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Yea, I didn't mean to sound harsh. I think that was a product of striving for brevity. Speculate away. Have fun.
What struck me is that I never carry any of this speculation into a home to tune a piano. It just has no part in my aural approach to tuning.

Sometimes for an interested client, I do a demonstration of the following kind:

Without sounding the note, I hold down the key of (say) C2. Then I strike C3 sharply, staccato. I draw attention to the echo of note C3 (130.8Hz) and show that it is coming from the unstruck strings of C2. I prove it by damping the C2 strings with my thumb, and immediately the sound stops.

Then I do the same with C2 and G3, and then with C2 and C4, and then C2 and E4. In each case, the frequency of the struck strings, is heard coming from the unstruck C2.

I tell the client that I am exciting the strings of C2, by resonance, to move as halves, thirds, quarters, and fifths of their fundamental length.

Is that not what I should tell them? What should I tell them?

That's what I tell clients too, more or less.

Oh good!

I vibrate; therefore I am partial to that!

Why, you're positively thrumming!

David,

That is precisely what is occurring. There is no need to wonder about it. In fact, all sounds (repeat ALL) are made up of harmonics (or have a harmonic structure)...barking dog, organ pipes, your voice...each has its own inique harmonic structure.

Ever wonder how an impressionist is able to sound just like another person? They have a unique capability of adapting their vocal cords/throat/oral cavity to duplicate (or nearly so) the harmonic structure of the person (or thing) they are imitating. Not everyone can do it. Some are better at it than others.

The piano's harmonic structure is unique in that it's "harmonics" are not actually harmonic but rather slightly inharmonic to the fundamental (when struck and allowed to vibrate freely). It is so unique that It cannot replicated electronically (as in synthesis) but rather it must be "sampled" (recorded from a real one) in order to sound realistic.

Pwg

Yes indeed. "Timbre".

And now some fun counter-examples:

• Cymbal crash (some kinda harmonics, but mostly chaotic noise)
• White noise (excites all frequencies, no harmonics) Think of the sound of rain, ocean waves, waterfalls, sandpaper, radio static, applause,...
• Gun shot (excites all frequencies, no harmonics)
• Many consonants (T, S, C/K, CH, SH, F, H, P, X)

Then there are the instruments that have harmonics but are extremely inharmonic like bells, timpani, gong, gamelan, etc.

The piano is one of the most successful instruments in terms of computer modelling. The more expensive Roland digital pianos use no sampling at all. They're no substitute for the real thing, but they're better than say, a modelled violin.

Yes, perhaps NOW with the tremendous computing power available, however I was thinking back several decades when synths were "synths" and Ray Kurzweil solved the "problem" with digital sampling of real instruments since it was basically impossible to realistically synthesize actual piano sound (it sounded cheesy). Sampling sounded REAL.

That was my thinking behind the statement.

Pwg

Not only that, you can excite any string into its first partial vibration by hitting the same note one octave higher, then touch the midway point of the lower string (node) to show that the node is not moving and the sound is not affected by touch the node. If that isn't a demonstration of partials, what is it?

Run all of those counter-examples through a spectrum analyzer and you will see that all of them can be decomposed into sines (with various time-domain envelopes). From a synthesis point of view, it might not be practical to recreate these using sines, but that's a whole other issue.

Paul.

I'll have to try that. Maybe I'll use a pencil eraser though to avoid marking up the string.

Pwg

When I teach guitar I use the same demonstration. The good thing about the low tension strings on a guitar is you can actually see the nodes very easily because the antinodes are 3-5mm wide up to the 3rd or 4th partial. I get the students to actually touch the nodes on my guitar so they can feel that they are stationary. I think guitarists are very accepting of the idea of partials because harmonics are used a lot in guitar music.

Put a musical tone, i.e., a tone with an easily identifiable pitch, through a spectrum analyzer, and you will see that the energy in the tone is at one or more discrete frequencies that are typically whole number ratios, or close to whole-number ratios. If that weren't the case, the sound wouldn't have a pitch. For example, is a cymbal crash at Bb, or E? The question is intuitively nonsensical. Now, put a nonmusical tone through a spectrum analyzer and instead of energy at discrete frequencies, you see a plot showing energy over broad sweeps of frequencies, often looking jagged and disorganized.
Although, in theory, one could decompose such a plot into sines, it is generally not helpful to attempt to do so. For noisy signals one usually hears terms like white, pink, brown, Gaussian, band-limited, among others. These terms are used to describe the frequency characteristics of the sound as a whole.