Talk:Kite's thoughts on fifthspans: Difference between revisions
m TallKite moved page Talk:Fifthspan to Talk:Kite's thoughts on fifthspans: Editor VectorGraphics has repeatedly edited pages I've written about my own research and inserted misinformation. On discord he is openly hostile to me. This move is necessary to avoid a toxic work environment for me. |
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:: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 12:48, 8 July 2024 (UTC) | :: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 12:48, 8 July 2024 (UTC) | ||
:: For instance, Mothra would be tricot, with the fifthspan to 7/4 being -1/3, and it would also be beta tri''quat'' (taking that for the moment as the fourths counterpart to tricot), with a double-octave-compounded-fourthspan to 7/4 being +1/3. Either way works the same (even on a fraction-named meantone such as quarter-comma meantone or even extended-limit Pythagorean tuning) as long as you don't try to apply it to an EDO having a fifth not divisible by 3 and demand that it produce an integer number of steps. | |||
:: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 06:12, 1 August 2024 (UTC) | |||
:: Actually, thinking about combining this with the [[Ploidacot]]/Ploidaquat concept reveals that it works even better than I thought. To take the 24EDO example, 24EDO is (haploid) dicot (with no boost prefix), so dividing the fifth (14\24) in half doesn't need any additional ploidacot/ploidaquat actions, and +3.5 fifths = +3.5 * 14 = 49\24 which octave-reduces to 1\24, as advertised; and -8.5 fifths = -8.5 * 14 = -119\24 which octave-reduces to 1\24, as advertised. But since 24EDO is dicot, it is thereby also (haploid) alpha-diquat, which means that you have to add a ploid (24) to the fourth (10\24) before performing the next steps, so the alpha-boosted fourth is 34 increments. Then we do the multiplication by the fractional number, and -3.5 alpha-boosted fourths = -3.5 * 34 = -119\17 which octave-reduces to 1\24, just like +3.5 fifths; and +8.5 alpha-boosted fourths = 289\24 which octave-reduces to 1\24, just like the -8.5 fifths. | |||
:: This works moving along the Dicot temperament, which is (haploid) dicot and (haploid) alpha-diquat and also includes the patent val of 17EDO, where the same thing works for +3.5 fifths (+3.5 * 10\17 = 35\17 octave which reduces to 1\17) and -3.5 alpha-boosted fourths (-3.5 * 24\17 = -84\17 which octave-reduces to 1\17). Of course, since 17EDO is odd, the progression in the reverse direction will come out to a whole number: -5.0 * 10\17 = -50\17 which octave-reduces to 1\17; and +5.0 * 24\17 (remember the alpha-boost to the fourth) = 120\17 which octave-reduces to 1\17. | |||
:: The Mothra example I gave above works the same way, but Mothra is tricot and beta-triquat, so you have to double-boost the fourths before performing further steps. And the Tetracot example that I fumbled above before I had this whole thing worked out functions the same way, but Tetracot is tetracot and gamma-tetraquat, so you have to triple-boost the fourths before performing further steps. This even works for a polyploid tempermant like Blackwood, which would be tricot and beta-triquat if not for the rule that explicitly declares it to be acot for having the fifth constituted of a whole number of ploids. | |||
:: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 06:08, 3 August 2024 (UTC) | |||
::: Edit for above: Forgot to multiply by ploidy for Blackwood, so if you bypass the rule that explicitly declares it to be acot, it would be tricot and iota-triquat. [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 18:46, 1 September 2024 (UTC) | |||