Why don't I hear overtones as a chord

Question

I play piano for a while now and I was used to the idea that every key there produces a single note. Recently I've started reading the lectures on music theory that explain music sounds as standing waves of a certain frequency. Such waves tend to come with the accompanying harmonics or overtones (with frequencies being 2x, 3x, ... of the fundamental frequency). In particular, when one plays C they also produce C,G,C,E,... which are the components of the major triad. However, when I play the major triad itself, it has a much more distinct color/sound to me. In a sense, I perceive a single C as something "neutral" while Cmaj triad/Cmin triad having fitting but different hues to the single C, both equally legit. How can this be if first overtones of C form a major triad though?

Answer 1

Many things in nature tend to allow for stable waves at more or less multiples of a base pitch. This is a result of simple physical limitations (if I have a vibating string I can only get waveforms that have a node at the ends, and such stuff). But this means that most simple sounds produced tend to feature more or less harmonic overtones. This means that our brain is used to experience them and will correct for them.

Hereby the more consonant a sound is, the easier it will be for the brain to interpret notes as harmonics of the lower ones. You can test this out yourself. If you play on a reasonably tuned piano root + octave + 12th + 15th + 17th + 19th ... this will sound quite pure (start from below and keep adding notes).

But if you play a simple C major triad — C-E-G — then clearly neither E nor G are harmonics of C. C and G could be both harmonics of the C an octave below (and the brain might even just assume it is), but the E could only be an harmonic of the C two octaves below.

Once you play chords you will find different effects affecting the sound, such as a beat between not only the notes, but also their overtones. Two sine waves in a 5th do sound quite pure (and even if you add a perfect 3rd it will sound quite pure). But if you look at their harmonics

you’ll find you get clashes between different combinations of the harmonics. This gets even more complex when you add the major third

C  -  c  - g - c' - e' - g' - bhf' - c''...
  E  -  e  -  b  -  e' -  g♯' - b'    - dhs'' ...
    G   -  g  - d'   -   g'  -  b'  -  d'' ...

(note that the b of the E is not the B of the G!) and even more if you have a minor third

C  -  c  - g - c' - e' - g' -  bhb' - c''...
  Eb  - eb - bb  - eb' - g' - bb'   - dhb'' ...
    G   -  g  - d'   -   g'  -   b'  -  d'' ...

This adds a lot vibrancy to the tone.

On top of this you have non linearity (the response of a combination is not the combination of the responses), which will actually create effects such as if you play a fifth the octave below the root sounding too (well observable at very high non linearity, such as heavy distortion).

Answer 2

Loosely speaking, one doesn't hear overtones, because the fundamental is too loud in comparison.

There are exceptions, however. When singers, for example, produce a chord perfectly in tune, it's not unusual to hear overtones, as though there was one or more additional singers producing additional chord tones.

When playing an holding a tone on the trumpet, one can train oneself to hear overtones "within" that tone. (Interesting note about the trumpet: It doesn't actually produce the fundamental pitch. Playing middle C on a trumpet is actually a first overtone. For more on this: Trumpet Peculiar Frequency spectrum, What are brass instrument "pedal tones" and "false tones", and how are they different?, and related links.)

Another way to hear overtones as a chord in themselves is a little piano trick.

1. C4 is middle C.
2. Without producing any sound, depress and hold the keys for G4, C5, and E5.
3. Very loudly, strike and immediately release C3.
4. You will hear a C major chord formed by the G4, C5, and E5.

Answer 3

That's an excellent question. The basic answer is that the accompanying harmonics of a single tone are much weaker than the fundamental tones you play on the keys. In addition, the fundamental tones of the keys are out of tune with the much weaker harmonics of the C, especially the E.

Answer 4

Slightly oversimplified answer

The perception issue comes down to sine waves, which are pure, "flavorless" pitches without overtones. Think of a very dull flute sound. If you have a Hammond organ handy, push in all the drawbars but the one labeled "8".

If you play a chord of three sine waves at C3, G4, and E5 (C below middle C, G above middle C, and E above that G) it will sound like a single note with a woody, clarinet-like sound, instead of three flutes, because those three sine waves are behaving as a fundamental and two overtones. The brain can hardly tell the difference.

But what if you play those same notes as a chord on a piano? It will most likely sound like a chord, because each of those notes has overtones of its own, and the brain easily picks those notes out as separate.