Gallery of combination product sets: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,262 edits
→Hexanies (6-tone): subheadings
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,262 edits
→Stellated hexanies (14-tone): update based on new pages since 23 may
 
(193 intermediate revisions by the same user not shown)
Line 1: Line 1:
This is a gallery of [[combination product set]] (CPS) 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.''


== Pentanies (5-tone) ==
== Pentanies (5-tone) ==
[[Category:5-tone scales]]
[[Category:5-tone scales]]
''Main page: [[Pentany]], see also: [[Ifdo]]''
''Main page: [[Pentany]]''
 
* [[4 from 1-3-5-7-11 pentany]] — ''sturdy, earthy''
* [[4 from 5-17-23-29-37 pentany]] — ''like anticipating the sunrise''
* [[4 from 5-17-23-29-41 pentany]] — ''ethereal, enchanting''
* [[4 from 5-17-23-31-41 pentany]] — ''sorrowful, warm''
* [[4 from 5-17-23-31-43 pentany]] — ''alert, tense''
 
== Hexanies (6-tone) ==
[[Category:6-tone scales]]
''Main page: [[Hexany]]''


=== In no-3s [[subgroup]]s ===


CPS (4 of 1 3 5 7 11)
==== 1.n ====
* Intervals: 11/10, 11/8, 11/7, 11/6, 2/1
* [[1-5-7-11 hexany]] — ''lopsided''
* Description: sturdy, grounded
* [[1-5-7-13 hexany]] — ''spicier whole tone scale''
* Subset of: [[11-limit]] JI, [[11ifdo]]
* [[1-7-11-13 hexany]] — ''extra [[xenharmonic]]''


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


CPS (4 of 5 17 23 29 37)
=== In no-5s subgroups ===
* Intervals: 37/34, 37/29, 37/23, 37/20, 2/1
* Description: like anticipation, sunrise
* Subset of: [[37-limit]] JI, [[37ifdo]]


==== 1.n ====
* [[1-3-7-9 hexany]] — ''a [[detempering]] of the [[archy]] scale''
* [[1-3-7-11 hexany]] — ''symmetrical shape; 2 strong tonal centres''
* [[1-3-7-13 hexany]] — ''extra xenharmonic''
* [[1-3-7-21 hexany]] — ''a [[detempering]] of the [[semaphore]] scale''
* [[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''


CPS (4 of 5 17 23 29 41)
==== 3.n ====
* Intervals: 41/40, 41/34, 41/29, 41/23, 2/1
* [[3-7-9-11 hexany]] — ''fresh [[11-limit]] JI version of the augmented scale''
* Description: enchanting, ethereal
* [[3-7-9-13 hexany]] — ''effective both at melody and harmony''
* Subset of: [[41-limit]] JI, [[41ifdo]]
* [[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''


CPS (4 of 5 17 23 31 41)
=== In no-7s subgroups ===
* Intervals: 41/40, 41/34, 41/31, 41/23, 2/1
* Description: sorrowful, warm
* Subset of: [[41-limit]] JI, [[41ifdo]]


==== 1.n ====
* [[1-3-5-9 hexany]] — ''difficult due to [[wolf interval|wolf fifth]] - better as a basis for building larger scales''
* [[1-3-5-11 hexany]] — ''stable chord roots + very xenharmonic''
* [[1-3-5-13 hexany]] — ''stable chord roots + very xenharmonic''
* [[1-3-5-15 hexany]] — ''difficult to use''
* [[1-3-5-45 hexany]] — ''very useful foundation for adding xenharmonic notes on top off; can play all ''Zelda'''s ocarina melodies''
* [[1-3-5-81 hexany]] — ''built around subtle pitch shifts''
* [[1-3-5-121 hexany]] — ''built-in beating effect that could be interesting''
* [[1-3-9-135 hexany]] — ''near identical to [[1-3-9-17 hexany]]''
* [[1-3-11-15 hexany]] — ''lopsided''
* [[1-3-13-15 hexany]] — ''lopsided''
* [[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''


