Gallery of combination product sets: Difference between revisions
Add pentadekany table |
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* [[1-5-7-11 hexany]] — ''lopsided'' | * [[1-5-7-11 hexany]] — ''lopsided'' | ||
* [[1-5-7-13 hexany]] — ''spicier whole tone scale'' | * [[1-5-7-13 hexany]] — ''spicier whole tone scale'' | ||
* [[1-5-7-17 hexany]] | |||
* [[1-7-11-13 hexany]] — ''extra [[xenharmonic]]'' | * [[1-7-11-13 hexany]] — ''extra [[xenharmonic]]'' | ||
* [[1-5-11-17 hexany]] - ''unwieldy'' | |||
==== 5.n ==== | ==== 5.n ==== | ||
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* [[1-3-7-11 hexany]] — ''symmetrical shape; 2 strong tonal centres'' | * [[1-3-7-11 hexany]] — ''symmetrical shape; 2 strong tonal centres'' | ||
* [[1-3-7-13 hexany]] — ''extra xenharmonic'' | * [[1-3-7-13 hexany]] — ''extra xenharmonic'' | ||
* [[1-3-7-17 hexany]] | |||
* [[1-3-7-21 hexany]] — ''a [[detempering]] of the [[semaphore]] scale'' | * [[1-3-7-21 hexany]] — ''a [[detempering]] of the [[semaphore]] scale'' | ||
* [[1-3-9-11 hexany]] — ''an even mix of xenharmonic and familiar'' | * [[1-3-9-11 hexany]] — ''an even mix of xenharmonic and familiar'' | ||
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* [[1-3-9-17 hexany]] — ''whole tone scale-like structure, but new unfamiliar melodies and harmonies'' | * [[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'' | * [[1-3-11-13 hexany]] — ''sounds surprisingly un-xenharmonic'' | ||
* [[1-3-11-17 hexany]] | |||
* [[1-3-13-17 hexany]] | |||
* [[:File:Hexany 1 3 21 29.png|1-3-21-29 hexany]] — ''fierce, groovy, dark'' | * [[: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'' | * [[1-3-21-49 hexany]] — ''a [[detempering]] of the [[slendric]] scale'' | ||
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* [[1-3-5-13 hexany]] — ''stable chord roots + very xenharmonic'' | * [[1-3-5-13 hexany]] — ''stable chord roots + very xenharmonic'' | ||
* [[1-3-5-15 hexany]] — ''difficult to use'' | * [[1-3-5-15 hexany]] — ''difficult to use'' | ||
* [[1-3-5-17 hexany]] | |||
* [[1-3-5-45 hexany]] — ''very useful foundation for adding xenharmonic notes on top off; can play all ''Zelda'''s ocarina melodies'' | * [[1-3-5-45 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'' | * [[1-3-5-81 hexany]] — ''built around subtle pitch shifts'' | ||
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* [[1-3-11-15 hexany]] — ''lopsided'' | * [[1-3-11-15 hexany]] — ''lopsided'' | ||
* [[1-3-13-15 hexany]] — ''lopsided'' | * [[1-3-13-15 hexany]] — ''lopsided'' | ||
* [[1-3-15-17 hexany]] | |||
* [[1-5-9-11 hexany]] — ''very lopsided and very xenharmonic'' | * [[1-5-9-11 hexany]] — ''very lopsided and very xenharmonic'' | ||
* [[1-5-9-13 hexany]] — ''easy to build [[bihexany]]s with'' | * [[1-5-9-13 hexany]] — ''easy to build [[bihexany]]s with'' | ||
* [[1-5-9-15 hexany]] — ''easy to build [[dekany]]s with'' | * [[1-5-9-15 hexany]] — ''easy to build [[dekany]]s with'' | ||
* [[1-5-9-17 hexany]] | |||
* [[1-5-11-13 hexany]] — ''an [[omniconsonant scale]]'' | * [[1-5-11-13 hexany]] — ''an [[omniconsonant scale]]'' | ||
* [[1-5-11-15 hexany]] — ''easy to build [[bihexany]]s with'' | * [[1-5-11-15 hexany]] — ''easy to build [[bihexany]]s with'' | ||
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=== Not yet categorised === | === Not yet categorised === | ||
* [[1-3-7-31-365 dekany]] | |||
* [[Deka1029]] | * [[Deka1029]] | ||
* [[Deka126]] | * [[Deka126]] | ||
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* [[1-3-5-9 by 17/12 bihexany]] — ''recommended'' | * [[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]] | ||
* [[1-5-9-17 by 10/7 bihexany]] — ''recommended'' | |||
* [[1-5-9-17 by 24/17 bihexany]] — ''recommended'' | |||
* [[3-5-7-15 by 17/14 bihexany]] | * [[3-5-7-15 by 17/14 bihexany]] | ||
* [[3-5-11-13 by 24/17 bihexany]] | * [[3-5-11-13 by 24/17 bihexany]] | ||
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* [[Bihexanymyna]] | * [[Bihexanymyna]] | ||
* [[GW Smith bihexany 14 Feb 2011]] | * [[GW Smith bihexany 14 Feb 2011]] | ||
==== 1-3-5-9 variations ==== | |||
* [[1-3-5-9 by 4/3 bihexany]] | |||
* [[1-3-5-9 by 6/5 bihexany]] | |||
* [[1-3-5-9 by 8/5 bihexany]] | |||
