User talk:SAKryukov: Difference between revisions

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::::: Sorry, I did not understand the answer, could you clarify? And what is "latter article"?No matter, I don't mind the use of "just intonation", only afraid of the situations when a reader understands it in some more concrete sense. I don't insist that my terms are better to coin them.

:::::: It would help if you followed the links in my last comment- I was telling you to follow the links to help you get a sense of what I meant, as the articles explained this better than I can. The term "latter" means the second of two, so the phrase "latter article" means "the second of two articles". --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 17:43, 27 November 2020 (UTC)

:::::Lastly, I was thinking about those commas and have some consideration. Roughly, we need to understand that in a rational-number interval i=A/B makes deep physical sense only if A and B are small enough. This is related to the nature of aural perception of any organisms or even devices. If the numbers became 3-digit numbers or more, the accuracy of the rational number doesn't play its role. Let's see: there are two physical traits: 1) the sense of harmonics in the interval with small A and B; it is based that two oscillators in the ear come in resonance, but not necessarily on their fundamental frequencies, but some low-order harmonics, if harmonics are high, the effect is unnoticeable, 2) the perception of logarithmic distances between frequencies as equal. Now, #1 and #2 are in fundamental contradiction: 1) if all intervals are rational numbers, their system is never ever equidistant, so the equivalence of tonalities is impossible, 2) if intervals are equidistant, the ratio values are never rational, so we won't feel the perfect sense of harmony. So, the question is: with this trade-off, where is the reasonable choice? The common-practice system has chosen the compromise and gave more preference to #2 than before. 12-EDO gives amazingly good compromise, but we pretty easily can perceive the deviation from harmony. At the same time, our trait #1 is more accurate than #2. What is my conclusion? It can be a bit complicated in practice, but this is nothing but some intermediate idea. First, everything depends on the composition. Where we value the sense of equidistant notes? I don't think it is absolutely important in most cases. That said, when your calculations lead you to big natural numbers, A/B, you can easily give up having a rational number for a certain degree and use a mixture of rational numbers and real numbers. I do understand how weird it can be, this is just a vague idea. Another vague idea is that you might extend some tonal system but then classify the resulting tones and their functional roles into two classes: "degrees" and "non-degrees". A "non-degree" tone can have a limited role, it cannot be, for example, used as a root of a chord, and so on. I do understand that this is very weird and not elegant, this is just for discussion. The main point is: the contradictions and trade-offs in the tonal systems are unavoidable in principle, by the very nature of thins, sorry for possible truism. — [[User:SAKryukov|SA]] 17:05, 27 November 2020 (UTC)

:::::: Given the trade off, I'd say that the reasonable choice is to try and approximate the rational values- especially 1-digit and 2-digit values- within a value of less than 3.5 cents wherever possible, as this is the kind of size difference where people won't really notice the deviation from harmony. As it happens, 159edo and a number of other EDOs in that area do a pretty good job with this from what I see. Yes, there are flaws, such as 159edo's inconsistent treatment of the 19 prime, but since 159edo represents the primes 5, 7 and 13 reasonably well, with the primes 3, 11, and 17 being represented by intervals that are less than a cent away from harmony, and since the primes 2, 3, 5, 7, 11 and 13, and 17 are the primes that have the most to really offer, I think we have the most important facets covered where it counts the most. I should point out that the reason I value the sense of equidistant notes is that it enables a sense of uniformity and provides some measure of simplicity, but using a set of equidistant notes that is too small causes problems and doesn't respect the unequal distances between 1-digit and 2-digit values within good enough reason. I definitely try to extend the tonal system but then classify the resulting tones and their functional roles into two classes: "main tones" (akin to your idea of "degrees") and "variant tones" (akin to your definition of "non-degrees"). As far as I'm concerned, "variant tones" mainly act as chord roots during modulation- that is, when you're in the middle of trying to change keys- and don't do anything like that under most other circumstances, so yes "variant tones" do indeed have a more limited role compared to "main tones". Does all of this make sense? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 17:43, 27 November 2020 (UTC)

