Gallery of combination product sets: Difference between revisions

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Complete 15-odd limit table
 
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This is a gallery of [[combination product set]] (CPS) scales, as well as subsets of, mergers of, or modifications of such scales.  
This is a gallery of [[combination product set]] (CPS) scales, as well as subsets of, mergers of, or modifications of such scales.


There are infinite possible CPS scales, so this list can never be complete.
There are infinite possible CPS scales, so this list can never be complete. If you find a CPS scale that you like, please document it here so that people can make music with it.


If you find a CPS scale that you like, please document it here so that people can make music with it.


See also [[:Category:Combination product sets]], which may include scales that have yet to be added to this list.
See also [[:Category:Combination product sets]], which may include scales that have yet to be added to this list.


 
''Italicised text following an em-dash beside a listed scale is a description by a wiki contributor of the subjective mood they personally feel when listening to the scale.''
(''In brackets beside listed scales are descriptions by wiki contributors of the subjective mood they personally feel when listening to the scale.'')


== Pentanies (5-tone) ==
== Pentanies (5-tone) ==
Line 15: Line 12:
''Main page: [[Pentany]]''
''Main page: [[Pentany]]''


* [[4 from 1-3-5-7-11 pentany]] (''sturdy, earthy'')
* [[4 from 1-3-5-7-11 pentany]] ''sturdy, earthy''
* [[4 from 5-17-23-29-37 pentany]] (''like anticipating the sunrise'')
* [[4 from 5-17-23-29-37 pentany]] ''like anticipating the sunrise''
* [[4 from 5-17-23-29-41 pentany]] (''ethereal, enchanting'')
* [[4 from 5-17-23-29-41 pentany]] ''ethereal, enchanting''
* [[4 from 5-17-23-31-41 pentany]] (''sorrowful, warm'')
* [[4 from 5-17-23-31-41 pentany]] ''sorrowful, warm''
* [[4 from 5-17-23-31-43 pentany]] (''alert, tense'')
* [[4 from 5-17-23-31-43 pentany]] ''alert, tense''


== Hexanies (6-tone) ==
== Hexanies (6-tone) ==
[[Category:6-tone scales]]
[[Category:6-tone scales]]
''Main page: [[Hexany]]''
''Main page: [[Hexany]]''
{| class="wikitable mw-collapsible mw-collapsed sortable" right-all"
|-
|-
! Combination Product Set
! Sum of factors
! Lowest common divisor
! Odd-limit
! Prime Limit
! Largest step size
! Smallest step size
! L/s step ratio
! Number of repeated notes
|-
| [[1-3-5-7 hexany]] || 16 || 3 || 7 || 7 || 266.871 || 84.467 || 3.159 || 0
|-
| [[1-3-5-9 hexany]] || 18 || 3 || 9 || 5 || 315.641 || 111.731 || 2.825 || 0
|-
| [[1-3-7-9 hexany]] || 20 || 3 || 9 || 7 || 266.871 || 62.961 || 4.238 || 0
|-
| [[1-5-7-9 hexany]] || 22 || 5 || 9 || 7 || 378.602 || 48.770 || 7.763 || 0
|-
| [[3-5-7-9 hexany]] || 24 || 15 || 9 || 7 || 315.641 || 84.467 || 3.736 || 0
|-
| [[1-3-5-11 hexany]] || 20 || 3 || 11 || 11 || 333.040 || 150.637 || 2.210 || 0
|-
| [[1-3-7-11 hexany]] || 22 || 3 || 11 || 11 || 284.447 || 80.537 || 3.531 || 0
|-
| [[1-3-9-11 hexany]] || 24 || 3 || 11 || 11 || 347.407 || 53.272 || 6.521 || 0
|-
| [[1-5-7-11 hexany]] || 24 || 5 || 11 || 11 || 386.313 || 31.194 || 12.384 || 0
|-
| [[1-5-9-11 hexany]] || 26 || 5 || 11 || 11 || 466.278 || 38.905 || 11.984 || 0
|-
| [[1-7-9-11 hexany]] || 28 || 7 || 11 || 11 || 231.174 || 116.233 || 1.988 || 0
|-
| [[3-5-7-11 hexany]] || 26 || 15 || 11 || 11 || 466.850 || 101.866 || 4.582 || 0
|-
| [[3-5-9-11 hexany]] || 28 || 15 || 11 || 11 || 536.950 || 31.766 || 16.903 || 0
|-
| [[3-7-9-11 hexany]] || 30 || 21 || 11 || 11 || 284.447 || 80.537 || 3.531 || 0
|-
| [[5-7-9-11 hexany]] || 32 || 35 || 11 || 11 || 270.079 || 165.004 || 1.636 || 0
|-
| [[1-3-5-13 hexany]] || 22 || 3 || 13 || 13 || 315.641 || 43.831 || 7.201 || 0
|-
| [[1-3-7-13 hexany]] || 24 || 3 || 13 || 13 || 573.656 || 92.601 || 6.194 || 0
|-
| [[1-3-9-13 hexany]] || 26 || 3 || 13 || 13 || 359.472 || 65.337 || 5.501 || 0
|-
| [[1-3-11-13 hexany]] || 28 || 3 || 13 || 13 || 412.745 || 138.572 || 2.980 || 0
|-
| [[1-5-7-13 hexany]] || 26 || 5 || 13 || 13 || 258.015 || 128.298 || 2.011 || 0
|-
| [[1-5-9-13 hexany]] || 28 || 5 || 13 || 13 || 250.303 || 177.068 || 1.413 || 0
|-
| [[1-5-11-13 hexany]] || 30 || 5 || 13 || 13 || 289.209 || 97.103 || 2.978 || 0
|-
| [[1-7-9-13 hexany]] || 30 || 7 || 13 || 13 || 405.443 || 75.611 || 5.362 || 0
|-
| [[1-7-11-13 hexany]] || 32 || 7 || 13 || 13 || 423.019 || 58.035 || 7.289 || 0
|-
| [[1-9-11-13 hexany]] || 34 || 9 || 13 || 13 || 347.407 || 12.064 || 28.796 || 0
|-
| [[3-5-7-13 hexany]] || 28 || 15 || 13 || 13 || 478.915 || 128.298 || 3.732 || 0
|-
| [[3-5-9-13 hexany]] || 30 || 15 || 13 || 13 || 315.641 || 43.831 || 7.201 || 0
|-
| [[3-5-11-13 hexany]] || 32 || 15 || 13 || 13 || 595.148 || 26.431 || 22.517 || 0
|-
| [[3-7-9-13 hexany]] || 32 || 21 || 13 || 13 || 369.746 || 128.298 || 2.881 || 0
|-
| [[3-7-11-13 hexany]] || 34 || 21 || 13 || 13 || 643.919 || 22.338 || 28.826 || 0
|-
| [[3-9-11-13 hexany]] || 36 || 27 || 13 || 13 || 412.745 || 138.572 || 2.978 || 0
|-
| [[5-7-9-13 hexany]] || 34 || 35 || 13 || 13 || 435.084 || 19.129 || 22.744 || 0
|-
| [[5-7-11-13 hexany]] || 36 || 35 || 13 || 13 || 328.278 || 36.705 || 8.943 || 0
|-
| [[5-9-11-13 hexany]] || 38 || 45 || 13 || 13 || 398.378 || 106.806 || 3.729 || 0
|-
| [[7-9-11-13 hexany]] || 40 || 63 || 13 || 13 || 289.209 || 128.298 || 2.254 || 0
|-
| [[1-3-5-15 hexany]] || 24 || 3 || 15 || 5 || 386.313 || 111.731 || 3.457 || 1
|-
| [[1-3-7-15 hexany]] || 26 || 3 || 15 || 7 || 582.512 || 111.731 || 5.213 || 0
|-
| [[1-3-9-15 hexany]] || 28 || 3 || 15 || 5 || 386.313 || 111.731 || 3.457 || 0
|-
| [[1-3-11-15 hexany]] || 30 || 3 || 15 || 11 || 386.313 || 38.905 || 9.929 || 0
|-
| [[1-3-13-15 hexany]] || 32 || 3 || 15 || 13 || 454.213 || 26.841 || 16.922 || 0
|-
| [[1-5-7-15 hexany]] || 28 || 5 || 15 || 7 || 470.781 || 111.731 || 4.213 || 0
|-
| [[1-5-9-15 hexany]] || 30 || 5 || 15 || 5 || 498.044 || 70.672 || 7.047 || 0
|-
| [[1-5-11-15 hexany]] || 32 || 5 || 15 || 11 || 386.313 || 53.272 || 7.251 || 0
|-
| [[1-5-13-15 hexany]] || 34 || 5 || 15 || 13 || 342.482 || 111.731 || 3.065 || 0
|-
| [[1-7-9-15 hexany]] || 32 || 7 || 15 || 7 || 653.184 || 84.467 || 7.733 || 0
|-
| [[1-7-11-15 hexany]] || 34 || 7 || 15 || 11 || 431.875 || 111.731 || 3.865 || 0
|-
| [[1-7-13-15 hexany]] || 36 || 7 || 15 || 13 || 721.084 || 16.566 || 43.527 || 0
|-
| [[1-9-11-15 hexany]] || 36 || 9 || 15 || 11 || 333.040 || 111.731 || 2.980 || 0
|-
| [[1-9-13-15 hexany]] || 38 || 9 || 15 || 13 || 524.866 || 43.831 || 11.974 || 0
|-
| [[1-11-13-15 hexany]] || 40 || 11 || 15 || 13 || 303.576 || 111.731 || 2.717 || 0
|-
| [[3-5-7-15 hexany]] || 30 || 15 || 15 || 7 || 266.871 || 119.442 || 2.234 || 0
|-
| [[3-5-9-15 hexany]] || 32 || 15 || 15 || 5 || 315.641 || 182.403 || 1.730 || 1
|-
| [[3-5-11-15 hexany]] || 34 || 15 || 15 || 11 || 347.407 || 150.637 || 2.306 || 0
|-
| [[3-5-13-15 hexany]] || 36 || 15 || 15 || 13 || 359.472 || 67.900 || 5.294 || 0
|-
| [[3-7-9-15 hexany]] || 34 || 21 || 15 || 7 || 378.602 || 48.770 || 7.763 || 0
|-
| [[3-7-11-15 hexany]] || 36 || 21 || 15 || 11 || 396.178 || 31.194 || 12.700 || 0
|-
| [[3-7-13-15 hexany]] || 38 || 21 || 15 || 13 || 685.388 || 19.129 || 35.829 || 0
|-
| [[3-9-11-15 hexany]] || 38 || 27 || 15 || 11 || 347.407 || 38.905 || 8.929 || 0
|-
| [[3-9-13-15 hexany]] || 40 || 27 || 15 || 13 || 250.313 || 138.572 || 1.806 || 0
|-
| [[3-11-13-15 hexany]] || 42 || 33 || 15 || 13 || 524.476 || 97.103 || 5.401 || 0
|-
| [[5-7-9-15 hexany]] || 36 || 35 || 15 || 7 || 315.641 || 62.961 || 5.103 || 0
|-
| [[5-7-11-15 hexany]] || 38 || 35 || 15 || 11 || 417.507 || 45.561 || 9.163 || 0
|-
| [[5-7-13-15 hexany]] || 40 || 35 || 15 || 13 || 369.746 || 119.442 || 3.095 || 0
|-
| [[5-9-11-15 hexany]] || 40 || 45 || 15 || 11 || 354.547 || 150.637 || 2.353 || 0
|-
| [[5-9-13-15 hexany]] || 42 || 45 || 15 || 13 || 315.641 || 65.337 || 4.830 || 0
|-
| [[5-11-13-15 hexany]] || 44 || 55 || 15 || 13 || 289.209 || 82.736 || 3.495 || 0
|-
| [[7-9-11-15 hexany]] || 42 || 63 || 15 || 11 || 315.641 || 101.866 || 3.098 || 0
|-
| [[7-9-13-15 hexany]] || 44 || 63 || 15 || 13 || 517.174 || 119.442 || 4.329 || 0
|-
| [[7-11-13-15 hexany]] || 46 || 77 || 15 || 13 || 534.750 || 119.442 || 4.477 || 0
|-
| [[9-11-13-15 hexany]] || 48 || 99 || 15 || 13 || 289.209 || 26.431 || 10.942 || 0
|}
=== In no-3s [[subgroup]]s ===


