User:Lucius Chiaraviglio/Musical Mad Science: Difference between revisions
→Musical Mad Science Musings on Diatonicized Third-Tone Sub-Chromaticism: More edits after filling in ~49/34 mappings |
→Musical Mad Science Musings on Diatonicized Third-Tone Sub-Chromaticism: Filled in ~75/52 mappings from 19edo through 201edo (safety save) |
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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 — will do this after filling in candidate generator mappings for EDOs already in this table). 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)''. | 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 — will do this after filling in candidate generator mappings for EDOs already in this table). 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]] = | {{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|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 = | {{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' val ~75/52 = 59; 'f' val ~75/52 = 59; ''patent ~384/265 = 60; b val ~384/255 = 61''; ''patent ~59049/40960 = 64; b val ~59049/40960 = 54'')}} | ||
{{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 = | {{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|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 = | {{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' val ~75/52 = 88; ''patent ~384/265 = 89''; ''patent ~59049/40960 = 91'')}} | ||
{{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 = | {{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|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 = | {{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|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 = | {{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|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 = | {{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|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 = | {{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|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 = | {{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' val ~75/52 = 106; ''patent ~384/265 = 108''; ''patent ~59049/40960 = 110'')}} | ||
{{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 = _; ''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 = _; ''patent ~384/265 = 78''; ''patent ~59049/40960 = 73'')}} | ||
{{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 = _; ''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 = _; ''patent ~384/265 = 127''; ''patent ~59049/40960 = 129'')}} | ||
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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]]) 06:52, 18 June 2025 (UTC) | ||