How do you incorporate math in music?
Is it by Rhythm…the notes on a scale…
Or via machinecode and other dsp methods.
I know comp programming uses algebra, permutations, and matrices for logic, among other things…but I’m not so sure about other maths like calculus, but also physics comes into play when you have hardware and are dealing with sampling and synthesis…regardless of whether or not you do circuit bending.
Have you ever read some of the stuff on audio analysis? There’s some really interesting math that they have for analyzing audio signals to extract data from it in order to do things like genre recognition or identify song changes or things like that.
This is actually a really good book that’s not overly technical while still touching on the math and stuff behind how it works:
Not really, I’ve always assumed math was implemented in the structure of some composition…
I.e. c maj, d maj, g maj…etc
Formula for chord progression
1+3=4
So basically the scale is built around sus4
But that is Awesome i/o thanks for the link.
Cheers.
Well, the equal tempered chromatic scale is based on 1/12th roots of 2, (i.e. n semitones above x = y = x*2^(1 + n/12)) so as to create smooth, even transitions between notes in order of the chromatic scale in order to mimic how the ear hears pitch, that is, exponentially. This is done in comparison to Pythagorean tuning, which uses ratios such as 2:1, 3:2, 4:3, etc. for different music intervals.
I don’t think there’s a lot of reason mathematically why certain chord progressions “work” and others don’t. Octaves, fifths, and fourths are supposed to be consonant, while thirds, seconds, sixths and sevenths are dissonant, though this also has a lot to do with the tastes of the listener and the musician’s intent as well, which is why I don’t believe there’s much math beyond the fact that you use numbers to identify the distances between notes.
If not by pitch then maybe math works better with rhythm, meters, and tempos…and most likely dsp…but I dont know enough code for dsp…
As for making different meters and rhythms and tempos fit together math does come into play at least in my experience.
You are correct about “taste” and “intent” … I would add “culture” and “experience” However there is more to “why certain chord progressions work” then your statement implies.
The first few harmonics of a fundamental note are heard as “consonant” simply because they physically, mathematically, blend with that fundamental.
So If C is your fundamental then G and F harmonize nicely. So does E (but E versus Eb is where it starts getting into “cultural” choices of what sounds “better”)
Taking this a step further… if you are in the key of C Major then C sounds like “home” or “at rest” CEG sounds like the “home” chord. BDF is Dissonant to the fundamental… The B at a half-step from C literally “needs” to resolve to C almost as if it is “out of tune.” The F, a half-step from E, similarly needs to resolve to the E. The D, a whole-step from the C or the E is less dissonant, but still needs resolution. Resolving the D down to to C is the stronger tendency.
This dance of tension and release between consonance and dissonance is what drives chord progressions… this is a bit oversimplified… but understanding this helps a lot with the “why does this work better than that?” When creating chord progressions.