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.

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

• 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

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

• 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

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
1-3-5-7-9 dekany	25	3	9	7	203.910	48.770	4.181	0
1-3-5-7-11 dekany	27	3	11	11	333.040	31.194	10.676	0
1-3-5-9-11 dekany	29	3	11	11	182.403	31.766	5.742	0
1-3-7-9-11 dekany	31	3	11	11	203.910	53.272	3.827	0
1-5-7-9-11 dekany	33	5	11	11	203.910	31.194	6.536	0
3-5-7-9-11 dekany	35	15	11	11	165.004	31.766	5.194	0
1-3-5-7-13 dekany	29	3	13	13	187.343	43.831	4.274	0
1-3-5-9-13 dekany	31	3	13	13	203.910	43.831	4.652	0
1-3-5-11-13 dekany	33	3	13	13	165.004	26.431	6.242	0
1-3-7-9-13 dekany	33	3	13	13	231.174	62.961	3.671	0
1-3-7-11-13 dekany	35	3	13	13	284.447	22.338	12.733	0
1-3-9-11-13 dekany	37	3	13	13	208.835	12.064	17.310	0
1-5-7-9-13 dekany	35	5	13	13	231.174	19.129	12.085	0
1-5-7-11-13 dekany	37	5	13	13	258.015	31.194	8.271	0
1-5-9-11-13 dekany	39	5	13	13	182.403	12.064	15.119	0
1-7-9-11-13 dekany	41	7	13	13	231.174	12.064	19.162	0
3-5-7-9-13 dekany	37	15	13	13	296.511	19.129	15.500	0
3-5-7-11-13 dekany	39	15	13	13	328.278	22.338	14.695	0
3-5-9-11-13 dekany	41	15	13	13	247.741	26.431	9.373	0
3-7-9-11-13 dekany	43	21	13	13	150.637	22.338	6.743	0
5-7-9-11-13 dekany	45	35	13	13	270.079	22.338	12.090	0
1-3-5-7-15 dekany	31	3	15	7	266.871	84.467	3.159	1
1-3-5-9-15 dekany	33	3	15	5	203.910	70.672	2.885	2
1-3-5-11-15 dekany	35	3	15	11	235.676	38.905	6.057	1
1-3-5-13-15 dekany	37	3	15	13	247.741	26.841	9.229	1
1-3-7-9-15 dekany	35	3	15	7	266.871	48.770	5.474	0
1-3-7-11-15 dekany	37	3	15	11	266.871	31.194	8.555	0
1-3-7-13-15 dekany	39	3	15	13	454.213	16.566	27.418	0
1-3-9-11-15 dekany	39	3	15	11	235.676	38.905	6.057	0
1-3-9-13-15 dekany	41	3	15	13	247.741	26.841	9.229	0
1-3-11-13-15 dekany	43	3	15	13	247.741	26.841	9.229	0
1-5-7-9-15 dekany	37	5	15	7	266.871	48.770	5.474	0
1-5-7-11-15 dekany	39	5	15	11	305.776	31.194	9.802	0
1-5-7-13-15 dekany	41	5	15	13	223.039	16.566	14.328	0
1-5-9-11-15 dekany	41	5	15	11	203.910	38.905	5.241	0
1-5-9-13-15 dekany	43	5	15	13	203.910	43.831	4.652	0
1-5-11-13-15 dekany	45	5	15	13	177.478	53.272	3.331	0
1-7-9-11-15 dekany	43	7	15	11	203.910	84.467	2.414	0
1-7-9-13-15 dekany	45	7	15	13	405.443	16.566	24.473	0
1-7-11-13-15 dekany	47	7	15	13	303.576	16.566	18.325	0
1-9-11-13-15 dekany	49	9	15	13	235.676	12.064	19.535	0
3-5-7-9-15 dekany	39	15	15	7	266.871	48.770	5.472	1
3-5-7-11-15 dekany	41	15	15	11	266.871	31.194	8.555	0
3-5-7-13-15 dekany	43	15	15	13	231.174	19.129	12.085	0
3-5-9-11-15 dekany	43	15	15	11	182.403	31.766	5.742	1
3-5-9-13-15 dekany	45	15	15	13	247.741	43.831	5.652	1
3-5-11-13-15 dekany	47	15	15	13	208.835	26.431	7.901	0
3-7-9-11-15 dekany	45	21	15	11	266.871	31.194	8.555	0
3-7-9-13-15 dekany	47	21	15	13	250.313	19.129	13.085	0
3-7-11-13-15 dekany	49	21	15	13	396.178	19.129	20.710	0
3-9-11-13-15 dekany	51	27	15	13	208.835	26.431	7.901	0
5-7-9-11-15 dekany	47	35	15	11	235.104	45.561	5.160	0
5-7-9-13-15 dekany	49	35	15	13	315.641	19.129	16.500	0
5-7-11-13-15 dekany	51	35	15	13	289.209	36.705	7.879	0
5-9-11-13-15 dekany	53	45	15	13	182.403	26.431	6.901	0
7-9-11-13-15 dekany	55	63	15	13	187.343	26.431	7.088	0

