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Is a recording of a chord merely a superposition of recordings of its constituent notes? Assuming the recording of its constituent notes are sufficiently clean.

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  • $\begingroup$ a chord created by simultaneous playing of monophonic instruments would be exactly the superposition, me thinks. i don't think that one flute's note would couple much into another flute. $\endgroup$ – robert bristow-johnson Dec 10 '17 at 2:47
  • $\begingroup$ You can never jump in the same river twice. The 16-bit sample array from the same flute played by the same player but recorded a day later are unlikely to be exactly identical to the first. $\endgroup$ – hotpaw2 Dec 10 '17 at 3:18
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    $\begingroup$ that is true. but that is not what i was thinking the question was about. $\endgroup$ – robert bristow-johnson Dec 10 '17 at 3:43
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    $\begingroup$ sometimes (if memory is cheap), sampling synths have multiple samples (or "sample arrays") of the same instrument at the same note and they pull one at random so that each note does not sound like an identical copy of the same thing. $\endgroup$ – robert bristow-johnson Dec 10 '17 at 3:44
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It's close enough for most practical synthesis purposes. However in real polyphonic instruments, there tends to be some coupling between the various oscillators that can, for example, synchronize notes that are close enough to whole number ratios.

For other ensemble instruments, the coupling can work via the hearing of the instrumentalists and minute corrections (of embouchure, fingering pitch, and so on).

And for nonlinear effects (like accordion bass mechanic sympathetic vibration or a distortion pedal for a guitar or a distorted amp), the results are definitely non-linear.

But more often than not, just adding the samples is a good enough approximation.

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Depends to some degree on the instrument: electronic versus mechanical, string versus reed versus pipe, etc. Typical electronic keyboards have no coupling between keys, and the DSP mixer is usually very close to linear (other than quantization effects, etc., unless the level is high enough to cause clipping, or kick in an AGC). But guitars and pianos do have physical coupling between strings, through the bridge as well as through instrument body or sound board resonances.

Coupling can change the individual notes to slightly different pitches as well as timbres (overtone series).

All bets are off for electric guitars fed though fuzz boxes (etc.).

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No, at least not exactly. It could be that linear superposition is a reasonable approximation of the actual physical processes, but that depends on many things. There are many sources of non-linearities, including the instrument itself and, obviously, the whole recording chain.

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For fretless instruments, in some situations, advanced players will modify the fingering slightly depending on the key or even the specific chord in order to improve the sound compared to the musical temperament built in to most instruments with quantized pitches. So in this case, the precise pitches of the constituent notes depends on the context in the music and one may need slightly different samples, or the ability to pitch shift samples a small amount to reproduce this effect.

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