Audio frequency and directionality question?

I'd guess between kHz and 3 kHz. That seems to be the selected range for best sensitivity and perhaps also for determining where the source is.

Probably, but there are - in fact - two mechanisms involved. At lowish frequencies - below about a kiloherz - you can get stuff from the ear-to-ear phase shift. At higher frequencies, the head and ear produce amplitude differences across the head, and the external ear can start functioning as directional antenna.

This means that there is a hole in your direction sensing system around one killoherz, as was dramatically illustrated by the private branch exchange system we had at Cambridge Instruments in the 1980's, where you could never tell whose phone was ringing in our open plan office space.

My wife's colleague at the then Applied Psychology Unit (now the Cogntion and Brain Science Unit) knew the whole story - the private branch exchnage system was widely used - and used it in their sales pitch. These days the unit doesn't work on this sort of stuff

and has shoved off the people who did to be professors elsewhere. Roy Patterson might be willing to tell you a bit about the subject, if you asked him nicely

He does appreciate good wine ....

-------------------- Bill Sloman, Nijmegen

1 kHz - 3 kHz

There's sure a hole in my own direction sensing right around there - I've occasionally been embarrassed by not being able to tell which side of a stereo pair was missing, using a 1kHz test tone. Always just figured it was a hideous defect in my hearing and stayed quiet about it :-) White/pink noise is a lot easier to localize.

I see here in Ballou's "Handbook for Sound Engineers", 2ed., in chapter 2 (by F. Alton Everest), that it says "experiments [by Shaw and by Batteau] demonstrate that the pinna is probably involved in localization of sounds, that the pinna gives direction-dependent filtering action, and that sounds above 7kHz are necessary for accurate localization." Everest goes on to discuss about the nulls of said filters, placing them by calculation between

1.67kHz at one extreme and 50kHz at the other (though the latter is far beyond the limit of perception).

By my read, nothing in Everest's chapter acknowledges nor strongly excludes the possibility of getting direction from low frequencies (via time-of-arrival info between ears). He's focused on single-ear localization. But he does seem to be agreeing with Bill that one needs frequencies quite a bit above 1kHz at least for single-ear localization to work.

I'd think it'd be centered around whatever the freq. is where 1/4 wave would be the width of a typical head. I wouldn't be surprised to know that a human cochlea/brain can resolve phase.

But this is speculation, of course. :-)

Cheers! Rich

If you had square waves (or triangle waves), then you had harmonic content well above the fundamental. If the effect went away when you switched to sine waves, I think you just demonstrated that it relies on frequencies higher than 1kHz, and that 1kHz tones by themselves couldn't be localized.

Why the effect faded out above 1.5kHz in your experiment is hard to say; but since both a square wave and a triangle wave contain only odd harmonics, and the harmonic series of a triangle wave rolls off quickly, (with 1/n^2), perhaps you just didn't have much energy content in the audible part of the spectrum. At 2kHz, for instance, the only audible harmonics would be at

6kHz, 10kHz, 14kHz; and the energy at 14kHz would be pretty low. At 3kHz, the audible harmonics would be 9kHz and 15kHz.

Hm. Never needed to use the information, but as I recall my Fourier prof from college (admittedly 45 years ago) the square wave has all the odd harmonics and the triangle has all the even harmonics. Am I really disremembering that or did my prof screw up?

Jim

but

[snip]

Since a square wave is the derivative of a triangle wave, my first thought would be that you are correct.

...Jim Thompson

--
|  James E.Thompson, P.E.                           |    mens     |
|  Analog Innovations, Inc.                         |     et      |
|  Analog/Mixed-Signal ASIC\'s and Discrete Systems  |    manus    |
|  Phoenix, Arizona            Voice:(480)460-2350  |             |
|  E-mail Address at Website     Fax:(480)460-2142  |  Brass Rat  |
|       http://www.analog-innovations.com           |    1962     |
             
I love to cook with wine.      Sometimes I even put it in the food.

