Gallery of combination product sets

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.

(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)

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)

Main page: Hexany

In no-3s subgroups

1.n

• 1-5-7-11 hexany (lopsided)
• 1-5-7-13 hexany (spicier whole tone scale)
• 1-7-11-13 hexany (extra xenharmonic)

5.n

• 5-7-11-13 hexany (melodically effective, contains a diminished chord)

In no-5s subgroups

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)
• 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)

3.n

• 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)
• 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

1.n

• 1-3-5-9 hexany (difficult due to 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 bihexanys with)
• 1-5-9-15 hexany (easy to build dekanys with)
• 1-5-11-13 hexany (an omniconsonant scale)
• 1-5-11-15 hexany (easy to build bihexanys 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)

3.n

• 3-5-9-11 hexany (very xenharmonic)
• 3-5-9-13 hexany (very useful both for melody and harmony; contains good barbados intervals)
• 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 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)

5.n

• 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

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 bihexanys)
• 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 dekanys)
• 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 bihexanys or dekanys)
• 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 bihexanys)

7.n

• 7-9-13-15 hexany (useful for building bihexanys or dekanys 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)

5.n

• 5-7-9-11 hexany (a neji of 6edo with an 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)

7.n

• 7-9-11-15 hexany (useful for building bihexanys)
• 7-11-17-45 hexany (dark, supernatural, metallic)

27.n

• 27-35-47-59 hexany (like melting rainbow ice cream in the sun)

In no-17s subgroups

7.n

• 7-11-13-15 hexany (useful for writing melody - expanding into a bihexany makes it more useful still)

Not yet categorised

• Hexany 1029
• Hexany 126
• Hexany 225
• Hexany 2401
• Hexany 245
• Hexany 3136
• Hexany 4375
• Hexany 5120
• Hexany 6144
• Hexany 65625
• Hexany 875
• User:BudjarnLambeth/My favourite hexanies using at least one odd greater than 15

Dekanies (10-tone)

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
• 1-3-7-9-29 dekany
• 1-7-9-11-13 dekany
• 3-7-9-11-13 dekany

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
• 1-3-5-11-15 dekany
• 1-3-5-13-15 dekany
• 1-3-9-11-15 dekany
• 1-3-9-13-15 dekany
• 1-3-11-13-15 dekany
• 1-5-9-11-13 dekany
• 1-5-9-11-15 dekany
• 1-5-9-13-15 dekany
• 1-5-11-13-15 dekany
• 1-9-11-13-15 dekany
• 3-5-9-11-13 dekany
• 3-5-9-11-15 dekany
• 3-5-9-13-15 dekany
• 3-5-11-13-15 dekany
• 3-9-11-13-15 dekany
• 5-9-11-13-15 dekany

In no-11s subgroups

• 1-3-5-7-9 dekany
• 1-3-5-7-13 dekany
• 1-3-5-7-15 dekany
• 1-3-5-9-15 dekany
• 1-3-7-9-13 dekany
• 1-3-7-9-15 dekany
• 1-3-7-13-15 dekany
• 1-5-7-9-13 dekany
• 1-5-7-9-15 dekany
• 1-5-7-13-15 dekany
• 1-7-9-13-15 dekany
• 3-5-7-9-13 dekany
• 3-5-7-9-15 dekany
• 3-5-7-13-15 dekany
• 3-7-9-13-15 dekany
• 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
• 1-7-9-11-15 dekany
• 3-5-7-9-11 dekany
• 3-5-7-11-15 dekany
• 3-7-9-11-15 dekany
• 5-7-9-11-15 dekany

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

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)

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
• 1-5-7-9 by 4/3 bihexany
• 3-5-7-9 by 5/4 bihexany

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
• 3-5-7-11 by 3/2 bihexany
• 3-5-9-11 by 5/4 bihexany

Generated by 13-odd-limit elements

• 1-3-5-9 by 13/9 bihexany
• 1-5-9-13 by 3/2 bihexany
• 1-7-9-13 by 4/3 bihexany
• 5-9-11-13 by 3/2 bihexany