; In no-3s [[subgroup]]s
==== 1.n ====
1.n
* [[1-5-7-11 hexany]] — ''lopsided''
* [[1-5-7-11 hexany]]
* [[1-5-7-13 hexany]] — ''spicier whole tone scale''
* [[1-5-7-13 hexany]]
* [[1-7-11-13 hexany]] — ''extra [[xenharmonic]]''
* [[1-7-11-13 hexany]]
 
5.n
* [[5-7-11-13 hexany]]


==== 5.n ====
* [[5-7-11-13 hexany]] — ''melodically effective, contains a diminished chord''


; In no-5s subgroups
=== In no-5s subgroups ===
1.n
* [[1-3-7-9 hexany]]
* [[1-3-7-11 hexany]]
* [[1-3-7-13 hexany]]
* [[1-3-7-21 hexany]]
* [[1-3-9-11 hexany]]
* [[1-3-9-13 hexany]]
* [[1-3-11-13 hexany]]
* [[:File:Hexany 1 3 21 29.png|1-3-21-29 hexany]] (''fierce, groovy, dark'')
* [[1-3-21-49 hexany]]
* [[1-7-9-11 hexany]]
* [[1-7-9-13 hexany]]


3.n
==== 1.n ====
* [[3-7-9-11 hexany]]
* [[1-3-7-9 hexany]] — ''a [[detempering]] of the [[archy]] scale''
* [[3-7-9-13 hexany]]
* [[1-3-7-11 hexany]] — ''symmetrical shape; 2 strong tonal centres''
* [[3-7-11-13 hexany]]
* [[1-3-7-13 hexany]] — ''extra xenharmonic''
* [[3-9-11-13 hexany]]
* [[1-3-7-21 hexany]] — ''a [[detempering]] of the [[semaphore]] scale''
* [[:File:Hexany 3 9 19 31.png|3-9-19-31 hexany]] (''sparkly, pretty'')
* [[1-3-9-11 hexany]] — ''an even mix of xenharmonic and familiar''
* [[1-3-9-13 hexany]] — ''an even mix of xenmelodic and familiar''
* [[1-3-9-17 hexany]] — ''whole tone scale-like structure, but new unfamiliar melodies and harmonies''
* [[1-3-11-13 hexany]] — ''sounds surprisingly un-xenharmonic''
* [[:File:Hexany 1 3 21 29.png|1-3-21-29 hexany]] — ''fierce, groovy, dark''
* [[1-3-21-49 hexany]] — ''a [[detempering]] of the [[slendric]] scale''
* [[1-7-9-11 hexany]] — ''warped xenharmonic whole tone scale''
* [[1-7-9-13 hexany]] ''lopsided''


