How many sound sources?

[pauln]

Imagine a recording studio...

One violin (sax, organ, whatever) plays a sustained tone at 2000 Hz. This creates a wave for the microphone, and other gear to process. On the scope it shows (for simplicity, let's make the simplifying assumption that the violin or whatever puts out a sine wave). So now we see the 2000 Hz wave on the scope.

Add a second instrument playing the same tone at 2000 Hz. Now the two waves are superimposed into a more complex wave. Since these are real instruments played by real musicians they will not be able to maintain any real phase-lock and the combined wave will have a strong component at 4000 Hz.

Add two more, 8000 Hz

Add four more, 16KHz

Add eight more, 32KHz (and this is only the fundamental sine waves, no harmonics or overtones)

Now think about the sound of masses orchestral violins...

Question is, as you see where I am going, when the orchestra, or choir, or whatever has enough sources sounding in unison, what happens to the frequencies in the complex wave? Seems to me that the power spectrum builds up greater and greater contributions in the very high end of the freq spectrum (The last time someone noticed and avoided a problem with increasing frequencies in the high end of the spectrum was when Max Planck initiated quantum phyics while studying black body radiation.) If it piles up like I show, what does this mean for orchestration (do you ever need more than 8 of anything? Can you hear it?) and what does this do to the Nyquist arguments about bandwidth limiting and sampling (what do 16 violins sound like if their combined fundamentals need 32KHz (much more for the harmonics) and the limit is 44.1KHz?)?

Is my composition assumption wrong?

[PrestonTom]

This is an easy one.Your assumption is incorrect!

Draw 2 sine waves of the same frequency, one above the other. Now add them together (add the vertical offsets). You now have a single resulting sine wave that is identical in frequency. It may be "taller" depending on the relative phases of the originals and it may have a different starting phase (again depending on the relative pahses of the originals).

There will not be any energy at 4000 Hz when you have two or more sources playing 2000 Hz. This is an approximately linear system and no additional harmonics will be produced (2000 Hz in, then only 2000 Hz out). As for non-linearities, these may or may not be at the 2nd harmonic. Even if they were, they would be 10s of dB down.

With this in mind, we don not need to bother with your final paragraph

-Tom

[Duke Spinner]

none of the pitch's will ever be closer than , say, 80 cent's

due to tuning, playing technique, interference

therefore they are not additive as volume goes

[pauln]

The example of two identical waves superimposed to make one bigger wave does not answer why I still hear two instruments. Here is an example I am thinking about...

http://www.lavryengineering.com/documents/Sampling_Theory.pdf

On p13-14 there is an illustration of the composition of four waves to make one complex wave. The problen to me is that the image of the four seperately drawn looks like a Jackson Pollock painting, but the resultant figure looks way too simple. Looking at the first one with the colored lines, just looking at the frequency with which peaks occur above and below in the first segment - I count 7 from 0 to 10, yet the resultant has only four!

If you tell me that some of them are being superimposed, does that mean of the four sound sources in the example that these as heard sources will be popping into and out of existence as I listen? That is, that I think I'm hearing four tones, but at any instant one or more of them combine to hide, then reappear?

[LarryC]

The example of two identical waves superimposed to make one bigger wave does not answer why I still hear two instruments...

If you tell me that some of them are being superimposed, does that mean of the four sound sources in the example that these as heard sources will be popping into and out of existence as I listen? That is, that I think I'm hearing four tones, but at any instant one or more of them combine to hide, then reappear?

I suspect the illustrations and examples from the paper are much too abstract. A musical tone will have a myriad of overtones, unlike these pure, electronically-generated sine waves. It will make the discussion much more complex, though.

Yes, absolutely you'll hear sound levels increase and decrease if two sources are slightly out of tune. This is called "beats." If the instruments are very close in pitch, the beats will be very slow, whereas they speed up if the diffference between the two pitches is increased. Gunther Schuller, a composer and french horn player, wrote that if multiple horn players sit too close together and play very high pitches at full volume, a physical vibration can be set up that will cause the notes from one or more of the players to "crack" or break up! That's a very strong, real-world example of "beats."

I can't explain the physics of why, say, two horns, two flutes or two violins sound different from only one, but they clearly do! Perhaps the individual signposts of a single instrument -- very fine details of bow movement, breath tones, or lip pressure variations -- seem to be blended away and the combo takes on a heavier, more anonymous quality than a single. It's very obvious to the experienced listener.

Is that what you meant by "hearing two instruments"? Naturally, it's very easy to hear two instruments if they are playing different parts, but it's harder to hear whether multiple instruments comprise 2, 3, 4, or more, if they are playing the same part in unison. No doubt whatever, though, about distinguishing only one soloist from more than one!

Do you ever need more than, say, eight? Absolutely!!! A section of only eight first violins or six cellos sounds very underpowered in a full orchestra compared with the standard complement of 14-16 firsts and 12 cellos.

