User:Lucius Chiaraviglio/Musical Mad Science: Difference between revisions
→Musical Mad Science Musings on Diatonicized Sixth-Tone Sub-Chromaticism(?): Complete the entries just added for right-most column of the 17L 2s tuning table |
Make table labels consistent; add some links; fix a couple of editing errors |
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==== My YouTube comments start here ==== | ==== My YouTube comments start here ==== | ||
I just had a crazy idea for your next musical mad science experiment (and it potentially includes 50edo): See if it is possible to retune some of the quarter-tone ([[24edo]], "diatonicized chromatic")11L 2s (L/s = 2) scale works of Ivan Wyschnegradsky into other tuning systems that support 11L 2s and have a good approximation and single circle of 11/8 (or 16/11). Plausible candidate tuning systems on the soft side are [[37edo]] (L/s = 3/2, and has a super-good 11/8), [[61edo]] (L/s = 5/3, but 61edo is big enough to be pushing the limits of plausibility), and [[50edo]] (L/s = 4/3 -- might be too soft). Plausible candidate tuning systems on the hard side are [[35edo]] (L/s = 3), [[59edo]] (L/s = 7/3, but 59edo is big enough to be pushing the limits of plausibility), and [[46edo]] (L/s = 4/1 -- might be too hard). | I just had a crazy idea for your next musical mad science experiment (and it potentially includes 50edo): See if it is possible to retune some of the quarter-tone ([[24edo]], "diatonicized chromatic")11L 2s (L/s = 2) scale works of Ivan Wyschnegradsky into other tuning systems that support 11L 2s and have a good approximation and single circle of [[11/8]] (or [[16/11]]). Plausible candidate tuning systems on the soft side are [[37edo]] (L/s = 3/2, and has a super-good 11/8), [[61edo]] (L/s = 5/3, but 61edo is big enough to be pushing the limits of plausibility), and [[50edo]] (L/s = 4/3 -- might be too soft). Plausible candidate tuning systems on the hard side are [[35edo]] (L/s = 3), [[59edo]] (L/s = 7/3, but 59edo is big enough to be pushing the limits of plausibility), and [[46edo]] (L/s = 4/1 -- might be too hard). | ||
Most of Ivan Wyschnegradsky's quarter-tone pieces are for 2 pianos tuned a quarter tone apart (in a few cases with other instruments); he did have a couple of quarter-tone pianos and even a quarter-tone harmonium built, but was not very satisfied with them (based on quarter-tone piano photos and video footage, I am going to hazard a guess that this was for ergonomic reasons); I think that with the way he wrote this music, it really does need the resonance and timbre of pianos. | Most of Ivan Wyschnegradsky's quarter-tone pieces are for 2 pianos tuned a quarter tone apart (in a few cases with other instruments); he did have a couple of quarter-tone pianos and even a quarter-tone harmonium built, but was not very satisfied with them (based on quarter-tone piano photos and video footage, I am going to hazard a guess that this was for ergonomic reasons); I think that with the way he wrote this music, it really does need the resonance and timbre of pianos. | ||
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Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 10:18, 25 January 2025 (UTC)<br> | Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 10:18, 25 January 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]]) 08:25, 26 April 2025 (UTC) | ||
=== Comma for getting the fifth on the circle of 11/8 or 16/11 in the middle of the 11L 2s tuning spectrum === | === Comma for getting the fifth on the circle of 11/8 or 16/11 in the middle of the 11L 2s tuning spectrum === | ||