* [[1-3-5-9 by 10/9 bihexany]] | |||
* [[1-3-5-9 by 13/10 bihexany]] | |||
* [[1-3-5-9 by 16/9 bihexany]] | |||
* [[1-3-5-9 by 16/15 bihexany]] | |||
* [[1-3-5-9 by 25/18 bihexany]] | |||
* [[1-3-5-9 by 27/20 bihexany]] | |||
* [[1-3-5-9 by 32/27 bihexany]] | |||
* [[1-3-5-9 by 11/9 bihexany]] | |||
== Duohexanies (12-tone) == | == Duohexanies (12-tone) == | ||
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* [[1-5-7-11 stellated hexany]] — ''recommended'' | * [[1-5-7-11 stellated hexany]] — ''recommended'' | ||
* [[1-5-7-13 stellated hexany]] | * [[1-5-7-13 stellated hexany]] | ||
* [[1-5-7-17 stellated hexany]] | |||
* [[1-5-11-13 stellated hexany]] | * [[1-5-11-13 stellated hexany]] | ||
* [[1-7-11-13 stellated hexany]] — ''recommended'' | * [[1-7-11-13 stellated hexany]] — ''recommended'' | ||
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* [[1-3-7-11 stellated hexany]] — ''recommended'' | * [[1-3-7-11 stellated hexany]] — ''recommended'' | ||
* [[1-3-7-13 stellated hexany]] — ''recommended'' | * [[1-3-7-13 stellated hexany]] — ''recommended'' | ||
* [[1-3-7-17 stellated hexany]] | |||
* [[1-3-9-11 stellated hexany]] | * [[1-3-9-11 stellated hexany]] | ||
* [[1-3-9-13 stellated hexany]] — ''recommended'' | * [[1-3-9-13 stellated hexany]] — ''recommended'' | ||
* [[1-3-9-17 stellated hexany]] | |||
* [[1-3-11-13 stellated hexany]] — ''recommended'' | * [[1-3-11-13 stellated hexany]] — ''recommended'' | ||
* [[1-3-11-17 stellated hexany]] | |||
* [[1-3-13-17 stellated hexany]] | |||
* [[1-7-9-11 stellated hexany]] | * [[1-7-9-11 stellated hexany]] | ||
* [[1-7-9-13 stellated hexany]] | * [[1-7-9-13 stellated hexany]] | ||
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* [[1-3-5-13 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'' | * [[1-3-5-15 stellated hexany]] — ''not recommended for xenharmony, but it's a good JI version of the 'Hungarian minor' scale if one wants that'' | ||
* [[1-3-5-17 stellated hexany]] | |||
* [[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]] — ''recommended but spicy'' | * [[1-3-13-15 stellated hexany]] — ''recommended but spicy'' | ||
* [[1-3-15-17 stellated hexany]] | |||
* [[1-5-9-11 stellated hexany]] | * [[1-5-9-11 stellated hexany]] | ||
* [[1-5-9-13 stellated hexany]] | * [[1-5-9-13 stellated hexany]] | ||
* [[1-5-9-15 stellated hexany]] | * [[1-5-9-15 stellated hexany]] | ||
* [[1-5-9-17 stellated hexany]] | |||
* [[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'' | * [[1-11-13-15 stellated hexany]] — ''recommended'' | ||
* [[1-15-45-75 stellated hexany]] — ''recommended'' | * [[1-15-45-75 stellated hexany]] — ''recommended'' | ||
* [[1-3-5-45 stellated hexany]] | |||
==== 3.n ==== | ==== 3.n ==== | ||
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== Eikosanies (20-tone) == | == Eikosanies (20-tone) == | ||
''Main page: [[Eikosany]]'' | ''Main page: [[Eikosany]]'' | ||
{| class="wikitable mw-collapsible mw-collapsed sortable" right-all" | |||
|- | |||
|- | |||
! 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.n === | ||
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== Other == | == Other == | ||
=== Enaeikosanies (21-tone) === | |||
* [[1-3-5-7-9-11-13 enaeikosany]] | * [[1-3-5-7-9-11-13 enaeikosany]] | ||
* [[1-3-5-7-9-11-15 enaeikosany]] | * [[1-3-5-7-9-11-15 enaeikosany]] | ||
| Line 1,155: | Line 1,260: | ||
* [[1-5-7-9-11-13-15 enaeikosany]] | * [[1-5-7-9-11-13-15 enaeikosany]] | ||
* [[3-5-7-9-11-13-15 enaeikosany]] | * [[3-5-7-9-11-13-15 enaeikosany]] | ||
=== Pentatriandekanies (35-tone) === | |||
* [[1-3-5-7-9-11-13 pentatriandekany]] | * [[1-3-5-7-9-11-13 pentatriandekany]] | ||
* [[1-3-5-7-9-11-15 pentatriandekany]] | * [[1-3-5-7-9-11-15 pentatriandekany]] | ||
| Line 1,163: | Line 1,270: | ||
* [[1-5-7-9-11-13-15 pentatriandekany]] | * [[1-5-7-9-11-13-15 pentatriandekany]] | ||
* [[3-5-7-9-11-13-15 pentatriandekany]] | * [[3-5-7-9-11-13-15 pentatriandekany]] | ||
=== Larger scales === | |||
* [[1-3-5-7-9-11-13-15 hexapenindasany]] | |||
* [[1-3-5-7-9-11-13-15 octaeikosany]] | * [[1-3-5-7-9-11-13-15 octaeikosany]] | ||
* [[1-3-5-7-9-11-13-15 evdomindasany]] | |||
{{navbox scale gallery}} | {{navbox scale gallery}} | ||