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 How much more players are needed to double the perceived volume?
Author: Luuk 
Date:   2025-01-30 14:04

In another thread Tom H wrote:

Quote:

As a retired band director I read somewhere that when you have more than one saxophone the volume tends to multiply. ie.- 6 trumpets together sound like 6 but 6 altos sound like way more than 6. I found this to be somewhat true. Has to do with it's curvy construction I believe.


When referring to perceived volume this observation is confusing to me. A doubling of the number of players brings a doubling of energy put into the sound (everything else left equal). It does not matter if the instruments involved are saxophones, flutes or clarinets. Of course, some instruments are more efficient in producing acoustic energy, thus in a complete band setting, adding a saxophone may add more to the output energy than adding a trumpet.

Now, lots of internet sites state that, in order to perceive a doubling of loudness, we need to put in ten (!) times as much power (for instance https://jlaudio.zendesk.com/hc/en-us/articles/217201737-Doubling-Power-vs-Doubling-Output, but there are many more sources).

Am I missing something? Maybe the frequency dependent sensitivity of the human ear is involved. When more energy is put in frequencies for which the ear is more sensitive, the subjective effect is more prominent. Could it be that the excess of overtones in saxophones when compared to trumpets lies at the root of the observation of Tom H?

Regards,

Luuk
Philharmonie Brainport
The Netherlands

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 Re: How much more players are needed to double the perceived volume?
Author: Philip Caron 
Date:   2025-01-30 17:36

If you add 6 altos, the trumpets are still going to be too loud.

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 Re: How much more players are needed to double the perceived volume?
Author: m1964 
Date:   2025-01-30 20:40

I was told that in order to double volume produced by a violin, you’d need to quadruple the number of instruments.

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 Re: How much more players are needed to double the perceived volume?
Author: Neil 
Date:   2025-01-31 04:01

Rather than speculating, I think the best approach is to actually measure the sound level. You can get a cheap sound level meter for less than $50.

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 Re: How much more players are needed to double the perceived volume?
Author: kdk 
Date:   2025-01-31 05:55

Even cheaper, for a rough idea, are the apps available on our phones.

One of the problems with so much discussion today is that so much of it starts with "They say..." or "I heard..." or "People say..." or even "I read somewhere that..."

Although they say that the only way to get two piccolos to play in tune with each other is to shoot one. But who knows??

Karl

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 Re: How much more players are needed to double the perceived volume?
Author: John Peacock 
Date:   2025-01-31 16:16

The quantitative answer to this question is perhaps surprising, since it concerns the human perception of the power in sound waves. Like so many things in the way humans work, this is on a logarithmic scale, measured in decibels. The very threshold of audibility is set at 0 dB, and the loudest sounds that can be tolerated are about 120 dB (as experienced say by someone in the middle of the hundreds of performers at one of the climaxes of Mahler 8). Normal conversation, or say a single violin playing mp, is reported to be at 60 dB. So in a sense Mahler 8 is twice as loud as one mp violin - but the way decibels work is that 10 dB is a factor 10 in acoustic power, so 120 dB is 1 million times the power of 60 dB.

That definition of "twice as loud" doesn't feel intuitively right to me, and that's probably because 0 dB is really astonishingly quiet. The quietest we ever experience in an everyday setting is something like a library reading room, and I've seen this quoted as 30 dB. So with that as a more realistic zero point, then twice as loud as our mp violin at 60dB would take us another 30 to 90 dB. But even that is 1000 times the power of the single violin, just to get a factor 2 in perceived volume. No wonder romantic composers rapidly moved from string quartets to massive symphony orchestras: you need a truly colossal boost in the number of players in order to achieve even a modest difference in how loud you feel things are.

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 Re: How much more players are needed to double the perceived volume?
Author: Philip DeVries 
Date:   2025-01-31 20:27

As noted, acoustic energy and perceived volume are not the same thing, and the OP is a question of perception, not actual sound power. Generally, it is a good rule of thumb that a 3dB (2x) increase in acoustic energy is roughly the threshold for you to notice that it became louder. If you suddenly notice “hey, those alto players are really cutting it”, it’s either a lot more than 2x acoustic energy, or it’s the physiology of hearing. If the observation in the OP is correct in general, it could indeed be something about the tonal content of the sax, which is more complex than the trumpet or the clarinet. My hunch, though, is that it is most likely the psychology of the players, with sax players playing more confidently in groups, but trumpet players blasting it, ever time.

