# Pitch vs Noise?

1. Nov 18, 2007

### NoiseQuestion

Hello everyone. I'm not a Physics major: I'm a Music major. And I have a question. I've read various books on acoustics, but I still haven't found the answer.

Ok. The way I see it, there are 2 basic types of sounds (I didn't get this out of a book, it's my own conclusion from everyday observation). One is pitch, the other is (for lack of a better word) noise.

Now every sound is a noise, right? True. But by pitch I mean a sound whose pitch we can determine. If I play a note on the piano, you can tell me "oh, that's a C", or you can give me some mathematical frequency for what we call "C".

By noise, I mean a sound whose pitch(es) cannot be determined. - And maybe I'm wrong about this, because I know next to nothing about Physics. But for example, say an airplane takes off and you have the unfortunate experience of standing behind it and you hear this EEEEEEEEEEEAAHHHHHHHHHHHH!!! or whatever. Now let's say you go to the piano and try to reproduce the "pitch(es)" of the engine going off. YOU CAN'T! Because the sound has no pitch we can determine. It's just noise.

Now here's my question. 1) Is everything I said above true? and 2) If it is, how do we describe, in scientific terms, what I have termed "noise?" If it has no defined pitch, what is it? What is the technical term for it, and how can we analyze it?

Thank you for your time!

2. Nov 19, 2007

### NeoDevin

What you call noise, rather than having a single pitch, has a spread of them. That is, the sound waves are a superposition of many waves with well defined pitches.

Relating back to music, have you ever heard two piccolo's (or even flutes, though not as bad) that are only slighly out of tune. They produce an awful wobbling sound (a beat). Imagine that with lots of different frequencies and you have your jet engine.

3. Nov 19, 2007

### NoiseQuestion

Great! Thanks for the reply!
1)So is there a technical term for this spread of pitches?
2)How can we determine what pitches are in the spread? Would a spectrogram analyze it?

4. Nov 19, 2007

### christianjb

5. Nov 19, 2007

### NoiseQuestion

Thank you. I had actually read those articles before, and found the 2nd one especially helpful. The Wikipedia article about white, red, and pink noise makes no sense to me, because it never really puts it into layman's terms by providing an example.

In the case of the jet engine, does white/pink/red/etc noise occur? In what way?

Are these "noise colors" in anyway related to the colors shown in some spectrograms? I came across this spectrogram software called Raven (developed at Cornell), and I was wondering why they are in shades of color? Check it out:

http://www.birds.cornell.edu/brp/raven/Raven.html

6. Nov 19, 2007

### billiards

1) No, a fair bit was untrue.

2) Sound is a type of energy, measured in decibels. Loosely, in music, the pitch is equal to the peak frequency, which is to say, it is the component of the sound with the most energy. In reality, an A played on a piano will have a frequency spectrum with its peak frequency at 440 Hz (or 220 Hz, or 880 Hz, etc... depending on octave) - the sound will not be composed of pure 440 Hz energy. Why do you think an A sounds different on a piano than it does on a guitar, or a violin? Because the frequency spectrum of these instruments is different.

In scientific terms, pitch means the same thing as frequency. Noise is a type of sound, although its definition is subjective, it is simply undesired signal. For example, if you made a recording and you noticed some background hiss, you might consider that to be noise. Noise will still have a frequency spectrum, sometimes, if the noise is of characteristic frequency, it is possible to apply some kind of "bandpass" filter to your recording so as to remove the noise.

7. Nov 19, 2007

### NoiseQuestion

Thank you! Your description of pitch/frequency was quite clear.

As for your definition of "noise", I am familiar with that textbook definition of noise as "unwanted sound" and that is not at all what I'm refering to. I used the term "noise" because I can't think of a better term for it, but I want to diferentiate it somehow from specific pitch. My main question is how can we analyze the frequencies of something like a jet engine roar?. In the case of a Mozart symphony, I can easily tell you note-by-note what the frequencies are. I can even write them down for you in musical notation. But how can we "describe" a get engine roar, if we cannot pin-point a specific pitch at any specific time?

8. Nov 19, 2007

### rbj

a few things need also to be fixed in your understanding, bill. or at least how you expressed it.

sound can be measured lotsa different ways to get various parameters. dB is one expression of a parameter called "loudness". dB SPL (Sound Pressure Level) is a different (but similar) expression that is the logarithm of physical amplitude of the sound intensity (power per unit area). the difference between the two is shown in the Fletcher-Munson relationship: http://en.wikipedia.org/wiki/Fletcher-Munson_curves (looks like ISO updated the data a little bit).

no, that is incorrect. on many levels.

just as dB SPL is a physical quantity while dB loudness is a perceptual quantity, pitch is a perceptual paramter (something that we measure with our ears and brains), while frequency is physical parameter and something that we (can) measure with electronic instruments.

in the case of a quasi-periodic tone (quasi-periodic tones are also harmonic, all frequency components are very close to integer multiples of a common fundamental frequency), the pitch we perceive (relative to some standard reference pitch) is closely related to the logarithm of the fundamental frequency. the might be zero energy at the fundamental (so it certainly will not be the peak frequency), but if the other odd-numbered harmonics do have sufficient energy, that fundamental still is deterministic. if $f_0$ is the fundamental of a tone that might be expressed as:

$$x(t) = \sum_{n=1}^{+\infty} r_n \cos(2 \pi n f_0 t + \phi_n)$$

then the pitch, measured in octaves and relative to A440, would be:

$$\log_2 \left( \frac{f_0}{\mathrm{440 Hz}} \right)$$

but even that expression becomes less accurate as the pitch gets very high in the musical scale (and slightly sharpened). i.e. the A that is 3 octaves above A440 is actually a teeny-weeny bit higher in fundemental frequency than 23 x 440 Hz. that is purely because of perceptual reasons and not because of physics. it's how a piano tuner tunes it.

