User:Lucius Chiaraviglio/Musical Mad Science: Difference between revisions
→Table of odd harmonics for various EDO values supporting 17L 2s: Fix typo in 320edo BrightGen |
Fix interval notation in mapping tables (all of 11L 2s; and first half of 17L 2s) |
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This table (actually a collection of tables for now) is for tracking trends in odd harmonics along the tuning spectrum of [[11L 2s]]; it is intended to match the organization of [[11L_2s#Scale_tree|the corresponding scale tree]]: | This table (actually a collection of tables for now) is for tracking trends in odd harmonics along the tuning spectrum of [[11L 2s]]; it is intended to match the organization of [[11L_2s#Scale_tree|the corresponding scale tree]]: | ||
{{Harmonics in equal|13|intervals=odd|prec=2|columns=28|title=[[13edo]] (L=1, s=1, ~[[16/11]] = 7) — Equalized 11L 2s}} | {{Harmonics in equal|13|intervals=odd|prec=2|columns=28|title=[[13edo]] (L=1, s=1, ~[[16/11]] = 7\13) — Equalized 11L 2s}} | ||
{{Harmonics in equal|76|intervals=odd|prec=2|columns=28|title=[[76edo]] (L=6, s=5, ~16/11 = 41)}} | {{Harmonics in equal|76|intervals=odd|prec=2|columns=28|title=[[76edo]] (L=6, s=5, ~16/11 = 41\76)}} | ||
{{Harmonics in equal|63|intervals=odd|prec=2|columns=28|title=[[63edo]] (L=5, s=4, ~16/11 = 34)}} | {{Harmonics in equal|63|intervals=odd|prec=2|columns=28|title=[[63edo]] (L=5, s=4, ~16/11 = 34\63)}} | ||
{{Harmonics in equal|113|intervals=odd|prec=2|columns=28|title=[[113edo]] (L=9, s=7, ~16/11 = 61)}} | {{Harmonics in equal|113|intervals=odd|prec=2|columns=28|title=[[113edo]] (L=9, s=7, ~16/11 = 61\113)}} | ||
{{Harmonics in equal|50|intervals=odd|prec=2|columns=28|title=[[50edo]] (L=4, s=3, ~16/11 = 27) — Supersoft 11L 2s}} | {{Harmonics in equal|50|intervals=odd|prec=2|columns=28|title=[[50edo]] (L=4, s=3, ~16/11 = 27\50) — Supersoft 11L 2s}} | ||
{{Harmonics in equal|137|intervals=odd|prec=2|columns=28|title=[[137edo]] (L=11, s=8, ~16/11 = 74)}} | {{Harmonics in equal|137|intervals=odd|prec=2|columns=28|title=[[137edo]] (L=11, s=8, ~16/11 = 74\137)}} | ||
{{Harmonics in equal|87|intervals=odd|prec=2|columns=28|title=[[87edo]] (L=7, s=5, ~16/11 = 47)}} | {{Harmonics in equal|87|intervals=odd|prec=2|columns=28|title=[[87edo]] (L=7, s=5, ~16/11 = 47\87)}} | ||
{{Harmonics in equal|124|intervals=odd|prec=2|columns=28|title=[[124edo]] (L=10, s=7, ~16/11 = 67)}} | {{Harmonics in equal|124|intervals=odd|prec=2|columns=28|title=[[124edo]] (L=10, s=7, ~16/11 = 67\124)}} | ||
{{Harmonics in equal|37|intervals=odd|prec=2|columns=28|title=[[37edo]] (L=3, s=2, ~16/11 is 20) — Soft 11L 2s}} | {{Harmonics in equal|37|intervals=odd|prec=2|columns=28|title=[[37edo]] (L=3, s=2, ~16/11 is 20\37) — Soft 11L 2s}} | ||
{{Harmonics in equal|135|intervals=odd|prec=2|columns=28|title=[[135edo]] (L=11, s=7, ~16/11 = 73)}} | {{Harmonics in equal|135|intervals=odd|prec=2|columns=28|title=[[135edo]] (L=11, s=7, ~16/11 = 73\135)}} | ||
{{Harmonics in equal|98|intervals=odd|prec=2|columns=28|title=[[98edo]] (L=8, s=5, ~16/11 = 53)}} | {{Harmonics in equal|98|intervals=odd|prec=2|columns=28|title=[[98edo]] (L=8, s=5, ~16/11 = 53\98)}} | ||
