User talk:SAKryukov: Difference between revisions

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:::::::::::::::::::::: Oh yes, I know all about that. In fact, while some consonances- such as those involving sum tones and difference tones- are based on a linear mathematical relationship (as noted by [[User:CritDeathX|Sam Pulley]] in [[User talk:CritDeathX #Ideas of Consonance|a conversation we had about the matter]]), there is an equivalent type of consonances that seems to be based on what I call a "contralinear" mathematical relationship- these particular tones being what I call "contrasum" and "contradifference" tones. We seem to need a new set of mathematical symbols in order to shorten the process of solving the mathematical problems involved in finding these contralinear tones. For example, a 10:12:15 minor triad is identical to a pitch relationship in which the frequencies are related the the following mathematical relationship 1/4:1/5:1/6. In order to solve for the contrasum and contradifference tones with the current set of mathematical relationships, we would currently need to take the multiplicative inverse of each of the fractions in the 1/4:1/5:1/6 ratio, solve for sum and difference tones among the resulting whole number ratios, and then take the multiplicative inverse of the answers we get- or something like that. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:34, 7 December 2020 (UTC)

::::::::::::::::::::::: 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''

:::::::::::::::::::::: 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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 :::::::::::::::::::::: Oh yes, I know all about that.  In fact, while some consonances- such as those involving sum tones and difference tones- are based on a linear mathematical relationship (as noted by [[User:CritDeathX|Sam Pulley]] in [[User talk:CritDeathX #Ideas of Consonance|a conversation we had about the matter]]), there is an equivalent type of consonances that seems to be based on what I call a "contralinear" mathematical relationship- these particular tones being what I call "contrasum" and "contradifference" tones.  We seem to need a new set of mathematical symbols in order to shorten the process of solving the mathematical problems involved in finding these contralinear tones.  For example, a 10:12:15 minor triad is identical to a pitch relationship in which the frequencies are related the the following mathematical relationship 1/4:1/5:1/6.  In order to solve for the contrasum and contradifference tones with the current set of mathematical relationships, we would currently need to take the multiplicative inverse of each of the fractions in the 1/4:1/5:1/6 ratio, solve for sum and difference tones among the resulting whole number ratios, and then take the multiplicative inverse of the answers we get- or something like that. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:34, 7 December 2020 (UTC)
+::::::::::::::::::::::: 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''
 :::::::::::::::::::::: 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)