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Theoretically, each addition of a sound identical to the previous one results in a 6db increase in the final sound result.
I ask: is that why in some orchestrations we see, for example, 6 clarinets playing the same passage in unison, that is, just to increase the final volume and highlight this passage beyond the other instruments?
Since the different instruments are not producing the exact same waveforms perfectly phase aligned, there is not nearly a 6 dB boost when the number of instruments playing the same part is doubled. It’s more complicated than that.
The doubling has two effects: first, there is a volume increase, and as some instruments are quieter than others, this can really help with the overall mix of the orchestra. It also helps with playing in bigger rooms. A modern version of this was that James Brown would have two drummers playing the same part so they could be loud enough without amplification. Or the drummers would take turns playing songs because they had to hit so hard they had to take breaks.
The second reason to double parts is to create a different timbre. A violin section playing in unison sounds very different from a single violin playing the same notes. And the size of the section makes a difference. Chamber strings sound “smaller” than symphonic strings.
I guess there’s a third reason which is if you want to create a note of arbitrary length, you can have a section sustain that note for a very long time assuming the players choose different times to breathe (which pros know to do without being asked). So the section sort of turns into a single instrument that has a different timbre and capabilities compared to a solo instrument.
In brief, certainly one reason for multiple instruments in unison is to achieve greater total signal (sound) power output.
In detail,
1) Two instruments will not add coherently, so the power ratio is additive, i.e. 2 are roughly twice the power (in linear units), three produces 3X the (linear) power. If they were coherent, the peak power would be 2^(number of instruments), except where the off-axis interference produced nulls.
2) Because the instruments are never perfectly in tune, nor do they produce exactly the same overtone ratios, the sound of, e.g., a 10-instrument first violin section sounds very different from the highly amplified sound from one violin.
3) Even if the instruments were identical in output, the tone quality is a function of the amplitude -- a clarinet played fortissimo does not sound like 10 clarinets played pianissimo.
