With the little knowledge I have about music and physics of sound, I believe that sound energy can either be enhanced or decreased based on the interference pattern that are formed due to the interacting frequencies. This may result in sounds that may be beyond limit of one's hearing capability. At high frequencies the negation becomes difficult as the energy of the wave is much higher and the loss is gradual.

Hi,

every electroacoustical transducer has maxumum sound pressure level (SPL) or power that can be transformed without or with very low distortions. The sound content is of no importance, it could be natural or unnatural sounds.

Hearing possibilities are well described in many books on psychoacoustics(see. e.g. Zwicker & Feldtkeller), including spectral, temporal and directional resolution and SPL limitations. 

Summing of many random sources of sound will create some noiselike sound. 

For closed volumes (as concert halls) among other things there is some minimal cubic volume per audience member.

Best regards

A fascinating question. Some of the issues may be logistical - since sound may take a large fraction of a second to cross such a large choir, you would need to segment your recording area to minimize the loss of musical content by delay. The large choir sang in unison, and it would be interesting to obtain the recordings no doubt made by individuals there on phones, and to combine them to answer one aspect of your question. The summation of so many sources of sound, even if each can be perceived as musical, will probably create something more like noise than discernible tones, as Mr. Gordon pointed out. There is another question of the boundary between perception of tone and perception of noise, which is largely dependent on subjective interpretation by the listener, and the acuity of the listener's hearing. Is there a definable boundary beyond which music is washed out in noise? Or is that always going to be subjective, or an individual condition?

So as long as clipping did not occur, I guess there's no technical limitations for quantity of sound energy sources "emitting" at once. Still intrigued by the perceptual boundaries though (and thanks Richard for your input here). At what point do sound atoms become a mash of indistinguishable noise ?

Thank you all   

Hi,

interesting question but (i think) the answer is quite simple: if you raise the amount of soundsources you will hear eventually (something like) white noise. If we consider the simplest sound source (a sine) from a spectral point of view we will get a line at a certain frequency. If we add more of the same signals (same frequency, same phase) nothing but the amplitude will change. If we add more (an infinte number of) sines with different frequencies we add more and more lines and we will get in the end a flat spectrum (= white noise). We can expand the example of sines to more natural sounds which can also be seen as just a summation of sinewaves (as shown by Fourier analysis) with different phase. So when we summarise natural sounds we will reach the white noise (or probably some other noise with a different spectrum) probably sooner. When we have reached this state, by adding more sources we will only alter the amplitude of our signal. And at some point we will get clipping but that's no "natural" limit but a matter of your recording/playback hardware.

So you can actually record and playback an infinite number of sound sources without any distortion as long as the overall volume of the resulting signal is at no point above you "clipping" limit.

At least that's my oppinion... ;)

Greets

Thank you so much Wolfgang, it does make sense - at least with the sine wave example (although I'm not sure how you'd be adding an infinite amount of sine waves as it'd take you forever to do so!) 

So there's frequency and phase and amplitude... but what about any and all other elements which make up each sound signature ?

If we were to combine many signatures (forests let's say)... how/when does each signature get diluted with the rest ? At what point does it all start being noise ? 

Are there any known or defined boundaries to this ? (both technical and perceptual)

Many thanks in advance

"although I'm not sure how you'd be adding an infinite amount of sine waves as it'd take you forever to do so!"

You're right, but that's of course just an example.

"but what about any and all other elements which make up each sound signature ?"

Actually EVERY sound is just comprised of these three elements. You can desompose any signal (or sound) into a number of sine waves with different frequency, amplitude and phase. So for example instead of one person talking you could also use a (high) number of (time variant) sine waves in a certain combination and the resulting signal would sound the same.

"At what point does it all start being noise ? Are there any known or defined boundaries to this ? (both technical and perceptual)"

Not really because noise is a very individual perception. What one person would define as noise is for another person maybe music. From a technical point of view noise is a sound with a flat spectrum or at least many overtones with no integer multiple of the fundamental frequency. A tone has a fundamental frequency and a number of integer partial tones which define the "characteristic sound" of it.

I think the most important point making the difference between noise and a tone is correlation. White noise is defined as the sum of all frequencies in a certain range (e.g., 20 Hz - 20 kHz) while level and phase are random.

