Gallery of combination product sets: Difference between revisions
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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. | ||
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) == | ||
| Line 15: | Line 12: | ||
''Main page: [[Pentany]]'' | ''Main page: [[Pentany]]'' | ||
* [[4 from 1-3-5-7-11 pentany]] | * [[4 from 1-3-5-7-11 pentany]] — ''sturdy, earthy'' | ||
* [[4 from 5-17-23-29-37 pentany]] | * [[4 from 5-17-23-29-37 pentany]] — ''like anticipating the sunrise'' | ||
* [[4 from 5-17-23-29-41 pentany]] | * [[4 from 5-17-23-29-41 pentany]] — ''ethereal, enchanting'' | ||
* [[4 from 5-17-23-31-41 pentany]] | * [[4 from 5-17-23-31-41 pentany]] — ''sorrowful, warm'' | ||
* [[4 from 5-17-23-31-43 pentany]] | * [[4 from 5-17-23-31-43 pentany]] — ''alert, tense'' | ||
== Hexanies (6-tone) == | == Hexanies (6-tone) == | ||
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=== In no-3s [[subgroup]]s === | === In no-3s [[subgroup]]s === | ||
5.n | ==== 1.n ==== | ||
* [[5-7-11-13 hexany]] | * [[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 === | === In no-5s subgroups === | ||
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]] | * [[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'' | |||
==== 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'' | |||
* [[:File:Hexany 3 9 19 31.png|3-9-19-31 hexany]] — ''sparkly, pretty'' | |||
7.n | ==== 7.n ==== | ||
* [[7-9-11-13 hexany]] | * [[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 === | ||
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'' | ||
* [[3-5-9-25 hexany]] | * [[1-3-5-15 hexany]] — ''difficult to use'' | ||
* [[3-5-9-27 hexany]] | * [[1-3-5-45 hexany]] — ''very useful foundation for adding xenharmonic notes on top off; can play all ''Zelda'''s ocarina melodies'' | ||
* [[3-5-11-13 hexany]] | * [[1-3-5-81 hexany]] — ''built around subtle pitch shifts'' | ||
* [[3-5-11-15 hexany]] | * [[1-3-5-121 hexany]] — ''built-in beating effect that could be interesting'' | ||
* [[3-5-13-15 hexany]] | * [[1-3-9-135 hexany]] — ''near identical to [[1-3-9-17 hexany]]'' | ||
* [[3-5-15-19 hexany]] | * [[1-3-11-15 hexany]] — ''lopsided'' | ||
* [[3-5-15-27 hexany]] | * [[1-3-13-15 hexany]] — ''lopsided'' | ||
* [[3-9-11-15 hexany]] | * [[1-5-9-11 hexany]] — ''very lopsided and very xenharmonic'' | ||
* [[3-9-13-15 hexany]] | * [[1-5-9-13 hexany]] — ''easy to build [[bihexany]]s with'' | ||
* [[3-11-13-15 hexany]] | * [[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'' | |||
==== 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 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'' | |||
5.n | ==== 5.n ==== | ||
* [[5-9-11-13 hexany]] | * [[5-9-11-13 hexany]] — ''useful for building melodies; an even mix of familiar and xenharmonic'' | ||
* [[5-9-11-15 hexany]] | * [[5-9-11-15 hexany]] — ''a [[detempering]] of the [[porcupine]] scale; nice melodies'' | ||
