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But this behavior happens for all the notes! It's not just the (C,C#), (C,B) combination, it's all (tone, semitone) combinations. So natural resonances are ruled out.

Bogs

You asked why some acoustic pianos and not others produce tones from adjacent strings that are not sympathetic vibrations. Please clarify why you rule out natural resonances.

Ian, natural resonances and sympathetic vibration only occurs when an identical or extremely close identical frequency is exiting an object. A truck passing on the street can cause a window pane to rattle on anearby home. The rattling will stop when they change speeds or gears on the vehicle.

When a note is struck on the piano and another note is undampened, the other note gets two distinctive types of excitation. The first to occur is the shock force from the hammer being transfered via the string to bridge to soundboard and the solid construction of these materials convey this initial attack force energy to other strings. This initial wave energy is not structured harmonically like strings are, and is extremely wide spectrum as far as frequencies go. It will create "noise" on another string but it lacks the transverse force of a hammer hit to really create any significant amplitude. This force is physically conveyed through the termination points (ends of the speaking length of the string) not at an ideal anti node location like where a hammer hits.

A secondary vibration energy occurs after this attack on the initially struck string and it does follow a structured spectrum of specific harmonics. This too will convey energy via the parts of the piano, as well as through the air around it. This energy will produce resonance and sympathetic vibration if it closely matches in fequency on any of the harmonics/partials. Two adjacent notes don't share any close harmonics on the lowest most audible portion of the ladder. This is why the sound some people are hearing is so faint in comparison to resonant produced sound on related notes.

On the pianos I listened to for these effects on adjacent notes, I actually pick up a lot more high fequency excitation than I do recognizable lower partials. It could be that high order partials might be close enough to each other because of varying inharmonicity that accompanies them, or, and I'm speculating here...the unstructured force wave of the initial hammer impact conveys a strong portion of high frequency energy in its spectrum.

you also could hear some of the wave produced by the back and forth move of the bridge (quadratic effecr is the name) but this is supposed to produce frequencies that are fundamental x 4 (or x2, I am just unsure).

What I heard is out of the spectra, so it can be longitudinal waves. Try to rub the strings with a resin impregnated cloth if you want to be sure. ( that isw a mean to evaluate moe of a string)

Emmery, agreed.

Your analogy with trucks and windows is a good one. The window rattles because it has a certain predisposition to do so.

As you will know better than me, the actual frequency spectra of piano notes can be far from the regular set of partials one might expect. There are the quadratic effects and longitudinal waves that Kamin mentions, along with phantom partials and other effects related to the bridge, soundboard resonances, etc.

Going back the Wikipedia quote, which puts it well, even small periodic driving forces can produce large amplitude oscillations at some unexpected frequency or other.

I have no idea why that Kawai digital piano sounds as it does or why any acoustic piano should behave in a similar way across the keyboard.

Why anyone considers Wikipedia even remotely reliable is beyond me. Seriously.

The analogy is not a good one as it is not an example of sympathetic vibration. It is an example mechanical vibration. The window pane rattles because it is loose in its frame, not because it is sympathetic to another source. The mechanical energy is being supplied by the passing truck, transmitted through the ground, into the house, and to the window frame which rattles the glass in contact with the window frame. The speed of the truck, or the gearing, would have no effect as the resonant fundamental frequency of the glass pane is far above the mechanical frequency of the truck. The glass pane rattles, and thus creates its own sonic projection.

A sympathetic vibration, at the same fundamental as the glass, with sufficient amplitude projected, would cause the glass to shatter and not rattle.

Marty, you are right in general, but Emmery's window was exhibiting sympathetic vibration for the sake of the argument!

Yes, you need to be judicious, but the passage I quoted is correct.

The Tahoma Bridge disaster is a famous example of natural resonance.

I believe you are incorrect Marty, the window pane is a good analogy of sympathetic vibration. If you google it specifically with the + sign and "sympathetic resonance", the exact analogy is present in numerous physics, science and acoustic articles...along with Wikipedia (under "sympathetic resonance"). It was not my own analogy, I was simply aware of it from reading it numerous times over the years.

The front hood on automobiles are actually constructed in such a way to avoid the same resonance caused from engine noise. Because it uses so much flat sheet steel, it needs to be constructed in a way to withstand the engines' entire RPM range.