Let's consider two examples:

1) In a beer tent of the "Oktoberfest" in Munic there are 5.000 people all talking to the people next to them. Everybody is saying something different. A listener receives the sum of many uncorrelated sound sources and receives this as noise.

2) In a football stadium 20.000 fans build up a speaking choir to cheer for their favorite player, that is, all 20.000 fans are shouting the name of the player synchronously. A listener receives the sum of many correlated sound sources and will be able to understand the name of the player the fans shout. The listener will perceive a large speaking choir, not noise.

Best regards

Thank you Albert, that´s very clarifying. How can I explore the concept of uncorrelated and correlated further ?

Many thanks 

Production. Sound consists of fast fluctuations of the air pressure around the atmospheric pressure. The air pressure cannot drop below zero (=vacuum), so you cannot produce arbitrarily high sound levels without strong distortion. This occurs with sonic booms, explosions, etc. The limit is ~194 dB SPL (decibel sound pressure level). This may look innocent, but decibels are a logarithmic scale! If each choir member produces 85 dB SPL (which is very loud), and when you ignore the logistic problems mentioned by others, your 121,440 member choir still "only" produces 136 dB SPL (which would destroy your hearing pretty fast anyway). In order to reach the atmospheric 194-dB-SPL limit you need a choir of 100 billion.

Recording. Good recording equipment adjusts its sensitivity to the intensity of the sound. The engineering term for this is "automatic gain control." The adjustment takes some time, so the equipment may have trouble with sudden outbursts. Of course a chain is as weak as its weakest link, so the microphone should be able to handle high intensities. There are special heavy duty microphones for industrial applications that can handle very high intensities (e.g. inside jet engines). There are no fundamental upper limits to the intensity a pressure sensor (microphone) can handle.

Hearing. Our inner ears have a built-in automatic gain control, which is pretty fast (reaction time < 1 ms). But our ears (and those of other mammals) do have their limits. Briefly, the louder a sound is, the shorter it takes to cause permanent hearing loss. The inner ears of many other vertebrates, e.g., frogs and lizards, can withstand much higher sound intensities without damage. It is not fully understood what makes mammalian ears more sensitive to acoustic trauma.

Dear Javi,

two sounds are perfectly correlated if "the same happens at the same time". For example, if two loudspeakers play identical sounds at the same time we perceive the sound as originating from the center ("phantom middle"). No correlation means that two sound sources "behave" completely independently one from the other.

Mathematically, two number series are (positively) correlated, if high values of one series go along with high values of the other and low values of the one with low values of the other. This can easily be adopted to audio signals since each audio signal can be represented as a number series by sampling.

Sincerely

If :played back "means sounding all at once in the same place, your question devolves mathematically into asking how many numbers can sum to, say, 3.  Mathematicians are inclined to invoke such ideas as infinity in such cases, though the answer is clearly larger than we can name.

If you at what point does adding yet another sound to a large mix become irrelevant, the answer is also clearly large, but far from infinite.  Having sung in large choruses, I opine that after about a hundred or two voice, the addition (or subtraction) one more (or less) hardly matters in any musical sense.  (The gospel choir at UCSD once numbered over 500, but their major problem was finding a space in which they could rehearse).

The interesting part of your question lies in between 0 and infinity.  Modern psycholofy and cognitive science both suggest that  7 plus or minus 2 is about the limit of our "attention".  But they also suggest we don't multitask, but scan, i.e., shift our focused attention rapidly among competing messages.  Any instrument-rated pilot can tell you that simultaneously scanning (meaning observing and understanding) 7 or so instruments (as well as looking out the window) stretches human capabilities.  Not impossible, but difficult, especially if your life depends on it.

So even though I can't truly answer your question, my best guess would be the well-established psychological number associated with short-term memory: seven plus or minus two.  Seems our brain - evolved over million of years - have figured that before that number, we stand a chance to figure things out.  After that number, run!

Thank you all, for some reason I stopped getting notifications with your latest responses...

Wolfang, that´s really interesting. I guess that by sound signature I mean other variables that make up for the context. Sounds always happen in both time and space and so even though the process of decomposing a sound into its forming sine waves is surely interesting and useful, it kind of removes it from its "habitat" :)

Hi Marcel, thanks so much for all that info, some of which I am new to !

