Why do some notes sound good together?
Notes whose frequencies stand in simple ratios share many of their overtones, so the ear has fewer clashing pairs to resolve — and the rest is what your culture has taught you to expect.
Simple intuition
The plain reason, in everyday words
A single musical note is not one frequency. A plucked string vibrates along its whole length and also in halves, thirds, quarters and so on, so it produces a whole stack of frequencies at once — a fundamental plus a series of overtones above it. Play two notes whose fundamentals are in a simple ratio, like 2:1 or 3:2, and many of those overtones land on exactly the same frequencies. The two sounds overlap and reinforce rather than interfering, and the combination sounds smooth and settled. Play two notes very close together instead and their overtones sit near each other without matching, producing a rapid wobbling beat that the ear registers as rough. So part of the answer is straightforwardly physical: it depends on how much of the two sounds coincide.
Consonance is purely mathematical and therefore universal.
The acoustic mechanism is real, but cross-cultural work finds societies without a preference for consonant intervals, while their sensitivity to roughness is unchanged. The preference is substantially learned.
Pianos are tuned to the simple ratios.
Equal temperament detunes almost every interval slightly so that music can be played in any key. What most listeners hear as a pure fifth is a few cents narrow.
Dissonance is a mistake or a failure.
It is a compositional resource. Tension and resolution depend on it, and what counts as dissonant has changed substantially over the history of Western music alone.
The same intervals sound good on any instrument.
Consonance depends on the overtone structure. Instruments with non-harmonic overtones, such as gamelan metallophones, work best with different tunings, and their traditions use them.
It is a rare question where a physical mechanism and a cultural convention are both real, both partly explanatory, and easy to confuse for one another. Getting the division right is the interesting part: roughness is measurable and largely universal, while the aesthetic preference built on it is not. That distinction — between a perceptual constraint and the convention erected on top of it — recurs in colour, in taste, and in typography.
Who worked it out
Pythagoras is credited with the observation that strings whose lengths stand in simple ratios sound harmonious together, tying musical pleasantness to number in a way that shaped Western thought for two millennia.
What problem forced it
Hermann von Helmholtz gave the first physical account in 1863, attributing dissonance to beating between partials and grounding musical consonance in the mechanics of hearing rather than in numerology.
How it changed since
Plomp and Levelt quantified roughness against critical bandwidth in 1965, deriving consonance curves from auditory data. Cross-cultural research from the 2010s onward, particularly work with the Tsimané, then established how much of the aesthetic preference is learned rather than given.
Why pianos are deliberately tuned slightly wrong
Equal temperament trades pure intervals for the freedom to change key, and the compromise is audible once you know to listen.
How gamelan tuning fits its instruments
A tradition where different overtone structures led to genuinely different intervals, which is the strongest evidence that timbre and tuning co-evolve.
Written for Curio rather than collected from a forum — it is part of the curated corpus that ships with the platform. The references it draws on are listed under Sources.