User talk:SAKryukov: Difference between revisions

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::::::::::::::::::::::: I would not be so sure. :-) What are you talking about? sum/difference frequencies need at least some mode interaction. But such interaction is by definition a non-linearity. The concept of "mode" fundamentally means that they are orthogonal, the subject of the superposition principle. Roughly speaking, modes don't see each other. When you project two laser lights on two different points and the beams pass across each other, none of the beams affect another one. Non-linearity can happen when the media is linear. For example, when the dielectric permittivity somehow depends on the value of the electric field of the wave, the change created by one beam warps the wave distribution of another beam, so it deflects. Normally, non-linearity happens with very high intensities (of anything). And yes, more sophisticated emission on sum/difference frequencies also takes place. Only all of it is non-linearity, again, by the definition. — [[User:SAKryukov|SA]], ''Monday 2020 December 7, 22:17 UTC''

:::::::::::::::::::::::: I'm talking about talking about [https://en.wikipedia.org/wiki/Combination_tone Combination tones], and also about additional pairs of tones that have a relationship to the logarithmic curve of sound perception akin to that to linear tones, only these other tones are along a decidedly non-linear curve. It would help more to go into an example, I think. Say you have a dyad (two note chord) consisting of frequencies of 440 Hz and 528 Hz. I imagine you know more about the combination tones that can result from this set of frequencies that I do, as well as how the frequencies of the combination tones are related to the actual tones by addition and subtraction, right? Well, Sam says that the linear relationship between the frequencies the actual tones and the combination tones leads to a sort of consonance, but, I'm saying that there are another set of tones related to that set of actual frequencies in a manner that is decidedly non-linear, yet is percieved to be just as consonant. In this case, we see the sum and difference tones resulting from 440 Hz and 528 Hz are 968 Hz and 88 Hz respectively, however, when we check the frequency relationships between all the pitches involved, we see a distinct set of intervals. The frequencies of 528 and 440 Hz form a 6/5 ratio, the frequencies of 528 Hz and 968 Hz form an 11/6 ratio, and the frequencies of 88 Hz and 440 Hz form a 5/1 ratio. If we take these ratios and line them up in such a way as to reflect the pitches involved from lowest to highest, we get a chord, that consists of the following steps 1/1-5/1-6/1-11/1, am I right? Now, if we take the multiplicative inverses of the ratios in the sequence, we get 1/1-1/5-1/6-1/11. Now, since we know that the interval between the 5/1 and 6/1 in the chord 1/1-5/1-6/1-11/1, is identical to the interval between the 1/55 and 1/6 in the chord 1/1-1/5-1/6-1/11- both being 6/5- and since we now want to find what I'm calling the "contrasum" and "contradifference" tones of 440 Hz and 528 Hz, we can assume that 440 Hz doubles as the 1/6 interval and that 528 Hz doubles as the 1/5 interval. Since multplying 440 by 6 gives you 2640, and since multiplying 528 by 5 also gives you 2640, that means that 2640 Hz is the "contradifference" tone to 440 Hz and 528 Hz. Since 2640 Hz corresponds to the 1/1 in the 1/1-1/5-1/6-1/11 chord, we now can solve for the "contrasum" tone in one of several ways- for the sake of simplicity, we'll just divide 2640 by 11 in order to find the frequency of the "contrasum" tone represented in the chord by the ratio of 1/11, and this tone turns out to be 240 Hz. Once you arrange the 2640 Hz frequency and the 240 Hz frequency in a chord together with the original 440 Hz and 528 Hz, you find that the resulting chord is just as consonant as the chord consisting of 88 Hz, 440 Hz, 528 Hz, and 968 Hz- once one takes the direction of chord construction into account. If you keep repeating this proceedure with different frequencies with different intervals, you'll eventually have a better idea as to the nature of the pitch relationships that I'm calling "contralinear". --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:12, 7 December 2020 (UTC)

