User talk:Lhearne: Difference between revisions

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::::::::::::::::::::"On the other hand, any scheme in which the major third is defined instead as an approximation to 5/4 does not preserve interval arithmetic in non-meantone systems, but may conserve existing associations between interval names and sound / size."

:::::::::::::::::::: I have my suspicions that something similar is ultimately true of both the 7-prime and the 13-prime. In fact, I'm fairly certain about the 7-prime having an even worse issue than the 5-prime since right off the bat it's rather hard to pin down the 7-prime's paradiatonic function as being consistently either a subminor seventh or an augmented sixth, meaning that 7/4 is perhaps best classified as being a type of "sinth" or "sixth-seventh". This in turn means that adding up the intervals of the prime chain properly with respect to the diatonic system is bound to be incredibly difficult.

:::::::::::::::::::: I have my suspicions that something similar is ultimately true of both the 7-prime and the 13-prime. In fact, I'm fairly certain about the 7-prime having an even worse issue than the 5-prime since right off the bat it's rather hard to pin down the 7-prime's paradiatonic function as being consistently either a subminor seventh or an augmented sixth, meaning that 7/4 is perhaps best classified as being a type of "sinth" or "sixth-seventh". This in turn means that adding up the intervals of the prime chain properly with respect to the diatonic system is bound to be incredibly difficult. On a related note, I must also point out that the concept of the "firth" interval is also bound to be incredibly useful as it can be used to mark enharmonic transitions like the one that occurs just about every time an interval chain crosses the 600-cent threshhold.

:::::::::::::::::::: Basically, I'm thinking that when it comes to which primes we support in our extension system, we need to deliberately look for primes that are really good at both maintaining well-ordered naming systems and conserving diatonic interval arithmetic by means of having small, relatively simple deviations from Pythagorean intervals even as they form chains of their own base interval, and the 11-prime so far seems to be the first prime after the famous 3-prime to actually have this property once we account for 33/32 having its own distinct identity as a musical interval- hence why I call both the 3-prime and the 11-prime "navigational primes". I'm sure there are other primes that do this, but something tells me that not every prime we encounter has this same exact property.

:::::::::::::::::::: Regarding your reservations concerning "Major" and "Minor" when it comes to Fourths and Fifths, I do share some of those same reservations, while at the same time, I, like the other people you mentioned, don't really think of of 11/8 as a neutral interval at all, hence my term "paramajor fourth" for 11/8. Given this, perhaps we should then denote the Paramajor and Paraminor intervals by using "L" for "Large" and "Little", which are more or less synonymous with "Major" and "Minor" in some ways. This would enable us to create more of a clear distinction between how Major and Minor intervals differ by the Apotome, and how Paramajor and Paraminor intervals differ by the Parapotome. Is this better? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 04:54, 11 February 2021 (UTC)

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 ::::::::::::::::::::"On the other hand, any scheme in which the major third is defined instead as an approximation to 5/4 does not preserve interval arithmetic in non-meantone systems, but may conserve existing associations between interval names and sound / size."
-:::::::::::::::::::: I have my suspicions that something similar is ultimately true of both the 7-prime and the 13-prime.  In fact, I'm fairly certain about the 7-prime having an even worse issue than the 5-prime since right off the bat it's rather hard to pin down the 7-prime's paradiatonic function as being consistently either a subminor seventh or an augmented sixth, meaning that 7/4 is perhaps best classified as being a type of "sinth" or "sixth-seventh".  This in turn means that adding up the intervals of the prime chain properly with respect to the diatonic system is bound to be incredibly difficult.
+:::::::::::::::::::: I have my suspicions that something similar is ultimately true of both the 7-prime and the 13-prime.  In fact, I'm fairly certain about the 7-prime having an even worse issue than the 5-prime since right off the bat it's rather hard to pin down the 7-prime's paradiatonic function as being consistently either a subminor seventh or an augmented sixth, meaning that 7/4 is perhaps best classified as being a type of "sinth" or "sixth-seventh".  This in turn means that adding up the intervals of the prime chain properly with respect to the diatonic system is bound to be incredibly difficult.  On a related note, I must also point out that the concept of the "firth" interval is also bound to be incredibly useful as it can be used to mark enharmonic transitions like the one that occurs just about every time an interval chain crosses the 600-cent threshhold.
 :::::::::::::::::::: Basically, I'm thinking that when it comes to which primes we support in our extension system, we need to deliberately look for primes that are really good at both maintaining well-ordered naming systems and conserving diatonic interval arithmetic by means of having small, relatively simple deviations from Pythagorean intervals even as they form chains of their own base interval, and the 11-prime so far seems to be the first prime after the famous 3-prime to actually have this property once we account for 33/32 having its own distinct identity as a musical interval- hence why I call both the 3-prime and the 11-prime "navigational primes".  I'm sure there are other primes that do this, but something tells me that not every prime we encounter has this same exact property.
 :::::::::::::::::::: Regarding your reservations concerning "Major" and "Minor" when it comes to Fourths and Fifths, I do share some of those same reservations, while at the same time, I, like the other people you mentioned, don't really think of of 11/8 as a neutral interval at all, hence my term "paramajor fourth" for 11/8.  Given this, perhaps we should then denote the Paramajor and Paraminor intervals by using "L" for "Large" and "Little", which are more or less synonymous with "Major" and "Minor" in some ways.  This would enable us to create more of a clear distinction between how Major and Minor intervals differ by the Apotome, and how Paramajor and Paraminor intervals differ by the Parapotome.  Is this better? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 04:54, 11 February 2021 (UTC)