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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?

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    No, you're misunderstanding the relationship between 'power', 'volume' & 'perception' See sengpielaudio.com/calculator-levelchange.htm which covers it better than I could here. – Tetsujin Aug 24 '19 at 16:31
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    @JimM 3 dB is a factor of two. 10dB is a factor of 100 -- just look up the definition of a decibel; and beware of the difference between amplitude and power. – Carl Witthoft Aug 24 '19 at 17:40
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    @JimM - Please ask your own question. – aparente001 Aug 25 '19 at 1:26
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    In grade school, one reason composers have six clarinetists play the same thing is that clarinet is a very popular instrument and it's good to have pieces where everyone gets to play. – aparente001 Aug 25 '19 at 1:28
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    To correct @CarlWitthoft's typo above: 10dB is a factor of 10. 20dB is a factor of 100. – Rosie F Aug 25 '19 at 6:30
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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.

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    Especially in choral singing, where the difference between one voice and two is staggering, even when everyone's trying to blend. And also similarly to a choir, the staggered breathing through long notes was something I was taught in third grade in a school choir. Good answer. – user45266 Aug 24 '19 at 19:45
  • For the second reason, "different timbre" is a nice way to put it. Less gloriously, having more players for the same part will often even out players that are slightly out of tune, and it will hide small mistakes and situations where one player messes up and stops playing for a while. Doing the same part with a solo player will make them much more "exposed", requiring a much higher skill of that one player to reliably play the part in tune with no errors and no safety net. And often it's easier to find 10 decent players than one excellent player, so... – a3nm Aug 25 '19 at 15:48
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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.

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  • The power ratio is always additive, not exponential. You can't get power out of nothing. One watt plus another watt yields two watts, wherever they come from. Answer is completely incorrect. – Marquis of Lorne Aug 26 '19 at 4:23
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    @user207421: Actually, you're both wrong. If they were coherent, n instruments would have n squared the power. The reason that this isn't a contradiction of the law of conservation of energy is that if n instruments interfere constructively at one point, they interfere destructively at another point, so the average power heard by a listener is n times the power of one instrument. – Peter Shor Aug 26 '19 at 12:42
  • +1 for your 2). So long as the difference in frequencies of the pitches they play isn't too great, the result is a richer sound. This is also why piano tuners deliberately tune the strings struck by the same hammer to very slightly different pitches. – Rosie F Aug 26 '19 at 13:52
  • @PeterShor That's what I meant with my " off-axis interference produced nulls" , but I certainly wasn't very clear on that point. – Carl Witthoft Aug 26 '19 at 14:07
  • @RosieF true -- an additional reason for that piano de-tuning is that it leads to vibrational energy transferring back and forth among the three (or two, for high notes) strings, generally lengthening the sustain. – Carl Witthoft Aug 26 '19 at 14:08

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