Xenharmonic Wiki:Cross-platform dialogue: Difference between revisions

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:: I also recognise/am aware that weighting in the way I suggested would lead to less mathematically elegant properties, if I recall discussions on the relationship between TE, complexity and rank correctly. I just wish to offer an alternate perspective to support the structure of my argument. --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 22:51, 15 March 2024 (UTC)

::: (Although, the goal of optimization should be optimizing the tuning we hear not optimizing mathematical elegance. Although it's nice for them to coincide as much as possible.) --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 23:09, 15 March 2024 (UTC)

:::: I can give you an example right now which is regarded by some as suboptimal: {128/125} (augmented) in CTE tuning is untempered, with pure 2, pure 3, and a 400-cent 5/4. It will have 6/5 at 302 cents whereas KE will have it more in tune at the expense of the purity of the 3. The logic of CTE is that since harmonic 3 isn't involved in the comma to be tempered out (128/125), of course it only makes sense that it should be pure, just as in 5-limit JI – and furthermore, any new prime added to this temperament should be pure. But POTE/KE also wanna take account of the sharp tendency induced by the sharp tuning of the 5. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 04:37, 16 March 2024 (UTC)

::::: Hmm... maybe it's a bad example for me because I think tempering 128/125 is unfeasible (maybe [[27edo]] does it well but that uses [[delta-rational chord]]s to justify itself so it's not really the thing temperaments were designed for because the target isn't a fixed point) but I will follow the spirit of the logic of the example. The issue seems to be rather that CTE isn't designed to handle the case where extra generators are independent of the commas tempered if you are valuing p/q over pq (because CTE choosing pure generators makes perfect sense if you want to weight them equally and in this sense it's the logical constraining of [[TE]] which assumes the same). But POTE certainly doesn't seem to be the right fix to prioritising p/q over pq. Rather it seems like (at least in this case) what's wanted is a metric that respects tendency (a desire I've voiced before actually). For example it's noted [[Constrained_tuning#CTE_tuning_vs_CTWE_tuning|here]] that "POTE tuning works as a quick approximation to CTWE" (AKA KE tuning), so maybe CTWE / KE tuning is desired? --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 18:23, 16 March 2024 (UTC)

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=== Mike's Response to All This ===

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 :: I also recognise/am aware that weighting in the way I suggested would lead to less mathematically elegant properties, if I recall discussions on the relationship between TE, complexity and rank correctly. I just wish to offer an alternate perspective to support the structure of my argument. --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 22:51, 15 March 2024 (UTC)
 ::: (Although, the goal of optimization should be optimizing the tuning we hear not optimizing mathematical elegance. Although it's nice for them to coincide as much as possible.) --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 23:09, 15 March 2024 (UTC)
 :::: I can give you an example right now which is regarded by some as suboptimal: {128/125} (augmented) in CTE tuning is untempered, with pure 2, pure 3, and a 400-cent 5/4. It will have 6/5 at 302 cents whereas KE will have it more in tune at the expense of the purity of the 3. The logic of CTE is that since harmonic 3 isn't involved in the comma to be tempered out (128/125), of course it only makes sense that it should be pure, just as in 5-limit JI – and furthermore, any new prime added to this temperament should be pure. But POTE/KE also wanna take account of the sharp tendency induced by the sharp tuning of the 5. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 04:37, 16 March 2024 (UTC)
+::::: Hmm... maybe it's a bad example for me because I think tempering 128/125 is unfeasible (maybe [[27edo]] does it well but that uses [[delta-rational chord]]s to justify itself so it's not really the thing temperaments were designed for because the target isn't a fixed point) but I will follow the spirit of the logic of the example. The issue seems to be rather that CTE isn't designed to handle the case where extra generators are independent of the commas tempered if you are valuing p/q over pq (because CTE choosing pure generators makes perfect sense if you want to weight them equally and in this sense it's the logical constraining of [[TE]] which assumes the same). But POTE certainly doesn't seem to be the right fix to prioritising p/q over pq. Rather it seems like (at least in this case) what's wanted is a metric that respects tendency (a desire I've voiced before actually). For example it's noted [[Constrained_tuning#CTE_tuning_vs_CTWE_tuning|here]] that "POTE tuning works as a quick approximation to CTWE" (AKA KE tuning), so maybe CTWE / KE tuning is desired? --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 18:23, 16 March 2024 (UTC)
 [[Category:Xenharmonic Wiki]]
 === Mike's Response to All This ===