7.n
==== 3.n ====
* [[7-9-11-13 hexany]]
* [[3-7-9-11 hexany]] — ''fresh [[11-limit]] JI version of the augmented scale''
* [[3-7-9-13 hexany]] — ''effective both at melody and harmony''
* [[3-7-11-13 hexany]] — ''very lopsided, very xenharmonic''
* [[3-9-11-13 hexany]] — ''lopsided but with lots of useful consonances''
* [[:File:Hexany 3 9 19 31.png|3-9-19-31 hexany]] — ''sparkly, pretty''


==== 7.n ====
* [[7-9-11-13 hexany]] — ''neat step pattern useful for melody and harmony, no [[5-limit]] intervals - forces xenharmony''


; In no-7s subgroups
=== In no-7s subgroups ===
1.n
* [[1-3-5-9 hexany]]
* [[1-3-5-11 hexany]]
* [[1-3-5-13 hexany]]
* [[1-3-5-15 hexany]]
* [[1-3-5-45 hexany]]
* [[1-3-5-81 hexany]]
* [[1-3-5-121 hexany]]
* [[1-3-11-15 hexany]]
* [[1-3-13-15 hexany]]
* [[1-5-9-11 hexany]]
* [[1-5-9-13 hexany]]
* [[1-5-9-15 hexany]]
* [[1-5-11-13 hexany]]
* [[1-5-11-15 hexany]]
* [[1-5-13-15 hexany]]
* [[1-9-11-15 hexany]]
* [[1-9-11-13 hexany]]
* [[1-9-13-15 hexany]]
* [[1-11-13-15 hexany]]
* [[1-15-45-75 hexany]]


3.n
==== 1.n ====
* [[3-5-9-11 hexany]]
* [[1-3-5-9 hexany]] — ''difficult due to [[wolf interval|wolf fifth]] - better as a basis for building larger scales''
* [[3-5-9-13 hexany]]
* [[1-3-5-11 hexany]] — ''stable chord roots + very xenharmonic''
* [[3-5-9-15 hexany]]
* [[1-3-5-13 hexany]] — ''stable chord roots + very xenharmonic''
* [[3-5-11-13 hexany]]
* [[1-3-5-15 hexany]] — ''difficult to use''
* [[3-5-11-15 hexany]]
* [[1-3-5-45 hexany]] — ''very useful foundation for adding xenharmonic notes on top off; can play all ''Zelda'''s ocarina melodies''
* [[3-5-13-15 hexany]]
* [[1-3-5-81 hexany]] — ''built around subtle pitch shifts''
* [[3-5-15-19 hexany]]
* [[1-3-5-121 hexany]] — ''built-in beating effect that could be interesting''
* [[3-5-15-27 hexany]]
* [[1-3-9-135 hexany]] — ''near identical to [[1-3-9-17 hexany]]''
* [[3-9-11-15 hexany]]
* [[1-3-11-15 hexany]] — ''lopsided''
* [[3-9-13-15 hexany]]
* [[1-3-13-15 hexany]] — ''lopsided''
* [[3-11-13-15 hexany]]
* [[1-5-9-11 hexany]] — ''very lopsided and very xenharmonic''
* [[1-5-9-13 hexany]] — ''easy to build [[bihexany]]s with''
* [[1-5-9-15 hexany]] — ''easy to build [[dekany]]s with''
* [[1-5-11-13 hexany]] — ''an [[omniconsonant scale]]''
* [[1-5-11-15 hexany]] — ''easy to build [[bihexany]]s with''
* [[1-5-13-15 hexany]] — ''big variety of consonances useful for emotionally expressive music''
* [[1-9-11-15 hexany]] — ''very melodically effective; all the chords will be unfamiliar''
* [[1-9-11-13 hexany]] — ''better to remove one note and use as a [[pentatonic]] scale instead''
* [[1-9-13-15 hexany]] — ''lopsided''
* [[1-11-13-15 hexany]] — ''very melodically effective; all the chords will be unfamiliar''
* [[1-15-45-75 hexany]] — ''a [[detempering]] of the blues scale with sweet simple [[just intonation]] harmonies that blend well''


5.n
==== 3.n ====
* [[5-9-11-13 hexany]]
* [[3-5-9-11 hexany]] — ''very xenharmonic''
* [[5-9-11-15 hexany]]
* [[3-5-9-13 hexany]] — ''very useful both for melody and harmony; contains good [[barbados]] intervals''
* [[5-9-13-15 hexany]]
* [[3-5-9-15 hexany]] — ''too similar to [[12edo]] to be interesting''
* [[5-11-13-15 hexany]]
* [[3-5-9-25 hexany]] — ''easy to build a [[bihexany]] or [[stellated hexany]] with''
* [[3-5-9-27 hexany]] — ''useful as a teaching tool, but not for making real music''
* [[3-5-11-13 hexany]] — ''unwieldy but xenharmonically interesting''
* [[3-5-11-15 hexany]] — ''both xenharmonic yet also highly accessible - recommended for beginner microtonalists''
* [[3-5-13-15 hexany]] — ''both xenharmonic yet also highly accessible - recommended for beginner microtonalists''
* [[3-5-15-19 hexany]] — ''useful for ear training; contains a [[wolf interval|wolf fifth]]''
* [[3-5-15-27 hexany]] — ''a worse version of the normal major scale''
* [[3-9-11-15 hexany]] — ''unfamiliar notes''
* [[3-9-13-15 hexany]] — ''very xenharmonic melodies; easy to learn the notes and intervals - especially audibly distinct from one another''
* [[3-11-13-15 hexany]] — ''unwieldy''


9.n
==== 5.n ====
* [[9-11-13-15 hexany]]
* [[5-9-11-13 hexany]] — ''useful for building melodies; an even mix of familiar and xenharmonic''
* [[5-9-11-15 hexany]] — ''a [[detempering]] of the [[porcupine]] scale; nice melodies''
* [[5-9-13-15 hexany]] — ''melodically interesting but harmonically unrewarding''
* [[5-11-13-15 hexany]] — ''highly recommended; an even mix of familiar and xenharmonic''


==== 9.n ====
* [[9-11-13-15 hexany]] — ''better used as a [[pentatonic]] scale by removing 1 note''


; In no-11s subgroups
=== In no-11s subgroups ===
1.n
* [[1-3-5-7 hexany]] (''cold, hazy'')
* [[1-3-7-15 hexany]]
* [[1-5-7-9 hexany]]
* [[1-7-9-15 hexany]]
* [[1-7-13-15 hexany]]


3.n
==== 1.n ====
* [[3-5-7-9 hexany]]
* [[1-3-5-7 hexany]] — ''cold, hazy''
* [[3-5-7-13 hexany]]
* [[1-3-7-15 hexany]] — ''lopsided''
* [[3-5-7-15 hexany]]
* [[1-5-7-9 hexany]] — ''whole tone scale-like but with a [[quarter tone]], making it very xenharmonic''
* [[3-5-15-21 hexany]]
* [[1-7-9-15 hexany]] — ''lopsided but useful for making [[bihexany]]s''
* [[3-7-9-15 hexany]]
* [[1-7-13-15 hexany]] — ''useful for making [[bihexany]] versions of [[10edo]], which would be a type of [[neji]]''
* [[3-7-13-15 hexany]]


