Talk:33/32

Name order

I'd like to change the order, making al-Farabi (Alpharabius) quarter tone first in the list. I think the math-derived names are less characteristic, and in addition we should be open to non-western music tradition because as they already tried lots of ideas we "now" have. --Xenwolf (talk) 09:35, 26 July 2020 (UTC)

Sure, despite that it's a long name (My same complaint about "Hunt minor submediant comma"). FloraC (talk) 14:16, 26 July 2020 (UTC)

I've been trying to do something about that. --Xenwolf (talk) 17:33, 26 July 2020 (UTC)

undecimal subminor second

This part was introduced by Aura[1] and reverted by FloraC [2]:

Because of its close proximity to 28/27, form which it differs only by 896/891, one could reasonably argue that 33/32 is the undecimal counterpart to 28/27, particularly if treated as an interval in its own right, in which case it could be analysed as the undecimal subminor second.

I'd like to remember that:
A Revert is felt however often as rude or unfriendly. If one considers that it needs hardly more than one mouse-click, whereas a substantial change costs sometimes very much effort, this becomes understandable.
Maybe the addition proposal should be further discussed? --Xenwolf (talk) 12:24, 18 September 2020 (UTC)

The same arguments seem to apply to 64/33 [3] [4]. --Xenwolf (talk) 12:32, 18 September 2020 (UTC)

Right, one thing that needs to be made clear here is that 33/32 really does serve multiple roles. Flora, you may not know this, but blues music does sometimes see 11/8 passed through on the way to roughly 15/11 as a means of further diminishing the flat fifth, before then resolving to 4/3. I know this because I've met a composer who's familiar with this aspect of blues music. When I introduced the idea of 11/8 as a fourth to him, he said he had never thought of resolving it up to 3/2 like I usually do. --Aura (talk) 14:13, 18 September 2020 (UTC)

Effectively, this shrinking of the flat fifth results in a just F-Demisharp being higher in pitch than a just G-Sesquiflat. It can be compared to the similar situation in which the Pythagorean Chromatic Semitone is larger than the Pythagorean Diatonic Semitone, with the result that C-Sharp is higher than D-Flat. (comment posted and modified by --Aura (talk) 14:36, 18 September 2020 (UTC))

No offense intended. Indeed I think it's fine to have different views present on the page, but you need to be coherent. To treat 33/32 a type of minor second, you have to further construct that 11/8 is a type of diminished fifth, and the "undecimal comma" in that system would be 8192/8019. So in total four pages need to be changed (33/32, 64/33, 11/8 and 16/11) and one need to be created (8192/8019). FloraC (talk) 15:15, 18 September 2020 (UTC)

For starters, if 33/32 is a type of second, it would be a subminor second, not a minor second. I should also point out 225/128, which serves as an augmented sixth in just Neapolitan Scales due to 256/255 serving as a diminished third. The common factor in all this? Both intervals fall in ranges where intervals are likely to see multiple functions on a fairly regular basis. In contrast, 11/8 more commonly functions as a fourth than as a fifth- in fact, I call it a "paramajor fourth" in a nod to both it's paradiatonic function and the term for that interval found on this page. You are right in pointing out the need for coherency- but does that mean we should then call 3/2 the "diminished sixth"? I mean, such a view is possible when one considers 12edo... On this front, I'm in the process of making a newer version of a guide to the diatonic and paradiatonic functions of various intervals. I showed Xenwolf the preliminary version of this map here. --Aura (talk) 16:04, 18 September 2020 (UTC)

Just a few comments. 1) I remember well the astonishing fact (when discovering "just" intonation) that the tones the de-tuned 12edo piano can be adjusted in different directions (meantone vs. pythagorean). 2) the categorization of interval pages as Third, Forth and so on, was meant only to get an idea of the size and has nothing to do with musical functions (maybe it should be replaced by cent ranges or something even better). 3) I'm often inconsistent in my edits to leave space for feedback (positive or negative) making the wiki a good place for discussion and participation. --Xenwolf (talk) 16:16, 18 September 2020 (UTC)

I understand being inconsistent in edits to leave space for feedback and you are right in doing so. However, it is also true that the listings as Third, Forth and so on do tend to reflect on their musical function, at least as far as I can see in light of my background as a composer. (comment posted and modified by --Aura (talk) 16:22, 18 September 2020 (UTC))

For the record, I can see keeping the listings of Prime, Second, Third and Forth and such as size listings, since that is how many microtonal composers from a background like mine tend to measure interval size. However, in the end, one of my main concerns in naming intervals- and even in coming up with the musical function map- is making things more accessible for microtonal composers with my type of background, while bridging to strikingly new areas of tonality such as treble-down tonality. Yes, this means coming up with new terminology in some respects. --Aura (talk) 16:39, 18 September 2020 (UTC)

As for how this should work on the wiki itself, I propose that if something can be classified as both a fourth and a fifth- as an example- it should be put under both "fourth" and "fifth" categories- specifically under a special subcategory for intervals with such an ambiguous nature... --Aura (talk) 16:42, 18 September 2020 (UTC)

Of course, I should point out that despite my proposals, I can't really be an admin of any sort, so you'll have to evaluate my proposal as you see fit. --Aura (talk) 16:45, 18 September 2020 (UTC)

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.
(above block was by: FloraC 10:37, 19 September 2020)

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... --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. --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. 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 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". 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... --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. 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? 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. FloraC (talk) 11:58, 21 April 2022 (UTC)