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)

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

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
• 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

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 stellated hexany	16	1	7	7	231.174	84.467	2.736	6
1-3-5-9 stellated hexany	18	1	9	5	203.910	92.178	2.212	6
1-3-7-9 stellated hexany	20	1	9	7	266.871	27.264	9.788	6
1-5-7-9 stellated hexany	22	1	9	7	378.602	27.274	14.409	6
3-5-7-9 stellated hexany	24	3	9	7	155.139	27.274	5.904	0
1-3-5-11 stellated hexany	20	1	11	11	333.040	53.272	6.251	6
1-3-7-11 stellated hexany	22	1	11	11	266.871	53.272	5.009	6
1-3-9-11 stellated hexany	24	1	11	11	294.134	53.272	5.521	6
1-5-7-11 stellated hexany	24	1	11	11	231.174	31.194	7.410	6
1-5-9-11 stellated hexany	26	1	11	11	203.910	38.905	5.241	6
1-7-9-11 stellated hexany	28	1	11	11	213.597	27.264	7.834	6
3-5-7-11 stellated hexany	26	3	11	11	165.004	4.502	36.651	0
3-5-9-11 stellated hexany	28	3	11	11	150.637	31.766	4.742	0
3-7-9-11 stellated hexany	30	3	11	11	150.637	27.264	5.525	0
5-7-9-11 stellated hexany	32	5	11	11	182.403	27.264	6.690	0
1-3-5-13 stellated hexany	22	1	13	13	315.641	26.841	11.759	6
1-3-7-13 stellated hexany	24	1	13	13	231.174	92.601	2.496	6
1-3-9-13 stellated hexany	26	1	13	13	203.910	65.337	3.120	6
1-3-11-13 stellated hexany	28	1	13	13	306.199	53.272	5.747	6
1-5-7-13 stellated hexany	26	1	13	13	231.174	26.841	8.612	6
1-5-9-13 stellated hexany	28	1	13	13	250.303	26.841	9.325	6
1-5-11-13 stellated hexany	30	1	13	13	262.368	26.841	9.774	6
1-7-9-13 stellated hexany	30	1	13	13	405.443	27.264	14.871	6
1-7-11-13 stellated hexany	32	1	13	13	231.174	39.328	5.878	6
1-9-11-13 stellated hexany	34	1	13	13	203.910	12.064	16.902	6
3-5-7-13 stellated hexany	28	3	13	13	187.343	16.566	11.308	0
3-5-9-13 stellated hexany	30	3	13	13	160.078	26.841	5.963	0
3-5-11-13 stellated hexany	32	3	13	13	138.572	26.431	5.242	0
3-7-9-13 stellated hexany	32	3	13	13	138.572	27.264	5.082	0
3-7-11-13 stellated hexany	34	3	13	13	138.572	22.338	6.203	0
3-9-11-13 stellated hexany	36	3	13	13	208.835	4.925	42.403	0
5-7-9-13 stellated hexany	34	5	13	13	203.910	19.129	10.659	0
5-7-11-13 stellated hexany	36	5	13	13	165.004	26.841	6.147	0