CPS (4 of 5 17 23 31 43)
==== 3.n ====
* Intervals: 43/40, 43/34, 43/31, 43/23, 2/1
* [[3-5-9-11 hexany]] — ''very xenharmonic''
* Description: tense, alert
* [[3-5-9-13 hexany]] — ''very useful both for melody and harmony; contains good [[barbados]] intervals''
* Subset of: [[43-limit]] JI, [[43ifdo]]
* [[3-5-9-15 hexany]] — ''too similar to [[12edo]] to be interesting''
* [[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''


== Hexanies (6-tone) ==
==== 5.n ====
[[Category:6-tone scales]]
* [[5-9-11-13 hexany]] — ''useful for building melodies; an even mix of familiar and xenharmonic''
''Main page: [[Hexany]]''
* [[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 ===
 
==== 1.n ====
* [[1-3-5-7 hexany]] — ''cold, hazy''
* [[1-3-7-15 hexany]] — ''lopsided''
* [[1-5-7-9 hexany]] — ''whole tone scale-like but with a [[quarter tone]], making it very xenharmonic''
* [[1-7-9-15 hexany]] — ''lopsided but useful for making [[bihexany]]s''
* [[1-7-13-15 hexany]] — ''useful for making [[bihexany]] versions of [[10edo]], which would be a type of [[neji]]''
 
==== 3.n ====
* [[3-5-7-9 hexany]] — ''useful for melody and harmony''
* [[3-5-7-13 hexany]] — ''useful for building [[dekany]]s''
* [[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]]''
 
==== 5.n ====
* [[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''
 
==== 7.n ====
* [[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 ===
 
==== 1.n ====
* [[1-7-11-15 hexany]] — ''a little unwieldy''
 
==== 3.n ====
* [[3-5-7-11 hexany]] — ''very xenharmonic''
* [[3-7-9-55 hexany]] — ''creates interesting complex beating when played in the bass or sub bass range''
* [[3-7-11-15 hexany]] — ''xenharmonic but also with sweet major thirds''


; No-3s
==== 5.n ====
* [[1-5-7-11 hexany]]
* [[5-7-9-11 hexany]] — ''a [[neji]] of [[6edo]] with an [[primodality|over-35 semiprime]] feel''
* [[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''


; No-5s
==== 7.n ====
* [[1-3-7-9 hexany]]
* [[7-9-11-15 hexany]] — ''useful for building [[bihexany]]s''
* [[1-3-7-11 hexany]]
* [[:File:Hexany 7 11 17 45 cents.png|7-11-17-45 hexany]] — ''dark, supernatural, metallic''
* [[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]]
* [[1-3-21-49 hexany]]
* [[1-7-9-11 hexany]]


; No-7s
==== 27.n ====
* [[1-3-5-9 hexany]]
* [[:File:Hexany 27 35 47 59 cents.png|27-35-47-59 hexany]] — ''like melting rainbow ice cream in the sun''
* [[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]]
* [[1-5-9-11 hexany]]
* [[1-5-9-15 hexany]]
* [[1-15-45-75 hexany]]
* [[3-5-15-19 hexany]]
* [[3-5-15-27 hexany]]


; No-11s
=== In no-17s subgroups ===
* [[1-3-5-7 hexany]]
* [[1-5-7-9 hexany]]
* [[3-5-7-9 hexany]]
* [[3-5-15-21 hexany]]
* [[9-25-49-81 hexany]]


; No-13s
==== 7.n ====
* [[3-7-9-55 hexany]]
* [[7-11-13-15 hexany]] — ''useful for writing melody - expanding into a [[bihexany]] makes it more useful still''
* [[5-7-9-33 hexany]]


; Not yet categorided
=== Not yet categorised ===
* [[Hexany 1029]]
* [[Hexany 1029]]
* [[Hexany 126]]
* [[Hexany 126]]
Line 96: Line 175:
* [[Hexany 65625]]
* [[Hexany 65625]]
* [[Hexany 875]]
* [[Hexany 875]]
* [[Hexanys-valentino]]
* [[User:BudjarnLambeth/My favourite hexanies using at least one odd greater than 15]]
 
