Topic by Jake Johnson

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  • Jake Johnson
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Topic: Research on the rate at which new partials replace existing partials?

Does anyone know of research about the speed at which or degree to which the partials of a newly struck string replace those of a sounding note on both the strings and the other physical components of a piano? I know that this is already part of the current PianoTeq model—striking a string that is already vibrating creates a different sound from striking an immobile string. (I‘m not sure if the model makes the soundboard vibrations\global resonance vary with repeated notes or when notes are played that contain partials that are the same as those that are already sounding.) No, I’m not building my own modeled piano—I’d just like to understand the phenomena better and thus be better able to know what I’m trying to emulate when working with either PianoTeq or samples.

In other words, what I’m trying to learn is: If one plays and sustains middle C, and then plays middle C again, at what rate do the new partials replace the existing partials\standing waves, and to what extent do the original sounding partials continue to play on the strings and soundboard, etc? How long do the standing waves on the soundboard and body and harp continue to sound after the new note is struck? What happens if the new note is not the same note, but instead contains some of the same partials as the previous note? I can guess at some of the variables: the physical composition of the soundboard, etc, the hammer hardness and velocity of the new strike, but I haven’t been able to find actual tests. (Does an increase in velocity = the rate at which the original standing waves are replaced by the new standing waves? Does the larger mass of the soundboard and body cause them to sustain existing standing waves longer?) One of my main interests is in trying to determine how the sound sources\modulators may vary in their response to the new strike--I can imagine that each of them (strings, body, harp, soundboard) may sustain given partials for different amounts of time, so that repeating a single note will mean that different partials will be playing\decaying from each source, and thus I will have another reason to feel overwhelmed by the complexity of how a piano creates a sound.

All of this comes from having a parameter on my old Ensoniq KS-32 that I’ve never seen on software samplers or modeled instruments—this Ensoniq parameter just lets you set the time that passes before the playing note dies after the same sample is struck again, so the notes overlap. In other words, striking a new note doesn’t immediately kill an existing note, which can instead continue to ring out for another few milliseconds. This feature doesn’t, of course, replicate the way partials may very briefly coexist. It only prolongs the sounding note slightly. On the other hand, it does increase the realism of the piano sound.

Reply by Philippe Guillaume

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Re: Research on the rate at which new partials replace existing partials?

Hi Jake, here are two remarks about these (difficult) questions:
- when a note is stroke a second time, the first one does not dye, it is still there, but it looses some of its energy because the hammer stays in contact with the string a certain time, hence works partially like a damper for the first note. Thus what was implemented in your Ensoniq KS-32 is consistent with the real thing,
- the second note has its own spectral content, it does not replace the previous note content, but it is added to it (precisely it’s added to what remains from the first note after the contact).

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Reply by Philippe Guillaume

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Re: Research on the rate at which new partials replace existing partials?

Btw, the JASA http://scitation.aip.org/JASA is probably the journal that has published the most papers on the piano. Among many other, one interesting series of papers from Anders Askenfelt and Erik V. Jansson:
- From touch to string vibrations—The initial course of the piano tone, J. Acoust. Soc. Am. 81, S61 (1987)
- From touch to string vibrations. I: Timing in the grand piano action, J. Acoust. Soc. Am. 88, 52 (1990)
- From touch to string vibrations. II: The motion of the key and hammer, J. Acoust. Soc. Am. 90, 2383 (1991)
- From touch to string vibrations. III: String motion and spectra, J. Acoust. Soc. Am. 93, 2181 (1993)

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Reply by Jake Johnson

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Re: Research on the rate at which new partials replace existing partials?

Thanks so much for the guidance. I hope you won't mind another question if you get the chance to answer: Since there is no damper on the soundboard (the hammer doesn't hit it to dampen the sound), do the standing waves on the soundboard just keep decaying in the same way that they would if no other notes are played?

Sorry for the complexities of these questions. I can see that I'm asking for the impossible, short answers about complex interactions of waves and sound sources\modifiers.

(From what I can gather, the patterns of standing waves on any planar surface are hard to map, and the patterns on a piano soundboard are very complex, influenced by so many factors that it's hard to imagine understanding them all: the placement and width and height of the bracings, the string struck, since each string initially vibrates a different part of the soundboard before the vibrations spread throughout the soundboard, the way the soundboard reflects vibrations back to the strings, which in turn revibrate (if that's a word) the soundboard in a sequence that only stops when all of the energy from the strike is expended, etc. Which may well explain why I'm having trouble understanding it all...)

Reply by Philippe Guillaume

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Re: Research on the rate at which new partials replace existing partials?

Jake Johnson wrote:

Thanks so much for the guidance. I hope you won't mind another question if you get the chance to answer: Since there is no damper on the soundboard (the hammer doesn't hit it to dampen the sound), do the standing waves on the soundboard just keep decaying in the same way that they would if no other notes are played?

Sorry for the complexities of these questions. I can see that I'm asking for the impossible, short answers about complex interactions of waves and sound sources\modifiers.

The complexity depends also on the point of view: things get simpler to understand if you think about the whole structure strings + soundboard + cabinet + outside as a single mechanical structure that has its proper modes (thus each mode concerns the whole structure, not isolated parts like single strings). Each mode has its proper decay rate, which is independent from everything else as long as the structure has no interaction with other elements like hammers and dampers. So the answer to your question is: the modes that were excited by the first stroke, once the second stroke is finished, will continue from this moment to vanish in the same way as if they were in this state after a first stroke. This of course can take into account the fact that each mode looses some energy during the contact time when the hammer strikes the strings for the second time, but once the contact is finished, the decay continues always in the same way. Another formulation: if one observes the vibrating structure (strings + soundboard +...) on a period where there is no interaction with the hammers or the dampers, it is almost impossible to tell whether a given note has bee stroke one or several times before that period. Hmm… Could not guess it would be so long, hope it’s not a complete confusion!

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