5-9-11-13 stellated hexany	38	5	13	13	165.004	9.441	17.477	0
7-9-11-13 stellated hexany	40	7	13	13	209.109	12.064	17.333	0
1-3-5-15 stellated hexany	24	1	15	5	274.582	111.731	2.457	7
1-3-7-15 stellated hexany	26	1	15	7	359.049	111.731	3.213	6
1-3-9-15 stellated hexany	28	1	15	5	386.313	92.178	4.190	6
1-3-11-15 stellated hexany	30	1	15	11	386.313	38.905	9.929	6
1-3-13-15 stellated hexany	32	1	15	13	247.741	26.841	9.229	6
1-5-7-15 stellated hexany	28	1	15	7	470.781	43.408	10.845	6
1-5-9-15 stellated hexany	30	1	15	5	498.044	70.672	7.047	6
1-5-11-15 stellated hexany	32	1	15	11	274.582	53.272	5.154	6
1-5-13-15 stellated hexany	34	1	15	13	342.482	26.841	12.759	6
1-7-9-15 stellated hexany	32	1	15	7	653.184	27.264	23.957	6
1-7-11-15 stellated hexany	34	1	15	11	305.776	111.731	2.736	6
1-7-13-15 stellated hexany	36	1	15	13	497.622	16.566	30.038	6
1-9-11-15 stellated hexany	36	1	15	11	333.040	92.178	3.613	6
1-9-13-15 stellated hexany	38	1	15	13	524.866	43.831	11.974	6
1-11-13-15 stellated hexany	40	1	15	13	247.741	80.114	3.092	6
3-5-7-15 stellated hexany	30	3	15	7	155.139	7.711	20.119	2
3-5-9-15 stellated hexany	32	3	15	5	203.911	70.672	2.885	3
3-5-11-15 stellated hexany	34	3	15	11	221.309	38.905	5.688	2
3-5-13-15 stellated hexany	36	3	15	13	203.910	26.841	7.596	2
3-7-9-15 stellated hexany	34	3	15	7	155.139	27.264	5.690	0
3-7-11-15 stellated hexany	36	3	15	11	155.139	31.194	4.973	0
3-7-13-15 stellated hexany	38	3	15	13	223.039	16.566	13.463	0
3-9-11-15 stellated hexany	38	3	15	11	182.403	38.905	4.688	0
3-9-13-15 stellated hexany	40	3	15	13	203.910	26.841	7.596	0
3-11-13-15 stellated hexany	42	3	15	13	194.468	26.841	7.245	0
5-7-9-15 stellated hexany	36	5	15	7	266.871	27.264	9.788	0
5-7-11-15 stellated hexany	38	5	15	11	155.139	31.194	4.973	0
5-7-13-15 stellated hexany	40	5	15	13	119.442	16.566	7.210	0
5-9-11-15 stellated hexany	40	5	15	11	150.137	38.905	3.859	0
5-9-13-15 stellated hexany	42	5	15	13	138.572	26.841	5.162	0
5-11-13-15 stellated hexany	44	5	15	13	150.137	14.627	10.264	0
7-9-11-15 stellated hexany	42	7	15	11	119.442	4.502	26.530	0
7-9-13-15 stellated hexany	44	7	15	13	293.712	16.566	17.729	0
7-11-13-15 stellated hexany	46	7	15	13	119.442	16.566	7.210	0
9-11-13-15 stellated hexany	48	9	15	13	191.845	12.064	15.902	0