5.n
==== 3.n ====
* [[5-7-9-13 hexany]]
* [[3-5-7-9 hexany]] — ''useful for melody and harmony''
* [[5-7-9-15 hexany]]
* [[3-5-7-13 hexany]] — ''useful for building [[dekany]]s''
* [[5-7-13-15 hexany]]
* [[3-5-7-15 hexany]] — ''the optimal configuration for maximising the number and variety of simple harmonies available in a hexatonic scale; strong melodically also''
* [[3-5-15-21 hexany]] — ''solidly rooted and consonant''
* [[3-7-9-15 hexany]] — ''big variety of chords available, both familiar and xenharmonic ones''
* [[3-7-13-15 hexany]] — ''related to the [[negri]] scale; useful for building [[bihexany]]s or [[dekany]]s''
* [[3-9-15-21 hexany]] — ''very similar to the [[1-3-5-7 hexany]]''


7.n
==== 5.n ====
* [[7-9-13-15 hexany]]
* [[5-7-9-13 hexany]] — ''very xenharmonic; easy to expand to a [[bihexany]] or [[dekany]]''
* [[5-7-9-15 hexany]] — ''potential for good compositions; a [[detempering]] of the [[starling]] scale''
* [[5-7-13-15 hexany]] — ''both harmonically and melodically strong, and useful for [[bihexany]]s''


9.n
==== 7.n ====
* [[9-25-49-81 hexany]]
* [[7-9-13-15 hexany]] — ''useful for building [[bihexany]]s or [[dekany]]s out of''


==== 9.n ====
* [[9-25-49-81 hexany]] — ''a diminished tetrad with built-in beating effects''


; In no-13s subgroups
=== In no-13s subgroups ===
1.n
* [[1-7-11-15 hexany]]


3.n
==== 1.n ====
* [[3-5-7-11 hexany]]
* [[1-7-11-15 hexany]] — ''a little unwieldy''
* [[3-7-9-55 hexany]]
* [[3-7-11-15 hexany]]


5.n
==== 3.n ====
* [[5-7-9-11 hexany]]
* [[3-5-7-11 hexany]] — ''very xenharmonic''
* [[5-7-9-33 hexany]]
* [[3-7-9-55 hexany]] — ''creates interesting complex beating when played in the bass or sub bass range''
* [[5-7-11-15 hexany]]
* [[3-7-11-15 hexany]] — ''xenharmonic but also with sweet major thirds''


7.n
==== 5.n ====
* [[7-9-11-15 hexany]]
* [[5-7-9-11 hexany]] — ''a [[neji]] of [[6edo]] with an [[primodality|over-35 semiprime]] feel''
* [[:File:Hexany 7 11 17 45 cents.png|7-11-17-45 hexany]] (''dark, supernatural, metallic'')
* [[5-7-9-33 hexany]] — ''though the small steps are mathematically distinct from one another, they don't sound audibly distinct''
* [[5-7-11-15 hexany]] ''lopsided''


27.n
==== 7.n ====
* [[:File:Hexany 27 35 47 59 cents.png|27-35-47-59 hexany]] (''like melting rainbow ice cream in the sun'')
* [[7-9-11-15 hexany]] — ''useful for building [[bihexany]]s''
* [[:File:Hexany 7 11 17 45 cents.png|7-11-17-45 hexany]] ''dark, supernatural, metallic''


==== 27.n ====
* [[:File:Hexany 27 35 47 59 cents.png|27-35-47-59 hexany]] — ''like melting rainbow ice cream in the sun''


; In no-17s subgroups
=== In no-17s subgroups ===
7.n
* [[7-11-13-15 hexany]]


==== 7.n ====
* [[7-11-13-15 hexany]] — ''useful for writing melody - expanding into a [[bihexany]] makes it more useful still''


; Not yet categorised
=== Not yet categorised ===
* [[Hexany 1029]]
* [[Hexany 1029]]
* [[Hexany 126]]
* [[Hexany 126]]
Line 173: Line 327:
* [[Hexany 65625]]
* [[Hexany 65625]]
* [[Hexany 875]]
* [[Hexany 875]]
* [[User:BudjarnLambeth/My favourite hexanies using at least one odd greater than 15]]


== Dekanies (10-tone) ==
== Dekanies (10-tone) ==
Line 178: Line 333:
''Main page: [[Dekany]]''
''Main page: [[Dekany]]''


; 1.3.5.x.y
=== In no-3s subgroups ===
* [[1-5-7-11-13 dekany]]
* [[5-7-9-11-13 dekany]]
 
=== In no-5s subgroups ===
* [[1-3-7-9-11 dekany]]
* [[1-3-7-11-13 dekany]]
* [[1-3-9-11-13 dekany]] — ''recommended''
* [[1-3-7-9-29 dekany]] — ''recommended''
* [[1-7-9-11-13 dekany]] — ''highly unusual but not necessarily bad''
* [[3-7-9-11-13 dekany]] — ''recommended''
 
=== In no-7s subgroups ===
* [[1-3-5-9-11 dekany]]
* [[1-3-5-9-13 dekany]]
* [[1-3-5-9-81 dekany]]
* [[1-3-5-11-13 dekany]] — ''recommended''
* [[1-3-5-11-15 dekany]] — ''recommended''
* [[1-3-5-13-15 dekany]] — ''recommended''
* [[1-3-9-11-15 dekany]] — ''recommended''
* [[1-3-9-13-15 dekany]]
* [[1-3-11-13-15 dekany]]
* [[1-5-9-11-13 dekany]]
* [[1-5-9-11-15 dekany]] — ''recommended''
* [[1-5-9-13-15 dekany]] — ''recommended''
* [[1-5-11-13-15 dekany]] — ''recommended''
* [[1-9-11-13-15 dekany]]
* [[3-5-9-11-13 dekany]]
* [[3-5-9-11-15 dekany]] — ''recommended''
* [[3-5-9-13-15 dekany]] — ''recommended''
* [[3-5-11-13-15 dekany]] — ''recommended''
* [[3-9-11-13-15 dekany]] — ''recommended''
* [[5-9-11-13-15 dekany]] — ''recommended''
 
=== In no-11s subgroups ===
* [[1-3-5-7-9 dekany]]
* [[1-3-5-7-9 dekany]]
* [[1-3-5-7-13 dekany]]
* [[1-3-5-7-13 dekany]]
* [[1-3-5-9-11 dekany]]
* [[1-3-5-7-15 dekany]] — ''recommended''
* [[1-3-5-9-81 dekany]]
* [[1-3-5-9-15 dekany]]
* [[1-3-7-9-13 dekany]] — ''recommended''
* [[1-3-7-9-15 dekany]]
* [[1-3-7-13-15 dekany]]
* [[1-5-7-9-13 dekany]] — ''recommended''
* [[1-5-7-9-15 dekany]]
* [[1-5-7-13-15 dekany]] — ''recommended''
* [[1-7-9-13-15 dekany]]
* [[3-5-7-9-13 dekany]]
* [[3-5-7-9-15 dekany]] — ''recommended''
* [[3-5-7-13-15 dekany]] — ''recommended''
* [[3-7-9-13-15 dekany]] — ''recommended''
* [[5-7-9-13-15 dekany]]
 