* [[5-9-13-15 hexany]] | * [[5-9-13-15 hexany]] — ''melodically interesting but harmonically unrewarding'' | ||
* [[5-11-13-15 hexany]] | * [[5-11-13-15 hexany]] — ''highly recommended; an even mix of familiar and xenharmonic'' | ||
9.n | ==== 9.n ==== | ||
* [[9-11-13-15 hexany]] | * [[9-11-13-15 hexany]] — ''better used as a [[pentatonic]] scale by removing 1 note'' | ||
=== In no-11s subgroups === | === In no-11s subgroups === | ||
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]] | |||
* [[3-9-15-21 hexany]] | ==== 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.n ==== | ||
* [[5-7-9-13 hexany]] | * [[5-7-9-13 hexany]] — ''very xenharmonic; easy to expand to a [[bihexany]] or [[dekany]]'' | ||
* [[5-7-9-15 hexany]] | * [[5-7-9-15 hexany]] — ''potential for good compositions; a [[detempering]] of the [[starling]] scale'' | ||
* [[5-7-13-15 hexany]] | * [[5-7-13-15 hexany]] — ''both harmonically and melodically strong, and useful for [[bihexany]]s'' | ||
7.n | ==== 7.n ==== | ||
* [[7-9-13-15 hexany]] | * [[7-9-13-15 hexany]] — ''useful for building [[bihexany]]s or [[dekany]]s out of'' | ||
9.n | ==== 9.n ==== | ||
* [[9-25-49-81 hexany]] | * [[9-25-49-81 hexany]] — ''a diminished tetrad with built-in beating effects'' | ||
=== In no-13s subgroups === | === In no-13s subgroups === | ||
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]] | ==== 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.n ==== | ||
* [[5-7-9-11 hexany]] | * [[5-7-9-11 hexany]] — ''a [[neji]] of [[6edo]] with an [[primodality|over-35 semiprime]] feel'' | ||
* [[5-7-9-33 hexany]] | * [[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]] | * [[5-7-11-15 hexany]] — ''lopsided'' | ||
7.n | ==== 7.n ==== | ||
* [[7-9-11-15 hexany]] | * [[7-9-11-15 hexany]] — ''useful for building [[bihexany]]s'' | ||
* [[:File:Hexany 7 11 17 45 cents.png|7-11-17-45 hexany]] | * [[:File:Hexany 7 11 17 45 cents.png|7-11-17-45 hexany]] — ''dark, supernatural, metallic'' | ||
27.n | ==== 27.n ==== | ||
* [[:File:Hexany 27 35 47 59 cents.png|27-35-47-59 hexany]] | * [[: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 === | ||
| Line 185: | Line 188: | ||
* [[1-3-7-9-11 dekany]] | * [[1-3-7-9-11 dekany]] | ||
* [[1-3-7-11-13 dekany]] | * [[1-3-7-11-13 dekany]] | ||
* [[1-3-9-11-13 dekany]] | * [[1-3-9-11-13 dekany]] — ''recommended'' | ||
* [[1-3-7-9-29 dekany]] | * [[1-3-7-9-29 dekany]] — ''recommended'' | ||
* [[1-7-9-11-13 dekany]] | * [[1-7-9-11-13 dekany]] — ''highly unusual but not necessarily bad'' | ||
* [[3-7-9-11-13 dekany]] | * [[3-7-9-11-13 dekany]] — ''recommended'' | ||
=== In no-7s subgroups === | === In no-7s subgroups === | ||
| Line 194: | Line 197: | ||
* [[1-3-5-9-13 dekany]] | * [[1-3-5-9-13 dekany]] | ||
* [[1-3-5-9-81 dekany]] | * [[1-3-5-9-81 dekany]] | ||
* [[1-3-5-11-13 dekany]] | * [[1-3-5-11-13 dekany]] — ''recommended'' | ||
* [[1-3-5-11-15 dekany]] | * [[1-3-5-11-15 dekany]] — ''recommended'' | ||