{{Harmonics in equal|159|intervals=odd|prec=2|columns=28|title=[[159edo]] (L=13, s=8, ~16/11 = 86)}} | {{Harmonics in equal|159|intervals=odd|prec=2|columns=28|title=[[159edo]] (L=13, s=8, ~16/11 = 86\159)}} | ||
{{Harmonics in equal|61|intervals=odd|prec=2|columns=28|title=[[61edo]] (L=5, s=3, ~16/11 = 33) — Semisoft 11L 2s}} | {{Harmonics in equal|61|intervals=odd|prec=2|columns=28|title=[[61edo]] (L=5, s=3, ~16/11 = 33) — Semisoft 11L 2s}} | ||
{{Harmonics in equal|146|intervals=odd|prec=2|columns=28|title=[[146edo]] (L=12, s=7, ~16/11 = 79)}} | {{Harmonics in equal|146|intervals=odd|prec=2|columns=28|title=[[146edo]] (L=12, s=7, ~16/11 = 79\146)}} | ||
{{Harmonics in equal|85|intervals=odd|prec=2|columns=28|title=[[85edo]] (L=7, s=4, ~16/11 = 46)}} | {{Harmonics in equal|85|intervals=odd|prec=2|columns=28|title=[[85edo]] (L=7, s=4, ~16/11 = 46\85)}} | ||
{{Harmonics in equal|109|intervals=odd|prec=2|columns=28|title=[[109edo]] (L=9, s=5, ~16/11 = 59)}} | {{Harmonics in equal|109|intervals=odd|prec=2|columns=28|title=[[109edo]] (L=9, s=5, ~16/11 = 59\109)}} | ||
{{Harmonics in equal|24|intervals=odd|prec=2|columns=28|title=[[24edo]] (L=2, s=1, ~16/11 = 13) — Basic 11L 2s}} | {{Harmonics in equal|24|intervals=odd|prec=2|columns=28|title=[[24edo]] (L=2, s=1, ~16/11 = 13\24) — Basic 11L 2s}} | ||
{{Harmonics in equal|107|intervals=odd|prec=2|columns=28|title=[[107edo]] (L=9, s=4, ~16/11 = 58)}} | {{Harmonics in equal|107|intervals=odd|prec=2|columns=28|title=[[107edo]] (L=9, s=4, ~16/11 = 58\107)}} | ||
{{Harmonics in equal|83|intervals=odd|prec=2|columns=28|title=[[83edo]] (L=7, s=3, ~16/11 = 45)}} | {{Harmonics in equal|83|intervals=odd|prec=2|columns=28|title=[[83edo]] (L=7, s=3, ~16/11 = 45\83)}} | ||
{{Harmonics in equal|142|intervals=odd|prec=2|columns=28|title=[[142edo]] (L=12, s=5, ~16/11 = 77)}} | {{Harmonics in equal|142|intervals=odd|prec=2|columns=28|title=[[142edo]] (L=12, s=5, ~16/11 = 77\142)}} | ||
{{Harmonics in equal|59|intervals=odd|prec=2|columns=28|title=[[59edo]] (L=5, s=2, ~16/11 = 32) — Semihard 11L 2s}} | {{Harmonics in equal|59|intervals=odd|prec=2|columns=28|title=[[59edo]] (L=5, s=2, ~16/11 = 32\59) — Semihard 11L 2s}} | ||
{{Harmonics in equal|153|intervals=odd|prec=2|columns=28|title=[[153edo]] (L=13, s=5, ~16/11 = 83)}} | {{Harmonics in equal|153|intervals=odd|prec=2|columns=28|title=[[153edo]] (L=13, s=5, ~16/11 = 83\153)}} | ||
{{Harmonics in equal|94|intervals=odd|prec=2|columns=28|title=[[94edo]] (L=8, s=3, ~16/11 = 51)}} | {{Harmonics in equal|94|intervals=odd|prec=2|columns=28|title=[[94edo]] (L=8, s=3, ~16/11 = 51\94)}} | ||
{{Harmonics in equal|129|intervals=odd|prec=2|columns=28|title=[[129edo]] (L=11, s=4, ~16/11 = 70)}} | {{Harmonics in equal|129|intervals=odd|prec=2|columns=28|title=[[129edo]] (L=11, s=4, ~16/11 = 70\129)}} | ||
{{Harmonics in equal|35|intervals=odd|prec=2|columns=28|title=[[35edo]] (L=3, s=1, ~16/11 = 19) — Hard 11L 2s}} | {{Harmonics in equal|35|intervals=odd|prec=2|columns=28|title=[[35edo]] (L=3, s=1, ~16/11 = 19\35) — Hard 11L 2s}} | ||