== Dekanies (10-tone) ==
[[Category:10-tone scales]]
''Main page: [[Dekany]]''
 
=== 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]]
* [[1-3-5-7-13 dekany]]
* [[1-3-5-7-15 dekany]] — ''recommended''
* [[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''
 
=== Related to [[regular temperament]] scales ===
* [[Dekany agni]]
* [[Dekany apollo]]
* [[Dekany guanyin]]
* [[Dekany indra]]
* [[Dekany jove]]
* [[Dekany laka]]
* [[Dekany marvel]]
* [[Dekany minerva]]
* [[Dekany pele]]
* [[Dekany portent]]
* [[Dekany prodigy]]
* [[Dekany sensamagic]]
* [[Dekany spectacle]]
* [[Dekany zeus]]
* [[Dekany-cs-marv]]
* [[Dekanymarvwoo]]
 
=== Not yet categorised ===
* [[Deka1029]]
* [[Deka126]]
* [[Deka1728]]
* [[Deka225]]
* [[Deka2401]]
* [[Deka245]]
* [[Deka3136]]
* [[Deka4375]]
* [[Deka5120]]
* [[Deka6144]]
* [[Deka65625]]
* [[Deka875]]
* [[Dekany-cs]]
 
== Bihexanies (12-tone) ==
[[Category:12-tone scales]]
''Main page: [[Bihexany]]''
 
=== 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]]
* [[1-3-7-9 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]]
* [[3-5-7-15 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''


CPS (2 of 1 3 5 7)
==== 23-odd ====
* [[3-5-7-15 by 23/14 bihexany]]


''Main page: [[1-3-5-7 hexany]].''
==== 25-odd ====
* Intervals: 7/6, 5/4, 35/24, 5/3, 7/4, 2/1
''(none documented)''
* Description: hazy, cold
* Subset of: [[7-limit]] JI


==== 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''


CPS (2 of 1 17 27 49)
==== 29-odd ====
* Intervals: 1323/1088, 49/34, 49/32, 27/17, 27/16, 2/1
* [[5-7-9-15 by 29/18 bihexany]]
* Description: clumsy, mischievous
* Subset of: [[17-limit]] JI, [[subgroup|2.3.7.17 subgroup]] JI


==== 31-odd ====
''(none documented)''


CPS (2 of 1 19 25 55)
==== 33-odd ====
* Intervals: 64/55, 25/19, 320/209, 32/19, 20/11, 2/1
* [[1-5-11-15 by 40/33 bihexany]]
* Description: vast, stern, robotic
* Subset of: [[19-limit]] JI, [[subgroup|2.5.11.19 subgroup]] JI


==== 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''


CPS (2 of 5 17 23 29)
==== 37-odd to 43-odd ====
* Intervals: 23/20, 23/17, 29/20, 29/17, 667/340, 2/1
''(none documented)''
* Description: dreamlike, hypnotic
* Subset of: [[29-limit]] JI, [[subgroup|2.5.17.23.29 subgroup]] JI


==== 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]]


CPS (2 of 5 17 23 31)
==== 47-odd to 53-odd ====
* Intervals: 713/680, 23/20, 23/17, 31/20, 31/17, 2/1
''(none documented)''
* Description: groovy, funky
* Subset of: [[31-limit]] JI, [[subgroup|2.5.17.23.31 subgroup]] JI


==== 55-odd ====
* [[1-9-11-15 by 72/55 bihexany]]


CPS (2 of 8 21 29 48)
==== 57-odd to 61-odd ====
* Intervals: 29/28, 8/7, 29/21, 3/2, 29/16, 2/1
''(none documented)''
* Description: funky, dark, fierce
* Subset of: [[29-limit]] JI, [[subgroup|2.3.7.29 subgroup]] JI


==== 63-odd ====
* [[1-3-5-7 by 80/63 bihexany]] — ''recommended''


CPS (2 of 19 31 36 48)
==== 65-odd ====
* Intervals: 36/31, 24/19, 864/589, 48/31, 36/19, 2/1
* [[3-5-11-13 by 96/65 bihexany]] — ''good for metallophone timbres like bells or Gamelan''
* Description: pretty, sparkly
* Subset of: [[31-limit]] JI, [[subgroup|2.3.19.31 subgroup]] JI


