 The Clarinet BBoard
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Author: Ginny
Date: 2002-08-05 16:07
What happened?
My son and I were playing duets last night, really matching tones well, playing with conviction.
We decided that the dog would like to join us (she also matchs pitches, such a musical family) and went to find her. My husband refers to this as a trio for two clarinets and basset hound. We seranaded her with a high C and the E above that, then switched to long B and G#, as the dog liked that key.
But in addition to the pup's lovely voice a VERY CLEAR FOURTH note was hear below the dog and clarinet pitches. It was not resonating from the piano, as we abandoned the dog and went about the house playing more notes and getting all sorts of these strange loud subtones. They sounded to both of us as if they were coming from within our eardrums, although my husband said he could hear them clearly and that these pitches sounded external to him.
Where we magically out of tune just the right amount?
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Author: Brian Peterson
Date: 2002-08-05 17:21
Ginny,
I haven't got a clue as to what the answer may be, but your question is the kind I live for on this BB!!
Brian Peterson
PS Maybe you should get your husband to videotape the three of you and submit it to World's Funniest Home Videos or the show like on Animal Planet.
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Author: Matt Locker
Date: 2002-08-05 19:17
I'll try to answer this one:
It's called the "beat" and it's what you get when 2 different frequencies are sounded at the same time. Each frequency has minimums and maximums - think of ocean waves. If they are integer multiples of each other (eg: 200Hz/400Hz) nothing horribly exciting happens - the faster one is just the octave (double) of the other. Consider what happens though when you play an A 440 against a slightly out of tune A 438. The crests/valleys (minimums/maximums) will correspond every 440x438 cycles basically a long time. You can hear this when tuning 2 instruments together - as the tuning gets closer the "beat" slows down until it basically disappears.
I think what you are hearing is the beat against 2 different freqencies - B & G#. I don't know how these 2 notes beat together when perfectly in tune but suspect that when played at either just the right tuning (whether in tune or not) a beat is created that sounds in the audible spectrum. Maybe it needs the dog's "song" as well to bring it out. Whatever, check it out by playing the notes and then lipping up or down to see if the 4th part gets louder or softer. It may also be that the room you are in has a harmonic fundamental at that particular frequency that really enhances that particular frequency.
My thoughts only.
Matt
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Author: JMcAulay
Date: 2002-08-05 21:35
A "Beat Frequency" is the sum *or* difference of two tones played simultaneously. Don't multiply; add or subtract. This effect only happens when there is a non-linear audio medium involved -- simply put, something that does not transmit or convey or respond to everything equally -- not too hard to find. So if one of you is playing A440 and the other is on C512, two other tones will appear, one at 72 Hertz and the other at 952 Hertz. Under perfect conditions for the effect to occur (often, it won't happen at all), these two beat notes would be of equal loudness. Under practical conditions, one or the other generally predominates by quite a bit.
While the effect is interesting, it can be very distracting. Audio and electronic engineers strive mightily for linearity in audio equipment and fixtures in presentation halls, so that the effect is minimized. The problem is that rarely will the beats bear close harmonic relationship to the original frequencies (i. e., no harmonious chord is usually produced), and it can sound awful.
Regards,
John
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Author: jez
Date: 2002-08-06 03:38
Listening to difference-tones can be very useful when thinking about intonation. There was a detailed discussion a while ago that you may enjoy. Do a 'search' for (believe it or not) "quiet bagpipes" No quotation marks
jez
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Author: Matt Locker
Date: 2002-08-06 12:18
JM:
I said that the waveforms for a 440 & 438 beat would line up every 440x438 cycles. I did not say that the beat frequency was 440x438 Hz. What this means is that the maxima is reached every 438 cycles of the 440Hz signal, or on the 440th cycle of the 438Hz signal. This would appear to be only 1 Hz but the definition of the beat (what I've found on the web anyway since my memory is faded on this issue) is that the beat "cycle" is defined to be the number of minima per cycle so that the number of minima per second is f1-f2 instead of (f1-f2)/2 (see http://hyperphysics.phy-astr.gsu.edu/hbase/sound/beat.html for a good description).
The beat equation is: f(beat) = magnitude(f1-f2).
This says that the beat for a 440 & 438 frequency pair would be 2 Hz. The beat for your example would be mag(440-512) = 72Hz only. I don't believe that you can't have a beat at a higher frequency than either of your other 2 frequencies.
MOO,
Matt
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Author: Bob
Date: 2002-08-06 12:52
Just the other day in the kitchen I was "trying out" a clarinet I was working on and experienced the "beat karma". Since it was the first time in many years of playing I then tried playing my "regular" clarinet...in the kitchen...and got the same effect.
Must be something about the acoustics in the kitchen or the fact that the egg beater is there. The incident is true, the attempt at joke probably weak.
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Author: george
Date: 2002-08-06 19:33
You can find a nice elementary discussion of the "beat" phenomenon in Section 1.3.3 of The Physics of Musical Instruments, by N. Fletcher & T. Rossing.
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Author: JMcAulay
Date: 2002-08-06 21:16
Matt, sorry your first posting was not clear to me, but I believe this one is. I apologize for the lack of accuracy in my first posting, which I will attempt to straighten out and clarify: f1 and f2 will produce beat frequencies at both their sum and difference, if they are in the presence of a non-linear medium. This effect is often essential to the functioning of certain electronic equipment, generally receivers or transmitters. Such a situation will also produce a number of frequencies of lesser amplitude, such as f1+2f2, etc., which can be troublesome and will occasionally require heroic measures to filter away. This situation is obviously to be avoided in sound transmission or reproduction (unless you're using a "Fuzzbox").
However, wave superposition will result in a difference *only* beat frequency even if perfect linearity prevails. The intensity of this beat note is greatest when f1 and f2 are exactly the same amplitude, and as their amplitude difference becomes greater, the amplitude of the beat note decreases.
While your cited reference is a good one, I believe most will find this one easier to understand:
http://www.cord.edu/dept/physics/p128/lecture99_34.html
Again, sorry for my foul-up. It happens. I'm not purrfict.
Regards,
John
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Author: Ginny
Date: 2002-08-07 01:51
Thanks for the link, John. The strange sound we made makes more sense. I still am
curious as to why both players felt as if they heard the beat frequency in the eardrum.
Speak placement (just kidding.)
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Author: Mark Charette
Date: 2002-08-07 02:01
Ginny wrote:
> I still am
> curious as to why both players felt as if they heard the beat
> frequency in the eardrum.
Phase differential. Hook up one of a pair of stereo loudspeakers "backwards" (reverse the leads) (even more fun is to miswire a set of headphones on purpose!). Sit between the speakers (or put on the headphones) and play your favorite music. The music will seem to be emanating from inside your head.
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