User:Lucius Chiaraviglio/Musical Mad Science: Difference between revisions
→Musical Mad Science Musings on Diatonicized Third-Tone Sub-Chromaticism: Add note about established recognition of ~13/9 and ~75/52 in Alphatricot 13-limit extensions |
→Table of odd harmonics for various EDO values supporting 17L 2s: Insert EDO values from the far right column of the 17L 2s scale tree, with provision for generator mappings (not yet filled in) (safety save) |
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=== Table of odd harmonics for various EDO values supporting 17L 2s === | === Table of odd harmonics for various EDO values supporting 17L 2s === | ||
The following table (actually a collection of tables for now) is for tracking trends in odd harmonics along the scale tree of [[17L 2s]]; it is intended to match the organization of [[17L_2s#Scale_tree|the corresponding scale tree]] (but this needs to be updated for addition of another column on 2025-05-12 — | The following table (actually a collection of tables for now) is for tracking trends in odd harmonics along the scale tree of [[17L 2s]]; it is intended to match the organization of [[17L_2s#Scale_tree|the corresponding scale tree]] (but this needs to be updated for addition of another column on 2025-05-12 — this is in a very early stage). For each EDO, it includes a list of plausible candidates for the 17L 2s bright generator (BrightGen), with ''candidates failing to map to the bright generator in italics, along with plausible wart fixes (if any)''. | ||
{{Harmonics in equal|19|intervals=odd|prec=2|columns=28|title=[[19edo]] (L=1, s=1, BrightGen is 10; patent ~[[13/9]] = 10; patent ~[[23/16]] = 10; ''patent ~[[49/34]] = 9''; patent ~[[62/43]] = 10; patent ~[[75/52]] = 10; patent ~[[384/265]] = 10; ''patent ~[[59049/40960]] = 9'') — Equalized 17L 2s}} | {{Harmonics in equal|19|intervals=odd|prec=2|columns=28|title=[[19edo]] (L=1, s=1, BrightGen is 10; patent ~[[13/9]] = 10; patent ~[[23/16]] = 10; ''patent ~[[49/34]] = 9''; patent ~[[62/43]] = 10; patent ~[[75/52]] = 10; patent ~[[384/265]] = 10; ''patent ~[[59049/40960]] = 9'') — Equalized 17L 2s}} | ||
{{Harmonics in equal|131|intervals=odd|prec=2|columns=28|title=[[131edo]] (L=7, s=6, BrightGen is 69; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | |||
{{Harmonics in equal|112|intervals=odd|prec=2|columns=28|title=[[112edo]] (L=6, s=5, BrightGen is 59; ''patent ~13/9 = 58; b val ~13/9 = 60''; patent ~23/16 = 59; ''patent ~49/34 = 58''; patent ~62/43 = 59; ''patent ~75/52 = 60'', 'b' or 'f' wart usable; ''patent ~384/265 = 60; b val ~384/255 = 61''; ''patent ~59049/40960 = 64; b val ~59049/40960 = 54'')}} | {{Harmonics in equal|112|intervals=odd|prec=2|columns=28|title=[[112edo]] (L=6, s=5, BrightGen is 59; ''patent ~13/9 = 58; b val ~13/9 = 60''; patent ~23/16 = 59; ''patent ~49/34 = 58''; patent ~62/43 = 59; ''patent ~75/52 = 60'', 'b' or 'f' wart usable; ''patent ~384/265 = 60; b val ~384/255 = 61''; ''patent ~59049/40960 = 64; b val ~59049/40960 = 54'')}} | ||
{{Harmonics in equal|205|intervals=odd|prec=2|columns=28|title=[[205edo]] (L=11, s=9, BrightGen is 108; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | |||
