by John Rosen
Posted with permission of the author.
Date: Thu, 11 Mar 2004 12:59:05 -0500
From: John Rosen <j-rosen@SBCGLOBAL.NET>
Subject: Difference/Combination Tones --LONG/Complete
Sorry, first msg went out before it was done.
The complexity level of difference tones (also called combination tones)is very high. They seem to be entirely psychoacoustic, and may have something to do with the little ear hairs that account for frequency perception.
A relatively accessible explanation is at https://en.wikipedia.org/wiki/Combination_tone . This site includes sound files with a ***SUPER*** demonstration of a difference tone, for headphones or speakers. Part of the goal here is to teach the listener to HEAR difference tones--good practice for us flutists. SET THE VOLUME HIGH, AS THE DIRECTIONS SAY. lOOK FOR THE SENTENCE, "Now listen to the two tones together. In this sample, the g3 plays for 1 second, then b3 joins it for five seconds."
Apparently harmonicas make very clear difference tones; listen to the sound files at "Remedial difference tone sample 1. Listen to these two harmonica notes played separately: 7draw, 8draw; then together: 78draw. Can you hear a faint tone at this pitch: diff? (This example and the stimuli are from Pat Missin's website, http://www.patmissin.com/ffaq/q26.html , accessed December 2002.)"
The next two paragraphs below the sentence above are ASTONISHING. I won't quote them because of length. Okay, enough gushing over this site; I bookmarked it, and I'll go back.
I found a web site that discusses "beats"--a pulsation in volume between two tones that aren't very different, slow enough to be noticed. I've heard these in tuning my clavichord (double-strung); the two strings of a note are in tune when the beats go away.
The web site (http://www2.sfu.ca/sonic-studio/handbook/Beats.html) includes several sound examples of beats--but you want broadband here, because the sound files are around one megabyte. The studio is Simon Fraser University, I believe, in Vancouver.
The example of beats totally freaked out my cat--woke him up and unsettled him. (He's used to music, of course.) So I'd say that cats hear difference tones two....
Beats are NOT difference tones, according to one web source (http://www.ptg.org/pipermail/pianotech/1999-September/051526.html - LINK NO LONGER VALID - 2011/03/01), a piano tuners' site. (With a keyboard instrument that actually makes a sound, unlike the permanently muted clavichord, tuners use beats within the octave to build a well-tempered scale, so this is important.) A quote:
Difference tones and beat frequencies, although they often have the same CPS numbers attached to them, are two completely different phenomena. Difference tones arise from nonlinearities in the auditory system, and when the real toned increase (or decrease) in volume, the difference tone increases (or decreases) in volume much more rapidly. For quiet tones, you may have beating but no difference tone. Even a 33Hz beat can be perceived without the slightest hint of a 33Hz tone. One additional phenomenon, the virtual pitch, is often close to the difference tone, and can beat against it. The understanding of these phenomena has increased tremendously since the 60's -- I suggest you go to the library and look up "psychoacoustics".
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I also found a web article that suggests difference tones are psychoacoustic, possibly arising in the physical ear. A quote:
Two pure tones presented simultaneously to the auditory system stimulate the basilar membrane at positions that are associated with their respective frequencies, but also at positions corresponding to frequencies that are the completion, toward lower frequencies, of the harmonic series. The causes and behavior of all these distortion products are not fully understood. However, it is easy to hear the difference tone that corresponds to the simple difference between the frequencies physically presented to the ear. This tone is all the more audible at higher levels. It has even been used compositionally, for example, in Gyorgy Ligeti's Zehn Stiicke fur Bldsserquinttet (1968). The phenomenon can be heard at the end of the first piece, for instance. The phenomenon can be heard at the end of the first piece, for instance. The difference tone belongs to the world of physiology and perception: even if it is not present in the stimulating waveform, it is created physically in the inner ear. It can also create auditory beats in the same way as a "real" sound since it is mechanically present on the basilar membrane.
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Sara Hennings wrote about her father's understanding of the effects of two different tones. I believe she was describing BEATS, which are acoustic, not DIFFERENCE TONES, which are psychoacoustic. But I'm not sure.
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APPENDICES:
Sthe definitions at (http://harada-sound.com/sound/handbook/basicterms.html):
Another effect experienced by the human listener is the interaction of tones with each other. Three situations can occur:
Beats - two tones separated only slightly (less than 30 Hz or so) and have approximately the same amplitude will produce beats-- literally, pulses-- alternating reinforcement and cancellation of amplitude-- at the ear equal to the difference between the two frequencies. As the difference between the frequency decreases, the speed of the beats decreases, too. Beats are the result of the ear's inability to separate closely-pitched notes.
Combination Tones - the sound two loud tones that differ by more than 50 Hz will be interpreted by the ear as a complex set of tones, including the two originals, and an additional set of tones that are equal to the sum and the difference of the two original tones. For example, 1 kHz and 1.5 kHz tones produce a difference tone of 500 Hz, and produce a sum tone of 2.5 kHz. Difference tones are easier to detect.
Masking - the phenomenon which prevents the ear from hearing softer sounds underneath loud tones. The effect is more pronounced when the frequencies in question are relatively close together. For example, a loud 4 kHz tone will mask a softer 3.5 kHz tone, but will have little effect on a soft 1 kHz tone.
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More on the physiological basis of difference tones http://www.zainea.com/Hearing,%20physiological%20and%20psychological%20aspects%20of.htm) No longer available 2019-01-13.
Furthermore, it is now known that the hair cells of the inner ear only react to vibrations in one direction, i.e. during one halfwave of a periodic vibration. This is an intrinsically nonlinear mechanism. When more than one frequency is present, this mode of response offers a highly elegant explanation to the phenomenon of <dfn>difference tones</dfn>, hybridization products which arise during the detection process of complex sounds. Earlier these were simply explained as resulting from the action of nonlinearities in the middle ear at loud volumes. Now it seems that that explanation does not really cover everything. Further, problems with the so called <dfn>missing fundamental</dfn> type tones (periodic sounds which take on the pitch of the first harmonic, even if the first (few) harmonic(s) is (are) not actually present) seem to benefit greatly from analyses which take into account this type of nonlinearity in the ear.
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I'm not vouching for this material that I only dimly understand. But it looks solid and is consistent.
Some implications for flutists seem to be:
People differ--presumably flutists and audience members alike--in their ability to hear difference tones, possibly because of physical differences in the ear. The difference tones aren't "there" in a sense of physical energy; our ears make them. Specific combinations of tones should make more or less noticeable perceptions of difference tones, depending on how the ear works.
I'm curious about how far the difference tones "project" or are audible. Even if two flutists can hear them, are the tones less noticeable to an audience? If two flutists "hear" a D-Bb-B yucky chord, does this mean that audience members 15' - 50' away will hear the chord? It sounds as if difference tones are perceived only at a high volume, so perhaps flutists duetting in large halls haven't anything to be concerned about--except their own sensibilities.
john
