Assume a looping sample of a sampled instrument, a tuba in this example.
A) The periodic wave shape at low A (A1) will differ from the wave shape at C4.
B) Additionally, the wave shape varies within the A1 sample as the flow pressure and therefore rate from the tubist's lungs through the instrument varies. This can be emperically verified through a simple gross examination of such a sample. This could be loosely correlated with "velocity" for percussion-based instruments.
Thus, wave shape is a function of A) pitch, and B) pressure.
The shape of the shaping function itself may be linear or nonlinear. For example, does the change in waveform shape progress regularly in relation to progression up the musical scale? Or does it change abruptly near the upper or lower extremes.
Lemma: I propose that, if the impact funtions along the pressure and pitch domains can be derived, there's really no need for huge multi-hundred MB deep sampling. One has only to generate the waves (using software that I'll have to write) based on a few "waypoints" along the pitch and pressure domains.
These simple waves can then be imported into the DAW as looped multisamples (tiny in size), and the ADSR set accordingly. Thus, you can have an orchestra-on-the-head-of-a-pin...
Thoughts?
Theoretical discussion of deep sampling
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bluebell
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Re: Theoretical discussion of deep sampling
There is another thing to be calculated: formants, some kind of resonance independent from the note's pitch
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Re: Theoretical discussion of deep sampling
Our understanding of sound waves in the digital world has become two dimensional - pitch and pressure, or amplitude. We can blame the computer screens for that. The pressure waves that actually reach our eardrums in the real world are three dimensional. The shape of the vibration in this third direction roughly corresponds to information about the character of sound known as "timbre", what bluebell calls "formants". And that is way more information than the four simple values of ADSR can imagine to emulate.These simple waves can then be imported into the DAW as looped multisamples (tiny in size), and the ADSR set accordingly. Thus, you can have an orchestra-on-the-head-of-a-pin...
Timbre is what contains information about how uniquely and beautifully imperfect the tube of the tuba was. How old the wood used in the cello was. How wet the leather on the kick was. That's what deep sampling attempts to capture. And hence all the money and effort spent by so many DAWs in 'recording' good samples, not 'generating' them. There could be an orchestra on the head of a pin the way you suggest it, and it may sound gorgeous, but it ain't ever sounding like an orchestra.