{{Harmonics in equal|93|intervals=odd|prec=2|columns=28|title=[[93edo]] (L=5, s=4, BrightGen is 49; ''patent ~13/9 = 50''; patent ~23/16 = 49; patent ~49/34 = 49; patent ~62/43 = 49; patent ~75/52 = 49; patent ~384/265 = 49; ''patent ~59049/40960 = 45'')}} | {{Harmonics in equal|93|intervals=odd|prec=2|columns=28|title=[[93edo]] (L=5, s=4, BrightGen is 49; ''patent ~13/9 = 50''; patent ~23/16 = 49; patent ~49/34 = 49; patent ~62/43 = 49; patent ~75/52 = 49; patent ~384/265 = 49; ''patent ~59049/40960 = 45'')}} | ||
{{Harmonics in equal|260|intervals=odd|prec=2|columns=28|title=[[260edo]] (L=14, s=11, BrightGen is 137; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | |||
{{Harmonics in equal|167|intervals=odd|prec=2|columns=28|title=[[167edo]] (L=9, s=7, BrightGen is 88; patent ~13/9 = 88; ''patent ~23/16 = 87''; patent ~49/34 = 88; patent ~62/43 = 88; ''patent ~75/52 = 89'', 'b' wart usable; ''patent ~384/265 = 89''; ''patent ~59049/40960 = 91'')}} | {{Harmonics in equal|167|intervals=odd|prec=2|columns=28|title=[[167edo]] (L=9, s=7, BrightGen is 88; patent ~13/9 = 88; ''patent ~23/16 = 87''; patent ~49/34 = 88; patent ~62/43 = 88; ''patent ~75/52 = 89'', 'b' wart usable; ''patent ~384/265 = 89''; ''patent ~59049/40960 = 91'')}} | ||
{{Harmonics in equal|241|intervals=odd|prec=2|columns=28|title=[[241edo]] (L=13, s=10, BrightGen is 127; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | |||
{{Harmonics in equal|74|intervals=odd|prec=2|columns=28|title=[[74edo]] (L=4, s=3, BrightGen is 39; ''patent ~13/9 = 40''; patent ~23/16 = 39; ''patent ~49/34 = 40, 'g' wart usable''; patent ~62/43 = 39; patent ~75/52 = 39; patent ~384/265 = 39; ''patent ~59049/40960 = 36'') — Supersoft 17L 2s}} | {{Harmonics in equal|74|intervals=odd|prec=2|columns=28|title=[[74edo]] (L=4, s=3, BrightGen is 39; ''patent ~13/9 = 40''; patent ~23/16 = 39; ''patent ~49/34 = 40, 'g' wart usable''; patent ~62/43 = 39; patent ~75/52 = 39; patent ~384/265 = 39; ''patent ~59049/40960 = 36'') — Supersoft 17L 2s}} | ||
{{Harmonics in equal|277|intervals=odd|prec=2|columns=28|title=[[277edo]] (L=15, s=11, BrightGen is 146; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | |||
{{Harmonics in equal|203|intervals=odd|prec=2|columns=28|title=[[203edo]] (L=11, s=8, BrightGen is 107; patent ~13/9 = 107; ''patent ~23/16 = 106''; patent ~49/34 = 107; patent ~62/43 = 107; patent ~75/52 = 107; ''patent ~384/265 = 109''; ''patent ~59049/40960 = 110'')}} | {{Harmonics in equal|203|intervals=odd|prec=2|columns=28|title=[[203edo]] (L=11, s=8, BrightGen is 107; patent ~13/9 = 107; ''patent ~23/16 = 106''; patent ~49/34 = 107; patent ~62/43 = 107; patent ~75/52 = 107; ''patent ~384/265 = 109''; ''patent ~59049/40960 = 110'')}} | ||
{{Harmonics in equal|332|intervals=odd|prec=2|columns=28|title=[[332edo]] (L=18, s=13, BrightGen is 175; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | |||
{{Harmonics in equal|129|intervals=odd|prec=2|columns=28|title=[[129edo]] (L=7, s=5, BrightGen is 68; ''patent ~13/9 = 69''; patent ~23/16 = 68; patent ~49/34 = 68; patent ~62/43 = 68; ''patent ~75/52 = 69''; patent ~384/265 = 68; ''patent ~59049/40960 = 63'')}} | {{Harmonics in equal|129|intervals=odd|prec=2|columns=28|title=[[129edo]] (L=7, s=5, BrightGen is 68; ''patent ~13/9 = 69''; patent ~23/16 = 68; patent ~49/34 = 68; patent ~62/43 = 68; ''patent ~75/52 = 69''; patent ~384/265 = 68; ''patent ~59049/40960 = 63'')}} | ||