Finally, I'm certain your assumption was incorrect -- adding instruments will not produce higher and higher multiples of their fundamental frequencies. One does not hear greater brilliance from instruments in multiples than singly.

Larry

[garyrc]

Stepping aside from the physics, and moving into physiological psychology, one reason you may want "more than 8 of anything," in an orchestra is to increase (and thus manipulate) cortical arousal. Ever-changing and fairly large changes in arousal in the cortex of the brain (and elsewhere, e.g., in the skin -- Yawns or Goose Bumps -- PWK), which are under approximate control of the composer, or other artist, look more and more like an important part of the experience of art, especially music.

Increasing Complexity of various kinds is one of the manipulations the composer can use to boost arousal. Massed instruments often sound incredibly complex, partly due to the human impossibility of everyone playing a certain part playing exactly alike. Add other parts with multiple players, and it's off to the arousal races. Personally, I find massed violins, seasoned by a large set of violas and cellos, to be a peak experience. You can guess (correctly) at variables used by artists to cause appreciable shifts (initially increases) in arousal, but it's nice that they were confirmed empirically by Berlyne and others. Some are: Loudness (massed instruments can be louder, right?), complexity, surprise (unbelievable transients, getting louder and louder; unexpected turns in melody or orchestration, unexpected discord), discord itself, novelty, uncertainty, ambiguity, brightness, size, and learned associations.

Cortical arousal boost itself often produces pleasure -- and sometimes discomfort, the relief of which is pleasurable -- and what Berlyne called "arousal boost-jag" in which both the rise and decline are pleasurable. Listen to the end of Beethoven's 7th symphony, very loudly, for a some of each or these effects! The artist, especially those who work in temporally unfolding arts, like cinema and music, can be thought of (metaphorically) as manipulating (or, if we think of the artist as having a baton, conducting) complex waves and swirls of arousal. A nice job, if you can get it.

A. E. Houseman's statement about poetry is true of all of the arts: "I can no more define poetry than a terrier can define a rat, but we both recognize the object by the symptoms which it provokes in us. Often, my skin bristles ... accompanied by a shiver down the spine ... there is a constriction of the throat and a precipitation of water to the eyes ... the hair of my flesh stands up."

Berlyne would understand.

[DrWho]

The problen to me is that the image of the four seperately drawn looks like a Jackson Pollock painting, but the resultant figure looks way too simple.

Sit down sometime and add the waveforms together by hand...you'll notice it comes out the same way.

What are you trying to get at with all this thinking? Or is it just purely academic?

[Rivendell61]

Gary,

Nice post!

Didn't put on the 7th--but I've been listening to Ireland, Butterworth, etc., settings of Housman for the last two hours.....

Mark

[pauln]

Mike, I'm just thinking out loud - trying to reconcile the simplicity of the superimposition wave against the actual experienced sound. It's hard to imagine that the mind differentiates a single wave into all the instruments of the orchestra, band, group, choir, whatever - it's just amazing to me still after being a musician most of my life - still amazing. I have spent hours playing with the ocilliscope.

I liked what Gary wrote - very 'perceptive'. It reminded me of the similar kinds of manipulation used for creative and artistic effect in liturature (narrators that lie), painting (use of symbolic images), etc. In music, the presentation is not controlled by the listener but by the music itself in real time. This is so different from the way one reads a book or observes a painting. Music demands and controls your attention in a special way because it goes through time with you. The dimensions of past, present, and anticipation of future allow music subject to great composers to demonstrate why music is the 'highest' of the arts.

[JJkizak]

I wonder what the difference is between multiple horn instruments cracking out to multiple "tweeter horns" in the same speaker?

JJK

[LarryC]

I wouldn't expect a similarity. The "cracking" horns refers to 2 or more players sitting close together and trying to play the same high note. A slight difference in pitch between the two will cause the beats I described above, and the physical force of the beats is supposed to be able to break up the note of one of the players. Probably by physically affecting the shape & pressure of his lips on the mouthpiece.

I can't see a similar effect occurring between two tweeter horns if they are playing the same note from an identical signal. Nor have I heard or read of an outside listenable high SPL creating a problem in another compression driver.

[Macho Nacho]

/

[ZAKO]

Stop playing with the ocilliscope. Music is a high art...But the scope can make you blind to perceptions.

[Marvel]

As Mike well knows, a common studio technique for voacalists was (assume it still is) to have the vocalist sing the exact same part at least twice. Slight disparites in the singing, when the track/parts are combined would still sound like the one vocalist, but the sound would be fatter, or more full.

This is often now done electronically, but doing an offset or other technique.

In my younger days, I was palying guitar with a brother/sister group, recording at the old RCA studios in Chicago (no longer there, btw) and the producer had Chuck repeat his vocal track. When the two were played back, you could here absolutely no difference. The issue wasn't that he sang so well, but that he sang the parts exactly the same each time. They were a little flabbergasted (and annoyed too, I think) that he could do that (he still sings pretty well, even though he has passed 60).