=== In no-13s subgroups ===
* [[1-3-5-7-11 dekany]]
* [[1-3-7-11-15 dekany]]
* [[1-5-7-9-11 dekany]]
* [[1-5-7-11-15 dekany]] — ''recommended but extra spicy''
* [[1-7-9-11-15 dekany]]
* [[3-5-7-9-11 dekany]]
* [[3-5-7-11-15 dekany]] — ''recommended''
* [[3-7-9-11-15 dekany]]
* [[5-7-9-11-15 dekany]] — ''recommended''


=== In no-17s subgroups ===
* [[1-7-11-13-15 dekany]]
* [[3-5-7-11-13 dekany]]
* [[3-7-11-13-15 dekany]]
* [[5-7-11-13-15 dekany]]
* [[7-9-11-13-15 dekany]] — ''recommended, but extra spicy''


; Not yet categorised
=== Related to [[regular temperament]] scales ===
* [[Deka1029]]
* [[Deka126]]
* [[Deka1728]]
* [[Deka225]]
* [[Deka2401]]
* [[Deka245]]
* [[Deka3136]]
* [[Deka4375]]
* [[Deka5120]]
* [[Deka6144]]
* [[Deka65625]]
* [[Deka875]]
* [[Dekany agni]]
* [[Dekany agni]]
* [[Dekany apollo]]
* [[Dekany apollo]]
Line 212: Line 418:
* [[Dekany spectacle]]
* [[Dekany spectacle]]
* [[Dekany zeus]]
* [[Dekany zeus]]
* [[Dekany-cs]]
* [[Dekany-cs-marv]]
* [[Dekany-cs-marv]]
* [[Dekanymarvwoo]]
* [[Dekanymarvwoo]]
=== Not yet categorised ===
* [[Deka1029]]
* [[Deka126]]
* [[Deka1728]]
* [[Deka225]]
* [[Deka2401]]
* [[Deka245]]
* [[Deka3136]]
* [[Deka4375]]
* [[Deka5120]]
* [[Deka6144]]
* [[Deka65625]]
* [[Deka875]]
* [[Dekany-cs]]


== Bihexanies (12-tone) ==
== Bihexanies (12-tone) ==
[[Category:12-tone scales]]
''Main page: [[Bihexany]]''
''Main page: [[Bihexany]]''
[[Category:12-tone scales]]


=== Generated by 7-odd-limit elements ===
* [[1-3-5-7 by 3/2 bihexany]]
* [[1-3-5-7 by 6/5 bihexany]]
* [[1-3-5-7 by 8/5 bihexany]]
* [[1-3-5-7 by 10/7 bihexany]]
* [[1-3-5-7 by 12/7 bihexany]]
=== Generated by 9-odd-limit elements ===
* [[1-3-5-7 by 9/5 bihexany]]
* [[1-3-5-7 by 9/7 bihexany]]
* [[1-3-5-7 by 9/8 bihexany]]
* [[1-3-5-9 by 7/5 bihexany]]
* [[1-3-5-9 by 7/5 bihexany]]
* [[1-5-9-13 by 3/2 bihexany]]
* [[1-3-7-9 by 5/4 bihexany]] — ''recommended''
* [[1-5-7-9 by 4/3 bihexany]]
* [[3-5-7-9 by 5/4 bihexany]] — ''recommended''
 
=== Generated by 11-odd-limit elements ===
* [[1-3-7-9 by 11/8 bihexany]]
* [[1-3-7-11 by 18/11 bihexany]]
* [[1-7-9-11 by 4/3 bihexany]] — ''recommended''
* [[3-5-7-11 by 3/2 bihexany]] — ''recommended''
* [[3-5-9-11 by 5/4 bihexany]]
 
=== Generated by 13-odd-limit elements ===
* [[1-3-5-9 by 13/9 bihexany]] — ''recommended''
* [[1-5-9-13 by 3/2 bihexany]] — ''recommended''
* [[1-7-9-13 by 4/3 bihexany]]
* [[5-9-11-13 by 3/2 bihexany]] — ''recommended''
 
=== Generated by 15-odd-limit elements ===
 
==== No-7s ====
* [[1-3-5-13 by 18/13 bihexany]] — ''recommended''
* [[1-3-9-15 by 11/8 bihexany]]
* [[1-3-11-15 by 6/5 bihexany]]
* [[1-3-13-15 by 18/13 bihexany]] — ''recommended''
* [[1-5-11-15 by 6/5 bihexany]]
* [[1-5-13-15 by 16/9 bihexany]]
* [[1-9-11-15 by 12/11 bihexany]]
* [[1-9-13-15 by 8/5 bihexany]]
* [[1-11-13-15 by 4/3 bihexany]]
* [[3-5-9-15 by 6/5 bihexany]]
* [[3-5-9-15 by 10/9 bihexany]]
* [[5-9-11-15 by 5/4 bihexany]]
* [[5-9-11-15 by 15/13 bihexany]]
* [[5-9-13-15 by 5/4 bihexany]] — ''recommended''
* [[5-11-13-15 by 11/9 bihexany]]
* [[9-11-13-15 by 3/2 bihexany]]
* [[9-11-13-15 by 33/26 bihexany]] — ''recommended''
 
==== No-11s ====
* [[1-3-5-7 by 15/14 bihexany]] — ''recommended''
* [[1-3-5-7 by 16/15 bihexany]]
* [[1-3-7-15 by 6/5 bihexany]]
* [[1-3-7-15 by 9/7 bihexany]] — ''recommended''
* [[1-3-9-15 by 7/6 bihexany]]
* [[1-5-7-15 by 6/5 bihexany]]
* [[1-7-9-15 by 4/3 bihexany]] — ''recommended''
* [[1-7-9-15 by 7/5 bihexany]]
* [[1-7-13-15 by 7/5 bihexany]] — ''recommended''
* [[3-5-7-15 by 9/5 bihexany]]
* [[3-5-7-15 by 9/8 bihexany]]
* [[3-7-13-15 by 4/3 bihexany]]
* [[3-7-13-15 by 7/5 bihexany]]
* [[5-7-9-15 by 5/4 bihexany]] — ''recommended''
* [[5-7-9-15 by 7/4 bihexany]]
* [[5-7-9-15 by 9/8 bihexany]]
* [[5-7-13-15 by 9/8 bihexany]]
* [[5-7-13-15 by 22/13 bihexany]]
 
==== No-13s ====
* [[3-5-7-15 by 11/7 bihexany]]
* [[3-7-11-15 by 7/5 bihexany]] — ''recommended''
* [[5-7-9-15 by 11/9 bihexany]]
* [[5-7-11-15 by 18/11 bihexany]]
* [[7-9-11-15 by 3/2 bihexany]]
 
==== No-17s ====
* [[7-11-13-15 by 7/5 bihexany]]
 
=== Generated by 17-odd-limit elements ===
* [[1-3-5-9 by 17/12 bihexany]] — ''recommended''
* [[1-5-9-15 by 17/12 bihexany]]
* [[3-5-7-15 by 17/14 bihexany]]
* [[3-5-11-13 by 24/17 bihexany]]
* [[3-11-13-15 by 24/17 bihexany]]
 