Thank you Richard ! (just seen your answer). Really interesting addition. So we have those proposed limits of conscious attention... what about subthreshold ?

Albert (thanks), so if we had a series of sine waves happening on the right speaker (for example 20, 30, 40 and 50 Hz), how would you create an uncorrelated series on the left speaker ? By changing the Hz altogether or just phase differences would make it uncorrelated too ? (I guess as ever, there'll be degrees here, from slight deviations to extreme ?)

I've just found a nice quote that somehow describes what I mean about "context" and "habitat" as opposed to decomposing/separating/analysing the constituents of sound:

"Even if there is only one possible unified theory, it is just a set of rules and equations. What is it that breathes fire into the equations and makes a universe for them to describe?"

~ Stephen Hawking

Dear Javi,

the best would be "no series" on the left speaker but somethin complelely different. Changing frequency would be o.k. in most cases. (Constant) phase differences would still provide a correlation.

Sincerely,

Albert

Thank you Albert ;)

Dear Javi,

if have no relevant cognitive numbers. Even it will not help alot, I try to figure out some problems or differences of natural sound events and creted events in its perception.

Let assume you have one sound source in a room. If you are in the room, you can locate the sound source and guess the acoustical behavior and the size of the room as all reflected sound waves (more correct: the first strong reflections) are 'recorded' by two ears and seperated by your brain. After a while the density of reflections is too high and can't be seperated in direction, it's the diffuse reverb of the room. 

So, now assume you recorded this source in a room with one microphone and as a playback setup you choose one loudspeaker. The direction of the reflected sound waves is lost, they all come from the loudspeaker. A three-dimensional soundfield is compressed to a one-dimensional sound event which is then influented by the playback room (if you are not in an anechoic chamber).

Even if you choose a 5.0 recording setup (maybe some coincidence microphone and a Hamasaki-square for reverb) and mix the result to a 5.1 setup you still lose one dimension, the height of the room as all loudspeakers are situated in one plane. The reflections were compressed to two dimensions.

In both record scenarios, the time, where sperarated sound reflections could be perceived is decreasing in comparison the the real room event. Nevertheless, you still have the impression of the size and acoustical behavior of the room, but now mixing several sound sources in the same way would produce a slighty  'muddier' result than the real event with several sources.

Technically, I would assume, that the number of sound events is not constant. In an anechoic chamber (or free field with fresh snow), where no room influences the sound it is much easier to perceive seperated sources than in a church with a high reverbaration time. Once I was in a church not seeing the orchestra and I could not figure out how many violins and cellos are playing (it were three violins and one chello - only four sources). Like others mentioned, it is also dependent on the correlation of the signals in time and frequency range.

Best regards,

André

Thank you André - so assuming most of us hear sounds in rooms that colour the perception of those sounds (and hence their recording and/or playback), recorded sounds fail to represent the original sound event (what about binaural recordings or any other 3D-type techniques ?) but still contain more information than frequency, phase and amplitude alone... right ?

"...but still contain more information than frequency, phase and amplitude alone... right?"

Very interesting question, Javi ... technically not. Phase, amplitude and frequency is all you need to define a single wave. A complex signal can be built out of these elementary waves, or Fourier would fail.

I think the key to define an answer is the definition of a 'sound event'. Maybe you could figure out that I'm more comfortible in the field of virtual acoustics.

Let's go back to the room. Is the reflection of the wall a new sound event just highly correlated to the primary source and attenuated by the acoustical parameters of the reflecting wall? Or is it just an 'Add-On' to the primary event and not a new one?*

Let's take your example of a hailstorm. If we assume, that every hailstone has the same size, weight, etc and is falling at the same speed to a plane ground ... then the events would also be highly correlated but have different sources, so they should be seperated events? A choir has even more degrees of freedom due to different singers.

It's getting philosophical ... sorry for that.

(*In a small room the first reflection can't be seperated due to the tiny difference in arrival time but it strenghtens or reinforce the direct sound. Otherwise, in a large room the first reflection (we don't take floor reflection into account) is perceived as a seperate event due to higher differences in arrival time.)

"what about binaural recordings ..."

It's great and can help alot. The best benefit and the highest immersion can be reached by individually recorded HRTFs (head-related transfer functions) and a head-tracker to compensate movements using another set of angular-dependent HRTFs.