Bruce

[Duke Spinner]

recording at the old RCA studios in Chicago (no longer there, btw)

ya know, Bruce ... I remember when you could go to 1841 Broadway, NYC.........

and see what was being recorded at Atlantic Studio's

[WMcD]

It is a good question. I don't think that quantum mechanics applied to sound waves, though.

A simplified presentation of the question is: Under which conditions can two sources of sine wave cause a new frequency.

The answer is that in a linear system, there are no new frequencies. This is pretty much like the graph you see in high school. The x axis it the input. The y axis is the output. The "transfer function" is the straight line. Hence, "linear".

This is a good thing for recording and transmission. You put in two frequencies. The output is two frequencies. Nothing more or less. Anything else would be distortion.

There are non linear systems. In the real world they are common. In fact it is difficult to make a perfectly linear system. We try to make amps, etc. linear.

One aspect of non-linear systems is that the output is F1 plus and minus F2, and F1 and F2. These are called hetrodynes, or beats, or intermod.

Guitar players use this The soundboard is not linear. The low E string is tuned to some freq.by twisting the peg to tension the string. The next string up is freted to what should be E. Both strings are plucked. If the second string is not at E, there is a wah, wah, wah. That is the difference F1 minus F2. Actully a bass note. The second string is adjusted so we dont have any difference or F1 minus F2 is zero. That happens when F1 and F2 (the strings) are putting out the same freq.

This is a little illustration that music and electical engineering are very close. But they often use different words for the same concepts. Bernard Shaw quipped that Americans and English are separated by a common language. It is like that.

The next question is whether :"air" is or is not linear. For the most part, it is. So there is not interaction of waveforms created by different instruments.

Even if you have a linear system making sound, is it "really" linear. PWK's work is that moving diaphragms suffer from Doppler distortion. This is like the whistle on a train. even though the whistle and the train are linear, the motion itself injects a modulation of F1 plus and minus F2.

But, let us assume there are the very high frequency components generated. Can we hear them? No. Our ears are in fact like little pianos or guitars. There are hairs of tuned lengths. The shortest are tuned to about 15 kHz. Regardless of Nyquest, the little hair in your ear can only act like a tuning fork for 15 kHz. It might be a Nyquest reconstruction filter. It feeds your brain.

Music is of course, quite wonderful. So this is a confabulation of our brain. Major chords are "happy". (Consider that all the machines in Las Vegas make a C major sound. Yup they're playing with us) Minor chords are sad.

Larry C. can tell us more. Take the opening notes of 2001. That is a minor chord, the second note of the three is a bit "off." Then it is followed immediately by a major chord. The second note is shifted a few Hertz. The overall effect is a rapid change from "sad" to "happy". I might have that backwards. The effect is wonderful.

There are some oddball things going on "in real time". Pardon: I'm gonna mangle spelling Rhimsky Korsakov. He puts together the best. At some parts he allows the violins to die down, and then hits a triangle. Really nice.

Gil

[LarryC]

Larry C. can tell us more.

Not without boring everyone to death and getting another "yawn." []

You exactly captured the minor-to-major shift in the opening of 2001, from Also Sprach Zarathustra by Richard Strauss. I think the music choices and settings in that movie were, still are, stunning.

[WMcD]

Thanks for the kind words, Larry.

BTW, WFMT reported that George Legetti passed away last month. Some of the most atmospheric (!) music in the movie were his works. They were not composed for the movie. Reportedly he was not entirely pleased with the use. I can only guess that a licensing agreement signed before the film made it legal.

I can't help but think of the young actress in the Sci-Fi classic, Beast from 20,000 Fathoms. She wished her other films were half as remembered. None the less, this was the vehicle for her film-based immortality.

I walk on eggs when I post anything about music theory. That is because Larry C. knows a heck of a lot. I tend to skate on the thin ice fringe of my understanding.

Awww. Come on Larry. Please write up your thoughts. I'd love to read them. I'm sure others here would too.

Do it, to it; at the old saying goes.

Gil

[LarryC]

Gil, I'm flattered and humbled, but honestly don't think I can add anything worthy to what you said in this particular case. I'll be happy to at some better opportunity.

Here is a link to detailed info about the music used in the film. Roger Ebert made these observations about the music and the film. He and others have noted that the film is almost like a silent movie -- extensive wordless action in a beautifully conceived musical context.

Any chance you can come to our Oct. 14 MD-DC-VA fest? Give it some thought as we see how many sign on. Sorry you didn't make it to Hope.

Larry

[pauln]

I love the movie. The original first scene was supposed to be a discussion/interview while standing in front of a huge computer (all the computers were big in the 60's). Turned out the noise made by the computer was so lound that a request was made to turn it off for a little while so the interview might be filmed. The answer to the request was that the computer was processing the payroll for a large company, but that it could be turned off if someone had about 150K pounds or some such large value to compensate for the time.

They decided not to shoot that scene...