User:Lucius Chiaraviglio/Musical Mad Science: Difference between revisions
Make table labels consistent; add some links; fix a couple of editing errors |
→Table of odd harmonics for various EDO values supporting 17L 2s: Make the 23rd harmonic more visible (including possible 'i' wart when appropriate) |
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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 tuning spectrum of [[17L 2s]]; it is intended to match the organization of [[17L_2s#Scale_tree|the corresponding scale tree]]. 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''. | |||
{{Harmonics in equal|19|intervals=odd|prec=2|columns=28|title=[[19edo]] (L=1, s=1, BrightGen is 10; patent ~[[13/9]] = 10; patent ~[[ | {{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 ~[[62/43]] = 10) — Equalized 17L 2s}} | ||
{{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 ~62/43 = 59)}} | {{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 ~62/43 = 59)}} | ||
{{Harmonics in equal|93|intervals=odd|prec=2|columns=28|title=[[93edo]] (L=5, s=4, BrightGen is 49; ''patent ~13/9 = 50''; patent ~62/43 = 49)}} | {{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 ~62/43 = 49)}} | ||
{{Harmonics in equal|167|intervals=odd|prec=2|columns=28|title=[[167edo]] (L=9, s=7, BrightGen is 88; patent ~13/9 = 88; patent ~ | {{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 ~62/43 = 88)}} | ||
{{Harmonics in equal|74|intervals=odd|prec=2|columns=28|title=[[74edo]] (L=4, s=3, BrightGen is 39; ''patent ~13/9 = 40''; patent ~62/43 = 39) — 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 ~62/43 = 39) — Supersoft 17L 2s}} | ||
{{Harmonics in equal|203|intervals=odd|prec=2|columns=28|title=[[203edo]] (L=11, s=8, BrightGen is 107; patent ~13/9 = 107; patent ~62/43 = 107)}} | {{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 ~62/43 = 107)}} | ||
{{Harmonics in equal|129|intervals=odd|prec=2|columns=28|title=[[129edo]] (L=7, s=5, BrightGen is 68; ''patent ~13/9 = 69''; patent ~62/43 = 68)}} | {{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 ~62/43 = 68)}} | ||
{{Harmonics in equal|184|intervals=odd|prec=2|columns=28|title=[[184edo]] (L=10, s=7, BrightGen is 97; patent ~13/9 = 97; patent ~62/43 = 97)}} | {{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 ~62/43 = 97)}} | ||
{{Harmonics in equal|55|intervals=odd|prec=2|columns=28|title=[[55edo]] (L=3, s=2, BrightGen is 29; ''patent ~13/9 = 30''; patent ~62/43 = 29) — 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 ~62/43 = 29) — Soft 17L 2s}} | ||
{{Harmonics in equal|201|intervals=odd|prec=2|columns=28|title=[[201edo]] (L=11, s=7, BrightGen is 106; patent ~13/9 = 106; patent ~62/43 = 106)}} | {{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 ~62/43 = 106)}} | ||
{{Harmonics in equal|146|intervals=odd|prec=2|columns=28|title=[[146edo]] (L=8, s=5, BrightGen is 77; ''patent ~13/9 = 78''; patent ~ | {{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 ~62/43 = 77)}} | ||
{{Harmonics in equal|237|intervals=odd|prec=2|columns=28|title=[[237edo]] (L=13, s=8, BrightGen is 125; patent ~13/9 = 125; patent ~62/43 = 125)}} | {{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 ~62/43 = 125)}} | ||
{{Harmonics in equal|91|intervals=odd|prec=2|columns=28|title=[[91edo]] (L=5, s=3, BrightGen is 48; ''patent ~13/9 = 49''; patent ~62/43 = 48) — 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 ~62/43 = 48) — Semisoft 17L 2s}} | ||
{{Harmonics in equal|218|intervals=odd|prec=2|columns=28|title=[[218edo]] (L=12, s=7, BrightGen is 115; patent ~13/9 = 115; patent ~62/43 = 115)}} | {{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 ~62/43 = 115)}} | ||
{{Harmonics in equal|127|intervals=odd|prec=2|columns=28|title=[[127edo]] (L=7, s=4, BrightGen is 67; ''patent ~13/9 = 68''; patent ~ | {{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 ~62/43 = 67)}} | ||
{{Harmonics in equal|163|intervals=odd|prec=2|columns=28|title=[[163edo]] (L=9, s=5, BrightGen is 86; ''patent ~13/9 = 87''; ''patent ~62/43 = 87 'k' wart usable'')}} | {{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 ~62/43 = 87 'k' wart usable'')}} | ||