NO! this is not true. not true at all.

No.

it is related, but it is not the same thing. it does not mean the same thing.

"noise" means a lot of things, a lot of different things to different people in different contexts. if "music" (particularly electronically synthesized music) or "pitch" is not the context, if you're just talking with some Joe on the street about other stuff, usually "noise" is synonymous with "racket" or "din" and is usually undesired. sometimes, in Communication Systems Theory (something that EE study in school), noise is this additive error signal that is also undesired (and we are trying to recover the signal or parameters about it before the noise was added by the transmission channel).

in acoustics, audio, and music synthesis, then often "noise" is "white noise" or "pink noise" or some other flavor and is a random process with certain statistical properties (as is the noise in Communication Theory), but in music, it might well be a component that is deliberately synthesized and made part of a signal. sometimes these noisy signals have a perceived pitch. and, remember: pitch is a perceptual parameter, in its definition, not a physical one. if you generated some broadbanded noise (which would be so wide and broadbanded, it would be hard to say it has any "pitch") and run that through a bandpass filter or a comb filter with a decent amount of resonance, the output of that filter would be "noisy" but still have a sense of pitch for people. that noise has pitch and it is not exactly a periodic function (but would have a strong component in it that has some statistical elements of periodicity).

BTW, guys, this is what i work in. i am not a physicist and i tread more lightly in the physics issues (particularly at the Relativity Forum), but in this area, i might be the resident guru here (unless someone else i know in the area is lurking).

Last edited: Nov 19, 2007
9. Nov 19, 2007

### NoiseQuestion

That's excellent, rbj. Thank you so much for taking the time to explain clarify these matters (and thank you again billiards for your reply!)
If you are indeed the guru on this matter (I do not doubt it!), then I would very much appreciate it if you would answer my main question: how can we analyze the sound of something like a jet engine? Another member here said that the roar of a jet engine is actually a "spread" of different pitches, resulting in no definite pitch. If that is so, is there some way we can discover (via some kind of software?) the exact pitches that make up this "spread" and graph how they change in time (as the jet becomes more distant)?

Last edited: Nov 19, 2007
10. Nov 19, 2007

### rbj

depends on what you mean by "analyze". one thing we can do is window off a segment (of finite length) of the jet engine sound and run it through a Fourier Transform of some manner. sometimes this is called the Short-Time Fourier Transform: http://en.wikipedia.org/wiki/Short-time_Fourier_transform .

that is what Fourier analysis is all about. it is about taking some arbiatrary waveform and breaking it up into component frequencies. more precisely: expressing the arbitrary waveform as some (possibly infinite) sum of sinusoidal waveforms, each having their own frequency parameter.

that may or may not be true. i tend to hear a "whine" from the engines in a commecial jet that could be assigned a pitch. definitely i can hear the pitch of a two-cycle motorcycle engine ("vrin, din, din, din"). the roar of fighter jets as they blast by me (Vermont Air National Guard) seem to be so broadbanded, i can't tell a specific pitch although whatever amorphous, indeterminite pitch they have does tend to lower (because of doppler) as they fly by. so do they have a pitch or not? that's like the old Clarol commercial (with a touch of sexual inuendo) those of us that are in our 50s remember: "Does she or doesn't she?" (hope so! )

yes, it's called a "spectrum analyzer" and its output is called a "spectogram". and it based, at least in some sense, on the STFT (this is true, even if your spectrum analyzer is a "filter bank", a collection of bandpass filters that are all tuned to variously spaced frequencies).

Last edited: Nov 19, 2007
11. Nov 19, 2007

### Staff: Mentor

I agree, jet engines "whine". I spent a very uncomfortable flight right next to an engine that was running at a frequency that was about 1-2 Hz away from the other engine. The resulting "beat" was very steady and irritating.

I guess I "whine" too

12. Nov 19, 2007

### FredGarvin

Jet engine noise is a very similar situation to a regular sound from any other source. It is the same in that it has components that will be picked up, i.e. fan tip noise, burner rumble and so on. However there is also turbulence induced noises that you simply will see no dominant source.

For example, on an FFT, you will see a nice solid peak at, what is referred to as blade pass frequency of the fan. It is one of the major noise contributors. However, the turbulent noise created at the rear of the engine due to exhaust is extremely random. If you looked at an FFT and a trace in the time domain, you won't be able to tell the difference. They are both a mess. So in that respect, I would say that noise would have to have some reference to randomness in the signal. But like has already been mentioned, "noise" is a pretty subjective term to my knowledge.

13. Nov 19, 2007

### NoiseQuestion

Thanks once again. By "analyze", I mean somehow capturing the unique characteristics of a given sound (jet engine, motorcylce, etc) in time in some kind of notation (like a graph). It is easy to notate music, because the pitches are very easy to distinguish. But in the case of an engine, it is impossible, at least in music notation. Can you recommend any spectogram/STFT software that you use? I have a Mac, and I need something user friendly (i.e. not MatLab!!! remember I'm not a Physics major, just a musician.)

14. Nov 19, 2007

### FredGarvin

15. Nov 19, 2007

### NoiseQuestion

Hmm. Very interesting. So you mean that there are some sounds (like turbulence) that have no dominant (outstanding) pitches? But if the signals of the noise are "random", doesn't that still imply that they exist? And if so, isn't there some kind of analysis software that could capture the sound and follow the exact pitch signals, however random they may be?

16. Nov 19, 2007

### NoiseQuestion

17. Nov 19, 2007

### FredGarvin

I just grabbed a couple of quick links. It appears that the Raven program will do exactly what you need.

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