{{Harmonics in equal|116|intervals=odd|prec=2|columns=28|title=[[116edo]] (L=10, s=3, ~16/11 = 63)}} | {{Harmonics in equal|116|intervals=odd|prec=2|columns=28|title=[[116edo]] (L=10, s=3, ~16/11 = 63\116)}} | ||
{{Harmonics in equal|81|intervals=odd|prec=2|columns=28|title=[[81edo]] (L=7, s=2, ~16/11 = 44)}} | {{Harmonics in equal|81|intervals=odd|prec=2|columns=28|title=[[81edo]] (L=7, s=2, ~16/11 = 44\81)}} | ||
{{Harmonics in equal|127|intervals=odd|prec=2|columns=28|title=[[127edo]] (L=11, s=3, ~16/11 = 69)}} | {{Harmonics in equal|127|intervals=odd|prec=2|columns=28|title=[[127edo]] (L=11, s=3, ~16/11 = 69\127)}} | ||
{{Harmonics in equal|46|intervals=odd|prec=2|columns=28|title=[[46edo]] (L=4, s=1, ~16/11 = 25) — Superhard 11L 2s}} | {{Harmonics in equal|46|intervals=odd|prec=2|columns=28|title=[[46edo]] (L=4, s=1, ~16/11 = 25\46) — Superhard 11L 2s}} | ||
{{Harmonics in equal|103|intervals=odd|prec=2|columns=28|title=[[103edo]] (L=9, s=2, ~16/11 = 56)}} | {{Harmonics in equal|103|intervals=odd|prec=2|columns=28|title=[[103edo]] (L=9, s=2, ~16/11 = 56\103)}} | ||
{{Harmonics in equal|57|intervals=odd|prec=2|columns=28|title=[[57edo]] (L=5, s=1, ~16/11 = 31)}} | {{Harmonics in equal|57|intervals=odd|prec=2|columns=28|title=[[57edo]] (L=5, s=1, ~16/11 = 31\57)}} | ||
{{Harmonics in equal|68|intervals=odd|prec=2|columns=28|title=[[68edo]] (L=6, s=1, ~16/11 = 37)}} | {{Harmonics in equal|68|intervals=odd|prec=2|columns=28|title=[[68edo]] (L=6, s=1, ~16/11 = 37\68)}} | ||
{{Harmonics in equal|11|intervals=odd|prec=2|columns=28|title=[[11edo]] (L=1, s=0, ~16/11 = 6) — Collapsed 11L 2s}} | {{Harmonics in equal|11|intervals=odd|prec=2|columns=28|title=[[11edo]] (L=1, s=0, ~16/11 = 6\11) — Collapsed 11L 2s}} | ||
Note that 11/8 (the dark generator, and thereby the bright generator 16/11) remains stable throughout the entire currently posted 11L 2s table &emdash; the worst relative error is -34.8%, at 127edo. | Note that 11/8 (the dark generator, and thereby the bright generator 16/11) remains stable throughout the entire currently posted 11L 2s table &emdash; the worst relative error is -34.8%, at 127edo. | ||
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Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:00, 9 April 2025 (UTC)<br> | Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:00, 9 April 2025 (UTC)<br> | ||
Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08: | Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:49, 21 June 2025 (UTC) | ||
== Musical Mad Science Musings on Diatonicized Third-Tone Sub-Chromaticism == | == Musical Mad Science Musings on Diatonicized Third-Tone Sub-Chromaticism == | ||
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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 — 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)''. | 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\19; patent ~[[13/9]] = 10\19; patent ~[[23/16]] = 10\19; ''patent ~[[49/34]] = 9\19''; patent ~[[62/43]] = 10\19; patent ~[[75/52]] = 10\19; patent ~[[384/265]] = 10\19; ''patent ~[[59049/40960]] = 9\19'') — 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|131|intervals=odd|prec=2|columns=28|title=[[131edo]] (L=7, s=6, BrightGen is 69\131; patent ~13/9 = _\131; patent ~23/16 = _\131\131\131; patent ~49/34 = _\131; patent ~62/43 = _\131\131; patent ~75/52 = _\131; patent ~384/265 = _\131\131; patent ~59049/40960 = _\131)}} | ||
