Talk:33/32: Difference between revisions

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::: I've voiced this already – "meantone grammar" should be avoided for JI intervals. For example, will you think of 7/4 when I say "augmented sixth" without context? In fact, 7/4 is an augmented sixth in septimal meantone, but not in JI, so "augmented sixth" should be avoided as a name for 7/4. Likewise, "12edo grammar" and others of specific temperaments should also be avoided. That answers why diminished sixth isn't really a name for 3/2.

::: Another meantone-centrist mindset is to think chromatic semitone is smaller than diatonic semitone. A demonstration of this is 28/27 and 21/20 being called septimal chroma, despite that both are diatonic in both size and function.

::: Another meantone-centrist mindset is to think chromatic semitone is smaller than diatonic semitone. A demonstration of this is 28/27 and 21/20 being called septimal chroma, despite that both are diatonic in both size and function. <small><br>(above block was by: FloraC 10:37, 19 September 2020)</small>

:::: What do you mean by "meantone centrist"? The fact is that when you refer to "meantone", I invariably think of those temperaments where the syntonic comma is tempered out... Dare I point out that 16/15 only differs from the apotome by the ''schisma'', and as far as I'm concerned, 16/15 is a diatonic semitone... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 11:22, 19 September 2020 (UTC)

:::: One more thing... the stuff I posted on your user page weighs in on this as well. In the end, I'm coming from the standpoint of how an interval functions relative to the Tonic. While you are right in pointing out that grammar of specific temperaments ought to be avoided, I'm forced to consider the fact that there's a general tendency for intervals to have specific functions depending on their size. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 11:33, 19 September 2020 (UTC)

::::: Sorry, but I meant talking about JI in the grammar of certain temperaments. As for the 16/15-problem, you do know that schisma is the difference between a major third and a dim fourth, right? So it is a dim second. Now adding a dim second to a chromatic semitone (aug unison) yields a diatonic semitone (minor second).

::::: I've read your Function Chart. Indeed, since 33/32 is 385/384 from 36/35 and 896/891 from 28/27, it can have ambiguous qualities. One of the chord progressions I've explored actually requires 245/243 be tempered out and effectively conflate them all. Nonetheless, 33/32 and 11/8 should function coherently. If 33/32 can be a subminor second in some circumstances, 11/8 can be a subdim fifth in the same way. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 12:54, 19 September 2020 (UTC)

:::::: After thinking on this a bit, it's clear to me that while one can reasonably construe 11/8 as a sort of sesqui-diminished fifth, this sort of thing is generally uncommon outside of blues music- plus a hemi-augmented fourth (or paramajor fourth) is not only the simpler notation for 11/8 but the more common. Thus we can keep 11/8 as is in terms of its names. I have also realized that 33/32 most commonly functions as a sort of parachroma- think something akin to a chroma, but involving primes like 7, 11, or 13- and thus, we can completely scratch the idea of referring to 33/32 as any sort of "undecimal subminor second". That said, I can see the article taking note that there are two corresponding paradiatonic intervals. One of these intervals is the real "undecimal subminor second", 512/495, and the other is 8192/8019- which runs a high risk of being conflated with 45/44 (another undecimal parachroma) due to only differing from it by a schisma. I can also see the article mentioning how when 16384/16335 is tempered out, 33/32 is equated with 512/495. Once that's done, we can worry about the 33/28 minor sixth and its octave counterpart 56/33. Does this sound more reasonable to you? (posted and edited by [[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:07, 19 September 2020 (UTC))

::::::: Yeah I've always thought there are some other ratios more suitable for the name "undecimal subminor second". [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 06:23, 20 September 2020 (UTC)

:: Oh, and Flora, no offense taken. Sorry I didn't say so earlier... Perhaps once I get the musical function map finalized, we can look over it and see if you also think it is a good guide for organizing the interval names- you know, such as whether 33/32 is a prime or a second, or even both at once... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:57, 18 September 2020 (UTC)

: So I'm in a program to add FJS names for intervals. I see [[11/10]] and [[20/11]] have inconsistent names. Currently I've added both to make them match, which may also need further discussion. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 07:21, 20 September 2020 (UTC)

== Comma ==

So if this is a formal comma in every major JI notation system, why is x31eq telling me it's so terrible to temper out? Why is it saying 729/704 is better? [[User:Bootmii|Bootmii]] ([[User talk:Bootmii|talk]]) 02:01, 21 April 2022 (UTC)

: Not sure about ''better'' but it's not surprising that the error of {729/704} is lower than {33/32}. 729/704 is much more complex and only a little bit larger than 33/32, so the corresponding temperaments introduce about the same magnitude of displacement in the lattice, but {729/704} has a longer path to evenly distribute it out, which implies less error for each step.