My second thought would be I am wrong ;-)

...Jim Thompson

--
|  James E.Thompson, P.E.                           |    mens     |
|  Analog Innovations, Inc.                         |     et      |
|  Analog/Mixed-Signal ASIC\'s and Discrete Systems  |    manus    |
|  Phoenix, Arizona            Voice:(480)460-2350  |             |
|  E-mail Address at Website     Fax:(480)460-2142  |  Brass Rat  |
|       http://www.analog-innovations.com           |    1962     |
             
I love to cook with wine.      Sometimes I even put it in the food.

Jim Thompson skrev:

;)

I've been wrong once, - I thought I was wrong ;)

-Lasse

I don't remember these things well enough to trust myself, but I do trust Wikipedia in this regard. "Like a square wave, the triangle wave contains only odd harmonics. However, the higher harmonics roll off much faster than in a square wave (proportional to the inverse square of the harmonic number as opposed to just the inverse), and so its sound is smoother than a square wave and is nearer to that of a sine wave." "A sawtooth wave's sound is harsh and clear and its spectrum contains both even and odd harmonics of the fundamental frequency."

What about the fundamental and all the even harmonics? Ignore the fundamental for a moment; now what you have is 2f, 4f, 6f, ... so that's the same as 1*(2f), 2*(2f), 3*(2f), ...; in other words, it's a sawtooth at twice the frequency. Add the fundamental sine wave back in, and you get something that looks sort of like a capacitor charging and discharging. Hmm.

A sawtooth is all of the even harmonics (well, plus the fundamental, of course). Just as a thought experiment, it looks like a triangle is a bunch of odd harmonics, but with weird phases.

What do you get if you add in _all_ of the harmonics? (at amplitudes proportioned like they are in the square and sawtooth, of course)

Thanks, Rich

I did a few experiments on the localisation of a tone fed to both ears, using an adjustable time difference in the feeds. Because we wanted it for other reasons, we were using a mixed triangular and square wave signal ( both the same frequency ), variable frequency between about 500 Hz to 1.5 Khz. Using headphones, you could definitely hear the sound move from side to side as the time delay was varied from zero to 400 microsec or so ( ie about the head width delay time ). The effect was most obvious below 1 Khz, and faded out above around 1.5 Khz. What wasnt obvious was whether the apparant source was in front or behind you, and we needed that too. Also the effect almost totally vanished when using speakers placed a couple of feet from the head. Since for the application we didnt want the user to have to wear phones, we abandoned the idea.

I think I also tried with sine waves, but it wasnt nearly as obvious without the sharp edges of the square waves.

--
Regards,

Adrian Jansen           adrianjansen at internode dot on dot net
Design Engineer         J & K Micro Systems
Microcomputer solutions for industrial control
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I generated a postscript printout of an FFT of a triangle wave at 1kHz. The odd harmonics are the spikes.

--
Regards,
  Bob Monsen

Cantorism (set theory) is a disease from which mathematics will have to 
recover.
- Henri Poincare

Agree with your comments about harmonic content. Since I cant hear much above 10 KHz ( getting old ! ) that would be logical. However I wonder whether the ear/brain is doing phase comparison or just time-of-arrival detection. I know that ultimately they are the same, but the fact that the localisation is much better for sharp edges than for sinewaves makes me think that the processing is extracting more info out of the edges that we might think.

One day when I've got nothing better to do ( Ha ! ), I might play with this a bit more.

--
Regards,

Adrian Jansen           adrianjansen at internode dot on dot net
Design Engineer         J & K Micro Systems
Microcomputer solutions for industrial control
Note reply address is invalid, convert address above to machine form.

D'oh!

--- Regards, Bob Monsen

The question of the ultimate foundations and the ultimate meaning of mathematics remains open; we do not know in what direction it will find its final solution or even whether a final objective answer can be expected at all. "Mathematizing" may well be a creative activity of man, like language or music, of primary originality, whose historical decisions defy complete objective rationalization.

- Hermann Weyl in 1944