.3
| [[5/4]], [[26/21]], ''[[16/13]]''
| Major 3rd
| M3
| F#
|-
| 15
| 400.0
| [[63/50]]
| Upmajor 3rd
| ^M3
| ^F#
|-
| 16
| 426.7
| [[9/7]]
| Augmented 3rd
| A3
| Fx
|-
| 17
| 453.3
| [[13/10]], ''[[21/16]]''
| Diminished 4th
| d4
| Gb
|-
| 18
| 480.0
| ''[[64/49]]''
| Down 4th
| v4
| vG
|-
| 19
| 506.7
| [[4/3]]
| Perfect 4th
| P4
| G
|-
| 20
| 533.3
| [[49/36]]
| Up 4th or Mid 4th
| ^4, ~4
| ^G
|-
| 21
| 560.0
| [[18/13]]
| Augmented 4th
| A4
| G#
|-
| 22
| 586.7
| [[7/5]]
| Upaugmented 4th
| ^A4
| ^G#
|-
|-
| rowspan="2" |Step #
| 23
| style="text-align:center;" |ET
| 613.3
| colspan="2" |Just
| [[10/7]]
|Difference <br> (ET minus Just)
| Downdiminshed 5th
| colspan="3" |[[Ups and Downs Notation]]
| vd5
| vAb
|-
|-
|Cents
| 24
|Interval
| 640.0
|Cents
| [[13/9]]
|
| Diminished 5th
|
| d5
|
| Ab
|
|-
|-
|0
| 25
|
| 666.7
| 1:1
| [[72/49]]
|0
| Down 5th or Mid 5th
|0
| v5, ~5
|Perfect Unison
| vA
|1
|D
|-
|-
|1
| 26
|26.666
| 693.3
|65:64
| [[3/2]]
|26.841
| Perfect 5th
| -0.174
| P5
|Up unison
| A
|
|D^
|-
|-
|2
| 27
|53.333
| 720.0
|33:32
| ''[[49/32]]''
|53.273
| Up 5th
|0.060
| ^5
|Augmented Unison
| ^A
|
|D#
|-
|-
|3
| 28
|80.0
| 746.7
|22:21
| [[20/13]], ''[[32/21]]''
|80.537
| Augmented 5th
| -0.537
| A5
|Upaugmented Unison
| A#
|
|D#^
|-
|-
|4
| 29
|106.666
| 773.3
|17:16
| [[14/9]]
|104.955
| Diminished 6th
|1.7112
| d6
|Downminor 2nd
| Bbb
|
|Ebv
|-
|-
|5
| 30
|133.333
| 800.0
|27:25
| [[100/63]]
|133.238
| Downminor 6th
|0.095
| vm6
| Minor 2nd
| vBb
|
|Eb
|-
|-
|6
| 31
|160
| 826.7
|11:10
| [[8/5]], [[21/13]], ''[[13/8]]''
|165.004
| Minor 6th
|<nowiki>-5.004</nowiki>
| m6
|Downmajor 2nd
| Bb
|
|Ev
|-
|-
|7
| 32
|186.666
| 853.3
|10:9
| [[49/30]], [[80/49]]
|182.404
| Mid 6th
|4.262
| ~6
|Major 2nd
| vB
|
|E
|-
|-
|8
| 33
|213.333
| 880.0
|9:8
| [[5/3]]
|203.910
| Major 6th
|9.423
| M6
|Upmajor 2nd
| B
|
|E^
|-
|-
|9
| 34
|240
| 906.7
|8:7
| [[42/25]]
|231.174
| Upmajor 6th
|8.826
| ^M6
|Augmented 2nd
| ^B
|
|E#
|-
|-
|10
| 35
|266.666
| 933.3
|7:6
| [[12/7]]
|266.871
| Augmented 6th
|<nowiki>-0.205</nowiki>
| A6
|Diminished 3rd
| B#
|
|Fb
|-
|-
|11
| 36
|293.333
| 960.0
|32:27
| [[7/4]], [[26/15]]
|294.135
| Diminished 7th
| -0.802
| d7
|Downminor 3rd
| Cb
|
|Fv
|-
|-
|12
| 37
|320
| 986.7
|6:5
|315.641
|4.359
|Minor 3rd
|  
|  
|F
| Downminor 7th
| vm7
| vC
|-
| 38
| 1013.3
| [[9/5]], ''[[16/9]]''
| Minor 7th
| m7
| C
|-
| 39
| 1040.0
| [[49/27]]
| Mid 7th
| ~7
| ^C
|-
| 40
| 1066.7
| [[13/7]], [[24/13]], [[50/27]], ''[[15/8]]''
| Major 7th
| M7
| C#
|-
| 41
| 1093.3
| [[28/15]]
| Upmajor 7th
| ^M7
| ^C#
|-
| 42
| 1120.0
| [[40/21]]
| Augmented 7th
| A7
| Cx
|-
| 43
| 1146.7
| [[35/18]], ''[[48/25]]'', ''[[63/32]]''
| Diminished 8ve
| d8
| Db
|-
|-
|13
| 44
|346.666
| 1173.3
|11:9
| [[49/25]], [[96/49]]
|347.408
| Down 8ve
| -0.741
| v8
|Mid 3rd
| vD
|
| F^
|-
|-
|14
| 45
|373.333
| 1200.0
|5:4-
| [[2/1]]
|386.314
| Perfect Octave
|<nowiki>-12.980</nowiki>
| P8
|Major 3rd
| D
|
|}
|F#
<nowiki/>* As a 2.3.5.7.13-subgroup temperament, using the 45f val
 
