| so, yes, pythagoras did not create a dead simple mathematical model that captures the entire complexity of human musical experience several thousand years ago. BUT i think the ongoing study of consonance/dissonance is a very interesting area of the intersection of math and music some key words/links to get you started: - "local consonance" - "consonance/dissonance curves" - a seminal paper: https://sethares.engr.wisc.edu/paperspdf/consonance.pdf - a more recent re-implementation with a cool video at the end: https://www.sebastianjiroschlecht.com/post/ondissonance/ the basic idea being, different timbres lend themselves differently to different tuning systems. so we can parameterize our models of tuning systems based on timbre an important thing to keep in mind: consonant/dissonant doesn't mean "good/bad" or "pleasant/unpleasant". they're the output values of a mathematical model which we have a complex intuitive relationship with. other ways of thinking about it might be "simple/complex", "resolved/unresolved", "release/tension", but all are inaccurate in their own way some areas i'd love to see progress in:
- the work i've seen focuses on computational models, i.e. take a simple mathematical model of timbre, and directly compute the consonance/dissonance curve from it. but real instruments' timbre varies across many dimensions, some prominent ones being pitch, time, and dynamics. can we instead burn some CPU cycles and generate curves from a waveform?
- what does this look like for triads? tetrads? ...?
- put this in the browser! would make it so much easier to play with and present the ideas to less technical audiences
- how can we use this to generate new instruments? can a synth automatically adjust its tuning system based on its parameters? can we start from a set of desired consonant/dissonant intervals and generate an instrument with a matching curve? |