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Gallery of combination product sets: Difference between revisions

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[[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 865: Line 990:
== 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 908: Line 1,102:
== 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 ===
Retrieved from "https://en.xen.wiki/w/Gallery_of_combination_product_sets"