== Notation ==
 
=== Ups and downs notation ===
Spoken as up, sharp, upsharp, etc. Note that up can be respelled as downsharp.
{{Ups and downs sharpness}}
 
=== Quarter-tone notation ===
Since a sharp raises by two steps, [[24edo#Notation|quarter-tone accidentals]] can also be used.
{{sharpness-sharp2}}
 
=== Sagittal notation ===
This notation uses the same sagittal sequence as EDOs [[52edo#Sagittal notation|52]] and [[59edo#Second-best fifth notation|59b]].
 
==== Evo flavor ====
<imagemap>
File:45-EDO_Evo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 543 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 140 106 [[36/35]]
rect 140 80 300 106 [[1053/1024]]
default [[File:45-EDO_Evo_Sagittal.svg]]
</imagemap>
 
==== Revo flavor ====
<imagemap>
File:45-EDO_Revo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 543 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 140 106 [[36/35]]
rect 140 80 300 106 [[1053/1024]]
default [[File:45-EDO_Revo_Sagittal.svg]]
</imagemap>
 
==== Evo-SZ flavor ====
<imagemap>
File:45-EDO_Evo-SZ_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 511 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 140 106 [[36/35]]
rect 140 80 300 106 [[1053/1024]]
default [[File:45-EDO_Evo-SZ_Sagittal.svg]]
</imagemap>
 
Because it contains no Sagittal symbols, this Evo-SZ Sagittal notation is also a Stein-Zimmerman notation.
 
In the following diagrams, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO.
 
== Approximation to JI==
=== Interval mappings ===
{{Q-odd-limit intervals|45}}{{Q-odd-limit intervals|44.9|apx=val|header=none|tag=none|title=15-odd-limit intervals by 45ef val mapping}}
 