{{Harmonics in equal|313|intervals=odd|prec=2|columns=28|title=[[313edo]] (L=17, s=12, BrightGen is 165; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | |||
{{Harmonics in equal|184|intervals=odd|prec=2|columns=28|title=[[184edo]] (L=10, s=7, BrightGen is 97; patent ~13/9 = 97; ''patent ~23/16 = 96, 'i' wart usable''; ''patent ~49/34 = 98''; patent ~62/43 = 97; patent ~75/52 = 97; ''patent ~384/265 = 99''; ''patent ~59049/40960 = 101'')}} | {{Harmonics in equal|184|intervals=odd|prec=2|columns=28|title=[[184edo]] (L=10, s=7, BrightGen is 97; patent ~13/9 = 97; ''patent ~23/16 = 96, 'i' wart usable''; ''patent ~49/34 = 98''; patent ~62/43 = 97; patent ~75/52 = 97; ''patent ~384/265 = 99''; ''patent ~59049/40960 = 101'')}} | ||
{{Harmonics in equal|239|intervals=odd|prec=2|columns=28|title=[[239edo]] (L=13, s=9, BrightGen is 126; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | |||
{{Harmonics in equal|55|intervals=odd|prec=2|columns=28|title=[[55edo]] (L=3, s=2, BrightGen is 29; ''patent ~13/9 = 30''; patent ~23/16 = 29; ''patent ~49/34 = 28''; patent ~62/43 = 29; patent ~75/52 = 29; patent ~384/265 = 29; ''patent ~59049/40960 = 27'') — Soft 17L 2s}} | {{Harmonics in equal|55|intervals=odd|prec=2|columns=28|title=[[55edo]] (L=3, s=2, BrightGen is 29; ''patent ~13/9 = 30''; patent ~23/16 = 29; ''patent ~49/34 = 28''; patent ~62/43 = 29; patent ~75/52 = 29; patent ~384/265 = 29; ''patent ~59049/40960 = 27'') — Soft 17L 2s}} | ||
{{Harmonics in equal|256|intervals=odd|prec=2|columns=28|title=[[256edo]] (L=14, s=9, BrightGen is 135; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | |||
{{Harmonics in equal|201|intervals=odd|prec=2|columns=28|title=[[201edo]] (L=11, s=7, BrightGen is 106; patent ~13/9 = 106; ''patent ~23/16 = 105''; ''patent ~49/34 = 105, 'g' wart usable''; patent ~62/43 = 106; ''patent ~75/52 = 107'', 'b' wart usable; ''patent ~384/265 = 108''; ''patent ~59049/40960 = 110'')}} | {{Harmonics in equal|201|intervals=odd|prec=2|columns=28|title=[[201edo]] (L=11, s=7, BrightGen is 106; patent ~13/9 = 106; ''patent ~23/16 = 105''; ''patent ~49/34 = 105, 'g' wart usable''; patent ~62/43 = 106; ''patent ~75/52 = 107'', 'b' wart usable; ''patent ~384/265 = 108''; ''patent ~59049/40960 = 110'')}} | ||
{{Harmonics in equal|347|intervals=odd|prec=2|columns=28|title=[[347edo]] (L=19, s=12, BrightGen is 183; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | |||
{{Harmonics in equal|146|intervals=odd|prec=2|columns=28|title=[[146edo]] (L=8, s=5, BrightGen is 77; ''patent ~13/9 = 78''; ''patent ~23/16 = 76''; patent ~49/34 = 77; patent ~62/43 = 77; patent ~75/52 = 77; ''patent ~384/265 = 78''; ''patent ~59049/40960 = 73'')}} | {{Harmonics in equal|146|intervals=odd|prec=2|columns=28|title=[[146edo]] (L=8, s=5, BrightGen is 77; ''patent ~13/9 = 78''; ''patent ~23/16 = 76''; patent ~49/34 = 77; patent ~62/43 = 77; patent ~75/52 = 77; ''patent ~384/265 = 78''; ''patent ~59049/40960 = 73'')}} | ||
{{Harmonics in equal|383|intervals=odd|prec=2|columns=28|title=[[383edo]] (L=21, s=13, BrightGen is 202; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | |||