:::::::::::::::::::::::: I'm talking about talking about [https://en.wikipedia.org/wiki/Combination_tone Combination tones], and also about additional pairs of tones that have a relationship to the logarithmic curve of sound perception akin to that of linear tones, only these other tones are along a decidedly non-linear curve. It would help more to go into an example, I think. Say you have a dyad (two note chord) consisting of frequencies of 440 Hz and 528 Hz. I imagine you know more about the combination tones that can result from this set of frequencies that I do, as well as how the frequencies of the combination tones are related to the actual tones by addition and subtraction, right? Well, Sam says that the linear relationship between the frequencies the actual tones and the combination tones leads to a sort of consonance, but, I'm saying that there are another set of tones related to that set of actual frequencies in a manner that is decidedly non-linear, yet is percieved to be just as consonant. In this case, we see the sum and difference tones resulting from 440 Hz and 528 Hz are 968 Hz and 88 Hz respectively, however, when we check the frequency relationships between all the pitches involved, we see a distinct set of intervals. The frequencies of 528 and 440 Hz form a 6/5 ratio, the frequencies of 528 Hz and 968 Hz form an 11/6 ratio, and the frequencies of 88 Hz and 440 Hz form a 5/1 ratio. If we take these ratios and line them up in such a way as to reflect the pitches involved from lowest to highest, we get a chord, that consists of the following steps 1/1-5/1-6/1-11/1, am I right? Now, if we take the multiplicative inverses of the ratios in the sequence, we get 1/1-1/5-1/6-1/11. Now, since we know that the interval between the 5/1 and 6/1 in the chord 1/1-5/1-6/1-11/1, is identical to the interval between the 1/55 and 1/6 in the chord 1/1-1/5-1/6-1/11- both being 6/5- and since we now want to find what I'm calling the "contrasum" and "contradifference" tones of 440 Hz and 528 Hz, we can assume that 440 Hz doubles as the 1/6 interval and that 528 Hz doubles as the 1/5 interval. Since multplying 440 by 6 gives you 2640, and since multiplying 528 by 5 also gives you 2640, that means that 2640 Hz is the "contradifference" tone to 440 Hz and 528 Hz. Since 2640 Hz corresponds to the 1/1 in the 1/1-1/5-1/6-1/11 chord, we now can solve for the "contrasum" tone in one of several ways- for the sake of simplicity, we'll just divide 2640 by 11 in order to find the frequency of the "contrasum" tone represented in the chord by the ratio of 1/11, and this tone turns out to be 240 Hz. Once you arrange the 2640 Hz frequency and the 240 Hz frequency in a chord together with the original 440 Hz and 528 Hz, you find that the resulting chord is just as consonant as the chord consisting of 88 Hz, 440 Hz, 528 Hz, and 968 Hz- once one takes the direction of chord construction into account. If you keep repeating this proceedure with different frequencies with different intervals, you'll eventually have a better idea as to the nature of the pitch relationships that I'm calling "contralinear". --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:12, 7 December 2020 (UTC)

:::::::::::::::::::::: Come to think of it, I think we actually need to speak to Sam about his [[User:CritDeathX/Sam's Idea Of Consonance|ideas of consonance]], as well as about how to flesh out the idea of "contralinear tones" based on our discussion. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:57, 7 December 2020 (UTC)