==== 67-odd to 97-odd ====
''(none documented)''


CPS (2 of 21 32 38 45)
==== 99-odd ====
* Intervals: 15/14, 19/16, 285/224, 45/32, 38/21, 2/1
* [[1-7-13-15 by 140/99 bihexany]]
* Description: playful, cheeky
* Subset of: [[19-limit]] JI, [[subgroup|2.3.5.7.19 subgroup]] JI


=== Bihexanies/Duohexanies (12-tone) ===
==== 101-odd to 133-odd ====
''Main page: [[Duohexany]]''
''(none documented)''
[[Category:12-tone scales]]


==== 135-odd ====
* [[1-3-9-135 by 57/34 bihexany]] — ''recommended''


* [[Bihexany]]
=== Not yet categorised ===
* [[Bihexanymyna]]
* [[Bihexanymyna]]
* [[GW Smith bihexany 14 Feb 2011]]
== Duohexanies (12-tone) ==
[[Category:12-tone scales]]
''Main page: [[Duohexany]]''
* [[Duohex]]
* [[Duohex]]
* [[Duohexmarvwoo]]
* [[Duohexmarvwoo]]
* [[Duohexmean]]
* [[Duohexmean]]
* [[Hexanys-valentino]]


=== 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 170: Line 558:
* [[Stellarhex]]
* [[Stellarhex]]


== Dekanies (10-tone) ==
== Pentadekanies (15-tone) ==
[[Category:10-tone scales]]
''Main page: [[Pentadekany]]''
''Main page: [[Dekany]]''
 
=== 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''


* [[1-3-5-7-9 dekany]]
=== 3.7.n ===
* [[1-3-5-7-13 dekany]]
* [[3-7-9-11-13-15 pentadekany]]
* [[1-3-5-9-11 dekany]]
* [[1-3-5-9-81 dekany]]
* [[Deka1029]]
* [[Deka126]]
* [[Deka1728]]
* [[Deka225]]
* [[Deka2401]]
* [[Deka245]]
* [[Deka3136]]
* [[Deka4375]]
* [[Deka5120]]
* [[Deka6144]]
* [[Deka65625]]
* [[Deka875]]
* [[Dekany agni]]
* [[Dekany apollo]]
* [[Dekany guanyin]]
* [[Dekany indra]]
* [[Dekany jove]]
* [[Dekany laka]]
* [[Dekany marvel]]
* [[Dekany minerva]]
* [[Dekany pele]]
* [[Dekany portent]]
* [[Dekany prodigy]]
* [[Dekany sensamagic]]
* [[Dekany spectacle]]
* [[Dekany zeus]]
* [[Dekany-cs]]
* [[Dekany-cs-marv]]
* [[Dekanymarvwoo]]


== Pentadekanies (15-tone) ==
=== 5.7.n ===
''Main page: [[Pentadekany]]''
* [[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]]


Latest revision as of 11:42, 3 June 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

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


View • Talk • EditScale galleries
JI scales 12-tone JI • Combination product set • Constant structure • Harry Partch-related • Maximal harmony epimorphic • MOS transversal • Non-octave JI • Wakalix • Z-polygon transversal • Other JI
Full list: Category:Just intonation scales
Tempered scales 11-tone MOS • 12-tone tempered • Chromatic pair • Clipper • Double mode • Essentially tempered • Fantasy detemper • Marvel woo • Meantone • Min ambiguity • MOS cradle • Negri-9 • Neutral third • Non-octave tempered • Scalesmith systematic • Ternary • Other tempered
Full list: Category:Tempered scales
Scales in EDOs in 10edo • 11 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 33 • 34 • 35 • 36 • 37 • 38 • 40 • 41 • 42 • 43 • 46 • 49 • 53 • 72 • 80
All other scale gallery pages are included in Category:Lists of scales
Retrieved from "https://en.xen.wiki/index.php?title=Gallery_of_combination_product_sets&oldid=231509"