{{Harmonics in equal|237|intervals=odd|prec=2|columns=28|title=[[237edo]] (L=13, s=8, BrightGen is 125; patent ~13/9 = 125; patent ~23/16 = 124; ''patent ~49/34 = 124''; patent ~62/43 = 125; patent ~75/52 = 125; ''patent ~384/265 = 127''; ''patent ~59049/40960 = 129'')}} | {{Harmonics in equal|237|intervals=odd|prec=2|columns=28|title=[[237edo]] (L=13, s=8, BrightGen is 125; patent ~13/9 = 125; patent ~23/16 = 124; ''patent ~49/34 = 124''; patent ~62/43 = 125; patent ~75/52 = 125; ''patent ~384/265 = 127''; ''patent ~59049/40960 = 129'')}} | ||
{{Harmonics in equal|328|intervals=odd|prec=2|columns=28|title=[[328edo]] (L=18, s=11, BrightGen is 173; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | |||
{{Harmonics in equal|91|intervals=odd|prec=2|columns=28|title=[[91edo]] (L=5, s=3, BrightGen is 48; ''patent ~13/9 = 49''; patent ~23/16 = 48; ''patent ~49/34 = 47''; patent ~62/43 = 48; ''patent ~75/52 = 47''; ''patent ~384/265 = 49''; ''patent ~59049/40960 = 46'') — Semisoft 17L 2s}} | {{Harmonics in equal|91|intervals=odd|prec=2|columns=28|title=[[91edo]] (L=5, s=3, BrightGen is 48; ''patent ~13/9 = 49''; patent ~23/16 = 48; ''patent ~49/34 = 47''; patent ~62/43 = 48; ''patent ~75/52 = 47''; ''patent ~384/265 = 49''; ''patent ~59049/40960 = 46'') — Semisoft 17L 2s}} | ||
{{Harmonics in equal|309|intervals=odd|prec=2|columns=28|title=[[309edo]] (L=17, s=10, BrightGen is 163; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | |||
{{Harmonics in equal|218|intervals=odd|prec=2|columns=28|title=[[218edo]] (L=12, s=7, BrightGen is 115; patent ~13/9 = 115; ''patent ~23/16 = 114''; patent ~49/34 = 115; patent ~62/43 = 115; patent ~75/52 = 115; ''patent ~384/265 = 117''; ''patent ~59049/40960 = 120'')}} | {{Harmonics in equal|218|intervals=odd|prec=2|columns=28|title=[[218edo]] (L=12, s=7, BrightGen is 115; patent ~13/9 = 115; ''patent ~23/16 = 114''; patent ~49/34 = 115; patent ~62/43 = 115; patent ~75/52 = 115; ''patent ~384/265 = 117''; ''patent ~59049/40960 = 120'')}} | ||
{{Harmonics in equal|345|intervals=odd|prec=2|columns=28|title=[[345edo]] (L=19, s=11, BrightGen is 182; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | |||
{{Harmonics in equal|127|intervals=odd|prec=2|columns=28|title=[[127edo]] (L=7, s=4, BrightGen is 67; ''patent ~13/9 = 68''; ''patent ~23/16 = 66, 'i' wart usable''; ''patent ~49/34 = 68''; patent ~62/43 = 67; patent ~75/52 = 67; ''patent ~384/265 = 68''; ''patent ~59049/40960 = 64'')}} | {{Harmonics in equal|127|intervals=odd|prec=2|columns=28|title=[[127edo]] (L=7, s=4, BrightGen is 67; ''patent ~13/9 = 68''; ''patent ~23/16 = 66, 'i' wart usable''; ''patent ~49/34 = 68''; patent ~62/43 = 67; patent ~75/52 = 67; ''patent ~384/265 = 68''; ''patent ~59049/40960 = 64'')}} | ||
{{Harmonics in equal|290|intervals=odd|prec=2|columns=28|title=[[290edo]] (L=16, s=9, BrightGen is 153; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | |||
{{Harmonics in equal|163|intervals=odd|prec=2|columns=28|title=[[163edo]] (L=9, s=5, BrightGen is 86; ''patent ~13/9 = 87''; ''patent ~23/16 = 85''; ''patent ~49/34 = 87''; ''patent ~62/43 = 87, 'k' wart usable''; ''patent ~75/52 = 85''; ''patent ~384/265 = 87''; ''patent ~59049/40960 = 83'')}} | {{Harmonics in equal|163|intervals=odd|prec=2|columns=28|title=[[163edo]] (L=9, s=5, BrightGen is 86; ''patent ~13/9 = 87''; ''patent ~23/16 = 85''; ''patent ~49/34 = 87''; ''patent ~62/43 = 87, 'k' wart usable''; ''patent ~75/52 = 85''; ''patent ~384/265 = 87''; ''patent ~59049/40960 = 83'')}} | ||