{{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\112; ''patent ~13/9 = 58\112; b val ~13/9 = 60\112''; patent ~23/16 = 59\112; ''patent ~49/34 = 58\112''; patent ~62/43 = 59\112; ''patent ~75/52 = 60\112'', 'b' or 'f' wart usable; ''patent ~384/265 = 60\112; b val ~384/255 = 61\112''; ''patent ~59049/40960 = 64\112; b val ~59049/40960 = 54\112'')}} | ||
{{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|205|intervals=odd|prec=2|columns=28|title=[[205edo]] (L=11, s=9, BrightGen is 108\205; patent ~13/9 = _\205; patent ~23/16 = _\205; patent ~49/34 = _\205; patent ~62/43 = _\205; patent ~75/52 = _\205; patent ~384/265 = _\205\205; patent ~59049/40960 = _\205)}} | ||
{{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\93; ''patent ~13/9 = 50\93''; patent ~23/16 = 49\93; patent ~49/34 = 49\93; patent ~62/43 = 49\93; patent ~75/52 = 49\93; patent ~384/265 = 49\93; ''patent ~59049/40960 = 45\93'')}} | ||
{{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|260|intervals=odd|prec=2|columns=28|title=[[260edo]] (L=14, s=11, BrightGen is 137\260; patent ~13/9 = _\260; patent ~23/16 = _\260; patent ~49/34 = _\260; patent ~62/43 = _\260; patent ~75/52 = _\260; patent ~384/265 = _\260; patent ~59049/40960 = _\260)}} | ||
{{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\167; patent ~13/9 = 88\167; ''patent ~23/16 = 87\167''; patent ~49/34 = 88\167; patent ~62/43 = 88\167; ''patent ~75/52 = 89\167'', 'b' wart usable; ''patent ~384/265 = 89\167''; ''patent ~59049/40960 = 91\167'')}} | ||
{{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|241|intervals=odd|prec=2|columns=28|title=[[241edo]] (L=13, s=10, BrightGen is 127\241; patent ~13/9 = _\241; patent ~23/16 = _\241; patent ~49/34 = _\241; patent ~62/43 = _\241; patent ~75/52 = _\241; patent ~384/265 = _\241; patent ~59049/40960 = _\241)}} | ||
{{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\74; ''patent ~13/9 = 40\74''; patent ~23/16 = 39\74; ''patent ~49/34 = 40\74, 'g' wart usable''; patent ~62/43 = 39\74; patent ~75/52 = 39\74; patent ~384/265 = 39\74; ''patent ~59049/40960 = 36\74'') — 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|277|intervals=odd|prec=2|columns=28|title=[[277edo]] (L=15, s=11, BrightGen is 146\277; patent ~13/9 = _\277; patent ~23/16 = _\277; patent ~49/34 = _\277; patent ~62/43 = _\277; patent ~75/52 = _\277; patent ~384/265 = _\277; patent ~59049/40960 = _\277)}} | ||
{{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\203; patent ~13/9 = 107\203; ''patent ~23/16 = 106''\203; patent ~49/34 = 107\203; patent ~62/43 = 107\203; patent ~75/52 = 107\203; ''patent ~384/265 = 109\203''; ''patent ~59049/40960 = 110\203'')}} | ||
{{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|332|intervals=odd|prec=2|columns=28|title=[[332edo]] (L=18, s=13, BrightGen is 175\332; patent ~13/9 = _\332; patent ~23/16 = _\332\332; patent ~49/34 = _\332; patent ~62/43 = _\332; patent ~75/52 = _\332; patent ~384/265 = _\332; patent ~59049/40960 = _\332)}} | ||