The decibel is an objective, scientific, logarithmic unit, for comparing relative amounts of power (acoustic energy or pressure, in the case of sound). A 10 decibel increase in acoustic energy corresponds to 10x power, but a 20 decibel increase in acoustic energy is 100x, and so on. A 3dB increase in acoustic energy corresponds to 2x. The sound pressure waves of multiple instruments are not in phase, so two instruments played at the same volume produce 2x acoustic energy, or a 3dB increase, over a single one. Actual sound energy doubles when the number of players double, if they all play the same way.

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 Re: How much more players are needed to double the perceived volume?
Author: Mark Charette 
Date:   2025-01-31 23:52

Apparent loudness is not linear with power output. See:
https://en.m.wikipedia.org/wiki/Equal-loudness_contour

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 Re: How much more players are needed to double the perceived volume?
Author: Burt 
Date:   2025-02-01 21:26

Philip DeVries described the situation perfectly.

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 Re: How much more players are needed to double the perceived volume?
Author: Chris P 
Date:   2025-02-02 19:54

If you're a military band arranger, just have all the solo and 1st clarinets screeching away up in the altissimo register at ff or more to make it all extra jarring. Meanwhile the Eb clarinet can be sat there twiddling their thumbs doing nothing.

Former oboe finisher
Howarth of London
1998 - 2010

The opinions I express are my own.

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 Re: How much more players are needed to double the perceived volume?
Author: kdk 
Date:   2025-02-02 20:07

Chris P wrote:

> If you're a military band arranger, just have all the solo and
> 1st clarinets screeching away up in the altissimo register at
> ff or more to make it all extra jarring. Meanwhile the Eb
> clarinet can be sat there twiddling their thumbs doing nothing.
>

Or you have the Eb clarinet double the piccolo part, adding to that intonation problem (now, whom do you shoot?).

:)

Karl



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 Re: How much more players are needed to double the perceived volume?
Author: Paul Aviles 
Date:   2025-02-02 20:18

Easy on the military clarinets! Ya know, besides clarinet, we are all weapons qualified.



:-)




………… Paul Aviles

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 Re: How much more players are needed to double the perceived volume?
Author: Chris P 
Date:   2025-02-02 20:29

Is that why military bands choose to tune to the solo clarinettist instead of the principal (or only) oboist?

Former oboe finisher
Howarth of London
1998 - 2010

The opinions I express are my own.

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 Re: How much more players are needed to double the perceived volume?
Author: SecondTry 
Date:   2025-02-02 21:45

I think one factor, certainly real and likely perceived is the volume...

...and this was at the very least alluded to above

that we start at.

As per Mark's linked article, there is a reason that a common scale of actual loudness, the decibel scale, is logarithmic in its design, like the earthquake Richter scale.

For the layperson this basically means that the degree of change between two adjacent value on the scale, say from "5" to "6" is significantly more the difference, say, between "3" and "4," just as sure as the difference between "6" and "7" is (exponentially) larger than "5" to "6."

That said though your inquiry deals with perception, and I imagine things that trigger human auditory response more--and frankly I don't know if that's a product of pitch, harmonics, or if it's even universal, I suspect are likely to be heard as louder with the addition of less instruments than sounds seen as more pleasing.

Does this mean that adding more piccolos or trumpets has greater effect than more violins....

I think so...?



Post Edited (2025-02-02 22:06)

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 Re: How much more players are needed to double the perceived volume?
Author: clarnibass 
Date:   2025-02-04 11:00

>> I read somewhere that when you have more than one saxophone the volume tends to multiply. ie.- 6 trumpets together sound like 6 but 6 altos sound like way more than 6 <<

Others already explained the volume "issue" well, but it sounds like it's more about expectation vs. reality and it's almost the other way around.
Meaning, the way (e.g.) six alto saxophones sound is the way they sound. If they don't sound the way you thought they would, then your expectation was different from reality for whatever reason.
Whether some instruments have a larger difference between expectation and reality than others is a statistics question... I guess it's possible. Or if certain sounds are likely to have this effect more than others, maybe someone has an explanation as to why.

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 Re: How much more players are needed to double the perceived volume?
Author: SecondTry 
Date:   2025-02-06 20:43

I might also suggest, somewhat tongue-in-cheek, that the perceived addition to volume with each new player might be directly correlated with the lack of intonation of the group with each other.  ;)

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