* [[1-3-5-13-15 dekany]] | * [[1-3-5-13-15 dekany]] — ''recommended'' | ||
* [[1-3-9-11-15 dekany]] | * [[1-3-9-11-15 dekany]] — ''recommended'' | ||
* [[1-3-9-13-15 dekany]] | * [[1-3-9-13-15 dekany]] | ||
* [[1-3-11-13-15 dekany]] | * [[1-3-11-13-15 dekany]] | ||
* [[1-5-9-11-13 dekany]] | * [[1-5-9-11-13 dekany]] | ||
* [[1-5-9-11-15 dekany]] | * [[1-5-9-11-15 dekany]] — ''recommended'' | ||
* [[1-5-9-13-15 dekany]] | * [[1-5-9-13-15 dekany]] — ''recommended'' | ||
* [[1-5-11-13-15 dekany]] | * [[1-5-11-13-15 dekany]] — ''recommended'' | ||
* [[1-9-11-13-15 dekany]] | * [[1-9-11-13-15 dekany]] | ||
* [[3-5-9-11-13 dekany]] | * [[3-5-9-11-13 dekany]] | ||
* [[3-5-9-11-15 dekany]] | * [[3-5-9-11-15 dekany]] — ''recommended'' | ||
* [[3-5-9-13-15 dekany]] | * [[3-5-9-13-15 dekany]] — ''recommended'' | ||
* [[3-5-11-13-15 dekany]] | * [[3-5-11-13-15 dekany]] — ''recommended'' | ||
* [[3-9-11-13-15 dekany]] | * [[3-9-11-13-15 dekany]] — ''recommended'' | ||
* [[5-9-11-13-15 dekany]] | * [[5-9-11-13-15 dekany]] — ''recommended'' | ||
=== In no-11s subgroups === | === 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]] | ||
* [[1-3-5-7-15 dekany]] | * [[1-3-5-7-15 dekany]] — ''recommended'' | ||
* [[1-3-5-9-15 dekany]] | * [[1-3-5-9-15 dekany]] | ||
* [[1-3-7-9-13 dekany]] | * [[1-3-7-9-13 dekany]] — ''recommended'' | ||
* [[1-3-7-9-15 dekany]] | * [[1-3-7-9-15 dekany]] | ||
* [[1-3-7-13-15 dekany]] | * [[1-3-7-13-15 dekany]] | ||
* [[1-5-7-9-13 dekany]] | * [[1-5-7-9-13 dekany]] — ''recommended'' | ||
* [[1-5-7-9-15 dekany]] | * [[1-5-7-9-15 dekany]] | ||
* [[1-5-7-13-15 dekany]] | * [[1-5-7-13-15 dekany]] — ''recommended'' | ||
* [[1-7-9-13-15 dekany]] | * [[1-7-9-13-15 dekany]] | ||
* [[3-5-7-9-13 dekany]] | * [[3-5-7-9-13 dekany]] | ||
* [[3-5-7-9-15 dekany]] | * [[3-5-7-9-15 dekany]] — ''recommended'' | ||
* [[3-5-7-13-15 dekany]] | * [[3-5-7-13-15 dekany]] — ''recommended'' | ||
* [[3-7-9-13-15 dekany]] | * [[3-7-9-13-15 dekany]] — ''recommended'' | ||
* [[5-7-9-13-15 dekany]] | * [[5-7-9-13-15 dekany]] | ||
| Line 234: | Line 237: | ||
* [[1-3-7-11-15 dekany]] | * [[1-3-7-11-15 dekany]] | ||
* [[1-5-7-9-11 dekany]] | * [[1-5-7-9-11 dekany]] | ||
* [[1-5-7-11-15 dekany]] | * [[1-5-7-11-15 dekany]] — ''recommended but extra spicy'' | ||
* [[1-7-9-11-15 dekany]] | * [[1-7-9-11-15 dekany]] | ||
* [[3-5-7-9-11 dekany]] | * [[3-5-7-9-11 dekany]] | ||
* [[3-5-7-11-15 dekany]] | * [[3-5-7-11-15 dekany]] — ''recommended'' | ||
* [[3-7-9-11-15 dekany]] | * [[3-7-9-11-15 dekany]] | ||
* [[5-7-9-11-15 dekany]] | * [[5-7-9-11-15 dekany]] — ''recommended'' | ||
=== In no-17s subgroups === | === In no-17s subgroups === | ||
| Line 246: | Line 249: | ||
* [[3-7-11-13-15 dekany]] | * [[3-7-11-13-15 dekany]] | ||
* [[5-7-11-13-15 dekany]] | * [[5-7-11-13-15 dekany]] | ||
* [[7-9-11-13-15 dekany]] | * [[7-9-11-13-15 dekany]] — ''recommended, but extra spicy'' | ||
=== Related to [[regular temperament]] scales === | === Related to [[regular temperament]] scales === | ||