{{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\129; ''patent ~13/9 = 69\129''; patent ~23/16 = 68\129; patent ~49/34 = 68\129; patent ~62/43 = 68\129; ''patent ~75/52 = 69\129''; patent ~384/265 = 68\129; ''patent ~59049/40960 = 63\129'')}} | ||
{{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|313|intervals=odd|prec=2|columns=28|title=[[313edo]] (L=17, s=12, BrightGen is 165\313; patent ~13/9 = _\313; patent ~23/16 = _\313; patent ~49/34 = _\313; patent ~62/43 = _\313; patent ~75/52 = _\313; patent ~384/265 = _\313; patent ~59049/40960 = _\313)}} | ||
{{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\184; patent ~13/9 = 97\184; ''patent ~23/16 = 96\184, 'i' wart usable''; ''patent ~49/34 = 98\184''; patent ~62/43 = 97\184; patent ~75/52 = 97\184; ''patent ~384/265 = 99\184''; ''patent ~59049/40960 = 101\184'')}} | ||
{{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|239|intervals=odd|prec=2|columns=28|title=[[239edo]] (L=13, s=9, BrightGen is 126\239; patent ~13/9 = _\239; patent ~23/16 = _\239; patent ~49/34 = _\239; patent ~62/43 = _\239; patent ~75/52 = _\239; patent ~384/265 = _\239; patent ~59049/40960 = _\239)}} | ||
{{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\55; ''patent ~13/9 = 30\55''; patent ~23/16 = 29\55; ''patent ~49/34 = 28\55''; patent ~62/43 = 29\55; patent ~75/52 = 29\55; patent ~384/265 = 29\55; ''patent ~59049/40960 = 27\55'') — 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|256|intervals=odd|prec=2|columns=28|title=[[256edo]] (L=14, s=9, BrightGen is 135\256; patent ~13/9 = _\256; patent ~23/16 = _\256; patent ~49/34 = _\256; patent ~62/43 = _\256; patent ~75/52 = _\256; patent ~384/265 = _\256; patent ~59049/40960 = _\256)}} | ||
{{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\201; patent ~13/9 = 106\201; ''patent ~23/16 = 105\201''; ''patent ~49/34 = 105\201, 'g' wart usable''; patent ~62/43 = 106\201; ''patent ~75/52 = 107\201'', 'b' wart usable; ''patent ~384/265 = 108\201''; ''patent ~59049/40960 = 110\201'')}} | ||
{{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|347|intervals=odd|prec=2|columns=28|title=[[347edo]] (L=19, s=12, BrightGen is 183\347; patent ~13/9 = _\347; patent ~23/16 = _\347; patent ~49/34 = _\347; patent ~62/43 = _\347; patent ~75/52 = _\347; patent ~384/265 = _\347; patent ~59049/40960 = _\347)}} | ||
{{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\146; ''patent ~13/9 = 78\146''; ''patent ~23/16 = 76\146\146''; patent ~49/34 = 77\146; patent ~62/43 = 77\146; patent ~75/52 = 77\146; ''patent ~384/265 = 78\146''; ''patent ~59049/40960 = 73\146'')}} | ||
{{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|383|intervals=odd|prec=2|columns=28|title=[[383edo]] (L=21, s=13, BrightGen is 202\383; patent ~13/9 = _\383; patent ~23/16 = _\383; patent ~49/34 = _\383; patent ~62/43 = _\383; patent ~75/52 = _\383; patent ~384/265 = _\383; patent ~59049/40960 = _\383)}} | ||
{{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\237; patent ~13/9 = 125\237; patent ~23/16 = 124\237; ''patent ~49/34 = 124\237''; patent ~62/43 = 125\237; patent ~75/52 = 125\237; ''patent ~384/265 = 127\237''; ''patent ~59049/40960 = 129\237'')}} | ||
