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If two sine waves can create harmony without the harmonics then what role/function does the harmonic series have in music outside of timbre? Is there any practical use for it?
Edit: What do the harmonics series explain/clarify?
I am a piano player at heart so if someone could connect their answer to the instrument as well I'd appreciate it. Its not necessary tho. I rather get a general understanding. Thanks.
The harmonic series doesn't really have an explicit 'role' in standard music theory.
However, as David Bowling says, understanding the harmonic series will help you understand - or give you another way to think about - :
If you were a computer musician, you could perhaps create sounds and pieces of music where you tailored your choice of notes to the harmonic series of your timbres - or perhaps you could only use individual harmonics, and not think in terms of 'notes' at all. If you read publications like the Computer Music Journal, you'll find people doing this kind of thing.
As a traditional pianist, I can't think of a way to directly give much of a role to the harmonic series in your music other than as an aid to understanding why the piano sounds like it does, why it's tuned how it is, why musical scales are as they are, and so on.
When you get into the scientific study of psychoacoustics of how pitch and consonance are perceived, you'll need to consider harmonics. Except for some synthesizers that generate pure sinusoids, all pitched instruments produce sounds that include significant overtones that are an important part of pitch perception. The main theory for consonance is that it is related to the perceived "beating" between the harmonics in the two sounds. So if you get into the quantitative study of this, or are just generally curious about how humans process sounds, then harmonics are a key feature to consider in explaining/clarifying these phenomena.
There are some sonic "magic tricks" that rely on understanding how partials are perceived, and thus can be manipulated. These include the missing fundamental effect, and Shepard tones.
If you consider polyphonic singing, which I consider magic, you probably don't need an intellectual understanding of overtones in order to execute or appreciate it. But if you want and idea of "how does she do that?", then you'd need to consider harmonics.
In terms of piano practice and performance itself, this kind of information is not really required (millions of pianists have been successful without really understanding any of it). If you get into piano tuning, it might be nice to know why the tuning is stretched, but as I understand it, in practice you want to do it by ear anyway.
The harmonic series isn't a tool or a set of instructions. Like so much of music 'theory' it's just a description of what happens.
Most musical notes have overtones. Many of them will approximate to the theoretical harmonic series - 2x, 3x, 4x etc. of the base frequency. (But on a real, physical instrument, they will ONLY approximate. So you'll come up against problems if you try to explain 'harmony' as coinciding overtones. Then there's the practical, imperfect systems of tuning we mostly use today... Music theory isn't actually very good at explaining WHY things sound good, though it can list and categorise lots of things that DO sound good.)
Maybe the nearest to a practical use of the harmonic series is found in brass instruments where the same length of tube can resonate to various pitches. On a trumpet it's Bb (tricky but possible), Bb (octave up), F, Bb, D, F, Ab (almost), Bb..... Which is the harmonic series based on the low Bb.
In real instruments (plucking a string, blowing a trumpet or clarinet, striking a piano string or bell), various overtones are excited; only flutes produce close to a pure sine wave. The exact set of overtones with amplitudes give the timbre of the instrument. Because strings have finite weight (as does the air column in a wind instrument), energy couples from one overtone to the others. Also, these overtones need not be exactly harmonic (especially piano and bells). It isn't so much as choosing to use overtones, one gets overtones anyway.