| Line 282: | Line 285: | ||
== Bihexanies (12-tone) == | == Bihexanies (12-tone) == | ||
[[Category:12-tone scales]] | |||
''Main page: [[Bihexany]]'' | ''Main page: [[Bihexany]]'' | ||
=== Generated by 7-odd-limit elements === | === Generated by 7-odd-limit elements === | ||
| Line 297: | Line 300: | ||
* [[1-3-5-7 by 9/8 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]] | ||
* [[1-3-7-9 by 5/4 bihexany]] | * [[1-3-7-9 by 5/4 bihexany]] — ''recommended'' | ||
* [[1-5-7-9 by 4/3 bihexany]] | * [[1-5-7-9 by 4/3 bihexany]] | ||
* [[3-5-7-9 by 5/4 bihexany]] | * [[3-5-7-9 by 5/4 bihexany]] — ''recommended'' | ||
=== Generated by 11-odd-limit elements === | === Generated by 11-odd-limit elements === | ||
* [[1-3-7-9 by 11/8 bihexany]] | * [[1-3-7-9 by 11/8 bihexany]] | ||
* [[1-3-7-11 by 18/11 bihexany]] | * [[1-3-7-11 by 18/11 bihexany]] | ||
* [[1-7-9-11 by 4/3 bihexany]] | * [[1-7-9-11 by 4/3 bihexany]] — ''recommended'' | ||
* [[3-5-7-11 by 3/2 bihexany]] | * [[3-5-7-11 by 3/2 bihexany]] — ''recommended'' | ||
* [[3-5-9-11 by 5/4 bihexany]] | * [[3-5-9-11 by 5/4 bihexany]] | ||
=== Generated by 13-odd-limit elements === | === Generated by 13-odd-limit elements === | ||
* [[1-3-5-9 by 13/9 bihexany]] | * [[1-3-5-9 by 13/9 bihexany]] — ''recommended'' | ||
* [[1-5-9-13 by 3/2 bihexany]] | * [[1-5-9-13 by 3/2 bihexany]] — ''recommended'' | ||
* [[1-7-9-13 by 4/3 bihexany]] | * [[1-7-9-13 by 4/3 bihexany]] | ||
* [[5-9-11-13 by 3/2 bihexany]] | * [[5-9-11-13 by 3/2 bihexany]] — ''recommended'' | ||
=== Generated by 15-odd-limit elements === | === Generated by 15-odd-limit elements === | ||
No-7s | |||
* [[1-3-5-13 by 18/13 bihexany]] | ==== No-7s ==== | ||
* [[1-3-5-13 by 18/13 bihexany]] — ''recommended'' | |||
* [[1-3-9-15 by 11/8 bihexany]] | * [[1-3-9-15 by 11/8 bihexany]] | ||
* [[1-3-11-15 by 6/5 bihexany]] | * [[1-3-11-15 by 6/5 bihexany]] | ||
* [[1-3-13-15 by 18/13 bihexany]] | * [[1-3-13-15 by 18/13 bihexany]] — ''recommended'' | ||
* [[1-5-11-15 by 6/5 bihexany]] | * [[1-5-11-15 by 6/5 bihexany]] | ||
* [[1-5-13-15 by 16/9 bihexany]] | * [[1-5-13-15 by 16/9 bihexany]] | ||
| Line 329: | Line 333: | ||
* [[5-9-11-15 by 5/4 bihexany]] | * [[5-9-11-15 by 5/4 bihexany]] | ||
* [[5-9-11-15 by 15/13 bihexany]] | * [[5-9-11-15 by 15/13 bihexany]] | ||
* [[5-9-13-15 by 5/4 bihexany]] | * [[5-9-13-15 by 5/4 bihexany]] — ''recommended'' | ||
* [[5-11-13-15 by 11/9 bihexany]] | * [[5-11-13-15 by 11/9 bihexany]] | ||
* [[9-11-13-15 by 3/2 bihexany]] | * [[9-11-13-15 by 3/2 bihexany]] | ||
* [[9-11-13-15 by 33/26 bihexany]] | * [[9-11-13-15 by 33/26 bihexany]] — ''recommended'' | ||
No-11s | ==== No-11s ==== | ||
* [[1-3-5-7 by 15/14 bihexany]] | * [[1-3-5-7 by 15/14 bihexany]] — ''recommended'' | ||
* [[1-3-5-7 by 16/15 bihexany]] | * [[1-3-5-7 by 16/15 bihexany]] | ||
* [[1-3-7-15 by 6/5 bihexany]] | * [[1-3-7-15 by 6/5 bihexany]] | ||
* [[1-3-7-15 by 9/7 bihexany]] | * [[1-3-7-15 by 9/7 bihexany]] — ''recommended'' | ||