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
|-
|-
|15
! rowspan="2" | [[Subgroup]]
|400
! rowspan="2" | [[Comma list]]
|5:4+
! rowspan="2" | [[Mapping]]
|386.314
! rowspan="2" | Optimal<br>8ve stretch (¢)
|13.686
! colspan="2" | Tuning error
| Upmajor 3rd
|
|F#^
|-
|-
|16
! [[TE error|Absolute]] (¢)
|426.666
! [[TE simple badness|Relative]] (%)
|9:7
|435.084
| -8.418
|Downdiminshed 4th
|
|Gbv
|-
|-
|17
| 2.3
|453.333
| {{Monzo| -71 45 }}
|13:10
| {{Mapping| 45 71 }}
|454.294
| +2.72
| -0.961
| 2.73
|Diminished 4th
| 10.2
|
|Gb
|-
|-
|18
| 2.3.5
|480
| 81/80, {{monzo| -27 1 11 }}
|21:16
| {{Mapping| 45 71 104 }}
|470.781
| +3.68
|9.219
| 2.61
|Down 4th
| 9.75
|
|Gv
|-
|-
|19
| 2.3.5.7
|506.666
| 81/80, 525/512, 2401/2400
|4:3
| {{Mapping| 45 71 104 126 }}
|498.045
| +3.55
|8.622
| 2.27
|Perfect 4th
| 8.49
|
|G
|-
|-
|20
| 2.3.5.7.13
|533.333
| 65/64, 81/80, 105/104, 2401/2400
|49:36
| {{Mapping| 45 71 104 126 166 }} (45f)
|533.742
| +3.59
| -0.409
| 2.03
|Up 4th
| 7.60
|
|}
|G^
 
=== Commas ===
This is a partial list of the [[commas]] that 45et [[tempering out|tempers out]] with its [[patent val]], {{val| 45 71 104 126 143 156 167 }}.
 
{| class="commatable wikitable center-1 center-2 right-4 center-5"
|-
|-
|21
! [[Harmonic limit|Prime<br>limit]]
|560
! [[Ratio]]<ref group="note">{{rd}}</ref>
|18:13
! [[Monzo]]
|563.382
! [[Cent]]s
|<nowiki>-3.382</nowiki>
! [[Color name]]
|Augmented 4th
! Name(s)
|
|G#
|-
|-
|22
| 5
|586.666
| [[81/80]]
|7:5
| {{Monzo| -4 4 -1 }}
|582.512
| 21.51
| 4.155
| Gu
|Upaugmented 4th
| Syntonic comma, Didymus' comma, meantone comma
|
|G#^
|-
|-
|23
| 5
|613.333
| <abbr title="7629394531250/7625597484987">(26 digits)</abbr>
|10:7
| {{Monzo| 1 -27 18 }}
|617.488
| 0.86
|<nowiki>-4.155</nowiki>
| Satritribiyo
|Downdiminshed 5th
| [[Ennealimma]]
|
|Abv
|-
|-
|24
| 7
|640
| [[16807/16384]]
|13:9
| {{Monzo| -14 0 0 5 }}
|636.618
| 44.13
|3.382
| Laquinzo
|Diminished 5th
| Cloudy comma
|
|Ab
|-
|-
|25
| 7
|666.666
| [[525/512]]
|72:49
| {{Monzo| -9 1 2 1 }}
|666.258
| 43.41
|0.409
| Lazoyoyo
|Down 5th
| Avicennma, Avicenna's enharmonic diesis
|
|Av
|-
|-
|26
| 7
| 693.333
| [[875/864]]
| 3:2
| {{Monzo| -5 -3 3 1 }}
|701.955
| 21.90
| -8.622
| Zotrigu
|Perfect 5th
| Keema
|
|A
|-
|-
|27
| 7
| 720
| [[3125/3087]]
| style="text-align:center;" |32:21
| {{Monzo| 0 -2 5 -3 }}
|729.219
| 21.18
|<nowiki>-9.219</nowiki>
| Triru-aquinyo
|Up 5th
| Gariboh comma
|
|A^
|-
|-
|28
| 7
|746.666
| <abbr title="40353607/40310784">(16 digits)</abbr>
|20:13
| {{Monzo| -11 -9 0 9 }}
|745.786
| 1.84
|0.961
| Tritrizo
|Augmented 5th
| [[Septimal ennealimma]]
|
|A#
|-
|-
|29
| 7
|773.333
| [[4375/4374]]
| style="text-align:center;" |14:9
| {{Monzo| -1 -7 4 1 }}
|764.916
| 0.40
|8.418
| Zoquadyo
|Upaugmented 5th
| Ragisma
|
|A#^
|-
|-
|30
| 11
|800
| [[45/44]]
| style="text-align:center;" |8:5-
| {{Monzo| -2 2 1 0 -1 }}
|813.686
| 38.91
|<nowiki>-13.686</nowiki>
| Luyo
|Downminor 6th
| Undecimal 1/5-tone
|
|Bbv
|-
|-
|31
| 11
|826.666
| [[385/384]]
| style="text-align:center;" |8:5+
| {{Monzo| -7 -1 1 1 1 }}
| 813.686
| 4.50
|12.980
| Lozoyo
|Minor 6th
| Keenanisma
|
|Bb
|-
|-
|32
| 11
|853.333
| <abbr title="117440512/117406179">(18 digits)</abbr>
| style="text-align:center;" |18:11
| {{Monzo| 24 -6 0 1 -5 }}
|852.592
| 0.51
|0.741
| Saquinlu-azo
|Mid 6th
| [[Quartisma]]
|
|}
| Bv
<references group="note" />
 
