Talk:Chords of pajara: Difference between revisions

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::: How exactly should the types of chords be prioritized? I propose jubilismic > archytas > mothwellsmic > ptolemismic > valinorsmic > marvel > pentacircle, and jubilismic11 > ares > apollo > minerva. --[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 20:06, 16 February 2026 (UTC)

::: Changed my mind; maybe it should be marvel > pentacircle > valinorsmic > ptolemismic > archytas > jubilismic and apollo > minerva > ares > jubilismic11. --[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 23:34, 17 February 2026 (UTC)

:::: So the more accurate ones come first? I suppose this will get rid of jubilismic and ares entirely. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 09:28, 18 February 2026 (UTC)

::::: I was just trying to make it fit; apollo is actually higher damage than minerva, even though 100/99 is smaller than 99/98, but it wouldn't be obvious to the reader. But I guess having the less accurate ones come first makes sense. As for pentacircle vs marvel, it's right on the edge. Calculating TOP damage from (size in cents)/log_2(num * denom), marvel has a TOP damage of 0.49366{{c}}, while pentacircle has a TOP damage of 0.49412{{c}}. The ordering might be different by metrics like minimum WE/CWE error. --[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 22:16, 18 February 2026 (UTC)

:::::: Nevermind, it seems like no chords can be tempered by both marvel and pentacircle, so it doesn't really matter.--[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 05:53, 20 February 2026 (UTC)

:::: I think the chord types should also be prioritized by prime limits, so jubilismic > archytas > marvel > mothwellsmic > ptolemismic > pentacircle. The triad from stacking two 5/4's is more recognizable as a marvel triad than a valinorsmic one. The nullity-2 ones should still be jubilismic11 > ares > apollo > minerva.--[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 06:59, 25 February 2026 (UTC)

::::: This one sounds most agreeable! —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 07:09, 25 February 2026 (UTC)

: There are chords essentially tempered by rank-2 [[miracle]] in the 11-limit (see [[miracle chords]]). I've been wondering for a while, are there any chords essentially tempered by a rank-1 temperament? Even further, are there chords which could by considered dyadically consonant by [[fudging]], but tempering out all the corresponding commas is impossible without mapping everything to the unison?--[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 01:38, 1 February 2026 (UTC)

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 ::: How exactly should the types of chords be prioritized? I propose jubilismic > archytas > mothwellsmic > ptolemismic > valinorsmic > marvel > pentacircle, and jubilismic11 > ares > apollo > minerva. --[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 20:06, 16 February 2026 (UTC)
+::: Changed my mind; maybe it should be marvel > pentacircle > valinorsmic > ptolemismic > archytas > jubilismic and apollo > minerva > ares > jubilismic11. --[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 23:34, 17 February 2026 (UTC)
+:::: So the more accurate ones come first? I suppose this will get rid of jubilismic and ares entirely. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 09:28, 18 February 2026 (UTC)
+::::: I was just trying to make it fit; apollo is actually higher damage than minerva, even though 100/99 is smaller than 99/98, but it wouldn't be obvious to the reader. But I guess having the less accurate ones come first makes sense. As for pentacircle vs marvel, it's right on the edge. Calculating TOP damage from (size in cents)/log_2(num * denom), marvel has a TOP damage of 0.49366{{c}}, while pentacircle has a TOP damage of 0.49412{{c}}. The ordering might be different by metrics like minimum WE/CWE error. --[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 22:16, 18 February 2026 (UTC)
+:::::: Nevermind, it seems like no chords can be tempered by both marvel and pentacircle, so it doesn't really matter.--[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 05:53, 20 February 2026 (UTC)
+:::: I think the chord types should also be prioritized by prime limits, so jubilismic > archytas > marvel > mothwellsmic > ptolemismic > pentacircle. The triad from stacking two 5/4's is more recognizable as a marvel triad than a valinorsmic one. The nullity-2 ones should still be jubilismic11 > ares > apollo > minerva.--[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 06:59, 25 February 2026 (UTC)
+::::: This one sounds most agreeable! —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 07:09, 25 February 2026 (UTC)
 : There are chords essentially tempered by rank-2 [[miracle]] in the 11-limit (see [[miracle chords]]). I've been wondering for a while, are there any chords essentially tempered by a rank-1 temperament? Even further, are there chords which could by considered dyadically consonant by [[fudging]], but tempering out all the corresponding commas is impossible without mapping everything to the unison?--[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 01:38, 1 February 2026 (UTC)