== Wiki ==

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 ::::: Sorry, I did not understand the answer, could you clarify? And what is "latter article"?No matter, I don't mind the use of "just intonation", only afraid of the situations when a reader understands it in some more concrete sense. I don't insist that my terms are better to coin them.
+:::::: It would help if you followed the links in my last comment- I was telling you to follow the links to help you get a sense of what I meant, as the articles explained this better than I can.  The term "latter" means the second of two, so the phrase "latter article" means "the second of two articles". --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 17:43, 27 November 2020 (UTC)
 :::::Lastly, I was thinking about those commas and have some consideration. Roughly, we need to understand that in a rational-number interval i=A/B makes deep physical sense only if A and B are small enough. This is related to the nature of aural perception of any organisms or even devices. If the numbers became 3-digit numbers or more, the accuracy of the rational number doesn't play its role. Let's see: there are two physical traits: 1) the sense of harmonics in the interval with small A and B; it is based that two oscillators in the ear come in resonance, but not necessarily on their fundamental frequencies, but some low-order harmonics, if harmonics are high, the effect is unnoticeable, 2) the perception of logarithmic distances between frequencies as equal. Now, #1 and #2 are in fundamental contradiction: 1) if all intervals are rational numbers, their system is never ever equidistant, so the equivalence of tonalities is impossible, 2) if intervals are equidistant, the ratio values are never rational, so we won't feel the perfect sense of harmony. So, the question is: with this trade-off, where is the reasonable choice? The common-practice system has chosen the compromise and gave more preference to #2 than before. 12-EDO gives amazingly good compromise, but we pretty easily can perceive the deviation from harmony. At the same time, our trait #1 is more accurate than #2. What is my conclusion? It can be a bit complicated in practice, but this is nothing but some intermediate idea. First, everything depends on the composition. Where we value the sense of equidistant notes? I don't think it is absolutely important in most cases. That said, when your calculations lead you to big natural numbers, A/B, you can easily give up having a rational number for a certain degree and use a mixture of rational numbers and real numbers. I do understand how weird it can be, this is just a vague idea. Another vague idea is that you might extend some tonal system but then classify the resulting tones and their functional roles into two classes: "degrees" and "non-degrees". A "non-degree" tone can have a limited role, it cannot be, for example, used as a root of a chord, and so on. I do understand that this is very weird and not elegant, this is just for discussion. The main point is: the contradictions and trade-offs in the tonal systems are unavoidable in principle, by the very nature of thins, sorry for possible truism. &mdash;&nbsp;[[User:SAKryukov|SA]] 17:05, 27 November 2020 (UTC)
+:::::: Given the trade off, I'd say that the reasonable choice is to try and approximate the rational values- especially 1-digit and 2-digit values- within a value of less than 3.5 cents wherever possible, as this is the kind of size difference where people won't really notice the deviation from harmony.  As it happens, 159edo and a number of other EDOs in that area do a pretty good job with this from what I see.  Yes, there are flaws, such as 159edo's inconsistent treatment of the 19 prime, but since 159edo represents the primes 5, 7 and 13 reasonably well, with the primes 3, 11, and 17 being represented by intervals that are less than a cent away from harmony, and since the primes 2, 3, 5, 7, 11 and 13, and 17 are the primes that have the most to really offer, I think we have the most important facets covered where it counts the most.  I should point out that the reason I value the sense of equidistant notes is that it enables a sense of uniformity and provides some measure of simplicity, but using a set of equidistant notes that is too small causes problems and doesn't respect the unequal distances between 1-digit and 2-digit values within good enough reason.  I definitely try to extend the tonal system but then classify the resulting tones and their functional roles into two classes: "main tones" (akin to your idea of "degrees") and "variant tones" (akin to your definition of "non-degrees"). As far as I'm concerned, "variant tones" mainly act as chord roots during modulation- that is, when you're in the middle of trying to change keys- and don't do anything like that under most other circumstances, so yes "variant tones" do indeed have a more limited role compared to "main tones".  Does all of this make sense? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 17:43, 27 November 2020 (UTC)
 == Wiki ==