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In my understanding, all sounds are technically made from a combination of sine waves together that form a timbre, and as such any sound can be represented as a combination of sine waves. Let's take additive synthesis, for example, like this one:

In this case, multiple waves are added to produce a timbre, but you don't hear the overtones, just the tonic bass.

So why when, say with a guitar, a chord is strummed, do the notes not blend together and produce a single tone with overtones? Why is the brain able to pick out individual notes here but not in additive synthesis? (Obviously you COULD listen for only the overtones and potentially pick them out but it's not like a chord where it's obvious there's multiple tones.)

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In my understanding, all sounds are technically made from a combination of sin waves together that form a timbre, and as such any sound can be represented as a combination of sin waves.

That's one of the ways that we can think about sound waves - and due to the way the ear is built, it probably is the best way for your question.

From a survival point of view, our ear has evolved to tell us about 'things that happen' in the world around us.

When 'an event' happens in the world - for example, an eagle cries in the distance - we tend to get a group of sine waves...

  • That are related to each other by their frequencies being multiples of each other
  • That are related to each other by their volume envelopes coinciding.

...and this is what our auditory system is listening for to tell us that "something has happened".

Of course it's more difficult to separate events that occur together in time. But we can still do it - for example, if the ear hears components at

100, 157, 200, 300, 314, 400, 471, 500, 600, 628, 700, 785.... Hz,

Our auditory system is "clever enough" to tell that they are actually two sets of multiples - one set of multiples of 157, and one set of multiples of 100. So there are two notes playing - one with a fundamental of 100 Hz, and one with a fundamental of 157 Hz.

But it's not always that easy. What if we had two sounds playing that are related to each other in pitch? It would be much harder to separate out 2 notes that were 100 and 150 Hz for example, as some of their harmonics (such as at 300 Hz and 600 Hz) would be in common to both notes. And in fact, when composers create harmonies, this is often what they do - play notes together that have simple frequency relationships, such that the notes 'blend together' and create one sound.

So when you say:

why when, say with a guitar, a chord is strummed, do the notes not blend together and produce a single tone with overtones?

I don't quite agree with the premise of your question - actually, I think the notes in a typical chord do tend to blend together in a way that many people without musical training find difficult to separate. With a guitar it's perhaps slightly easier as the notes are typically struck at slightly different times when strummed, but when someone plays a chord on a piano, it is hard - without musical experience - to pick out the individual notes, especially if it's a big jazzy chord with more than 3 notes. With musical experience, we learn the 'feel' of particular combinations of notes, and can then do the reverse process of associating the 'feel' of a sound that we hear with a combination of notes. But it's certainly not something that everyone can do without practice.

In a way, you've put your finger on what harmony is - it's taking a number of sounds, each with their own sonic signature related to their harmonic structures, and putting them together in a way that you create another 'bigger' sound, with a more interesting (but often still coherent) harmonic structure. In a way, you could say that 'harmony' is the plural of 'timbre'!

It's probably worth mentioning a couple of simplifications that I'm making here:

... and yet our ears cope with this too.

  • Are you guys meaning to say sine waves? I've never heard of a sin wave what is that? – Timinycricket Mar 4 '18 at 9:06
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    @Timinycricket we're talking about sinusoidal waves - yes, 'sine' is the abbreviation you'll find in the dictionary, while 'sin' is the one you'll see on your calculator I guess! – topo morto Mar 4 '18 at 9:26
  • @DavidBowling I'm sure you're right - I've edited my usages. – topo morto Mar 4 '18 at 10:33
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    Also look up Tartini tones (multiple videos on Youtube). This is a phenomenon where multiple pitches played at the same time produce the illusion of a lower note, because your brain thinks that the two real notes are overtones of the same nonexistent fundamental. – MattPutnam Mar 4 '18 at 17:24
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    Pipe organs use this resultant to create the effect of a 32' or 64' stop: "For a 32' stop, the two ranks are 16' and 10-2/3'; for a 64' stop, the two ranks are 32' and 21-1/3'. This effect was first used in the organ by Abt Vogler (1749-1814)." --organstops.org/r/resultant.html – E. Douglas Jensen Mar 6 '18 at 19:00
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With training you can actually hear the overtones. A good introduction to this is listening to polyphonic overtone singing. This is a singing technique in with the overtones of the voice are amplified by creating a 2nd resonance chamber in the mouth with tongue positioning.

Here is an example of that:

From listening to that you should know what they sound like, and then listen to a constant pitch and try to pick out the overtones. Once you notice them it's kind of hard to unnoticed them. I hear overtones in almost every steady pitch now.

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