User talk:Lhearne: Difference between revisions

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::::::::::::::::::: diaschisma-narrow min 2, classic minor 3, diaschisma-Wide Major 3, Perfect 5, diaschisma-narrow minor 6, classic minor 6, classic Major 7, diaschisma-Wide Major 7, Perfect 8.

::::::::::::::::::: the diaschismic intervals are like 5-limit super and sub intervals, and when 225/224 is tempered out they are equivalent, but we need it because 225/224 is not always tempered out, and these intervals are relatively simple. --[[User:Lhearne|Lhearne]] ([[User talk:Lhearne|talk]]) 03:40, 11 February 2021 (UTC)

:::::::::::::::::::: For the record, while we do need to support 2.5 and 2.7, and even 2.13 in some ways, I do have questions as to what sorts of simple commas can be used for maintaining well-ordered naming systems for these, as I distinctly remember reading this on the [[Extended-diatonic interval names]] page:

::::::::::::::::::::"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. Basically, I'm thinking that in our extension system, we need to deliberately look for primes that are really good at conserving diatonic interval arithmetic by means of 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- 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/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)

@@ Line 144: / Line 144: @@
 ::::::::::::::::::: diaschisma-narrow min 2, classic minor 3, diaschisma-Wide Major 3, Perfect 5, diaschisma-narrow minor 6, classic minor 6, classic Major 7, diaschisma-Wide Major 7, Perfect 8.
 ::::::::::::::::::: the diaschismic intervals are like 5-limit super and sub intervals, and when 225/224 is tempered out they are equivalent, but we need it because 225/224 is not always tempered out, and these intervals are relatively simple. --[[User:Lhearne|Lhearne]] ([[User talk:Lhearne|talk]]) 03:40, 11 February 2021 (UTC)
+:::::::::::::::::::: For the record, while we do need to support 2.5 and 2.7, and even 2.13 in some ways, I do have questions as to what sorts of simple commas can be used for maintaining well-ordered naming systems for these, as I distinctly remember reading this on the [[Extended-diatonic interval names]] page:
+::::::::::::::::::::"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.  Basically, I'm thinking that in our extension system, we need to deliberately look for primes that are really good at conserving diatonic interval arithmetic by means of 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- 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/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)