{{Harmonics in equal|199|intervals=odd|prec=2|columns=28|title=[[199edo]] (L=11, s=6, BrightGen is 105; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | |||
{{Harmonics in equal|36|intervals=odd|prec=2|columns=28|title=[[36edo]] (L=2, s=1, BrightGen is 19; patent ~13/9 = 19; patent ~23/16 = 19; patent ~49/34 = 19; patent ~62/43 = 19; patent ~75/52 = 20; patent ~384/265 = 19; ''patent ~59049/40960 = 18'') — Basic 17L 2s}} | {{Harmonics in equal|36|intervals=odd|prec=2|columns=28|title=[[36edo]] (L=2, s=1, BrightGen is 19; patent ~13/9 = 19; patent ~23/16 = 19; patent ~49/34 = 19; patent ~62/43 = 19; patent ~75/52 = 20; patent ~384/265 = 19; ''patent ~59049/40960 = 18'') — Basic 17L 2s}} | ||
{{Harmonics in equal|___|intervals=odd|prec=2|columns=28|title=[[___edo]] (L=_, s=_, BrightGen is __; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | |||
{{Harmonics in equal|161|intervals=odd|prec=2|columns=28|title=[[161edo]] (L=9, s=4, BrightGen is 85; ''patent ~13/9 = 86''; ''patent ~23/16 = 84''; patent ~49/34 = 85; patent ~62/43 = 85; patent ~75/52 = 85; ''patent ~384/265 = 86''; ''patent ~59049/40960 = 83'')}} | {{Harmonics in equal|161|intervals=odd|prec=2|columns=28|title=[[161edo]] (L=9, s=4, BrightGen is 85; ''patent ~13/9 = 86''; ''patent ~23/16 = 84''; patent ~49/34 = 85; patent ~62/43 = 85; patent ~75/52 = 85; ''patent ~384/265 = 86''; ''patent ~59049/40960 = 83'')}} | ||
{{Harmonics in equal|___|intervals=odd|prec=2|columns=28|title=[[___edo]] (L=_, s=_, BrightGen is __; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | |||
{{Harmonics in equal|125|intervals=odd|prec=2|columns=28|title=[[125edo]] (L=7, s=3, BrightGen is 66; ''patent ~13/9 = 67, 'f' wart usable''; ''patent ~23/16 = 65''; patent ~49/34 = 66; patent ~62/43 = 66; patent ~75/52 = 65, 'f' wart usable; ''patent ~384/265 = 67''; ''patent ~59049/40960 = 65'')}} | {{Harmonics in equal|125|intervals=odd|prec=2|columns=28|title=[[125edo]] (L=7, s=3, BrightGen is 66; ''patent ~13/9 = 67, 'f' wart usable''; ''patent ~23/16 = 65''; patent ~49/34 = 66; patent ~62/43 = 66; patent ~75/52 = 65, 'f' wart usable; ''patent ~384/265 = 67''; ''patent ~59049/40960 = 65'')}} | ||
{{Harmonics in equal|___|intervals=odd|prec=2|columns=28|title=[[___edo]] (L=_, s=_, BrightGen is __; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | |||
{{Harmonics in equal|214|intervals=odd|prec=2|columns=28|title=[[214edo]] (L=12, s=5, BrightGen is 113; ''patent ~13/9 = 114''; ''patent ~23/16 = 112''; patent ~49/34 = 113; patent ~62/43 = 113; patent ~75/52 = 113; ''patent ~384/265 = 114''; ''patent ~59049/40960 = 111'')}} | {{Harmonics in equal|214|intervals=odd|prec=2|columns=28|title=[[214edo]] (L=12, s=5, BrightGen is 113; ''patent ~13/9 = 114''; ''patent ~23/16 = 112''; patent ~49/34 = 113; patent ~62/43 = 113; patent ~75/52 = 113; ''patent ~384/265 = 114''; ''patent ~59049/40960 = 111'')}} | ||
{{Harmonics in equal|___|intervals=odd|prec=2|columns=28|title=[[___edo]] (L=_, s=_, BrightGen is __; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | |||
