Xenharmonic Wiki:Cross-platform dialogue: Difference between revisions
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:: I appreciate your in-depth response a lot. Sorry if I came across as hostile, it was not my intention. The thing about POTE being the tuning with a unique property is interesting; I hadn't heard it before. If I may offer my own thoughts: I agree that likely the reason POTE seems to be a good approximation is to do with [[delta-rational chord]]s (which from what I understand is the appropriate and nontrivial generalisation of isoharmonic chords, in that delta-rational chords sound like JI without being JI while isoharmonic chords are JI tunings of delta-rational chords); in my mind though it would make more sense to devise a different measure entirely if you wanted to optimise that sort of thing like how you noted that one could devise measures of triadic/tetradic/etc. chords. I have a hypothesis to do with the divide between POTE and CTE, or I think more aptly, between weighting p/q over pq and weighting them the same. It seems to me that the lower accuracy a temperament is, the more we prioritise p/q over pq, so that CTE becomes increasingly worse, while the higher accuracy a temperament is, the more it makes sense to also want to model pq with p/q; maybe this caused an impression here that CTE made more sense. For example, I myself wouldn't usually look at temperaments like tempering [[256/243]] (Blackwood) or [[128/125]] (Augmented) because if I wanted something like that, I would instead investigate a DR (Delta-Rational) chord phenomenon rather than using CTE. Kind regards, --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 20:51, 17 March 2024 (UTC) | :: I appreciate your in-depth response a lot. Sorry if I came across as hostile, it was not my intention. The thing about POTE being the tuning with a unique property is interesting; I hadn't heard it before. If I may offer my own thoughts: I agree that likely the reason POTE seems to be a good approximation is to do with [[delta-rational chord]]s (which from what I understand is the appropriate and nontrivial generalisation of isoharmonic chords, in that delta-rational chords sound like JI without being JI while isoharmonic chords are JI tunings of delta-rational chords); in my mind though it would make more sense to devise a different measure entirely if you wanted to optimise that sort of thing like how you noted that one could devise measures of triadic/tetradic/etc. chords. I have a hypothesis to do with the divide between POTE and CTE, or I think more aptly, between weighting p/q over pq and weighting them the same. It seems to me that the lower accuracy a temperament is, the more we prioritise p/q over pq, so that CTE becomes increasingly worse, while the higher accuracy a temperament is, the more it makes sense to also want to model pq with p/q; maybe this caused an impression here that CTE made more sense. For example, I myself wouldn't usually look at temperaments like tempering [[256/243]] (Blackwood) or [[128/125]] (Augmented) because if I wanted something like that, I would instead investigate a DR (Delta-Rational) chord phenomenon rather than using CTE. Kind regards, --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 20:51, 17 March 2024 (UTC) | ||
[[Category:Xenharmonic Wiki]] | [[Category:Xenharmonic Wiki]] | ||
:: Also, if you haven't seen it already, you may want to look at [[Talk:POTE_tuning#Justification]] - it seems relevant to this discussion, as [[User:Sintel]] comments there, although I'm not sure if the comments are outdated. --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 21:19, 17 March 2024 (UTC) | |||