But: Front-Back-Confusion is still a problem (not so much using a head tracker). The discrepancy between recording and play back room has an influence to the immersion. Even the loudness of recorded and played back signal should be matched. Using headphones can also have a negative impact to the immersion .... just because you know, that you are wearing headphones and the sound is coming from them. And ... it's a single user experience.

" ... or any other 3D-type techniques?"

Yes, Wave Field Synthesis and Ambisonics work fine with some limitations, if you are willing to have a huge loudspeaker setup.

Sorry, this is not answering your question.

Thank you André and no worries at all - the "meat" is often where things get philosophical, have no problems with that :)

Yes I guess defining a sound event is not easy within that example: A hailstorm could then be a finite (yet ambiguous) moment-to-moment (acoustic) experience of hailstones falling. A complex agglomeration of similar yet unique (self-similar) and minimally spaced vibrations, whose combined happening (effect?) is able to spark an ever-changing yet recognisable soundscape.

In such an example. even thought the time-arrival differences between the first group of hailstones and the last could be massive, wouldn´t we tend to perceive the event as just one ?

In any case, thanks for your clarifications and insights. Very much appreciated.

From the perceptual side, one thing that wasn't mentioned yet are the masking effects (in time and frequency) in the auditory path that probably define up to what limits sound events can still be perceived as separate.

This is a really fascinating question and I dare say not solved by the science yet. All the former answers were excellent and each of them puts the problem in a bit different perspective.

In fact your question is about the limit of information that the ear can make use of. Auditory perception is a very complex mechanism and the answer depends on the kind of sounds that are to be listened simultaneously. In some cases approximate quantitative answers can be given.

In the simplest case of individual sinusoids, but only being part of the so called harmonic complex tone (HTC), that is when their respective frequencies are multiples of the lowest one, it is well established that we can "hear out", that is sense the pitches, of five to seven lowest sinusoids. They are called "resolvable" harmonics, the higher harmonics are unresolvable. However, shoud we hear more than one HTC this rule does not work, the task becomes much more difficult for the ear. On the other hand, when there are about 10 sinusoids randomly spaced over the one-third octave band, their sound is more similar to that of the band of noise of the same width, than to some sinusoids. Certainly, 10 sinusoids in one-third octave band is beyond what you have called "the limit", our ear fails to analyse them.

Another, rather well investigated kind of sounds is speech. If we hear to simultaneously spoken words, our ability to understand is between two and three words. We can follow more simultaneous musical instruments, assuming each of them plays a different melodic line, but it is not easy to give a number and 7 given by F. Richard Moore is a realistic approximation.

The above numbers can be obtained in anechoic/headphone listening and as Andre Siegel correctly noticed, would be more difficult to obtain in reverberant listening conditions.

Your example with a 120,000 people choir is yet something else. All these people produce an approximation of correlated sound sources, not in the mathematical sense but in a perceptual sense, under some conditions. Assuming you are a listener (or you put a microphone), what you would hear depends on your distance to the choir and the choir's arrangement. Should they form 346 rows of 346 singers in each row, they would be spread over a square of about 150x150 meters, a very complex sound source to analyse. Finally, your example with hailstorms: assuming you hear the fall of each piece with the same intensity, I can imagine if each succeeding fall arrives to your ear below some 2 ms (miliseconds) then what you hear is just noise.

Thank you all so much for your answers.

So going back to the hailstorm example, don't you all think that if I created a track made of may recordings of hailstones crashing against the ground, even though technically at some point in the iteration the spectrum would be "equal" to any digitally created white noise, the resulting soundscape would both be and feel quite different than listening to white noise alone ?

And I guess this is applicable to the choir I imagined too. Andre said it quite clearly: "Phase, amplitude and frequency is all you need to define a single wave". But, are they enough to define complex sounds too ?

Why is it that some sounds sound more "alive" than others ?

Many thanks !

Densifying sound events would definitely not end up in white noise. How the differences in character between sound textures could be perceived and represented by humans is the subject of McDermott's seminal work, culminating in below article in Nature:

Article Sound Texture Perception via Statistics of the Auditory Peri...

Article Summary statistics in auditory perception

Thanks ever so much Diemo, looking forward to check his work up !