* [[1-3-9-15 by 7/6 bihexany]] | * [[1-3-9-15 by 7/6 bihexany]] | ||
* [[1-5-7-15 by 6/5 bihexany]] | * [[1-5-7-15 by 6/5 bihexany]] | ||
* [[1-7-9-15 by 4/3 bihexany]] | * [[1-7-9-15 by 4/3 bihexany]] — ''recommended'' | ||
* [[1-7-9-15 by 7/5 bihexany]] | * [[1-7-9-15 by 7/5 bihexany]] | ||
* [[1-7-13-15 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 9/5 bihexany]] | ||
* [[3-5-7-15 by 9/8 bihexany]] | * [[3-5-7-15 by 9/8 bihexany]] | ||
* [[3-7-13-15 by 4/3 bihexany]] | * [[3-7-13-15 by 4/3 bihexany]] | ||
* [[3-7-13-15 by 7/5 bihexany]] | * [[3-7-13-15 by 7/5 bihexany]] | ||
* [[5-7-9-15 by 5/4 bihexany]] | * [[5-7-9-15 by 5/4 bihexany]] — ''recommended'' | ||
* [[5-7-9-15 by 7/4 bihexany]] | * [[5-7-9-15 by 7/4 bihexany]] | ||
* [[5-7-9-15 by 9/8 bihexany]] | * [[5-7-9-15 by 9/8 bihexany]] | ||
| Line 354: | Line 358: | ||
* [[5-7-13-15 by 22/13 bihexany]] | * [[5-7-13-15 by 22/13 bihexany]] | ||
No-13s | ==== No-13s ==== | ||
* [[3-5-7-15 by 11/7 bihexany]] | * [[3-5-7-15 by 11/7 bihexany]] | ||
* [[3-7-11-15 by 7/5 bihexany]] | * [[3-7-11-15 by 7/5 bihexany]] — ''recommended'' | ||
* [[5-7-9-15 by 11/9 bihexany]] | * [[5-7-9-15 by 11/9 bihexany]] | ||
* [[5-7-11-15 by 18/11 bihexany]] | * [[5-7-11-15 by 18/11 bihexany]] | ||
* [[7-9-11-15 by 3/2 bihexany]] | * [[7-9-11-15 by 3/2 bihexany]] | ||
No-17s | ==== No-17s ==== | ||
* [[7-11-13-15 by 7/5 bihexany]] | * [[7-11-13-15 by 7/5 bihexany]] | ||
=== Generated by 17-odd-limit elements === | === Generated by 17-odd-limit elements === | ||
* [[1-3-5-9 by 17/12 bihexany]] | * [[1-3-5-9 by 17/12 bihexany]] — ''recommended'' | ||
* [[1-5-9-15 by 17/12 bihexany]] | * [[1-5-9-15 by 17/12 bihexany]] | ||
* [[3-5-7-15 by 17/14 bihexany]] | * [[3-5-7-15 by 17/14 bihexany]] | ||
| Line 372: | Line 376: | ||
=== Generated by 19-odd-limit elements === | === Generated by 19-odd-limit elements === | ||
* [[1-3-9-17 by 19/16 bihexany]] | * [[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]] | * [[3-5-7-15 by 19/14 bihexany]] | ||
* [[3-5-13-15 by 19/17 bihexany]] | * [[3-5-13-15 by 19/17 bihexany]] | ||
* [[3-7-9-15 by 19/17 bihexany]] | * [[3-7-9-15 by 19/17 bihexany]] — ''recommended'' | ||
=== Higher odd-limit elements === | === Higher odd-limit elements === | ||
21-odd | |||
==== 21-odd ==== | |||
* [[1-3-5-7 by 21/16 bihexany]] | * [[1-3-5-7 by 21/16 bihexany]] | ||
* [[1-3-5-7 by 40/21 bihexany]] | * [[1-3-5-7 by 40/21 bihexany]] | ||
* [[3-5-11-15 by 21/11 bihexany]] | * [[3-5-11-15 by 21/11 bihexany]] | ||
* [[3-7-13-15 by 21/13 bihexany]] | * [[3-7-13-15 by 21/13 bihexany]] | ||
* [[7-9-13-15 by 21/13 bihexany]] | * [[7-9-13-15 by 21/13 bihexany]] — ''recommended'' | ||
23-odd | |||
==== 23-odd ==== | |||
* [[3-5-7-15 by 23/14 bihexany]] | * [[3-5-7-15 by 23/14 bihexany]] | ||
25-odd | |||
27-odd | ==== 25-odd ==== | ||
''(none documented)'' | |||
==== 27-odd ==== | |||
* [[1-5-7-15 by 32/27 bihexany]] | * [[1-5-7-15 by 32/27 bihexany]] | ||