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 ::::::::::::::::::::::: I would not be so sure. :-) What are you talking about? sum/difference frequencies need at least some mode interaction. But such interaction is by definition a non-linearity. The concept of "mode" fundamentally means that they are orthogonal, the subject of the superposition principle. Roughly speaking, modes don't see each other. When you project two laser lights on two different points and the beams pass across each other, none of the beams affect another one. Non-linearity can happen when the media is linear. For example, when the dielectric permittivity somehow depends on the value of the electric field of the wave, the change created by one beam warps the wave distribution of another beam, so it deflects. Normally, non-linearity happens with very high intensities (of anything). And yes, more sophisticated emission on sum/difference frequencies also takes place. Only all of it is non-linearity, again, by the definition. &mdash;&nbsp;[[User:SAKryukov|SA]],&nbsp;''Monday&nbsp;2020&nbsp;December&nbsp;7,&nbsp;22:17&nbsp;UTC''
-:::::::::::::::::::::::: I'm talking about talking about [https://en.wikipedia.org/wiki/Combination_tone Combination tones], and also about additional pairs of tones that have a relationship to the logarithmic curve of sound perception akin to that to linear tones, only these other tones are along a decidedly non-linear curve.  It would help more to go into an example, I think.  Say you have a dyad (two note chord) consisting of frequencies of 440 Hz and 528 Hz.  I imagine you know more about the combination tones that can result from this set of frequencies that I do, as well as how the frequencies of the combination tones are related to the actual tones by addition and subtraction, right?  Well, Sam says that the linear relationship between the frequencies the actual tones and the combination tones leads to a sort of consonance, but, I'm saying that there are another set of tones related to that set of actual frequencies in a manner that is decidedly non-linear, yet is percieved to be just as consonant.  In this case, we see the sum and difference tones resulting from 440 Hz and 528 Hz are 968 Hz and 88 Hz respectively, however, when we check the frequency relationships between all the pitches involved, we see a distinct set of intervals.  The frequencies of 528 and 440 Hz form a 6/5 ratio, the frequencies of 528 Hz and 968 Hz form an 11/6 ratio, and the frequencies of 88 Hz and 440 Hz form a 5/1 ratio.  If we take these ratios and line them up in such a way as to reflect the pitches involved from lowest to highest, we get a chord, that consists of the following steps 1/1-5/1-6/1-11/1, am I right?  Now, if we take the multiplicative inverses of the ratios in the sequence, we get 1/1-1/5-1/6-1/11.  Now, since we know that the interval between the 5/1 and 6/1 in the chord 1/1-5/1-6/1-11/1, is identical to the interval between the 1/55 and 1/6 in the chord 1/1-1/5-1/6-1/11- both being 6/5- and since we now want to find what I'm calling the "contrasum" and "contradifference" tones of 440 Hz and 528 Hz, we can assume that 440 Hz doubles as the 1/6 interval and that 528 Hz doubles as the 1/5 interval.  Since multplying 440 by 6 gives you 2640, and since multiplying 528 by 5 also gives you 2640, that means that 2640 Hz is the "contradifference" tone to 440 Hz and 528 Hz.  Since 2640 Hz corresponds to the 1/1 in the 1/1-1/5-1/6-1/11 chord, we now can solve for the "contrasum" tone in one of several ways- for the sake of simplicity, we'll just divide 2640 by 11 in order to find the frequency of the "contrasum" tone represented in the chord by the ratio of 1/11, and this tone turns out to be 240 Hz.  Once you arrange the 2640 Hz frequency and the 240 Hz frequency in a chord together with the original 440 Hz and 528 Hz, you find that the resulting chord is just as consonant as the chord consisting of 88 Hz, 440 Hz, 528 Hz, and 968 Hz- once one takes the direction of chord construction into account.  If you keep repeating this proceedure with different frequencies with different intervals, you'll eventually have a better idea as to the nature of the pitch relationships that I'm calling "contralinear". --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:12, 7 December 2020 (UTC)
+:::::::::::::::::::::::: I'm talking about talking about [https://en.wikipedia.org/wiki/Combination_tone Combination tones], and also about additional pairs of tones that have a relationship to the logarithmic curve of sound perception akin to that of linear tones, only these other tones are along a decidedly non-linear curve.  It would help more to go into an example, I think.  Say you have a dyad (two note chord) consisting of frequencies of 440 Hz and 528 Hz.  I imagine you know more about the combination tones that can result from this set of frequencies that I do, as well as how the frequencies of the combination tones are related to the actual tones by addition and subtraction, right?  Well, Sam says that the linear relationship between the frequencies the actual tones and the combination tones leads to a sort of consonance, but, I'm saying that there are another set of tones related to that set of actual frequencies in a manner that is decidedly non-linear, yet is percieved to be just as consonant.  In this case, we see the sum and difference tones resulting from 440 Hz and 528 Hz are 968 Hz and 88 Hz respectively, however, when we check the frequency relationships between all the pitches involved, we see a distinct set of intervals.  The frequencies of 528 and 440 Hz form a 6/5 ratio, the frequencies of 528 Hz and 968 Hz form an 11/6 ratio, and the frequencies of 88 Hz and 440 Hz form a 5/1 ratio.  If we take these ratios and line them up in such a way as to reflect the pitches involved from lowest to highest, we get a chord, that consists of the following steps 1/1-5/1-6/1-11/1, am I right?  Now, if we take the multiplicative inverses of the ratios in the sequence, we get 1/1-1/5-1/6-1/11.  Now, since we know that the interval between the 5/1 and 6/1 in the chord 1/1-5/1-6/1-11/1, is identical to the interval between the 1/55 and 1/6 in the chord 1/1-1/5-1/6-1/11- both being 6/5- and since we now want to find what I'm calling the "contrasum" and "contradifference" tones of 440 Hz and 528 Hz, we can assume that 440 Hz doubles as the 1/6 interval and that 528 Hz doubles as the 1/5 interval.  Since multplying 440 by 6 gives you 2640, and since multiplying 528 by 5 also gives you 2640, that means that 2640 Hz is the "contradifference" tone to 440 Hz and 528 Hz.  Since 2640 Hz corresponds to the 1/1 in the 1/1-1/5-1/6-1/11 chord, we now can solve for the "contrasum" tone in one of several ways- for the sake of simplicity, we'll just divide 2640 by 11 in order to find the frequency of the "contrasum" tone represented in the chord by the ratio of 1/11, and this tone turns out to be 240 Hz.  Once you arrange the 2640 Hz frequency and the 240 Hz frequency in a chord together with the original 440 Hz and 528 Hz, you find that the resulting chord is just as consonant as the chord consisting of 88 Hz, 440 Hz, 528 Hz, and 968 Hz- once one takes the direction of chord construction into account.  If you keep repeating this proceedure with different frequencies with different intervals, you'll eventually have a better idea as to the nature of the pitch relationships that I'm calling "contralinear". --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:12, 7 December 2020 (UTC)
 :::::::::::::::::::::: Come to think of it, I think we actually need to speak to Sam about his [[User:CritDeathX/Sam's Idea Of Consonance|ideas of consonance]], as well as about how to flesh out the idea of "contralinear tones" based on our discussion. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:57, 7 December 2020 (UTC)