{{Harmonics in equal|89|intervals=odd|prec=2|columns=28|title=[[89edo]] (L=5, s=2, BrightGen is 47; patent ~13/9 = 47; patent ~23/16 = 47; patent ~49/34 = 47; patent ~62/43 = 47; ''patent ~75/52 = 48''; patent ~384/265 = 47; ''patent ~59049/40960 = 46'') — Semihard 17L 2s}} | {{Harmonics in equal|89|intervals=odd|prec=2|columns=28|title=[[89edo]] (L=5, s=2, BrightGen is 47; patent ~13/9 = 47; patent ~23/16 = 47; patent ~49/34 = 47; patent ~62/43 = 47; ''patent ~75/52 = 48''; patent ~384/265 = 47; ''patent ~59049/40960 = 46'') — Semihard 17L 2s}} | ||
{{Harmonics in equal|___|intervals=odd|prec=2|columns=28|title=[[___edo]] (L=_, s=_, BrightGen is __; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | |||
{{Harmonics in equal|231|intervals=odd|prec=2|columns=28|title=[[231edo]] (L=13, s=5, BrightGen is 122; ''patent ~13/9 = 123''; ''patent ~23/16 = 121''; ''patent ~49/34 = 121''; patent ~62/43 = 122; ''patent ~75/52 = 121''; ''patent ~384/265 = 124''; ''patent ~59049/40960 = 121'')}} | {{Harmonics in equal|231|intervals=odd|prec=2|columns=28|title=[[231edo]] (L=13, s=5, BrightGen is 122; ''patent ~13/9 = 123''; ''patent ~23/16 = 121''; ''patent ~49/34 = 121''; patent ~62/43 = 122; ''patent ~75/52 = 121''; ''patent ~384/265 = 124''; ''patent ~59049/40960 = 121'')}} | ||
{{Harmonics in equal|___|intervals=odd|prec=2|columns=28|title=[[___edo]] (L=_, s=_, BrightGen is __; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | |||
{{Harmonics in equal|142|intervals=odd|prec=2|columns=28|title=[[142edo]] (L=8, s=3, BrightGen is 75; patent ~13/9 = 75; ''patent ~23/16 = 74''; ''patent ~49/34 = 76''; ''patent ~62/43 = 74, 'k' wart usable''; ''patent ~75/52 = 76'', 'f' wart usable; ''patent ~384/265 = 76''; ''patent ~59049/40960 = 74'')}} | {{Harmonics in equal|142|intervals=odd|prec=2|columns=28|title=[[142edo]] (L=8, s=3, BrightGen is 75; patent ~13/9 = 75; ''patent ~23/16 = 74''; ''patent ~49/34 = 76''; ''patent ~62/43 = 74, 'k' wart usable''; ''patent ~75/52 = 76'', 'f' wart usable; ''patent ~384/265 = 76''; ''patent ~59049/40960 = 74'')}} | ||
{{Harmonics in equal|___|intervals=odd|prec=2|columns=28|title=[[___edo]] (L=_, s=_, BrightGen is __; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | |||
{{Harmonics in equal|195|intervals=odd|prec=2|columns=28|title=[[195edo]] (L=11, s=4, BrightGen is 103; ''patent ~13/9 = 104, 'f' wart usable but requires 'e' wart for 11th harmonic''; ''patent ~23/16 = 102''; patent ~49/34 = 102; patent ~62/43 = 103; patent ~75/52 = 103; ''patent ~384/265 = 104''; ''patent ~59049/40960 = 102'')}} | {{Harmonics in equal|195|intervals=odd|prec=2|columns=28|title=[[195edo]] (L=11, s=4, BrightGen is 103; ''patent ~13/9 = 104, 'f' wart usable but requires 'e' wart for 11th harmonic''; ''patent ~23/16 = 102''; patent ~49/34 = 102; patent ~62/43 = 103; patent ~75/52 = 103; ''patent ~384/265 = 104''; ''patent ~59049/40960 = 102'')}} | ||
{{Harmonics in equal|___|intervals=odd|prec=2|columns=28|title=[[___edo]] (L=_, s=_, BrightGen is __; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | |||
