What physically happens when notes in singing or an instrument harmonise? Why do those certain notes sound good together and others sound awful?
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Turns out our ears and brains are excellent at detecting wave harmonics; we can detect when sounds are in harmony and when they are not;
[https://en.wikipedia.org/wiki/Inharmonicity](https://en.wikipedia.org/wiki/Inharmonicity)
Hearing an inharmonic sound is grating to people, while harmonic waves are pleasing;
[https://en.wikipedia.org/wiki/Harmonic#:~:text=A%20harmonic%20of%20such%20a,are%20known%20as%20higher%20harmonics](https://en.wikipedia.org/wiki/Harmonic#:~:text=A%20harmonic%20of%20such%20a,are%20known%20as%20higher%20harmonics).
Say you play two notes of wildly different pitches, that is, the higher note has a faster frequency and the lower note has a slower frequency. If the higher frequency note is a positive integer multiple (so you can multiply the base frequency by some whole number and equal something close to the frequency of the higher pitched note) of the lower note that music is in harmony. It sounds like the two notes are playing well together in the sandbox, while inharmonic pitches make you want to cry.
Professional vocalists who have ‘perfect pitch’, so basically anyone whose name is not Miley Cyrus, can hit the note’s pitch with their voice very accurately – which is important if instruments are playing at the same time and they need to be harmonious. This is why timing is so crucial, if you are off tempo, even if the music is written with and performed with harmony it will sound like crap because the pitches don’t line up.
Pluck a string, it will vibrate. There will be a main vibration, say, 110 times a second, but most of the times there will also be other quieter vibrations happening at multiples of that main vibration. The higher the number of vibrations per second, the higher in pitch the sound. That’s called an [harmonic series](https://en.wikipedia.org/wiki/Harmonic_series_%28music%29).
So, let’s start with this set of vibrations:
* 110 times a second.
* 220 times a second.
* 330 times a second.
* 440 times a second.
* 550 times a second.
* …
When talking about music, we seldom use the number of vibrations per second; instead we have note names:
* 110 times a second: A₃
* 220 times a second: A₄
* 330 times a second: E₄
* 440 times a second: A₅
* 550 times a second: C♯₅
* …
It just happens our ear/brain *really* likes combinations of those first vibrations. A₃ to A₄ is an octave, which is the most consonant pair. A₄ to E₄ is a fifth, which is the second most consonant pair. E₄ to A₅ is a fourth; again, very consonant, but less. A₅ to C♯₅ is a major third, sounds good too, but less than all the previous. The farther you go in the vibration set, the more dissonant it will sound.
Note that frequency ratios that are very simple sound consonant; A₃ to A₄ is 1:2; A₄ to E₄ is 2:3; E₄ to A₅ is 3:4; A₅ to C♯₅ is 4:5.
tl;dr: A choir where singers sing the notes A, C♯ and E sounds good, because the notes they sing are in simple ratios to each other.
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Music geeks: this explanation obviously draws on just intonation; equal temperament breaks the elegance of the idea but our ears have been accustomed to the margin of error introduced by non-pure intervals.
Sound is air wiggling like a wave. “Every” sound is comprised of a big wiggle, a wiggle half that size, another half that size, another half *that* size, and so on, pretty much forever. What we hear and notice of all those wiggles, the that first biggest wiggle in the wiggle party, that’s what we recognize as, for example, middle c.
When we think a harmony sounds pretty with a note, it’s because you are actually already hearing that note within the original wiggles of the first note, only several octaves higher. So your brain is going “hey! Those match!” When the two notes don’t sound good together, it’s because none of the “mini wiggles” match with each other.
This isn’t a precise explanation of it (and I may have done wiggle math wrong) but, from my understanding, this is essentially what’s happening.
Also, an interesting tidbit, in western music the music scale was based around the wiggles in one particular note. Where as bagpipes’ tuning is based around the actual hertz(?) values and is “perfect tuning” based on the math values of the first (lowest) wiggle of the sound, not taking all the note’s mini wiggles into account. That’s why bagpipe music sounds so funny to many western ears; it’s tuned it’s wiggles totally differently to the way we’re used to!
Edit: u/waptaff has kindly provided the correct wiggle math in another comment that I was struggling to remember for those who would like a more precise explanation 🙂
I think with all things that “align” it’s a matter of frequency our brain recognizes – just like in nature some of the phenomena we see we recognize and understand now – the same reason a tornado occurs when we have a low and a high system. It’s just a consequence of just the right combinations.
I’d be interested to see someone with a music background maybe give better terminology to this phenomena, lol.
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