Re:Music theory for nerds (2016)
by PaulDavisThe1st on Wednesday February 16, 2022 @03:31PM
(#30365284)
Unfortunately, nobody said "western musical ideas of consonance is rooted in simple harmonic ratios". The whole point of Plomb & Levelt's work (recommended if you have no read it) is that provides an explanation for consonance that has simple harmonic ratios as an existential but insufficient component. From their work, what matters is not the ratios of the two fundamentals, because there are essentially no natural tones that consist of only the fundamental (1). Instead, consonance/dissonance is a result of the sum of the consonsance relationships between each pair of partials in the two tones.
Sethares extended their conclusions a bit by noting that since the partial spectrum is the definition of timbre, the most consonant/dissonant intervals would vary by timbre, which they claimed is observed in the real world.
(1) Indeed, the first step of their work, defining the "human dissonance response curve" relies on being able to use a signal generator to create pure sine tones.
This is a good overview (linked elsewhere in the comments): https://sethares.engr.wisc.edu/consemi.html
Sethares extended their conclusions a bit by noting that since the partial spectrum is the definition of timbre, the most consonant/dissonant intervals would vary by timbre, which they claimed is observed in the real world.
(1) Indeed, the first step of their work, defining the "human dissonance response curve" relies on being able to use a signal generator to create pure sine tones.