{{Harmonics in equal|53|intervals=odd|prec=2|columns=28|title=[[53edo]] (L=3, s=1, BrightGen is 28; patent ~13/9 = 28; patent ~23/16 = 28; patent ~49/34 = 28; patent ~62/43 = 28; patent ~75/52 = 28; patent ~384/265 = 28; patent ~59049/40960 = 28) — Hard 17L 2s}} | {{Harmonics in equal|53|intervals=odd|prec=2|columns=28|title=[[53edo]] (L=3, s=1, BrightGen is 28; patent ~13/9 = 28; patent ~23/16 = 28; patent ~49/34 = 28; patent ~62/43 = 28; patent ~75/52 = 28; patent ~384/265 = 28; patent ~59049/40960 = 28) — Hard 17L 2s}} | ||
{{Harmonics in equal|___|intervals=odd|prec=2|columns=28|title=[[___edo]] (L=_, s=_, BrightGen is __; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | |||
{{Harmonics in equal|176|intervals=odd|prec=2|columns=28|title=[[176edo]] (L=10, s=3, BrightGen is 93; patent ~13/9 = 93; ''patent ~23/16 = 92''; patent ~49/34 = 93; patent ~62/43 = 93; ''patent ~75/52 = 94''; ''patent ~384/265 = 94''; patent ~59049/40960 = 93)}} | {{Harmonics in equal|176|intervals=odd|prec=2|columns=28|title=[[176edo]] (L=10, s=3, BrightGen is 93; patent ~13/9 = 93; ''patent ~23/16 = 92''; patent ~49/34 = 93; patent ~62/43 = 93; ''patent ~75/52 = 94''; ''patent ~384/265 = 94''; patent ~59049/40960 = 93)}} | ||
{{Harmonics in equal|___|intervals=odd|prec=2|columns=28|title=[[___edo]] (L=_, s=_, BrightGen is __; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | |||
{{Harmonics in equal|123|intervals=odd|prec=2|columns=28|title=[[123edo]] (L=7, s=2, BrightGen is 65; patent ~13/9 = 65; ''patent ~23/16 = 64, 'i' wart is usable''; ''patent ~49/34 = 64''; patent ~62/43 = 65; ''patent ~75/52 = 66''; patent ~384/265 = 65; patent ~59049/40960 = 65)}} | {{Harmonics in equal|123|intervals=odd|prec=2|columns=28|title=[[123edo]] (L=7, s=2, BrightGen is 65; patent ~13/9 = 65; ''patent ~23/16 = 64, 'i' wart is usable''; ''patent ~49/34 = 64''; patent ~62/43 = 65; ''patent ~75/52 = 66''; patent ~384/265 = 65; patent ~59049/40960 = 65)}} | ||
{{Harmonics in equal|___|intervals=odd|prec=2|columns=28|title=[[___edo]] (L=_, s=_, BrightGen is __; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | |||
{{Harmonics in equal|193|intervals=odd|prec=2|columns=28|title=[[193edo]] (L=11, s=3, BrightGen is 102; patent ~13/9 = 102; ''patent ~23/16 = 101''; patent ~49/34 = 102; patent ~62/43 = 102; patent ~75/52 = 102; ''patent ~384/265 = 104''; ''patent ~59049/40960 = 103'')}} | {{Harmonics in equal|193|intervals=odd|prec=2|columns=28|title=[[193edo]] (L=11, s=3, BrightGen is 102; patent ~13/9 = 102; ''patent ~23/16 = 101''; patent ~49/34 = 102; patent ~62/43 = 102; patent ~75/52 = 102; ''patent ~384/265 = 104''; ''patent ~59049/40960 = 103'')}} | ||
{{Harmonics in equal|___|intervals=odd|prec=2|columns=28|title=[[___edo]] (L=_, s=_, BrightGen is __; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | |||
{{Harmonics in equal|70|intervals=odd|prec=2|columns=28|title=[[70edo]] (L=4, s=1, BrightGen is 37; patent ~13/9 = 37; patent ~23/16 = 37; patent ~49/34 = 38; patent ~62/43 = 37; ''patent ~75/52 = 38''; patent ~384/265 = 37; patent ~59049/40960 = 37) — Superhard 17L 2s}} | {{Harmonics in equal|70|intervals=odd|prec=2|columns=28|title=[[70edo]] (L=4, s=1, BrightGen is 37; patent ~13/9 = 37; patent ~23/16 = 37; patent ~49/34 = 38; patent ~62/43 = 37; ''patent ~75/52 = 38''; patent ~384/265 = 37; patent ~59049/40960 = 37) — Superhard 17L 2s}} | ||
{{Harmonics in equal|___|intervals=odd|prec=2|columns=28|title=[[___edo]] (L=_, s=_, BrightGen is __; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | |||
