Talk:Kite's thoughts on fifthspans: Difference between revisions
→Fifthward and fourthward distances for multi-ring EDOs?: Add example of how to make Fourthspan work with fractional Fifthspans |
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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:: Based upon the [[Ploidacot]] explanation, it shouldn't be a surprise that a fourthspan wouldn't work the same way as a negative fifthspan, since to get a fourthspan from a negative fifthspan, you need to add an equave, which might not be dividible by the same number as the fifthspan. In 24EDO you can divide both by 2, but in 34EDO, you can divide the fifth (20\34) by 4 (as part of 34EDO being tetracot), but you can't divide the fourth (14\34) by 4. So you would just have to accept that fifthspan and fourthspan won't have a simple relationship to each other. | :: Based upon the [[Ploidacot]] explanation, it shouldn't be a surprise that a fourthspan wouldn't work the same way as a negative fifthspan, since to get a fourthspan from a negative fifthspan, you need to add an equave, which might not be dividible by the same number as the fifthspan. In 24EDO you can divide both by 2, but in 34EDO, you can divide the fifth (20\34) by 4 (as part of 34EDO being tetracot), but you can't divide the fourth (14\34) by 4. So you would just have to accept that fifthspan and fourthspan won't have a simple relationship to each other. | ||
:: [[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. | :: 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) | :: [[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) | |||