{{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|328|intervals=odd|prec=2|columns=28|title=[[328edo]] (L=18, s=11, BrightGen is 173\328; patent ~13/9 = _\328; patent ~23/16 = _\328; patent ~49/34 = _\328; patent ~62/43 = _\328; patent ~75/52 = _\328; patent ~384/265 = _\328; patent ~59049/40960 = _\328)}} | ||
{{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\91; ''patent ~13/9 = 49\91''; patent ~23/16 = 48\91; ''patent ~49/34 = 47\91''; patent ~62/43 = 48\91; ''patent ~75/52 = 47\91''; ''patent ~384/265 = 49\91''; ''patent ~59049/40960 = 46\91'') — 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|309|intervals=odd|prec=2|columns=28|title=[[309edo]] (L=17, s=10, BrightGen is 163\309; patent ~13/9 = _\309; patent ~23/16 = _\309; patent ~49/34 = _\309; patent ~62/43 = _\309; patent ~75/52 = _\309; patent ~384/265 = _\309; patent ~59049/40960 = _\309)}} | ||
{{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\218; patent ~13/9 = 115\218; ''patent ~23/16 = 114\218''; patent ~49/34 = 115\218; patent ~62/43 = 115\218; patent ~75/52 = 115\218; ''patent ~384/265 = 117\218''; ''patent ~59049/40960 = 120\218'')}} | ||
{{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|345|intervals=odd|prec=2|columns=28|title=[[345edo]] (L=19, s=11, BrightGen is 182\345; patent ~13/9 = _\345; patent ~23/16 = _\345; patent ~49/34 = _\345; patent ~62/43 = _\345; patent ~75/52 = _\345; patent ~384/265 = _\345; patent ~59049/40960 = _\345)}} | ||
{{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\127; ''patent ~13/9 = 68\127''; ''patent ~23/16 = 66\127, 'i' wart usable''; ''patent ~49/34 = 68\127''; patent ~62/43 = 67\127; patent ~75/52 = 67\127; ''patent ~384/265 = 68\127''; ''patent ~59049/40960 = 64\127'')}} | ||
{{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|290|intervals=odd|prec=2|columns=28|title=[[290edo]] (L=16, s=9, BrightGen is 153\290; patent ~13/9 = _\290; patent ~23/16 = _\290; patent ~49/34 = _\290; patent ~62/43 = _\290; patent ~75/52 = _\290; patent ~384/265 = _\290; patent ~59049/40960 = _\290)}} | ||
{{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\163; ''patent ~13/9 = 87\163''; ''patent ~23/16 = 85\163''; ''patent ~49/34 = 87\163;''; ''patent ~62/43 = 87\163, 'k' wart usable''; ''patent ~75/52 = 85\163''; ''patent ~384/265 = 87\163''; ''patent ~59049/40960 = 83\163'')}} | ||
{{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|199|intervals=odd|prec=2|columns=28|title=[[199edo]] (L=11, s=6, BrightGen is 105\199; patent ~13/9 = _\199; patent ~23/16 = _\199; patent ~49/34 = _\199; patent ~62/43 = _\199; patent ~75/52 = _\199; patent ~384/265 = _\199; patent ~59049/40960 = _\199)}} | ||
{{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|197|intervals=odd|prec=2|columns=28|title=[[197edo]] (L=11, s=5, BrightGen is 104; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | {{Harmonics in equal|197|intervals=odd|prec=2|columns=28|title=[[197edo]] (L=11, s=5, BrightGen is 104; patent ~13/9 = _; patent ~23/16 = _; patent ~49/34 = _; patent ~62/43 = _; patent ~75/52 = _; patent ~384/265 = _; patent ~59049/40960 = _)}} | ||