A truly perfect unison
Two notes are two notes. At least, it seems that way. When people play two notes at two frequencies, they sound like two notes, even when they're playing in unison. There are a variety of factors causing this. How close can two human players of an instrument realistically get to playing a truly perfect unison?
By a "truly perfect unison", I mean that the two notes are observed to be one louder note, indistinguishable from a single note of a higher volume.
Please don't hesitate to get into complicated explanations; it may take me a while, but I'll probably figure it out.
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In practice this is nearly impossible without using mechanical (computer or the like) means. Not only must the amplitudes match but the frequency must be very close and stay that close for the whole duration. The other problem that affects the previous would in matching the phase. Note that a violin section may play almost perfectly in tune but will still sound different from a single violin playing loudly. This to a large extent due to phase differences among the players. Trivially a phase change changes relative loudness continuously. Letting Sin(At) represent a pure tone of frequency A as function of time, one can change phase and get Sin(At+b) where b is the phase. This becomes (through elementary trigonometric identities) Sin(At)Cos(b)+Cos(At)Sin(b). The pure form has split into two parts with one part out of phase with the other.
@user452 ...
Note that I'm looping in the fact question is also tagged as pychoacoustic:
If you have the same pitch/note, all waveform arguments are moot.
Theoretically, two humans such as two twin humans, highly and similarly trained, are most likely than most to indistinguishably attack the target note than 2 unrelated, highly and similarly trained musicians.
I really do think this is a great question, and I for one would be up on this so-called so-wiki more often if I saw more questions like it.
Thank you for posting,
-R
If we first assumme that we are taking about two acoustic instruments being played in a real space, there are a few things we have to do to get this to happen, all of which are hard:
We have to find two instruments that can produce very similar waveforms, and play them with very similar technique such that they produce those very similar waveforms. This is very hard, as all real acoustic instruments have complex behavior, producing waveforms consisting of many harmonic and inharmonic partials that can shift in amplitude and frequency; slight variations in playing technique will change how each of those behaves. Any slight difference in the frequency of a prominent partial between our two instruments may produce an audible chorusing effect.
We have to start the notes at exactly the same time when we play them, by which i mean down to a tiny fraction of a millisecond, otherwise you will get comb filtering effects, and possibly a smearing of the initial transient (to which the ear is very sensitive).
The two instruments have to seem to be in the same place. The auditory system has a variety of ways of locating and separating sounds, and in any real environment, it is likely to have enough clues to separate two sound sources playing the same thing.
If we can somehow overcome those issues, then possibly we could get two instruments to sound like one. It's just that all those things are hard to overcome.
As Tetsujin says in the comment, a computer playing back samples can easily make two notes sound like one - precisely because it can overcome all these issues. It can ensure that both parts play the same waveform; it can start playback at the same point in discrete (sampled) time; and it can mix the waveforms in a way unaffected by acoustic space.
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