SAKryukov
Joined 23 November 2020
Nonlinear effects |
m "I saw a simple marimba example" typo fixed |
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:::::::::::::::::::: I do in fact disagree with you when it comes to the idea of the fundamental frequency being entirely outside the problems of tonal systems. The way I see it, the Tonic is at its strongest when it not only has the smallest possible rational intervals relative to all the notes in the scale, but is also the note that can generate all the other notes in the set purely through its own overtone series and undertone series. It's not just one of these facets that provides a sense of tonality but both. If tonality is like an entire building, then fundamental frequencies matching the tonic's pitch class are like the type of material that makes for the strongest type of foundation- does this analogy make any practical sense? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:53, 7 December 2020 (UTC) | :::::::::::::::::::: I do in fact disagree with you when it comes to the idea of the fundamental frequency being entirely outside the problems of tonal systems. The way I see it, the Tonic is at its strongest when it not only has the smallest possible rational intervals relative to all the notes in the scale, but is also the note that can generate all the other notes in the set purely through its own overtone series and undertone series. It's not just one of these facets that provides a sense of tonality but both. If tonality is like an entire building, then fundamental frequencies matching the tonic's pitch class are like the type of material that makes for the strongest type of foundation- does this analogy make any practical sense? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:53, 7 December 2020 (UTC) | ||
::::::::::::::::::::: I never meant "the idea of the fundamental frequency being entirely outside...", it was a typo, sorry. Please see above: <EDIT>...<end EDIT>. Are you sure you understand the phenomenon correctly? In this Wikipedia article, some important considerations are missing. It needs some time to describe the idea and the questionable parts. It actually comes to theoretical mechanics (not "theoretical mechanics" learned by engineers, but the real thing, mostly the formalism of Lagrange, Hamilton, and then Emmy Noether), where the orthogonal space of modes can be understood, as well as the role of linearity and non-linear effects. (The usual myth of musicians is to call the physical-mathematics basis of music "acoustics", but in fact, there is next to nothing about real acoustics in music theory, but there is a lot of theoretical mechanics, abstract algebra, infinite-dimension functional spaces, theory of numbers, and the like.) Even for linear mechanics, this Wikipedia article considers only the sets of "similar" modes, like string or air vibrations with different number of nodes. Real life is more complicated. On this site, or maybe on some referenced sites, I | ::::::::::::::::::::: I never meant "the idea of the fundamental frequency being entirely outside...", it was a typo, sorry. Please see above: <EDIT>...<end EDIT>. Are you sure you understand the phenomenon correctly? In this Wikipedia article, some important considerations are missing. It needs some time to describe the idea and the questionable parts. It actually comes to theoretical mechanics (not "theoretical mechanics" learned by engineers, but the real thing, mostly the formalism of Lagrange, Hamilton, and then Emmy Noether), where the orthogonal space of modes can be understood, as well as the role of linearity and non-linear effects. (The usual myth of musicians is to call the physical-mathematics basis of music "acoustics", but in fact, there is next to nothing about real acoustics in music theory, but there is a lot of theoretical mechanics, abstract algebra, infinite-dimension functional spaces, theory of numbers, and the like.) Even for linear mechanics, this Wikipedia article considers only the sets of "similar" modes, like string or air vibrations with different number of nodes. Real life is more complicated. On this site, or maybe on some referenced sites, I saw a simple marimba example with some unrelated modes (all real modes do not interact due to linearity, but some modes are also "unrelated"). Now, we can always have a fundamental on an unrelated type of modes, which is lower than the most perceivable fundamental, and, in this case, these frequencies can be also totally unrelated, without any integer-number fractions. ...I understand my text is messy here. If you are interested, I can explain it properly. — [[User:SAKryukov|SA]], ''Monday 2020 December 7, 20:35 UTC'' | ||
::::::::::::::::::::: By the way, do you know about the nonlinear properties of our aural system? It was even used in historical organs. I mean, the phenomenon has nothing to do with brain processing. The sound is physically generated in the head out of the sound waves. It can generate a sound which does not physically present in the air, say, combination frequencies which cannot appear in any linear systems due to the superposition principle. — [[User:SAKryukov|SA]], ''Monday 2020 December 7, 20:35 UTC'' | ::::::::::::::::::::: By the way, do you know about the nonlinear properties of our aural system? It was even used in historical organs. I mean, the phenomenon has nothing to do with brain processing. The sound is physically generated in the head out of the sound waves. It can generate a sound which does not physically present in the air, say, combination frequencies which cannot appear in any linear systems due to the superposition principle. — [[User:SAKryukov|SA]], ''Monday 2020 December 7, 20:35 UTC'' | ||