=== Generated by 19-odd-limit elements ===
* [[1-3-9-17 by 19/16 bihexany]] — ''recommended''
* [[3-5-15-19 by 9/8 bihexany]]
* [[3-5-15-19 by 9/8 bihexany]]
* [[3-5-7-15 by 19/14 bihexany]]
* [[3-5-13-15 by 19/17 bihexany]]
* [[3-7-9-15 by 19/17 bihexany]] — ''recommended''
=== Higher odd-limit elements ===
==== 21-odd ====
* [[1-3-5-7 by 21/16 bihexany]]
* [[1-3-5-7 by 40/21 bihexany]]
* [[3-5-11-15 by 21/11 bihexany]]
* [[3-7-13-15 by 21/13 bihexany]]
* [[7-9-13-15 by 21/13 bihexany]] — ''recommended''
==== 23-odd ====
* [[3-5-7-15 by 23/14 bihexany]]
==== 25-odd ====
''(none documented)''
==== 27-odd ====
* [[1-5-7-15 by 32/27 bihexany]]
* [[3-5-7-15 by 27/14 bihexany]] — ''recommended''
* [[3-9-13-15 by 27/26 bihexany]] — ''recommended''
==== 29-odd ====
* [[5-7-9-15 by 29/18 bihexany]]
==== 31-odd ====
''(none documented)''
==== 33-odd ====
* [[1-5-11-15 by 40/33 bihexany]]
==== 35-odd ====
* [[1-3-5-7 by 36/35 bihexany]]
* [[1-3-5-7 by 48/35 bihexany]]
* [[1-3-5-7 by 64/35 bihexany]] — ''recommended''
* [[1-3-7-15 by 48/35 bihexany]] — ''recommended''
==== 37-odd to 43-odd ====
''(none documented)''
==== 45-odd ====
* [[1-3-5-7 by 56/45 bihexany]]
* [[1-3-5-9 by 64/45 bihexany]]
* [[1-5-9-15 by 64/45 bihexany]]
* [[3-5-7-15 by 45/28 bihexany]]
==== 47-odd to 53-odd ====
''(none documented)''
==== 55-odd ====
* [[1-9-11-15 by 72/55 bihexany]]
==== 57-odd to 61-odd ====
''(none documented)''
==== 63-odd ====
* [[1-3-5-7 by 80/63 bihexany]] — ''recommended''
==== 65-odd ====
* [[3-5-11-13 by 96/65 bihexany]] — ''good for metallophone timbres like bells or Gamelan''
==== 67-odd to 97-odd ====
''(none documented)''
==== 99-odd ====
* [[1-7-13-15 by 140/99 bihexany]]
==== 101-odd to 133-odd ====
''(none documented)''
==== 135-odd ====
* [[1-3-9-135 by 57/34 bihexany]] — ''recommended''
=== Not yet categorised ===
* [[Bihexanymyna]]
* [[Bihexanymyna]]
* [[GW Smith bihexany 14 Feb 2011]]
* [[GW Smith bihexany 14 Feb 2011]]


== Duohexanies (12-tone) ==
== Duohexanies (12-tone) ==
[[Category:12-tone scales]]
''Main page: [[Duohexany]]''
''Main page: [[Duohexany]]''
[[Category:12-tone scales]]


* [[Duohex]]
* [[Duohex]]
Line 236: Line 619:


== Stellated hexanies (14-tone) ==
== Stellated hexanies (14-tone) ==
[[Category:14-tone scales]]
''Main page: [[Stellated hexany]]''
''Main page: [[Stellated hexany]]''
[[Category:14-tone scales]]


=== In no-3s subgroups ===
* [[1-5-7-11 stellated hexany]] — ''recommended''
* [[1-5-7-13 stellated hexany]]
* [[1-5-11-13 stellated hexany]]
* [[1-7-11-13 stellated hexany]] — ''recommended''
=== In no-5s subgroups ===
* [[1-3-7-9 stellated hexany]]
* [[1-3-7-11 stellated hexany]] — ''recommended''
* [[1-3-7-13 stellated hexany]] — ''recommended''
* [[1-3-9-11 stellated hexany]]
* [[1-3-9-13 stellated hexany]] — ''recommended''
* [[1-3-11-13 stellated hexany]] — ''recommended''
* [[1-7-9-11 stellated hexany]]
* [[1-7-9-13 stellated hexany]]
* [[3-7-9-11 stellated hexany]] — ''recommended''
* [[3-7-9-13 stellated hexany]] — ''recommended, but with 2 notes removed - read article''
* [[3-7-11-13 stellated hexany]] — ''recommended''
* [[3-9-11-13 stellated hexany]]
=== In no-7s subgroups ===
==== 1.n ====
* [[1-3-5-9 stellated hexany]]
* [[1-3-5-11 stellated hexany]]
* [[1-3-5-13 stellated hexany]]
* [[1-3-5-15 stellated hexany]] — ''not recommended for xenharmony, but it's a good JI version of the 'Hungarian minor' scale if one wants that''
* [[1-3-9-15 stellated hexany]]
* [[1-3-11-15 stellated hexany]]
* [[1-3-13-15 stellated hexany]] — ''recommended but spicy''
* [[1-5-9-11 stellated hexany]]
* [[1-5-9-13 stellated hexany]]
* [[1-5-9-15 stellated hexany]]
* [[1-5-11-15 stellated hexany]]
* [[1-5-13-15 stellated hexany]]
* [[1-11-13-15 stellated hexany]]  — ''recommended''
* [[1-15-45-75 stellated hexany]] — ''recommended''
==== 3.n ====
* [[3-5-9-11 stellated hexany]] — ''recommended''
* [[3-5-9-13 stellated hexany]] — ''recommended''
* [[3-5-9-15 stellated hexany]]
* [[3-5-9-25 stellated hexany]] — ''recommended''
* [[3-5-9-27 stellated hexany]]
* [[3-5-11-13 stellated hexany]] — ''recommended''
* [[3-5-11-15 stellated hexany]] — ''recommended''
* [[3-5-13-15 stellated hexany]]
* [[3-9-11-15 stellated hexany]] — ''recommended''
* [[3-9-13-15 stellated hexany]]
* [[3-9-25-625 stellated hexany]] — ''recommended''
* [[3-11-13-15 stellated hexany]] — ''recommended''
==== 5.n ====
* [[5-9-11-13 stellated hexany]]
* [[5-9-11-15 stellated hexany]] — ''recommended (rotate it)''
* [[5-9-13-15 stellated hexany]] — ''recommended with 2 steps optionally removed (see article)''
* [[5-11-13-15 stellated hexany]] — ''recommended but spicy''
=== In no-11s subgroups ===
* [[1-3-5-7 stellated hexany]] — ''recommended''
* [[1-3-7-15 stellated hexany]]
* [[1-5-7-9 stellated hexany]]
* [[1-5-7-15 stellated hexany]]
* [[1-7-9-15 stellated hexany]]
* [[1-7-13-15 stellated hexany]]
* [[3-5-7-9 stellated hexany]] — ''recommended with 2 notes removed - read article''
* [[3-5-7-13 stellated hexany]] — ''recommended''
* [[3-5-7-15 stellated hexany]]
* [[3-7-9-15 stellated hexany]] — ''recommended with 2 notes removed - read article''
* [[3-7-13-15 stellated hexany]] — ''recommended''
* [[3-9-15-21 stellated hexany]] — ''recommended''
* [[5-7-9-13 stellated hexany]]
* [[5-7-9-15 stellated hexany]] — ''recommended (rotate it above 3/2)''
=== In no-13s subgroups ===
* [[1-7-11-15 stellated hexany]]
* [[3-5-7-11 stellated hexany]] — ''recommended''
* [[3-7-11-15 stellated hexany]]
* [[5-7-9-11 stellated hexany]]
* [[5-7-11-15 stellated hexany]] — ''recommended''
=== Not yet categorised ===
* [[Stelhex]]
* [[Stelhex]]
* [[Stelhex-catakleismic]]
* [[Stelhex-catakleismic]]
Line 247: Line 712:
== Pentadekanies (15-tone) ==
== Pentadekanies (15-tone) ==
''Main page: [[Pentadekany]]''
''Main page: [[Pentadekany]]''
=== 1.3.n ===
* [[1-3-5-7-9-11 pentadekany]]
* [[1-3-5-7-9-13 pentadekany]] — ''recommended''
* [[1-3-5-7-9-15 pentadekany]]
* [[1-3-5-7-11-13 pentadekany]]
* [[1-3-5-7-11-15 pentadekany]] — ''recommended''
* [[1-3-5-7-13-15 pentadekany]]
* [[1-3-5-9-11-13 pentadekany]]
* [[1-3-5-9-11-15 pentadekany]]
* [[1-3-5-9-13-15 pentadekany]]
* [[1-3-5-11-13-15 pentadekany]] — ''recommended but only for advanced composers''
* [[1-3-7-9-11-13 pentadekany]] — ''recommended''
* [[1-3-7-9-11-15 pentadekany]] — ''recommended''
* [[1-3-7-9-13-15 pentadekany]]
* [[1-3-7-11-13-15 pentadekany]]
* [[1-3-9-11-13-15 pentadekany]]
=== 1.5.n ===
* [[1-5-7-9-11-13 pentadekany]]
* [[1-5-7-9-11-15 pentadekany]] — ''recommended''
* [[1-5-7-9-13-15 pentadekany]] — ''recommended''
* [[1-5-7-11-13-15 pentadekany]]
* [[1-5-9-11-13-15 pentadekany]]
=== 1.7.n ===
* [[1-7-9-11-13-15 pentadekany]]
=== 3.5.n ===
* [[3-5-7-9-11-13 pentadekany]]
* [[3-5-7-9-11-15 pentadekany]] — ''recommended''
* [[3-5-7-9-13-15 pentadekany]]
* [[3-5-7-11-13-15 pentadekany]] — ''recommended''
* [[3-5-9-11-13-15 pentadekany]] — ''recommended''
=== 3.7.n ===
* [[3-7-9-11-13-15 pentadekany]]
=== 5.7.n ===
* [[5-7-9-11-13-15 pentadekany]]