Generated by 15-odd-limit elements

No-7s

• 1-3-5-13 by 18/13 bihexany
• 1-3-9-15 by 11/8 bihexany
• 1-3-11-15 by 6/5 bihexany
• 1-3-13-15 by 18/13 bihexany
• 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
• 5-11-13-15 by 11/9 bihexany
• 9-11-13-15 by 3/2 bihexany
• 9-11-13-15 by 33/26 bihexany

No-11s

• 1-3-5-7 by 15/14 bihexany
• 1-3-5-7 by 16/15 bihexany
• 1-3-7-15 by 6/5 bihexany
• 1-3-7-15 by 9/7 bihexany
• 1-3-9-15 by 7/6 bihexany
• 1-5-7-15 by 6/5 bihexany
• 1-7-9-15 by 4/3 bihexany
• 1-7-9-15 by 7/5 bihexany
• 1-7-13-15 by 7/5 bihexany
• 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
• 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
• 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
• 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
• 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

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

23-odd

• 3-5-7-15 by 23/14 bihexany

25-odd
27-odd

• 1-5-7-15 by 32/27 bihexany
• 3-5-7-15 by 27/14 bihexany
• 3-9-13-15 by 27/26 bihexany

29-odd

• 5-7-9-15 by 29/18 bihexany

31-odd
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
• 1-3-7-15 by 48/35 bihexany

37...43
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...53
55-odd

• 1-9-11-15 by 72/55 bihexany

57...61
63-odd

• 1-3-5-7 by 80/63 bihexany

65-odd

• 3-5-11-13 by 96/65 bihexany

67...97
99-odd

• 1-7-13-15 by 140/99 bihexany

101...133
135-odd

• 1-3-9-135 by 57/34 bihexany

Not yet categorised

• Bihexanymyna
• GW Smith bihexany 14 Feb 2011

Duohexanies (12-tone)

Main page: Duohexany

• Duohex
• Duohexmarvwoo
• Duohexmean
• Hexanys-valentino

Stellated hexanies (14-tone)

Main page: Stellated hexany

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
• 3-7-11-13 stellated hexany
• 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
• 1-3-9-15 stellated hexany
• 1-3-11-15 stellated hexany
• 1-3-13-15 stellated hexany
• 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
• 1-15-45-75 stellated hexany (recommended)

3.n

• 3-5-9-11 stellated hexany (recommended)
• 3-5-9-13 stellated hexany
• 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
• 3-5-11-15 stellated hexany
• 3-5-13-15 stellated hexany
• 3-9-11-15 stellated hexany
• 3-9-13-15 stellated hexany
• 3-9-25-625 stellated hexany (recommended)
• 3-11-13-15 stellated hexany

5.n

• 5-9-11-13 stellated hexany
• 5-9-11-15 stellated hexany
• 5-9-13-15 stellated hexany
• 5-11-13-15 stellated hexany

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
• 3-5-7-15 stellated hexany
• 3-7-9-15 stellated hexany
• 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

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

Not yet categorised

• Stelhex
• Stelhex-catakleismic
• Stelhex2
• Stelhex5
• Stellarhex

Pentadekanies (15-tone)

Main page: Pentadekany

1.3.n

• 1-3-5-7-9-11 pentadekany
• 1-3-5-7-9-13 pentadekany
• 1-3-5-7-9-15 pentadekany
• 1-3-5-7-11-13 pentadekany
• 1-3-5-7-11-15 pentadekany
• 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
• 1-3-7-9-11-13 pentadekany
• 1-3-7-9-11-15 pentadekany
• 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
• 1-5-7-9-13-15 pentadekany
• 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
• 3-5-7-9-13-15 pentadekany
• 3-5-7-11-13-15 pentadekany
• 3-5-9-11-13-15 pentadekany

3.7.n

• 3-7-9-11-13-15 pentadekany

5.7.n

• 5-7-9-11-13-15 pentadekany

Eikosanies (20-tone)

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