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)

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::::: 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 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 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? --[[User:Aura|Aura]] ~~(posted and edited by~~ ([[User talk:Aura|talk]]) 19:07, 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)

@@ Line 37: / Line 37: @@
 ::: 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)
@@ Line 47: / Line 47: @@
 ::::: 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 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 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? --[[User:Aura|Aura]] (posted and edited by ([[User talk:Aura|talk]]) 19:07, 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)