== Eikosanies (20-tone) ==
== Eikosanies (20-tone) ==
''Main page: [[Eikosany]]''
''Main page: [[Eikosany]]''
=== 1.3.n ===
* [[1-3-5-7-9-11 eikosany]]
* [[1-3-5-7-9-13 eikosany]]
* [[1-3-5-7-9-15 eikosany]]
* [[1-3-5-7-11-13 eikosany]]
* [[1-3-5-7-11-15 eikosany]]
* [[1-3-5-7-13-15 eikosany]]
* [[1-3-5-9-11-13 eikosany]]
* [[1-3-5-9-11-15 eikosany]]
* [[1-3-5-9-13-15 eikosany]]
* [[1-3-5-11-13-15 eikosany]]
* [[1-3-7-9-11-13 eikosany]]
* [[1-3-7-9-11-15 eikosany]]
* [[1-3-7-9-13-15 eikosany]]
* [[1-3-7-11-13-15 eikosany]]
* [[1-3-9-11-13-15 eikosany]]
=== 1.5.n ===
* [[1-5-7-9-11-13 eikosany]]
* [[1-5-7-9-11-15 eikosany]]
* [[1-5-7-9-13-15 eikosany]]
* [[1-5-7-11-13-15 eikosany]]
* [[1-5-9-11-13-15 eikosany]]
=== 1.7.n ===
* [[1-7-9-11-13-15 eikosany]]
=== 3.5.n ===
* [[3-5-7-9-11-13 eikosany]]
* [[3-5-7-9-11-15 eikosany]]
* [[3-5-7-9-13-15 eikosany]]
* [[3-5-7-11-13-15 eikosany]]
* [[3-5-9-11-13-15 eikosany]]
=== 3.7.n ===
* [[3-7-9-11-13-15 eikosany]]
=== 5.7.n ===
* [[5-7-9-11-13-15 eikosany]]
=== Other ===
* [[Eikosanyplusop]]
* [[Eikosanyplusop]]
== Other ==
* [[1-3-5-7-9-11-13 enaeikosany]]
* [[1-3-5-7-9-11-15 enaeikosany]]
* [[1-3-5-7-9-13-15 enaeikosany]]
* [[1-3-5-7-11-13-15 enaeikosany]]
* [[1-3-5-9-11-13-15 enaeikosany]]
* [[1-3-7-9-11-13-15 enaeikosany]]
* [[1-5-7-9-11-13-15 enaeikosany]]
* [[3-5-7-9-11-13-15 enaeikosany]]
* [[1-3-5-7-9-11-13 pentatriandekany]]
* [[1-3-5-7-9-11-15 pentatriandekany]]
* [[1-3-5-7-9-13-15 pentatriandekany]]
* [[1-3-5-7-11-13-15 pentatriandekany]]
* [[1-3-5-9-11-13-15 pentatriandekany]]
* [[1-3-7-9-11-13-15 pentatriandekany]]
* [[1-5-7-9-11-13-15 pentatriandekany]]
* [[3-5-7-9-11-13-15 pentatriandekany]]
* [[1-3-5-7-9-11-13-15 octaeikosany]]


{{navbox scale gallery}}
{{navbox scale gallery}}

Latest revision as of 09:14, 5 July 2026

This is a gallery of combination product set (CPS) scales, as well as subsets of, mergers of, or modifications of such scales.

There are infinite possible CPS scales, so this list can never be complete. If you find a CPS scale that you like, please document it here so that people can make music with it.


See also Category:Combination product sets, which may include scales that have yet to be added to this list.

Italicised text following an em-dash beside a listed scale is a description by a wiki contributor of the subjective mood they personally feel when listening to the scale.

Pentanies (5-tone)

Main page: Pentany

Hexanies (6-tone)