: If you enjoy more of this kind of convo plz consider joining our Dicord or FB group. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 11:58, 21 April 2022 (UTC)

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 ::: I've voiced this already – "meantone grammar" should be avoided for JI intervals. For example, will you think of 7/4 when I say "augmented sixth" without context? In fact, 7/4 is an augmented sixth in septimal meantone, but not in JI, so "augmented sixth" should be avoided as a name for 7/4. Likewise, "12edo grammar" and others of specific temperaments should also be avoided. That answers why diminished sixth isn't really a name for 3/2.
-::: Another meantone-centrist mindset is to think chromatic semitone is smaller than diatonic semitone. A demonstration of this is 28/27 and 21/20 being called septimal chroma, despite that both are diatonic in both size and function.
+::: Another meantone-centrist mindset is to think chromatic semitone is smaller than diatonic semitone. A demonstration of this is 28/27 and 21/20 being called septimal chroma, despite that both are diatonic in both size and function. <small><br>(above block was by: FloraC 10:37, 19 September 2020)</small>
 :::: What do you mean by "meantone centrist"?  The fact is that when you refer to "meantone", I invariably think of those temperaments where the syntonic comma is tempered out...  Dare I point out that 16/15 only differs from the apotome by the ''schisma'', and as far as I'm concerned, 16/15 is a diatonic semitone... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 11:22, 19 September 2020 (UTC)
+:::: One more thing... the stuff I posted on your user page weighs in on this as well.  In the end, I'm coming from the standpoint of how an interval functions relative to the Tonic.  While you are right in pointing out that grammar of specific temperaments ought to be avoided, I'm forced to consider the fact that there's a general tendency for intervals to have specific functions depending on their size. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 11:33, 19 September 2020 (UTC)
+::::: Sorry, but I meant talking about JI in the grammar of certain temperaments. As for the 16/15-problem, you do know that schisma is the difference between a major third and a dim fourth, right? So it is a dim second. Now adding a dim second to a chromatic semitone (aug unison) yields a diatonic semitone (minor second).
+::::: I've read your Function Chart. Indeed, since 33/32 is 385/384 from 36/35 and 896/891 from 28/27, it can have ambiguous qualities. One of the chord progressions I've explored actually requires 245/243 be tempered out and effectively conflate them all. Nonetheless, 33/32 and 11/8 should function coherently. If 33/32 can be a subminor second in some circumstances, 11/8 can be a subdim fifth in the same way. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 12:54, 19 September 2020 (UTC)
+:::::: After thinking on this a bit, it's clear to me that while one can reasonably construe 11/8 as a sort of sesqui-diminished fifth, this sort of thing is generally uncommon outside of blues music- plus a hemi-augmented fourth (or paramajor fourth) is not only the simpler notation for 11/8 but the more common.  Thus we can keep 11/8 as is in terms of its names.  I have also realized that 33/32 most commonly functions as a sort of parachroma- think something akin to a chroma, but involving primes like 7, 11, or 13- and thus, we can completely scratch the idea of referring to 33/32 as any sort of "undecimal subminor second".  That said, I can see the article taking note that there are two corresponding paradiatonic intervals.  One of these intervals is the real "undecimal subminor second", 512/495, and the other is 8192/8019- which runs a high risk of being conflated with 45/44 (another undecimal parachroma) due to only differing from it by a schisma.  I can also see the article mentioning how when 16384/16335 is tempered out, 33/32 is equated with 512/495.  Once that's done, we can worry about the 33/28 minor sixth and its octave counterpart 56/33.  Does this sound more reasonable to you? (posted and edited by [[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:07, 19 September 2020 (UTC))
+::::::: Yeah I've always thought there are some other ratios more suitable for the name "undecimal subminor second". [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 06:23, 20 September 2020 (UTC)
 :: Oh, and Flora, no offense taken.  Sorry I didn't say so earlier...  Perhaps once I get the musical function map finalized, we can look over it and see if you also think it is a good guide for organizing the interval names- you know, such as whether 33/32 is a prime or a second, or even both at once... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:57, 18 September 2020 (UTC)
+: So I'm in a program to add FJS names for intervals. I see [[11/10]] and [[20/11]] have inconsistent names. Currently I've added both to make them match, which may also need further discussion. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 07:21, 20 September 2020 (UTC)
+== Comma ==
+So if this is a formal comma in every major JI notation system, why is x31eq telling me it's so terrible to temper out? Why is it saying 729/704 is better? [[User:Bootmii|Bootmii]] ([[User talk:Bootmii|talk]]) 02:01, 21 April 2022 (UTC)
+: Not sure about ''better'' but it's not surprising that the error of {729/704} is lower than {33/32}. 729/704 is much more complex and only a little bit larger than 33/32, so the corresponding temperaments introduce about the same magnitude of displacement in the lattice, but {729/704} has a longer path to evenly distribute it out, which implies less error for each step.
+: If you enjoy more of this kind of convo plz consider joining our Dicord or FB group. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 11:58, 21 April 2022 (UTC)