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Gallery of combination product sets: Difference between revisions

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|-
|-
| [[7-9-11-13 hexany]] || 40 || 63 || 13 || 13 || 289.209 || 128.298 || 2.254 || 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 [[subgroup]]s ===
=== In no-3s [[subgroup]]s ===
Line 109: Line 179:
* [[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 ====
Line 120: Line 192:
* [[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''
Line 125: Line 198:
* [[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''
Line 147: Line 222:
* [[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''
Line 153: Line 229:
* [[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''
Line 262: Line 340:
[[Category:10-tone scales]]
[[Category:10-tone scales]]
''Main page: [[Dekany]]''
''Main page: [[Dekany]]''
 
{| 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 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 ===
=== In no-3s subgroups ===
* [[1-5-7-11-13 dekany]]
* [[1-5-7-11-13 dekany]]
Line 352: Line 555:


=== Not yet categorised ===
=== Not yet categorised ===
* [[1-3-7-31-365 dekany]]
* [[Deka1029]]
* [[Deka1029]]
* [[Deka126]]
* [[Deka126]]
Line 453: Line 657:
* [[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]]
Line 538: Line 744:
* [[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) ==
Line 551: Line 770:
[[Category:14-tone scales]]
[[Category:14-tone scales]]
''Main page: [[Stellated hexany]]''
''Main page: [[Stellated hexany]]''
{| 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 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 ===
=== In no-3s subgroups ===
* [[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''
Line 562: Line 935:
* [[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]]
Line 579: Line 956:
* [[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 ====
Line 642: Line 1,023:
== Pentadekanies (15-tone) ==
== Pentadekanies (15-tone) ==
''Main page: [[Pentadekany]]''
''Main page: [[Pentadekany]]''
 
{| 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 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.n ===
* [[1-3-5-7-9-11 pentadekany]]
* [[1-3-5-7-9-11 pentadekany]]
Line 685: Line 1,135:
== 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 ===
Line 730: Line 1,250:


== 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 738: 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 746: 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}}
Retrieved from "https://en.xen.wiki/w/Gallery_of_combination_product_sets"