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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]] | {{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|76|intervals=odd|prec=2|columns=28|title=[[76edo]] (L=6, s=5, 16/11 | {{Harmonics in equal|76|intervals=odd|prec=2|columns=28|title=[[76edo]] (L=6, s=5, ~16/11 = 41)}} | ||
{{Harmonics in equal|63|intervals=odd|prec=2|columns=28|title=[[63edo]] (L=5, s=4, 16/11 | {{Harmonics in equal|63|intervals=odd|prec=2|columns=28|title=[[63edo]] (L=5, s=4, ~16/11 = 34)}} | ||
{{Harmonics in equal|113|intervals=odd|prec=2|columns=28|title=[[113edo]] (L=9, s=7, 16/11 | {{Harmonics in equal|113|intervals=odd|prec=2|columns=28|title=[[113edo]] (L=9, s=7, ~16/11 = 61)}} | ||
{{Harmonics in equal|50|intervals=odd|prec=2|columns=28|title=[[50edo]] (L=4, s=3, 16/11 | {{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|137|intervals=odd|prec=2|columns=28|title=[[137edo]] (L=11, s=8, 16/11 | {{Harmonics in equal|137|intervals=odd|prec=2|columns=28|title=[[137edo]] (L=11, s=8, ~16/11 = 74)}} | ||
{{Harmonics in equal|87|intervals=odd|prec=2|columns=28|title=[[87edo]] (L=7, s=5, 16/11 | {{Harmonics in equal|87|intervals=odd|prec=2|columns=28|title=[[87edo]] (L=7, s=5, ~16/11 = 47)}} | ||
{{Harmonics in equal|124|intervals=odd|prec=2|columns=28|title=[[124edo]] (L=10, s=7, 16/11 | {{Harmonics in equal|124|intervals=odd|prec=2|columns=28|title=[[124edo]] (L=10, s=7, ~16/11 = 67)}} | ||
{{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) — Soft 11L 2s}} | ||
{{Harmonics in equal|135|intervals=odd|prec=2|columns=28|title=[[135edo]] (L=11, s=7, 16/11 | {{Harmonics in equal|135|intervals=odd|prec=2|columns=28|title=[[135edo]] (L=11, s=7, ~16/11 = 73)}} | ||
{{Harmonics in equal|98|intervals=odd|prec=2|columns=28|title=[[98edo]] (L=8, s=5, 16/11 | {{Harmonics in equal|98|intervals=odd|prec=2|columns=28|title=[[98edo]] (L=8, s=5, ~16/11 = 53)}} | ||
{{Harmonics in equal|159|intervals=odd|prec=2|columns=28|title=[[159edo]] (L=13, s=8, 16/11 | {{Harmonics in equal|159|intervals=odd|prec=2|columns=28|title=[[159edo]] (L=13, s=8, ~16/11 = 86)}} | ||
{{Harmonics in equal|61|intervals=odd|prec=2|columns=28|title=[[61edo]] (L=5, s=3, 16/11 | {{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 | {{Harmonics in equal|146|intervals=odd|prec=2|columns=28|title=[[146edo]] (L=12, s=7, ~16/11 = 79)}} | ||
{{Harmonics in equal|85|intervals=odd|prec=2|columns=28|title=[[85edo]] (L=7, s=4, 16/11 | {{Harmonics in equal|85|intervals=odd|prec=2|columns=28|title=[[85edo]] (L=7, s=4, ~16/11 = 46)}} | ||
{{Harmonics in equal|109|intervals=odd|prec=2|columns=28|title=[[109edo]] (L=9, s=5, 16/11 | {{Harmonics in equal|109|intervals=odd|prec=2|columns=28|title=[[109edo]] (L=9, s=5, ~16/11 = 59)}} | ||
{{Harmonics in equal|24|intervals=odd|prec=2|columns=28|title=[[24edo]] (L=2, s=1, 16/11 | {{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|107|intervals=odd|prec=2|columns=28|title=[[107edo]] (L=9, s=4, 16/11 | {{Harmonics in equal|107|intervals=odd|prec=2|columns=28|title=[[107edo]] (L=9, s=4, ~16/11 = 58)}} | ||
{{Harmonics in equal|83|intervals=odd|prec=2|columns=28|title=[[83edo]] (L=7, s=3, 16/11 | {{Harmonics in equal|83|intervals=odd|prec=2|columns=28|title=[[83edo]] (L=7, s=3, ~16/11 = 45)}} | ||
{{Harmonics in equal|142|intervals=odd|prec=2|columns=28|title=[[142edo]] (L=12, s=5, 16/11 | {{Harmonics in equal|142|intervals=odd|prec=2|columns=28|title=[[142edo]] (L=12, s=5, ~16/11 = 77)}} | ||
{{Harmonics in equal|59|intervals=odd|prec=2|columns=28|title=[[59edo]] (L=5, s=2, 16/11 | {{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|153|intervals=odd|prec=2|columns=28|title=[[153edo]] (L=13, s=5, 16/11 | {{Harmonics in equal|153|intervals=odd|prec=2|columns=28|title=[[153edo]] (L=13, s=5, ~16/11 = 83)}} | ||