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-catakleismic
• Stelhex2
• Stelhex5
• Stellarhex

Pentadekanies (15-tone)

Main page: Pentadekany

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
1-3-5-7-9-11 pentadekany	36	3	11	11	150.637	31.194	4.829	0
1-3-5-7-9-13 pentadekany	38	3	13	13	138.572	19.129	7.244	0
1-3-5-7-11-13 pentadekany	40	3	13	13	138.572	22.338	6.203	0
1-3-5-9-11-13 pentadekany	42	3	13	13	165.004	12.064	13.677	0
1-3-7-9-11-13 pentadekany	44	3	13	13	138.572	12.064	11.486	0
1-5-7-9-11-13 pentadekany	46	5	13	13	165.004	12.064	13.677	0
3-5-7-9-11-13 pentadekany	48	15	13	13	150.637	19.129	7.874	0
1-3-5-7-9-15 pentadekany	40	3	15	7	155.139	48.770	3.181	2
1-3-5-7-11-15 pentadekany	42	3	15	11	165.004	31.194	5.289	1
1-3-5-7-13-15 pentadekany	44	3	15	13	138.572	16.566	8.364	1
1-3-5-9-11-15 pentadekany	44	3	15	11	165.004	31.194	5.289	2
1-3-5-9-13-15 pentadekany	46	3	15	13	203.910	26.841	7.596	2
1-3-5-11-13-15 pentadekany	48	3	15	13	150.637	26.841	5.612	1
1-3-7-9-11-15 pentadekany	46	3	15	11	119.442	31.194	3.829	0
1-3-7-9-13-15 pentadekany	48	3	15	13	138.572	16.566	8.364	0
1-3-7-11-13-15 pentadekany	50	3	15	13	165.004	16.566	9.960	0
1-3-9-11-13-15 pentadekany	52	3	15	13	165.004	12.064	13.677	0
1-5-7-9-11-15 pentadekany	48	5	15	11	165.004	31.194	5.289	0
1-5-7-9-13-15 pentadekany	50	5	15	13	203.910	16.566	12.308	0
1-5-7-11-13-15 pentadekany	52	5	15	13	138.572	16.566	8.364	0
1-5-9-11-13-15 pentadekany	54	5	15	13	138.572	12.064	11.486	0
1-7-9-11-13-15 pentadekany	56	7	15	13	119.442	12.064	9.900	0
3-5-7-9-11-15 pentadekany	50	15	15	11	165.004	31.194	5.289	1
3-5-7-9-13-15 pentadekany	52	15	15	13	128.298	19.129	6.706	1
3-5-7-11-13-15 pentadekany	54	15	15	13	150.637	19.129	7.874	0
3-5-9-11-13-15 pentadekany	56	15	15	13	150.637	26.431	5.699	1
3-7-9-11-13-15 pentadekany	58	21	15	13	138.572	19.129	7.244	0
5-7-9-11-13-15 pentadekany	60	35	15	13	150.637	19.129	7.874	0

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)

Main page: Eikosany

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
1-3-5-7-9-11 eikosany	36	15	11	11	102.043	31.194	3.271	0
1-3-5-7-9-13 eikosany	38	15	13	13	111.731	16.566	6.744	0
1-3-5-7-11-13 eikosany	40	15	13	13	128.298	22.338	5.743	0
1-3-5-9-11-13 eikosany	42	15	13	13	138.572	12.064	11.486	0
1-3-7-9-11-13 eikosany	44	21	13	13	116.233	12.064	9.634	0
1-5-7-9-11-13 eikosany	46	35	13	13	128.298	12.064	10.634	0
3-5-7-9-11-13 eikosany	48	105	13	13	131.507	19.129	6.874	0
1-3-5-7-9-15 eikosany	40	15	15	7	119.442	7.711	15.489	4
1-3-5-7-11-15 eikosany	42	15	15	11	119.442	9.864	12.108	2
1-3-5-7-13-15 eikosany	44	15	15	13	128.298	16.566	7.744	2
1-3-5-9-11-15 eikosany	44	15	15	11	165.004	17.399	9.483	4
1-3-5-9-13-15 eikosany	46	15	15	13	138.572	26.841	5.162	4
1-3-5-11-13-15 eikosany	48	15	15	13	138.572	12.064	11.486	2
1-3-7-9-11-15 eikosany	46	21	15	11	116.233	31.194	3.726	0
1-3-7-9-13-15 eikosany	48	21	15	13	119.442	16.566	7.210	0
1-3-7-11-13-15 eikosany	50	21	15	13	128.298	16.566	7.744	0
1-3-9-11-13-15 eikosany	52	27	15	13	111.731	12.064	9.261	0
1-5-7-9-11-15 eikosany	48	35	15	11	123.372	31.194	3.954	0
1-5-7-9-13-15 eikosany	50	35	15	13	119.442	16.566	7.210	0
1-5-7-11-13-15 eikosany	52	35	15	13	119.442	16.566	7.210	0
1-5-9-11-13-15 eikosany	54	45	15	13	121.173	4.925	24.603	0
1-7-9-11-13-15 eikosany	56	63	15	13	111.731	12.064	9.261	0
3-5-7-9-11-15 eikosany	50	105	15	11	119.442	31.194	3.829	2
3-5-7-9-13-15 eikosany	52	105	15	13	128.298	19.129	6.706	2
3-5-7-11-13-15 eikosany	54	105	15	13	128.298	19.129	6.706	0
3-5-9-11-13-15 eikosany	56	135	15	13	138.572	12.064	11.486	2
3-7-9-11-13-15 eikosany	58	189	15	13	119.442	19.129	6.244	0
5-7-9-11-13-15 eikosany	60	315	15	13	128.298	12.638	10.151	0

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

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