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
|-
|33
! Periods<br>per 8ve
|880
! Generator*
| style="text-align:center;" |5:3
! Cents*
|884.359
! Associated<br>ratio*
|<nowiki>-4.359</nowiki>
! Temperament
|Major 6th
|
|B
|-
|-
|34
| 1
|906.666
| 1\45
| style="text-align:center;" |27:16
| 26.7
|905.865
| 49/48
|0.802
| [[Sfourth]]
|Upmajor 6th
|
|B^
|-
|-
|35
| 1
|933.333
| 2\45
| style="text-align:center;" |12:7
| 53.3
|933.129
| 36/35
|0.205
| [[Chromo]]
|Augmented 6th
|
|B#
|-
|-
|36
| 1
|960
| 7\45
| style="text-align:center;" | 7:4
| 186.7
|968.826
| 10/9
|<nowiki>-8.826</nowiki>
| [[Mintone]]
|Diminished 7th
|
|Cb
|-
|-
|37
| 1
| 986.666
| 11\45
| style="text-align:center;" | 16:9
| 293.3
|996.089
| 25/21
|<nowiki>-9.423</nowiki>
| [[Quasitemp]]
|Downminor 7th
|
|Cv
|-
|-
|38
| 1
|1013.333
| 14\45
| style="text-align:center;" |9:5
| 373.3
|1017.596
| 5/4
|<nowiki>-4.262</nowiki>
| [[Submerged]]
|Minor 7th
|
|C
|-
|-
|39
| 1
|1040
| 16\45
| style="text-align:center;" |20:11
| 426.7
|1034.996
| 9/7
|5.004
| [[Squares]]
| Upminor 7th
|
|C^
|-
|-
|40
| 1
| 1066.666
| 23\45
| style="text-align:center;" |50:27
| 453.3
|1066.762
| 13/10
|<nowiki>-0.095</nowiki>
| [[Maja]]
|Major 7th
|
|C#
|-
|-
|41
| 1
|1093.333
| 19\45
| style="text-align:center;" |32:17
| 506.7
|1095.044
| 4/3
| -1.7112
| [[Flattone]]
|Upmajor 7th
|
|C#^
|-
|-
|42
| 3
|1120
| 19\45<br>(4\45)
| style="text-align:center;" |21:11
| 506.7<br>(106.7)
|1119.463
| 4/3<br>(15/14)
|0.537
| [[Lithium]]
|Downdiminshed 8ve
|
|Dbv
|-
|-
|43
| 5
|1146.666
| 19\45<br>(1\45)
| style="text-align:center;" |64:33
| 506.7<br>(26.7)
|1146.727
| 4/3<br>(49/48)
|<nowiki>-0.060</nowiki>
| [[Cloudtone]]
|Diminished 8ve
|
|Db
|-
|-
|44
| 9
|1173.333
| 12\45<br>(2\45)
| style="text-align:center;" |128:65
| 320.0<br>(53.3)
|1173.158
| 6/5<br>(36/35)
|0.174
| [[Ennealimmal]]
|Down 8ve
|
|Dv
|-
|-
|45
| 15
|1200
| 19\45<br>(1\45)
| style="text-align:center;" |2:1
| 506.7<br>(26.7)
|1200
| 4/3<br>(126/125)
|0
| [[Pentadecal]]
|Perfect Octave
|
|D
|}
|}
<nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct
== Octave stretch and compression ==
