4 ms·

W.r.t. combinatorics: I was thinking of tuning systems and scales. I have always thought about the theory, but never written it down. Some other people actually

W.r.t. combinatorics: I was thinking of tuning systems and scales. I have always thought about the theory, but never written it down. Some other people actually did a much better job than me: http://andrewduncan.net/cmt/ http://andrewduncan.net/cmt/ W.r.t. linear algebra: mostly in relation to sound synthesis, but also in relation to music composition, theory of overtones, piano tunings... You ask, I'll explain.

kian 5y ago
I'd love to hear your explanations re linear algebra on all of the above, but most especially with respect to music composition.
- edejong 5y ago
  Sound synthesis: mostly when I was playing with PD (Pure Data). Linear algebra comes up all the time in sampling theory. Music composition: this is a bit more far fetched, but I always thought of composition as a combination of vectors which can vary semi-independently. We want to pick some plane through that vector space and move within the plane. For example, we can vary in harmonic complexity, melodic complexity, rhythmic complexity, dynamics, tempo. But it wouldn't make sense to do all at the same time. So we pick one plane, say harmonic complexity and dynamics, and move within that plane. This allows the listener to get used to the 'space' that is opened by the composition. We can then slowly add more vectors, to keep the interest. A very visual representation of this is the trackpads that you can see on certain modular synthesizers. Often there is a complex setup, but the variables of the setup are reduced to two dimensions, which allows the composers to vary within this projected plane. Piano tunings: well, basically you have a vector of 230 piano strings of which the overtones are all slightly out of tune. To tune a piano 'correctly', you need to minimise set of equations of strings and overtones (matrix).

4 ms·

W.r.t. combinatorics: I was thinking of tuning systems and scales. I have always thought about the theory, but never written it down. Some other people actually

by edejong 5y ago

kian 5y ago
I'd love to hear your explanations re linear algebra on all of the above, but most especially with respect to music composition.
- edejong 5y ago
  Sound synthesis: mostly when I was playing with PD (Pure Data). Linear algebra comes up all the time in sampling theory. Music composition: this is a bit more far fetched, but I always thought of composition as a combination of vectors which can vary semi-independently. We want to pick some plane through that vector space and move within the plane. For example, we can vary in harmonic complexity, melodic complexity, rhythmic complexity, dynamics, tempo. But it wouldn't make sense to do all at the same time. So we pick one plane, say harmonic complexity and dynamics, and move within that plane. This allows the listener to get used to the 'space' that is opened by the composition. We can then slowly add more vectors, to keep the interest. A very visual representation of this is the trackpads that you can see on certain modular synthesizers. Often there is a complex setup, but the variables of the setup are reduced to two dimensions, which allows the composers to vary within this projected plane. Piano tunings: well, basically you have a vector of 230 piano strings of which the overtones are all slightly out of tune. To tune a piano 'correctly', you need to minimise set of equations of strings and overtones (matrix).