Main page: Hexany

Combination Product Set Sum of factors Lowest common divisor Odd-limit Prime Limit Largest step size Smallest step size L/s step ratio Number of repeated notes
1-3-5-7 hexany 16 3 7 7 266.871 84.467 3.159 0
1-3-5-9 hexany 18 3 9 5 315.641 111.731 2.825 0
1-3-7-9 hexany 20 3 9 7 266.871 62.961 4.238 0
1-5-7-9 hexany 22 5 9 7 378.602 48.770 7.763 0
3-5-7-9 hexany 24 15 9 7 315.641 84.467 3.736 0
1-3-5-11 hexany 20 3 11 11 333.040 150.637 2.210 0
1-3-7-11 hexany 22 3 11 11 284.447 80.537 3.531 0
1-3-9-11 hexany 24 3 11 11 347.407 53.272 6.521 0
1-5-7-11 hexany 24 5 11 11 386.313 31.194 12.384 0
1-5-9-11 hexany 26 5 11 11 466.278 38.905 11.984 0
1-7-9-11 hexany 28 7 11 11 231.174 116.233 1.988 0
3-5-7-11 hexany 26 15 11 11 466.850 101.866 4.582 0
3-5-9-11 hexany 28 15 11 11 536.950 31.766 16.903 0
3-7-9-11 hexany 30 21 11 11 284.447 80.537 3.531 0
5-7-9-11 hexany 32 35 11 11 270.079 165.004 1.636 0
1-3-5-13 hexany 22 3 13 13 315.641 43.831 7.201 0
1-3-7-13 hexany 24 3 13 13 573.656 92.601 6.194 0
1-3-9-13 hexany 26 3 13 13 359.472 65.337 5.501 0
1-3-11-13 hexany 28 3 13 13 412.745 138.572 2.980 0
1-5-7-13 hexany 26 5 13 13 258.015 128.298 2.011 0
1-5-9-13 hexany 28 5 13 13 250.303 177.068 1.413 0
1-5-11-13 hexany 30 5 13 13 289.209 97.103 2.978 0
1-7-9-13 hexany 30 7 13 13 405.443 75.611 5.362 0
1-7-11-13 hexany 32 7 13 13 423.019 58.035 7.289 0
1-9-11-13 hexany 34 9 13 13 347.407 12.064 28.796 0
3-5-7-13 hexany 28 15 13 13 478.915 128.298 3.732 0
3-5-9-13 hexany 30 15 13 13 315.641 43.831 7.201 0
3-5-11-13 hexany 32 15 13 13 595.148 26.431 22.517 0
3-7-9-13 hexany 32 21 13 13 369.746 128.298 2.881 0
3-7-11-13 hexany 34 21 13 13 643.919 22.338 28.826 0
3-9-11-13 hexany 36 27 13 13 412.745 138.572 2.978 0
5-7-9-13 hexany 34 35 13 13 435.084 19.129 22.744 0
5-7-11-13 hexany 36 35 13 13 328.278 36.705 8.943 0
5-9-11-13 hexany 38 45 13 13 398.378 106.806 3.729 0
7-9-11-13 hexany 40 63 13 13 289.209 128.298 2.254 0
1-3-5-15 hexany 24 3 15 5 386.313 111.731 3.457 1
1-3-7-15 hexany 26 3 15 7 582.512 111.731 5.213 0
1-3-9-15 hexany 28 3 15 5 386.313 111.731 3.457 0
1-3-11-15 hexany 30 3 15 11 386.313 38.905 9.929 0
1-3-13-15 hexany 32 3 15 13 454.213 26.841 16.922 0
1-5-7-15 hexany 28 5 15 7 470.781 111.731 4.213 0
1-5-9-15 hexany 30 5 15 5 498.044 70.672 7.047 0
1-5-11-15 hexany 32 5 15 11 386.313 53.272 7.251 0
1-5-13-15 hexany 34 5 15 13 342.482 111.731 3.065 0
1-7-9-15 hexany 32 7 15 7 653.184 84.467 7.733 0
1-7-11-15 hexany 34 7 15 11 431.875 111.731 3.865 0
1-7-13-15 hexany 36 7 15 13 721.084 16.566 43.527 0
1-9-11-15 hexany 36 9 15 11 333.040 111.731 2.980 0
1-9-13-15 hexany 38 9 15 13 524.866 43.831 11.974 0
1-11-13-15 hexany 40 11 15 13 303.576 111.731 2.717 0
3-5-7-15 hexany 30 15 15 7 266.871 119.442 2.234 0
3-5-9-15 hexany 32 15 15 5 315.641 182.403 1.730 1
3-5-11-15 hexany 34 15 15 11 347.407 150.637 2.306 0
3-5-13-15 hexany 36 15 15 13 359.472 67.900 5.294 0
3-7-9-15 hexany 34 21 15 7 378.602 48.770 7.763 0
3-7-11-15 hexany 36 21 15 11 396.178 31.194 12.700 0
3-7-13-15 hexany 38 21 15 13 685.388 19.129 35.829 0
3-9-11-15 hexany 38 27 15 11 347.407 38.905 8.929 0
3-9-13-15 hexany 40 27 15 13 250.313 138.572 1.806 0
3-11-13-15 hexany 42 33 15 13 524.476 97.103 5.401 0
5-7-9-15 hexany 36 35 15 7 315.641 62.961 5.103 0
5-7-11-15 hexany 38 35 15 11 417.507 45.561 9.163 0
5-7-13-15 hexany 40 35 15 13 369.746 119.442 3.095 0
5-9-11-15 hexany 40 45 15 11 354.547 150.637 2.353 0
5-9-13-15 hexany 42 45 15 13 315.641 65.337 4.830 0
5-11-13-15 hexany 44 55 15 13 289.209 82.736 3.495 0
7-9-11-15 hexany 42 63 15 11 315.641 101.866 3.098 0
7-9-13-15 hexany 44 63 15 13 517.174 119.442 4.329 0
7-11-13-15 hexany 46 77 15 13 534.750 119.442 4.477 0
9-11-13-15 hexany 48 99 15 13 289.209 26.431 10.942 0

In no-3s subgroups

1.n

5.n

In no-5s subgroups

1.n

3.n

7.n

In no-7s subgroups

1.n

3.n

5.n

9.n

In no-11s subgroups

1.n

3.n

5.n

7.n

9.n

In no-13s subgroups

1.n

3.n

5.n

7.n

27.n

In no-17s subgroups

7.n

Not yet categorised

Dekanies (10-tone)

Main page: Dekany

In no-3s subgroups

In no-5s subgroups

In no-7s subgroups

In no-11s subgroups

In no-13s subgroups

In no-17s subgroups

Related to regular temperament scales

Not yet categorised

Bihexanies (12-tone)

Main page: Bihexany

Generated by 7-odd-limit elements

Generated by 9-odd-limit elements

Generated by 11-odd-limit elements

Generated by 13-odd-limit elements

Generated by 15-odd-limit elements

No-7s

No-11s

No-13s

No-17s

Generated by 17-odd-limit elements

Generated by 19-odd-limit elements

Higher odd-limit elements

21-odd

23-odd

25-odd

(none documented)

27-odd

29-odd

31-odd

(none documented)

33-odd

35-odd

37-odd to 43-odd

(none documented)

45-odd

47-odd to 53-odd

(none documented)

55-odd

57-odd to 61-odd

(none documented)

63-odd

65-odd

67-odd to 97-odd

(none documented)

99-odd

101-odd to 133-odd

(none documented)

135-odd

Not yet categorised

Duohexanies (12-tone)

Main page: Duohexany

Stellated hexanies (14-tone)

Main page: Stellated hexany

In no-3s subgroups

In no-5s subgroups

In no-7s subgroups

1.n

3.n

5.n

In no-11s subgroups

In no-13s subgroups

Not yet categorised

Pentadekanies (15-tone)

Main page: Pentadekany

1.3.n

1.5.n

1.7.n

3.5.n

3.7.n

5.7.n

Eikosanies (20-tone)

Main page: Eikosany

1.3.n

1.5.n

1.7.n

3.5.n

3.7.n

5.7.n

Other

Other


ViewTalkEditScale galleries
JI scales 12-tone JICombination product setConstant structureHarry Partch-relatedMaximal harmony epimorphicMOS transversalNon-octave JIWakalixZ-polygon transversalOther JI
Full list: Category:Just intonation scales
Tempered scales 11-tone MOS12-tone temperedChromatic pairClipperDouble modeEssentially temperedFantasy detemperMarvel wooMeantoneMin ambiguityMOS cradleNegri-9Neutral thirdNon-octave temperedScalesmith systematicTernaryOther tempered
Full list: Category:Tempered scales
Scales in EDOs in 10edo1113141516171819202122232425262728293031333435363738404142434649537280
All other scale gallery pages are included in Category:Lists of scales