Oscilloscope. E1.

What I notice most is that the beating in Pianoteq is much, much faster. At least twice as fast on most pairs of partials? (I'm not sure why the beating is present on a single string when listening to two partials, but it's clearly there.)

https://youtu.be/4AhqKPLf2nk
Suddenly there was a phase offset between the left and right channels. And also there was a phase of the sound in overtones Pianoteq in opposition.
The ear is sensitive to the phase change. Related to this is the feeling of pitch. The perception of integrity and pitch.
http://clippu.net/threads/tembr.967/
(Here the phases described experiment)

Helmholtz wrote that phase is inaudible, but later writers say that this is only true for sine waves or sounds with few partials. When there are multiple inharmonic partials, particularly, phase differences are audible. Sorry not to have access to the modern quotes right now, but I think the general agreement, now, is that for a piano note, which has both many inharmonic partials, and has two to three, slightly out of unison, strings sounding at once, and with the phase of each string rapidly changing as it bounces off each termination point, the phase is not just audible, but a major component of the timbre. (And there are the bridges to consider. I get lost there. They serve as termination points? Not exactly, since the strings vibrate on both sides of the bridges? And it is the vibrations of the soundboard that we hear, for the most part. On various parts of the soundboard, which itself responds with differing amounts of impedance as it thickens and thins. And then there is the phase change where these various thicknesses and thinesses of wood meet the curving rim...)

Still don't understand the difference in the beat rate that is so audible on these mono-string recordings of two partials. What's going on there? I do understand why there is beating. I don't understand why the beat rates differ so much between the piano note and the modelled note. Is the variation in the pitch of the partials that wide? If so, wouldn't the timbre of the notes sound still more different? The beat rate is much, much faster between partials in the model. Sounds at least twice as fast. Cant imagine how that is possible.

(I still want to talk more about the regularity of the beats in the modelled notes, compared to the "acoustic" notes, too. And the sustain time of the lower partials.)

Very valuable discussion going on. (Only by getting lost can one get found?)

Back to the the subject matter at hand:  Some explanations why the amplitude vs. time traces might be different.

I know of no definitive cause for the difference  in traces between piano sources, but here are a few musings on this subject.

Yes, of course, one source is a digital recording of a Model B Steinway and the other source is a Pianoteq virtual model of a 7' Steinway studio grand piano. 

Strike point:
Choosing a different strike point along a given string, virtual or otherwise, will give rise to emphasizing and suppressing any number of upper harmonics.  For example, many piano makers desire the strike point to be one-seventh the distance from the end of a string, so as to force that 7th harmonic to be suppressed.

Who's to say that the strike point of the Pianoteq note was precisely the same strike point as the piano used in the sample library?

Hammer Hardness:
Harder hammers give rise to brighter tone, including overtones ... especially overtones of notes in the lowest piano octave.

Hammer Mass:
In the virtual world, any value of hammer mass is possible; it will change the amplitude ratio of fundamental frequency to amplitudes of the natural harmonic series.

String Mass and Tension:
Of course, this comparison is of the same note E1, but who's to say the Pianoteq virtual string is identical to the given sampled piano?

Vibrational Mode of Piano String:
The nature of an agraffe in the grand piano's soundboard bridge is to cause the vibrational mode to change from purely vertical (as in struck from beneath in an upward direction) to one that has a horizontal component to it as well.  We do not know whether the sampled piano was taken before- or after the string had gone into the horizontal component.  An experienced listener can hear the change in the overtone series that results from the string's vibrational mode with a horizontal component to it.

I submit that vibrational mode of a string is constantly changing, in the case of Pianoteq -- but might be a looped and relatively unchanging snippet from the sampled piano library.  Why so?  That's because it's harder to loop the sound of a vibrating string whose vibrational mode includes vertical- and horizontal components.  (It's easier to hear the looping point unless a relatively unchanging mode is sampled.)

Food for thought.

Cheers,

Joe

Hello Jake,

According to the original statement in this thread, the non-Pianoteq sound came from "Pianowave Steinway B samples" rather than a live recording from a real acoustic Model B at hand.  While this might sound as though I am being picky, it is possible that any samples from a piano library may have been processed with noise reduction, compression or EQ.