I believe you have the point ther..(while I heard windows vibrating with piano tones )I will try to test more tomorrow, but yet, what I hear is either longitudinal waves exited by the bridge, ore a mix of high partials creating new sounds (those are not high treble ringing, and certainly not a little segment of wire exited somewhere)

It is easy to test so to know which sound is heard..
There is also indeed a part of fundamental exited just because the bridge vibrates enough (small grand Pleyel) clearly audible, on a large part of the scale for those last)

All those unsuspected tones are what makes the sound of real pianos lively and rich.

....or sound rinky tink, like many spinets.

If some pianos have this effect then there may be implications for the sonority of the piano when using the sustain pedal. I would imagine increased cacophony if many adjacent un-dampened notes are more easily excited at their fundamental.

It is not a good analogy as a rattle of a window pane is not caused by sympathetic vibration. Rattle is the key word. A "rattle" is due to mechanical vibration, through direct, or conveyed, contact with the source of the mechanical energy.

I need not check additional sources in reference to my expertise in the properties of acoustic dynamics.

Check out "Musica Ricercata" by Ligeti which does just that often esp. in the first two pieces which are the only ones I can play.

I would guess to enhance "realism" they just added a cheap tweak to excite other notes a bit when you strike any key. Sounds more random, i.e., like the real thing.

Kees

Kees, I've heard linguolabial trills with more depth and musical quality than what Musica Ricercata has to offer...I'm sad to say. When an artist gathers enough recognition to put out trash or nothing as an example of their work...the only thing more silly are the critics who waste their breath talking about it.

Its in the same league as Cages' 4' 33" (opening and closing the piano lid)....

http://www.youtube.com/watch?v=HypmW4Yd7SY

and Robert Rauschenbergs' "White Paintings"...

Tastes differ. I like Musica Ricercata quite a bit and so did Stanley Kubrick who used it (mvmt 2) in his last movie.

Regarding Cages' 4' 33" I performed it once in a version lasting 3 minutes (4'33' is just the title, the piece can be any length) on recorder (the piece is for any instruments, not piano as many people think). Instead of closing the piano lid during the piece as David Tudor did I took my recorder apart.

Needless to say it was tuned in an unequal temperament.

Kees

I like LIGETI probably pne of the best composers, much humor, no much posture .

I hate "music" that have as a prerequisite to put the metronome at 120

Well, I was just going to lurk, but I had to try this on the two working pianos I have at hand. The effect is very clear on the Lester spinet. After testing C4, I played a few other random keys, and G4 rings very prominently when held silently and the adjacent semitones are played. So, I went to the Haddorff upright. The C4 does not ring very prominently when tested this way (though it does ring), and, when tested, G4 rings very prominently against the semitones. I am not educted enough to speculate on the cause--mechanical, sympathetic, angelic. Anyway, Bogs, thought you'd want to know. It seems that it is a property of my two old acoustic pianos, at least, and from a previous discussion in Pianist Corner, I will throw my hat into the ring with those who suppose that what you discovered is a deliberate decision by the DP designers to try to get the right piano noises into the DP...

--Andy

Just about every disaster and miscalculation involving the oversite of "experts", was preceded with the famous words in your quote I have put in bold. The expertise of the numerous people using the definition I used is known...you not bothering to verify it does not make it invalid..other than in your own mind. Your own "expertise" however appears self proclaimed, and not important enough to even put in your signature.

Marty, the word "rattle" has numerous different meanings definatively. "to make a rapid succession of short sharp noises" is the most common, and it is not quantified with a source of the noise being mechanically coupled, or indirectly through air pressure waves, nor any other mode of transmission, resonant or not. Its use in "resonance" explanation therefore is not definatively excluded.

I have heard snare drums "rattle" in the same way as window panes do, and it can be sympathetic resonance or simply excitation from a drumstick. The contact of the drum skin to the snares produces the sound, the sympathetic resonance of the skin or the snare can be the source of the driving amplitude for it. Air pressure waves of resonant frequency from a nearby speaker can induce it. Non resonant vibration forces from a stage floor can also induce it...neither excludes the other, in regards to a "rattle" being heard.
Marty, the cited definition bothers you in regards to accuracy because perhaps you are ignoring a key componant of it. The fact that the "rattle" occurs as the engine speed of the truck is at a specific RPM, and then dissapears when this RPM slows or speeds up is what defines its resonant relationship. If the truck produced a vibration that caused a rattle, regardles off engine speed, then I would agree with you that there is some other mechanical vibration going on that is not sympathetic in nature.