{{Harmonics in equal|157|intervals=odd|prec=2|columns=28|title=[[157edo]] (L=9, s=2, BrightGen is 83; patent ~13/9 = 83; ''patent ~23/16 = 82''; patent ~49/34 = 83; patent ~62/43 = 83; ''patent ~75/52 = 84''; ''patent ~384/265 = 84''; ''patent ~59049/40960 = 84'')}} | {{Harmonics in equal|157|intervals=odd|prec=2|columns=28|title=[[157edo]] (L=9, s=2, BrightGen is 83; patent ~13/9 = 83; ''patent ~23/16 = 82''; patent ~49/34 = 83; patent ~62/43 = 83; ''patent ~75/52 = 84''; ''patent ~384/265 = 84''; ''patent ~59049/40960 = 84'')}} | ||
{{Harmonics in equal|___|intervals=odd|prec=2|columns=28|title=[[___edo]] (L=_, s=_, BrightGen is __; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | |||
{{Harmonics in equal|87|intervals=odd|prec=2|columns=28|title=[[87edo]] (L=5, s=1, BrightGen is 46; patent ~13/9 = 46 ; patent ~23/16 = 46; ''patent ~49/34 = 45''; patent ~62/43 = 46; patent ~75/52 = 46; ''patent ~384/265 = 47''; ''patent ~59049/40960 = 47'')}} | {{Harmonics in equal|87|intervals=odd|prec=2|columns=28|title=[[87edo]] (L=5, s=1, BrightGen is 46; patent ~13/9 = 46 ; patent ~23/16 = 46; ''patent ~49/34 = 45''; patent ~62/43 = 46; patent ~75/52 = 46; ''patent ~384/265 = 47''; ''patent ~59049/40960 = 47'')}} | ||
{{Harmonics in equal|___|intervals=odd|prec=2|columns=28|title=[[___edo]] (L=_, s=_, BrightGen is __; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | |||
{{Harmonics in equal|104|intervals=odd|prec=2|columns=28|title=[[104edo]] (L=6, s=1, BrightGen is 55; patent ~13/9 = 55; ''patent ~23/16 = 54''; patent ~49/34 = 55; patent ~62/43 = 55; ''patent ~75/52 = 54''; ''patent ~384/265 = 56''; ''patent ~59049/40960 = 57'')}} | {{Harmonics in equal|104|intervals=odd|prec=2|columns=28|title=[[104edo]] (L=6, s=1, BrightGen is 55; patent ~13/9 = 55; ''patent ~23/16 = 54''; patent ~49/34 = 55; patent ~62/43 = 55; ''patent ~75/52 = 54''; ''patent ~384/265 = 56''; ''patent ~59049/40960 = 57'')}} | ||
{{Harmonics in equal|___|intervals=odd|prec=2|columns=28|title=[[___edo]] (L=_, s=_, BrightGen is __; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | |||
{{Harmonics in equal|17|intervals=odd|prec=2|columns=28|title=[[17edo]] (L=1, s=0, BrightGen is 9; patent ~13/9 = 9; patent ~23/16 = 9; ''patent ~49/34 = 10, 'g' wart usable but requires 'c' wart for 5th harmonic''; patent ~62/43 = 9; ''patent ~75/52 = 8''; ''patent ~384/265 = 10''; c val ~384/265 = 9; ''patent ~59049/40960 = 10''; c val ~59049/40960 = 9) — Collapsed 17L 2s}} | {{Harmonics in equal|17|intervals=odd|prec=2|columns=28|title=[[17edo]] (L=1, s=0, BrightGen is 9; patent ~13/9 = 9; patent ~23/16 = 9; ''patent ~49/34 = 10, 'g' wart usable but requires 'c' wart for 5th harmonic''; patent ~62/43 = 9; ''patent ~75/52 = 8''; ''patent ~384/265 = 10''; c val ~384/265 = 9; ''patent ~59049/40960 = 10''; c val ~59049/40960 = 9) — Collapsed 17L 2s}} | ||
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Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:42, 8 April 2025 (UTC)<br> | Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:42, 8 April 2025 (UTC)<br> | ||
Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) | Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 05:41, 19 June 2025 (UTC) | ||