45edo's approximations of 3/1, 5/1, 7/1, 11/1 and 13/1 and 17/1 are all improved by a [[Octave stretch|stretched-octave]] version of 45edo, such as [[ed12|161ed12]] or [[ed6|116ed6]]. The trade-off is a slightly worse 2/1. [[207zpi]] also improves on all of those harmonics except for 17/1.
The tuning [[equal tuning|183ed17]] may also be used, it improves 3/1, 5/1, 7/1, 11/1, 13/1 ''and'' 17/1 (with different mappings for many) but at the cost of a noticeably worse 2/1 than the others.
== Scales ==
* [[Cloudtone]][10] - recommended by [[Maeve Gutierrez]]: 8 1 8 1 8 1 8 1 8 1
* [[JUMBLE]]'s "moment of chaos scale": 3 9 6 1 4 7 2 5 8 (used in several works including [https://www.youtube.com/watch?v=WqEOi4cd1Og ''Archipelago Arpeggio''] and [https://www.youtube.com/watch?v=4iwJFVIWEII ''FERAL (45edo microtonal ambient track)''])
* 13-tone 5&9edo scale: 5 4 1 5 3 2 5 2 3 5 1 4 5
* 12-tone 5&9edo scale{{idio}}: 5 4 1 5 3 2 5 2 3 5 5 5
== Instruments ==
'''Lumatone'''
See [[Lumatone mapping for 45edo]]
== Music ==
; [[Bryan Deister]]
* [https://www.youtube.com/shorts/33tKBiWZvXM ''(short clip) Fantasy in 45edo''] (2025)
* [https://www.youtube.com/watch?v=Xblr-4aGBtM ''<nowiki>Twin Arrows [45edo]</nowiki>''] (2026)
; [[JUMBLE]]
* [https://www.youtube.com/watch?v=tbc_OxHp-ec ''Fishbowl''] (2023)
* [https://www.youtube.com/watch?v=WqEOi4cd1Og ''Archipelago Arpeggio''] (2024)
* [https://www.youtube.com/watch?v=Kd4t_iKiKMA ''Fallen Angel''] (2024)
* [https://www.youtube.com/watch?v=DPztb8W6ykY ''Solar Guardian''] (2024)
* [https://www.youtube.com/watch?v=24gnhAbHtiw ''Qúchze úzeq Qávka''] (2025)
* [https://www.youtube.com/watch?v=K2p7HOI3TUE ''Sodium Light (45edo Microtonal Chillwave)''] (2026)
* [https://www.youtube.com/watch?v=ex9WfmWVibY ''Yēú Zee Kiidhai (45edo microtonal ambient)''] (2026)
* [https://www.youtube.com/watch?v=4iwJFVIWEII ''FERAL (45edo microtonal ambient track)''] (2026)
* [https://www.youtube.com/watch?v=cXZ3RkTDE-I ''Chmelui-Múzeq - Haoýoze (45edo Microtonal Ambient)''] (2026)
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[[Category:Meantone]]
[[Category:Meantone]]
[[Category:Ennealimmal]]
[[Category:Quartismic]]
[[Category:Listen]]
[[Category:Todo:add rank 2 temperaments table]]