Gallery of combination product sets

Revision as of 07:03, 5 July 2026 by Yourmusic Productions (talk | contribs) (13-odd limit table entries)

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

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