Regarding the trace, I refer to the top photograph (oscilloscope) in the original thread.  The author also mentioned "the timbre of sounding splits into separate sounds in a long sound."  By this, I believe he has heard the virtual Pianoteq string change from purely from a vertical vibrational mode to one that has a horizontal component to it, i.e., he is now hearing the effects of the soundboard resonance.  It is very possible that the soundboard resonance (an its own associated overtones) might be the origin of those extra lines observed in the oscilloscope trace.

Cheers,

Joe

The following thoughts emerged:
1. Communication sound amplitude with frequency. Since a small change in frequency is manifested as phase shift. Accordingly, the connection with the phase amplitude. Fluctuating transition from one to another. It looks like the effect when whirling skater pulls in his hands and begins to spin faster.
2. Swinging nodes and anti-nodes along a vibrating string and relative to each other. Since it is an overtone oscillation of several parts of the string, then the rocking nodes and anti-nodes, they may be subject to change in amplitude and phase with respect to each other. Perhaps with this and related effect of changes in the composition of overtones when playing repeated notes on the open string.
3. Manifestation swinging phase shift between the left and right channel. Perhaps this is due to the direction of rotation of the vibrating string.
4. The presence of some common, unifying force that connects, magnetizing phase of the overtones together. A kind of gravity between the phases of the overtones. (At the piano Lissajous trajectory lines resemble the trajectory around the sun of planets, planets from Pianoteq trajectory without star .. Fancy comparison)))
5. Often there are overtones in Pianoteq sounding completely opposite. This creates a feeling of extra sound an octave higher. If this occurs in the sound of overtone, that phantom sound may be different from the other notes and overtones cause strangeness tone.
6. How it manifests itself vibration cast iron frame? More precisely vibration system: cast iron frame, all the strings. It's a massive facility with a large internal stress. Perhaps the vibration spectrum extends from the fluctuations of a few seconds up to a much higher than the highest strings .. I personally, after the piano, I want to add a sympathetic resonance when I sit down at Pianoteq. Can frame as the sun around which everything spins?)

Listening to the piano impression that the cast-iron frame makes a sound of what is happening inside the string with the external vibrations. This adds a "nasal" tone and high frequency "hiss" and shine. The steinway is a combination between a cast-iron frame and the outer casing without touching the deck. The outer housing is a cavity for a frame? So interesting..

Probably a varying cancellation effect between the two tines.

Surely that IS the difference in phase between two very similar signals reaching the ONE ear ?
It is about the simplest and "purist" experiment that shows it.
Almost every other experience includes reflected sound and (as we all KNOW) sound reflectors change timbre.

On reflection "Spin" may have not been the best word for me to have chosen for the tuning fork experiment.
I had NOT meant a fast spin, merely a slow rolling of the tang between thumb and forefinger, a revolution or two per second.
Turning the fork at SLOW speed doesn't introduce the Doppler effect, it just illustrates that phase is audible.

You'd still get subtle but audible tremolo effect. And you can still think of it as being due to the superposition of two very subtle equal and opposite Doppler shifts (too subtle to be audible if you could listen to one tine at a time). Or you can think of it as being due to small relative phase shifts. Mathematically the two are equivalent. Phase is not really audible though. If you listened to the tuning fork in two different fixed orientations (slightly different relative phases for the two sources), they would sound identical (except for a very small change in volume). You only hear the 1-2 Hz sinusoidal variation in the phases while the tuning fork is rotating. But anyway it's a two sources + one detector (ear) situation, which if carefully set up could theoretically result in strong enhancements or cancellations (not with a tuning fork but say two loudspeakers). That's not relevant to phases of a superposition of pure tones in a mono signal though, where one can't hear phase except at the lowest frequencies.

It was made in Gnuplot, just typing explicit expressions in. The frequencies I chose to best illustrate what's happening. In a realistic scenario there would be a lot more difference in tremolo and tuning fork pitch frequencies and the Doppler shift would be a lot more subtle. But then the plot would be way too busy to see what's happening.

There is no Doppler effect if you PAUSE the rotation of the tang.
It is possible to hear the phase difference - - separately and in addition to the changing of phase difference.
I don't regard the changing of phase difference as the Doppler effect - YMMV, etc.