{{Harmonics in equal|36|intervals=odd|prec=2|columns=28|title=[[36edo]] (L=2, s=1, BrightGen is 19; patent ~13/9 = 19; patent ~62/43 = 19) — 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 ~62/43 = 19) — Basic 17L 2s}} | ||
{{Harmonics in equal|161|intervals=odd|prec=2|columns=28|title=[[161edo]] (L=9, s=4, BrightGen is 85; ''patent ~13/9 = 86''; patent ~62/43 = 85)}} | {{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 ~62/43 = 85)}} | ||
{{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 ~62/43 = 66)}} | {{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 ~62/43 = 66)}} | ||
{{Harmonics in equal|214|intervals=odd|prec=2|columns=28|title=[[214edo]] (L=12, s=5, BrightGen is 113; ''patent ~13/9 = 114''; patent ~62/43 = 113)}} | {{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 ~62/43 = 113)}} | ||
{{Harmonics in equal|89|intervals=odd|prec=2|columns=28|title=[[89edo]] (L=5, s=2, BrightGen is 47; patent ~13/9 = 47; patent ~ | {{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 ~62/43 = 47) — Semihard 17L 2s}} | ||
{{Harmonics in equal|231|intervals=odd|prec=2|columns=28|title=[[231edo]] (L=13, s=5, BrightGen is 122; ''patent ~13/9 = 123''; patent ~62/43 = 122)}} | {{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 ~62/43 = 122)}} | ||
{{Harmonics in equal|142|intervals=odd|prec=2|columns=28|title=[[142edo]] (L=8, s=3, BrightGen is 75; patent ~13/9 = 75; ''patent ~62/43 = 74, 'k' wart usable'')}} | {{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 ~62/43 = 74, 'k' wart usable'')}} | ||
{{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 | {{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 ~62/43 = 103)}} | ||
{{Harmonics in equal|53|intervals=odd|prec=2|columns=28|title=[[53edo]] (L=3, s=1, BrightGen is 28; patent ~13/9 = 28; patent ~62/43 = 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 ~62/43 = 28) — Hard 17L 2s}} | ||
{{Harmonics in equal|176|intervals=odd|prec=2|columns=28|title=[[176edo]] (L=10, s=3, BrightGen is 93; patent ~13/9 = 93; patent ~62/43 = 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 ~62/43 = 93)}} | ||
{{Harmonics in equal|123|intervals=odd|prec=2|columns=28|title=[[123edo]] (L=7, s=2, BrightGen is 65; patent ~13/9 = 65; patent ~ | {{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 ~62/43 = 65)}} | ||
{{Harmonics in equal|193|intervals=odd|prec=2|columns=28|title=[[193edo]] (L=11, s=3, BrightGen is 102; patent ~13/9 = 102; patent ~62/43 = 102)}} | {{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 ~62/43 = 102)}} | ||
{{Harmonics in equal|70|intervals=odd|prec=2|columns=28|title=[[70edo]] (L=4, s=1, BrightGen is 37; patent ~13/9 = 37; patent ~62/43 = 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 ~62/43 = 37) — Superhard 17L 2s}} | ||
{{Harmonics in equal|157|intervals=odd|prec=2|columns=28|title=[[157edo]] (L=9, s=2, BrightGen is 83; patent ~13/9 = 83; patent ~62/43 = 83)}} | {{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 ~62/43 = 83)}} | ||
{{Harmonics in equal|87|intervals=odd|prec=2|columns=28|title=[[87edo]] (L=5, s=1, BrightGen is 46; patent ~13/9 = 46; patent ~62/43 = 46)}} | {{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 ~62/43 = 46)}} | ||
{{Harmonics in equal|104|intervals=odd|prec=2|columns=28|title=[[104edo]] (L=6, s=1, BrightGen is 55; patent ~13/9 = 55; patent ~62/43 = 55)}} | {{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 ~62/43 = 55)}} | ||
{{Harmonics in equal|17|intervals=odd|prec=2|columns=28|title=[[17edo]] (L=1, s=0, BrightGen is 9; patent ~13/9 = 9; patent ~62/43 = 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 ~62/43 = 9) — Collapsed 17L 2s}} | ||
(Need a way to combine the collection of tables into a single table for better readability.) | (Need a way to combine the collection of tables into a single table for better readability.) | ||
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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]]) 21:30, 26 April 2025 (UTC) | ||