User talk:TallKite: Difference between revisions

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: So your categories seem to correspond to various regions of the lattice, which makes sense to me. Not sure I understand the positive/negative classification. Personally I loosely classify imperfect intervals as supermajor-major-neutral-minor-subminor, 5ths as superperfect-perfect-halfdim-dim-(subdim) and 4ths as (superaug)-aug-halfaug-perfect-subperfect. So basically 5-limit and deviations from there, very 31-edo-like. One could add submajor, superminor, superperfect 4th, etc. to get it down to 3-limit, very 41-edo-like. If you sharpen the 5th, then in the 3-limit chain of 5ths major sounds like supermajor and minor sounds subminor. If you flatten it, you get submajor and superminor, and if you flatten a lot, neutral. Is that the logic behind positive/negative? If so, that might be a better way to describe it, rather than referring to edos. Also note that to get 11/8 and 16/11, you are presumably flattening the 5th by a quartertone. This makes the major 2nd sound minor, and the major 3rd sound diminished! --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 07:23, 2 August 2021 (UTC)

:: Thank you so much for your response! Yes, the logic is that positive polarity refers to intervals generated by sharp fifths while negative polarity refers to intervals generated by flat fifths. I appreciate all of your input and the connection between color notation and intervallic polarity makes a lot of sense. On the other hand, I still wonder if there is something related to the dissonance, harmonic entropy, or complexity of an interval that could be used to derive its intervallic polarity. (This could allow intervallic polarity to possibly be generalized to chords and/or intervals played with different timbres) --[[User:Userminusone|Userminusone]] ([[User talk:Userminusone|talk]]) 21:11, 2 August 2021 (UTC)

== having torsion vs. being enfactored ==

Hi Kite. Per your request I'm continuing discussion with you on your user page where you are more likely to see it sooner. This is a continuation of the discussion started here: [[Talk:Color notation/Temperament Names]]

I'm glad you agree about torsion. I like the way you explained it, pointing to the name of RTT itself. As a nit-pick, though, I can't agree with the statement that "you can't hear periodicity blocks". That wasn't what I was trying to say. In fact, I was trying to say something like the opposite. My point was that using e.g. {{vector|-8 8 -2}} instead of {{vector|-4 4 -1}} has an audible effect on periodicity blocks but not on temperaments. For a periodicity block, it causes the size of the scale to double, but half of the notes are a redundant copy of the other half, simply offset. Because this is a real audible effect, and I understand there are maybe even some uses for it or cases where it's desirable, it has a name, "torsion". But for a temperament, though, where the comma is by definition tempered out, there is no audible effect, and thus using {{vector|-8 8 -2}} instead of {{vector|-4 4 -1}} is meaningless. It's just pathological enfactoring that is removed when the comma-basis is put into canonical form.

I'm glad you agree about contorsion too. I'm not sure we do, though, because your statement about 12- and 24- ET is not how I would describe it. I would say something more like this: "Calling {{map|24 38 56}} a 'temperament' is misleading because everything it does as a temperament is already done by the simpler {{map|12 19 28}}. In other words, all of its notes are real and audible, but half of them are not used for tempering, or we could say that it is 2-enfactored. Therefore it should not be listed as a strict 'temperament'; perhaps we could call it a 'temperoid' or something like that instead." Does that check out with you?

I found this page of yours this morning which uses the word "torsion" a lot: [[Catalog of rank two temperaments]]. Per my explanation above, would you mind if I renamed uses of "torsion" to "enfactored" there? If you prefer, I could include a footnote on the first one that explains it has historically sometimes been called torsion. Alternatively... why does it matter if they are enfactored? Does anyone need to care? Just defactor them. Maybe it'd be better to just include the canonical form of these temperaments. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 16:56, 30 September 2021 (UTC)

@@ Line 399: / Line 399: @@
 : So your categories seem to correspond to various regions of the lattice, which makes sense to me. Not sure I understand the positive/negative classification. Personally I loosely classify imperfect intervals as supermajor-major-neutral-minor-subminor, 5ths as superperfect-perfect-halfdim-dim-(subdim) and 4ths as (superaug)-aug-halfaug-perfect-subperfect. So basically 5-limit and deviations from there, very 31-edo-like. One could add submajor, superminor, superperfect 4th, etc. to get it down to 3-limit, very 41-edo-like. If you sharpen the 5th, then in the 3-limit chain of 5ths major sounds like supermajor and minor sounds subminor. If you flatten it, you get submajor and superminor, and if you flatten a lot, neutral. Is that the logic behind positive/negative? If so, that might be a better way to describe it, rather than referring to edos. Also note that to get 11/8 and 16/11, you are presumably flattening the 5th by a quartertone. This makes the major 2nd sound minor, and the major 3rd sound diminished! --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 07:23, 2 August 2021 (UTC)
 :: Thank you so much for your response! Yes, the logic is that positive polarity refers to intervals generated by sharp fifths while negative polarity refers to intervals generated by flat fifths. I appreciate all of your input and the connection between color notation and intervallic polarity makes a lot of sense. On the other hand, I still wonder if there is something related to the dissonance, harmonic entropy, or complexity of an interval that could be used to derive its intervallic polarity. (This could allow intervallic polarity to possibly be generalized to chords and/or intervals played with different timbres) --[[User:Userminusone|Userminusone]] ([[User talk:Userminusone|talk]]) 21:11, 2 August 2021 (UTC)
+== having torsion vs. being enfactored ==
+Hi Kite. Per your request I'm continuing discussion with you on your user page where you are more likely to see it sooner. This is a continuation of the discussion started here: [[Talk:Color notation/Temperament Names]]
+I'm glad you agree about torsion. I like the way you explained it, pointing to the name of RTT itself. As a nit-pick, though, I can't agree with the statement that "you can't hear periodicity blocks". That wasn't what I was trying to say. In fact, I was trying to say something like the opposite. My point was that using e.g. {{vector|-8 8 -2}} instead of {{vector|-4 4 -1}} has an audible effect on periodicity blocks but not on temperaments. For a periodicity block, it causes the size of the scale to double, but half of the notes are a redundant copy of the other half, simply offset. Because this is a real audible effect, and I understand there are maybe even some uses for it or cases where it's desirable, it has a name, "torsion". But for a temperament, though, where the comma is by definition tempered out, there is no audible effect, and thus using {{vector|-8 8 -2}} instead of {{vector|-4 4 -1}} is meaningless. It's just pathological enfactoring that is removed when the comma-basis is put into canonical form.
+I'm glad you agree about contorsion too. I'm not sure we do, though, because your statement about 12- and 24- ET is not how I would describe it. I would say something more like this: "Calling {{map|24 38 56}} a 'temperament' is misleading because everything it does as a temperament is already done by the simpler {{map|12 19 28}}. In other words, all of its notes are real and audible, but half of them are not used for tempering, or we could say that it is 2-enfactored. Therefore it should not be listed as a strict 'temperament'; perhaps we could call it a 'temperoid' or something like that instead." Does that check out with you?
+I found this page of yours this morning which uses the word "torsion" a lot: [[Catalog of rank two temperaments]]. Per my explanation above, would you mind if I renamed uses of "torsion" to "enfactored" there? If you prefer, I could include a footnote on the first one that explains it has historically sometimes been called torsion. Alternatively... why does it matter if they are enfactored? Does anyone need to care? Just defactor them. Maybe it'd be better to just include the canonical form of these temperaments. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 16:56, 30 September 2021 (UTC)