{{Harmonics in equal|94|intervals=odd|prec=2|columns=28|title=[[94edo]] (L=8, s=3, 16/11 | {{Harmonics in equal|94|intervals=odd|prec=2|columns=28|title=[[94edo]] (L=8, s=3, ~16/11 = 51)}} | ||
{{Harmonics in equal|129|intervals=odd|prec=2|columns=28|title=[[129edo]] (L=11, s=4, 16/11 | {{Harmonics in equal|129|intervals=odd|prec=2|columns=28|title=[[129edo]] (L=11, s=4, ~16/11 = 70)}} | ||
{{Harmonics in equal|35|intervals=odd|prec=2|columns=28|title=[[35edo]] (L=3, s=1, 16/11 | {{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|116|intervals=odd|prec=2|columns=28|title=[[116edo]] (L=10, s=3, 16/11 | {{Harmonics in equal|116|intervals=odd|prec=2|columns=28|title=[[116edo]] (L=10, s=3, ~16/11 = 63)}} | ||
{{Harmonics in equal|81|intervals=odd|prec=2|columns=28|title=[[81edo]] (L=7, s=2, 16/11 | {{Harmonics in equal|81|intervals=odd|prec=2|columns=28|title=[[81edo]] (L=7, s=2, ~16/11 = 44)}} | ||
{{Harmonics in equal|127|intervals=odd|prec=2|columns=28|title=[[127edo]] (L=11, s=3, 16/11 | {{Harmonics in equal|127|intervals=odd|prec=2|columns=28|title=[[127edo]] (L=11, s=3, ~16/11 = 69)}} | ||
{{Harmonics in equal|46|intervals=odd|prec=2|columns=28|title=[[46edo]] (L=4, s=1, 16/11 | {{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|103|intervals=odd|prec=2|columns=28|title=[[103edo]] (L=9, s=2, 16/11 | {{Harmonics in equal|103|intervals=odd|prec=2|columns=28|title=[[103edo]] (L=9, s=2, ~16/11 = 56)}} | ||
{{Harmonics in equal|57|intervals=odd|prec=2|columns=28|title=[[57edo]] (L=5, s=1, 16/11 | {{Harmonics in equal|57|intervals=odd|prec=2|columns=28|title=[[57edo]] (L=5, s=1, ~16/11 = 31)}} | ||
{{Harmonics in equal|68|intervals=odd|prec=2|columns=28|title=[[68edo]] (L=6, s=1, 16/11 | {{Harmonics in equal|68|intervals=odd|prec=2|columns=28|title=[[68edo]] (L=6, s=1, ~16/11 = 37)}} | ||
{{Harmonics in equal|11|intervals=odd|prec=2|columns=28|title=[[11edo]] (L=1, s=0, 16/11 | {{Harmonics in equal|11|intervals=odd|prec=2|columns=28|title=[[11edo]] (L=1, s=0, ~16/11 = 6) — 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]]) | Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:25, 26 April 2025 (UTC) | ||
== Musical Mad Science Musings on Diatonicized Sixth-Tone Sub-Chromaticism(?) == | == Musical Mad Science Musings on Diatonicized Sixth-Tone Sub-Chromaticism(?) == | ||
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Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:20, 4 April 2025 (UTC)<br> | Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:20, 4 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]]) 08:25, 26 April 2025 (UTC) | ||
=== Table of odd harmonics for various EDO values supporting 17L 2s === | === Table of odd harmonics for various EDO values supporting 17L 2s === | ||
This 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]]: | This 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]]: | ||
{{Harmonics in equal|19|intervals=odd|prec=2|columns=28|title=[[19edo]] (L=1, s=1, BrightGen is 10; patent ~13/9 = 10; patent ~62/43 = 10) — 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 ~[[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 ~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 ~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 ~62/43 = 88)}} | {{Harmonics in equal|167|intervals=odd|prec=2|columns=28|title=[[167edo]] (L=9, s=7, BrightGen is 88; patent ~13/9 = 88; 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'' | {{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|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 ~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 ~62/43 = 68)}} | ||
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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]]) 08: | Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:25, 26 April 2025 (UTC) | ||