Pythagoras' ideas about tuning only make sense with instruments that have harmonic or almost harmonic timbres, which is true for most instruments. However, tune

Pythagoras' ideas about tuning only make sense with instruments that have harmonic or almost harmonic timbres, which is true for most instruments. However, tuned percussion is typically inharmonic. It's long been known that inharmonic instruments sound most consonant in chords using non-integer frequency ratios. William Sethares developed a model of consonance and dissonance that accounts for this: https://sethares.engr.wisc.edu/paperspdf/consonance.pdf https://sethares.engr.wisc.edu/paperspdf/consonance.pdf Informal explanation: https://sethares.engr.wisc.edu/consemi.html https://sethares.engr.wisc.edu/consemi.html