Hi Robert, Pipe organs have been using resultant pitches for eons. Typically in the bass where they feel they need a 32ft pedal stop. The 16ft C and G are played together. Giving the resultant C at 32ft pitch. Since the volume is continuous, it's a some what different case than the piano decay. Regards Roger At 04:39 PM 12/3/02 -0500, you wrote: >Here's an experiment you can all do, and all you need is a piano. > >Play C6 and F#6 together, as loudly as you can. If the theory is correct, >the resultant between F#6 (1484 Hz) and C6 (1050.5 Hz) will be 433.5 Hz, >which is just 25 cents below A4. > >I tried this, not expecting to hear any resultant. I was quite surprised >to hear a faint A4, or something like it. But as I listened, I noticed >that the A4 resultant behaved strangely. As soon as the C6 and F#6 began >to decay, the A4 resultant suddenly dropped out. It did not gradually >decay. And if I play C6 and F#6 together softly, I hear no A4 resultant >at all. This leads me to believe that the A4 resultant is not being >caused by C6 and F#6 beating together in the usual fashion. If that were >the case, the resultant would decay exactly the same as the two primary >notes. Instead, I think this is a case of non-linear mixing (as alluded >to by Sarah Fox several days ago). When the volume level falls below the >threshold for making the distortion or buzzing, then the resultant tone >suddenly stops. > >There are lots of opportunities for non-linear mixing when playing two >notes on a piano. No piano is perfectly solid. If there is a loose screw >somewhere, or if two parts of the piano are just barely touching, then you >will have non-linear mixing. (In the extreme case, these conditions cause >noticeable buzzing.) At high volume levels, there can even be non-linear >mixing in our ears, when the bones that carry the sound from the eardrum >reach the limit of their travel. In fact it is difficult to guarantee a >purely linear addition of two tones. Any distortion of the sound causes >the component sounds to interact non-linearly, and thus produce real >acoustic energy at the resultant frequency. For example, Don Mannino's >suggestion: > >>....Back to your original question, Ric. I made a recording for you, and >>you can hear the resultant tone. I made a wav file of 20K and 20.5K >>tones, one in each ear. Then I combined them into a single mono >>file. If you play it in good headphones and turn up the volume loud, you >>can just hear the 500hz tone as a pitch. > >The process of making wav files includes time-sampling and quantization, >both of which are somewhat non-linear. If there is a 500 Hz resultant in >Don's wav file, it is probably an artifact of the imperfections of the >recording process. If it were possible to record 20 kHz and 20.5 kHz >tones and mix them with no distortion at all, then there would be no 500 >Hz resultant. Since it is hard to find such a perfect recording system, >then the theory can perhaps be tested by finding a poorer recording system >- one with more distortion. If my theory is correct, the resultant tone >should be even stronger when played on such a system with more distortion. > >-Bob Scott > Ypsilanti, MI > >_______________________________________________ >pianotech list info: https://www.moypiano.com/resources/#archives
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