Why is the harmonic series presented as a succession rather than a chord? And has it been definitely proven that all partials sound at once?

Question

It is my understanding from so far limited research that all whole number integer ratios sound simultaneously with the fundamental, but has this been proven beyond all doubt? Is it possible that the partials sound in succession even if it so rapid that to the human ear it sounds as a chord rather than an arpeggio? Are there any ways to measure this?

Answer 1

It is my understanding from so far limited research that all whole number integer ratios sound simultaneously with the fundamental

It depends on exactly what situation/instrument you're talking about. With many acoustic instruments, you often see an initial 'chaotic' part of the sound that quickly turns into a pitched sound as the energy driving the sound becomes subject to the resonances of the system. It's entirely possible that one partial might reach some threshold of audibility before another, so I don't think your statement is necessarily true.

Is it possible that the partials sound in succession even if it so rapid that to the human ear it sounds as a chord rather than an arpeggio?

Do you mean such that each partial stops before the next starts, or just that they start in succession? Either is possible, but both are probably easier to achieve with electronic than acoustic instruments.

Are there any ways to measure this?

The fourier transform is the most usual way to see where in the frequency spectrum the energy in an audio signal is.

Answer 2

Sound consists of individual sine waves, meaning that any waveform that occurs in the physical world can be decomposed into a number of single-frequency waves.

A sound can consist of only a single frequency. For example, a sine wave produced by a synthesizer's sine oscillator is like that. In that case there are no overtones, there are no partials. Only a fundamental.

If there are overtones in addition to a fundamental in an instrument's sound, then the overtones do sound simultaneously together with the fundamental.

This can be seen in a spectrum analyzer. And it can be heard by the human ear https://en.wikipedia.org/wiki/Hearing#Inner_ear The ear contains small hairs which react to the incoming sound, and different areas or cells are sensitive to different frequencies.

Whatever kind of sound waveform you produce, say, by playing an instrument, using a synthesizer, or by drawing a waveform (that you could store in a WAV file) in an audio application and playing it back with your computer, the sound output will "contain" one or more partials, sine waves. This can be "proven" in many ways. You could for example filter the sound with very narrow band filters and notice that more than one of the filters lets something through it. Or you could have resonators that resonate at different frequencies, and you would see that a sound with overtones excites several of them, not just one. Or you could use a spectrum analyzer, if you believe what it's showing to you.

Let's take a square wave as an example https://en.wikipedia.org/wiki/Square_wave

(Picture from Wikipedia https://en.wikipedia.org/wiki/Square_wave#/media/File:Fourier_series_for_square_wave.gif)

A perfect square wave has infinitely sharp edges, the corners of the squares. Such a sound cannot "exist" in the real world - any observer with finite resolution would perceive it as consisting of a number of sine waves, without being able to tell if the sound was really a square, or if the non-squareness is just beyond their capabilities to perceive. In the above picture, a square wave (blue curve) is synthesized by adding more and sine partials with different frequencies, and as more and more partials are added, the sum of the partials gets closer and closer to a theoretical square. Or as Wikipedia puts it, "An ideal mathematical square wave changes between the high and the low state instantaneously, and without under- or over-shooting. This is impossible to achieve in physical systems, as it would require infinite bandwidth."

Answer 3

I don't think it's always presented that way. The Wikipedia page has three different graphical representations.

Of those representations the one in staff notation presents it like a series I think to simply allow space for labeling. I know that I don't read it and think it's literally presenting pitches in time, like it was a melody.