Talk:7/4: Difference between revisions

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::: I read ''half a step'' as 50% of 1\edo? Concerning the prime harmonics (their octave complements share the exact same table), is it actually that indisputable? I know the concept of [[consistency]] but I find it questionable already in cases like [[7/5]]: this interval can probably be used independently of the fact that it can be derived from [[7/4]] and [[5/4]]; another example is the great approximation of [[11/7]] in [[23edo]]. Whatever, would you say that tables would useful to you if there was this column with the amount of repetitions within the limit you described? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:53, 25 October 2020 (UTC)

:::: You are correct in your reading of half a step as 1\edo. While it is true that 7/5 ~~can be used independently~~ can be used independently of the fact that it can be derived from 7/4 and 5/4, consistency is my main concern with these intervals, as wherever the p-limits from which intervals like 7/5 are derived are poorly represented and or subject to contortion in any given EDO, ~~it seems to either call~~ the consistency of the derived intervals into question and or ~~open up~~ multiple possible representations in a given EDO. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:14, 25 October 2020 (UTC)

:::: You are correct in your reading of half a step as 50% of 1\edo. While it is true that 7/5 can be used independently of the fact that it can be derived from 7/4 and 5/4, consistency is my main concern with these intervals. In my own work, it seems that wherever the p-limits from which intervals like 7/5 are derived are poorly represented and or subject to contortion in any given EDO, the consistency of the derived intervals is called the into question and or multiple possible representations in a given EDO occur. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:14, 25 October 2020 (UTC)

:::: My end goal with including a table containing the number of times the tempered p-limit interval in question can be stacked without the absolute error between the tempered stack and its just counterpart exceeding 3.5 cents (or half a step- whichever is smaller), has more to do with mapping out the usable portions of the harmonic lattice for any given EDO. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:19, 25 October 2020 (UTC)

::::: I have the impression that we still have little experience in generalizing the multiplication of intervals, so the combinability of fifths is certainly undisputed, but on the other hand it is strongly oriented towards functional harmony since the Baroque. I don't know any other interval that could perform such an axis function, although I can imagine that one could try it with the third. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 22:45, 25 October 2020 (UTC)

:::::: Remember what I said about the 11-limit being mathematically derivable as an excellent representation for quartertones in terms of ratio simplicity? One of the implications of this excellent representation- particualarly in light of the way it plays out- is that the paramajor fourth (that is, 11/8) can- and indeed it does- perform an axis function where quartertones are concerned. I've since checked the 11-limit's representation of quartertones against that of the other rational intervals called "quarter tones" [https://en.wikipedia.org/wiki/List_of_pitch_intervals on Wikipedia's list of pitch intervals] and found the 11-limit's 33/32 to be better than any of them in terms of ratio simplicity. (multiple comments combined and edited by --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:02, 25 October 2020 (UTC))

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 ::: I read ''half a step'' as 50% of 1\edo? Concerning the prime harmonics (their octave complements share the exact same table), is it actually that indisputable? I know the concept of [[consistency]] but I find it questionable already in cases like [[7/5]]: this interval can probably be used independently of the fact that it can be derived from [[7/4]] and [[5/4]]; another example is the great approximation of [[11/7]] in [[23edo]]. Whatever, would you say that tables would useful to you if there was this column with the amount of repetitions within the limit you described? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:53, 25 October 2020 (UTC)
-:::: You are correct in your reading of half a step as 1\edo.  While it is true that 7/5 can be used independently can be used independently of the fact that it can be derived from 7/4 and 5/4, consistency is my main concern with these intervals, as wherever the p-limits from which intervals like 7/5 are derived are poorly represented and or subject to contortion in any given EDO, it seems to either call the consistency of the derived intervals into question and or open up multiple possible representations in a given EDO. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:14, 25 October 2020 (UTC)
+:::: You are correct in your reading of half a step as 50% of 1\edo.  While it is true that 7/5 can be used independently of the fact that it can be derived from 7/4 and 5/4, consistency is my main concern with these intervals.  In my own work, it seems that wherever the p-limits from which intervals like 7/5 are derived are poorly represented and or subject to contortion in any given EDO, the consistency of the derived intervals is called the into question and or multiple possible representations in a given EDO occur. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:14, 25 October 2020 (UTC)
+:::: My end goal with including a table containing the number of times the tempered p-limit interval in question can be stacked without the absolute error between the tempered stack and its just counterpart exceeding 3.5 cents (or half a step- whichever is smaller), has more to do with mapping out the usable portions of the harmonic lattice for any given EDO. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:19, 25 October 2020 (UTC)
+::::: I have the impression that we still have little experience in generalizing the multiplication of intervals, so the combinability of fifths is certainly undisputed, but on the other hand it is strongly oriented towards functional harmony since the Baroque. I don't know any other interval that could perform such an axis function, although I can imagine that one could try it with the third. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 22:45, 25 October 2020 (UTC)
+:::::: Remember what I said about the 11-limit being mathematically derivable as an excellent representation for quartertones in terms of ratio simplicity?  One of the implications of this excellent representation- particualarly in light of the way it plays out- is that the paramajor fourth (that is, 11/8) can- and indeed it does- perform an axis function where quartertones are concerned.  I've since checked the 11-limit's representation of quartertones against that of the other rational intervals called "quarter tones" [https://en.wikipedia.org/wiki/List_of_pitch_intervals on Wikipedia's list of pitch intervals] and found the 11-limit's 33/32 to be better than any of them in terms of ratio simplicity. (multiple comments combined and edited by --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:02, 25 October 2020 (UTC))