* [[3-5-7-15 by 27/14 bihexany]] | * [[3-5-7-15 by 27/14 bihexany]] — ''recommended'' | ||
* [[3-9-13-15 by 27/26 bihexany]] | * [[3-9-13-15 by 27/26 bihexany]] — ''recommended'' | ||
29-odd | |||
==== 29-odd ==== | |||
* [[5-7-9-15 by 29/18 bihexany]] | * [[5-7-9-15 by 29/18 bihexany]] | ||
31-odd | |||
33-odd | ==== 31-odd ==== | ||
''(none documented)'' | |||
==== 33-odd ==== | |||
* [[1-5-11-15 by 40/33 bihexany]] | * [[1-5-11-15 by 40/33 bihexany]] | ||
35-odd | |||
==== 35-odd ==== | |||
* [[1-3-5-7 by 36/35 bihexany]] | * [[1-3-5-7 by 36/35 bihexany]] | ||
* [[1-3-5-7 by 48/35 bihexany]] | * [[1-3-5-7 by 48/35 bihexany]] | ||
* [[1-3-5-7 by 64/35 bihexany]] | * [[1-3-5-7 by 64/35 bihexany]] — ''recommended'' | ||
* [[1-3-7-15 by 48/35 bihexany]] | * [[1-3-7-15 by 48/35 bihexany]] — ''recommended'' | ||
37 | |||
45-odd | ==== 37-odd to 43-odd ==== | ||
''(none documented)'' | |||
==== 45-odd ==== | |||
* [[1-3-5-7 by 56/45 bihexany]] | * [[1-3-5-7 by 56/45 bihexany]] | ||
* [[1-3-5-9 by 64/45 bihexany]] | * [[1-3-5-9 by 64/45 bihexany]] | ||
* [[1-5-9-15 by 64/45 bihexany]] | * [[1-5-9-15 by 64/45 bihexany]] | ||
* [[3-5-7-15 by 45/28 bihexany]] | * [[3-5-7-15 by 45/28 bihexany]] | ||
47 | |||
55-odd | ==== 47-odd to 53-odd ==== | ||
''(none documented)'' | |||
==== 55-odd ==== | |||
* [[1-9-11-15 by 72/55 bihexany]] | * [[1-9-11-15 by 72/55 bihexany]] | ||
57 | |||
63-odd | ==== 57-odd to 61-odd ==== | ||
* [[1-3-5-7 by 80/63 bihexany]] | ''(none documented)'' | ||
65-odd | |||
* [[3-5-11-13 by 96/65 bihexany]] | ==== 63-odd ==== | ||
67 | * [[1-3-5-7 by 80/63 bihexany]] — ''recommended'' | ||
99-odd | |||
==== 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]] | * [[1-7-13-15 by 140/99 bihexany]] | ||
101 | |||
135-odd | ==== 101-odd to 133-odd ==== | ||
* [[1-3-9-135 by 57/34 bihexany]] | ''(none documented)'' | ||
==== 135-odd ==== | |||
* [[1-3-9-135 by 57/34 bihexany]] — ''recommended'' | |||
=== Not yet categorised === | === Not yet categorised === | ||
| Line 428: | Line 458: | ||
== Duohexanies (12-tone) == | == Duohexanies (12-tone) == | ||
[[Category:12-tone scales]] | |||
''Main page: [[Duohexany]]'' | ''Main page: [[Duohexany]]'' | ||
* [[Duohex]] | * [[Duohex]] | ||
| Line 437: | Line 467: | ||
== Stellated hexanies (14-tone) == | == Stellated hexanies (14-tone) == | ||
[[Category:14-tone scales]] | |||
''Main page: [[Stellated hexany]]'' | ''Main page: [[Stellated hexany]]'' | ||
=== In no-3s subgroups === | === In no-3s subgroups === | ||
* [[1-5-7-11 stellated hexany]] | * [[1-5-7-11 stellated hexany]] — ''recommended'' | ||
* [[1-5-7-13 stellated hexany]] | * [[1-5-7-13 stellated hexany]] | ||
* [[1-5-11-13 stellated hexany]] | * [[1-5-11-13 stellated hexany]] | ||
* [[1-7-11-13 stellated hexany]] | * [[1-7-11-13 stellated hexany]] — ''recommended'' | ||
=== In no-5s subgroups === | === In no-5s subgroups === | ||
* [[1-3-7-9 stellated hexany]] | * [[1-3-7-9 stellated hexany]] | ||
* [[1-3-7-11 stellated hexany]] | * [[1-3-7-11 stellated hexany]] — ''recommended'' | ||
* [[1-3-7-13 stellated hexany]] | * [[1-3-7-13 stellated hexany]] — ''recommended'' | ||
* [[1-3-9-11 stellated hexany]] | * [[1-3-9-11 stellated hexany]] | ||
* [[1-3-9-13 stellated hexany]] | * [[1-3-9-13 stellated hexany]] — ''recommended'' | ||
* [[1-3-11-13 stellated hexany]] | * [[1-3-11-13 stellated hexany]] — ''recommended'' | ||
* [[1-7-9-11 stellated hexany]] | * [[1-7-9-11 stellated hexany]] | ||
* [[1-7-9-13 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 === | === In no-7s subgroups === | ||
==== 1.n ==== | |||
* [[1-3-5-9 stellated hexany]] | * [[1-3-5-9 stellated hexany]] | ||
* [[1-3-5-11 stellated hexany]] | * [[1-3-5-11 stellated hexany]] | ||
* [[1-3-5-13 stellated hexany]] | * [[1-3-5-13 stellated hexany]] | ||
* [[1-3-5-15 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]] | * [[1-3-9-15 stellated hexany]] | ||
* [[1-3-11-15 stellated hexany]] | * [[1-3-11-15 stellated hexany]] | ||
* [[1-3-13-15 stellated hexany]] | * [[1-3-13-15 stellated hexany]] — ''recommended but spicy'' | ||
* [[1-5-9-11 stellated hexany]] | * [[1-5-9-11 stellated hexany]] | ||
* [[1-5-9-13 stellated hexany]] | * [[1-5-9-13 stellated hexany]] | ||
| Line 469: | Line 505: | ||
* [[1-5-11-15 stellated hexany]] | * [[1-5-11-15 stellated hexany]] | ||
* [[1-5-13-15 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 === | === In no-11s subgroups === | ||
* [[1-3-5-7 stellated hexany]] | * [[1-3-5-7 stellated hexany]] — ''recommended'' | ||
* [[1-3-7-15 stellated hexany]] | * [[1-3-7-15 stellated hexany]] | ||
* [[1-5-7-9 stellated hexany]] | * [[1-5-7-9 stellated hexany]] | ||
* [[1-5-7-15 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 === | === In no-13s subgroups === | ||
* [[1-7-11-15 stellated hexany]] | * [[1-7-11-15 stellated hexany]] | ||
* [[3-5-7-11 stellated hexany]] — ''recommended'' | |||
* [[3-5-7-11 stellated hexany]] | |||
* [[3-7-11-15 stellated hexany]] | * [[3-7-11-15 stellated hexany]] | ||
* [[5-7-9-11 stellated hexany]] | * [[5-7-9-11 stellated hexany]] | ||
* [[5-7 | * [[5-7-11-15 stellated hexany]] — ''recommended'' | ||
=== Not yet categorised === | |||
* [[Stelhex]] | * [[Stelhex]] | ||
* [[Stelhex-catakleismic]] | * [[Stelhex-catakleismic]] | ||
| Line 523: | Line 561: | ||
''Main page: [[Pentadekany]]'' | ''Main page: [[Pentadekany]]'' | ||
=== 1.3.n === | |||
* [[1-3-5-7-9-11 pentadekany]] | * [[1-3-5-7-9-11 pentadekany]] | ||
* [[1-3-5-7-9-13 pentadekany]] | * [[1-3-5-7-9-13 pentadekany]] — ''recommended'' | ||
* [[1-3-5-7-9-15 pentadekany]] | * [[1-3-5-7-9-15 pentadekany]] | ||
* [[1-3-5-7-11-13 pentadekany]] | * [[1-3-5-7-11-13 pentadekany]] | ||
* [[1-3-5-7-11-15 pentadekany]] | * [[1-3-5-7-11-15 pentadekany]] — ''recommended'' | ||
* [[1-3-5-7-13-15 pentadekany]] | * [[1-3-5-7-13-15 pentadekany]] | ||
* [[1-3-5-9-11-13 pentadekany]] | * [[1-3-5-9-11-13 pentadekany]] | ||
* [[1-3-5-9-11-15 pentadekany]] | * [[1-3-5-9-11-15 pentadekany]] | ||
* [[1-3-5-9-13-15 pentadekany]] | * [[1-3-5-9-13-15 pentadekany]] | ||
* [[1-3-5-11-13-15 pentadekany]] | * [[1-3-5-11-13-15 pentadekany]] — ''recommended but only for advanced composers'' | ||
* [[1-3-7-9-11-13 pentadekany]] | * [[1-3-7-9-11-13 pentadekany]] — ''recommended'' | ||
* [[1-3-7-9-11-15 pentadekany]] | * [[1-3-7-9-11-15 pentadekany]] — ''recommended'' | ||
* [[1-3-7-9-13-15 pentadekany]] | * [[1-3-7-9-13-15 pentadekany]] | ||
* [[1-3-7-11-13-15 pentadekany]] | * [[1-3-7-11-13-15 pentadekany]] | ||
* [[1-3-9-11-13-15 pentadekany]] | * [[1-3-9-11-13-15 pentadekany]] | ||
=== 1.5.n === | |||
* [[1-5-7-9-11-13 pentadekany]] | * [[1-5-7-9-11-13 pentadekany]] | ||
* [[1-5-7-9-11-15 pentadekany]] | * [[1-5-7-9-11-15 pentadekany]] — ''recommended'' | ||
* [[1-5-7-9-13-15 pentadekany]] | * [[1-5-7-9-13-15 pentadekany]] — ''recommended'' | ||
* [[1-5-7-11-13-15 pentadekany]] | * [[1-5-7-11-13-15 pentadekany]] | ||
* [[1-5-9-11-13-15 pentadekany]] | * [[1-5-9-11-13-15 pentadekany]] | ||
=== 1.7.n === | |||
* [[1-7-9-11-13-15 pentadekany]] | * [[1-7-9-11-13-15 pentadekany]] | ||
=== 3.5.n === | |||
* [[3-5-7-9-11-13 pentadekany]] | * [[3-5-7-9-11-13 pentadekany]] | ||
* [[3-5-7-9-11-15 pentadekany]] | * [[3-5-7-9-11-15 pentadekany]] — ''recommended'' | ||
* [[3-5-7-9-13-15 pentadekany]] | * [[3-5-7-9-13-15 pentadekany]] | ||
* [[3-5-7-11-13-15 pentadekany]] | * [[3-5-7-11-13-15 pentadekany]] — ''recommended'' | ||
* [[3-5-9-11-13-15 pentadekany]] | * [[3-5-9-11-13-15 pentadekany]] — ''recommended'' | ||
=== 3.7.n === | |||
* [[3-7-9-11-13-15 pentadekany]] | * [[3-7-9-11-13-15 pentadekany]] | ||
=== 5.7.n === | |||
* [[5-7-9-11-13-15 pentadekany]] | * [[5-7-9-11-13-15 pentadekany]] | ||
| Line 566: | Line 604: | ||
''Main page: [[Eikosany]]'' | ''Main page: [[Eikosany]]'' | ||
=== 1.3.n === | |||
* [[1-3-5-7-9-11 eikosany]] | * [[1-3-5-7-9-11 eikosany]] | ||
* [[1-3-5-7-9-13 eikosany]] | * [[1-3-5-7-9-13 eikosany]] | ||
| Line 583: | Line 621: | ||
* [[1-3-9-11-13-15 eikosany]] | * [[1-3-9-11-13-15 eikosany]] | ||
=== 1.5.n === | |||
* [[1-5-7-9-11-13 eikosany]] | * [[1-5-7-9-11-13 eikosany]] | ||
* [[1-5-7-9-11-15 eikosany]] | * [[1-5-7-9-11-15 eikosany]] | ||
| Line 590: | Line 628: | ||
* [[1-5-9-11-13-15 eikosany]] | * [[1-5-9-11-13-15 eikosany]] | ||
=== 1.7.n === | |||
* [[1-7-9-11-13-15 eikosany]] | * [[1-7-9-11-13-15 eikosany]] | ||
=== 3.5.n === | |||
* [[3-5-7-9-11-13 eikosany]] | * [[3-5-7-9-11-13 eikosany]] | ||
* [[3-5-7-9-11-15 eikosany]] | * [[3-5-7-9-11-15 eikosany]] | ||
| Line 600: | Line 638: | ||
* [[3-5-9-11-13-15 eikosany]] | * [[3-5-9-11-13-15 eikosany]] | ||
=== 3.7.n === | |||
* [[3-7-9-11-13-15 eikosany]] | * [[3-7-9-11-13-15 eikosany]] | ||
=== 5.7.n === | |||
* [[5-7-9-11-13-15 eikosany]] | * [[5-7-9-11-13-15 eikosany]] | ||
=== Other === | |||
* [[Eikosanyplusop]] | * [[Eikosanyplusop]] | ||