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  • #46
    Re: 64' resultants



    [quote user="sesquialtera16"]</P>


    play the 32 bourdon at tc</P>


    add the bass f below it</P>


    see what happens [/quote]</P>


    I think you are just trying to pull our chainby inducing us to invert our thinking.. [] What you have suggestedis merely F+fifth which resultsina sub F. []</P>
    2008: Phoenix III/44

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    • #47
      Re: 64' resultants



      In response to Al,</P>


      Your first question concerns resultant tones, where some nonlinear element is present - here (pun intended) the human hearing system, when we are listening to any type of organ, pipe or pipeless. Yes, there are additive tones, but they are usually masked by the harmonics of the initiating sounds, as you have surmised. I think it would be very hard to perceive them.</P>


      Your last question concerns beats, and the answer is again, yes. The waves reinforce or partially cancel at the beat rate.</P>


      I am not sure what you mean by "true mixing". </P>


      The Wiki article referred to in an earlier post says that resultant tones can be "heard" when using headphones to feed one tone into the right ear and the other tone into the left ear. If this is really the case, then it means that the nonlinearity of our hearing is a very complex matter indeed, and that any attempt to compare it to more straightforward nonlinearity (e.g. in a loudspeaker) is probably conjectural.</P>


      John Reimer</P>

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      • #48
        Re: 64' resultants

        Perhaps then this is the basis for the latest directed energy non lethal weapon system whereupon two powerful ultrasonic beams having frequency difference in the audio range are simultaneously directed at a target, causing pain and nausia, rendering the opponent ineffective.I have heard that this is adefense tool on many modern ships. I imagine one of those could generate a pretty good 64' resultant.We'll wait and see if one comes on Craig's list or eBay soon.Any ideas?

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        • #49
          Re: 64' resultants

          [quote user="j reimer"]

          To reply to cosmicpanda -</p>


          When we play together a C and the G above it (for example), we do hear a beat (assuming they are not in perfect tune as "fifths"). This is consistent with my statement about similar pitch and amplitude, for what we are hearing is not a beat between the fundamentals of the two notes. It is a beat between the third harmonic of the C and the second harmonic of the G.</p>


          The fact that we can hear a beat between two sounds of similar pitch and amplitude does not mean that our ear is responding to a "new sound" in the real world. What is happening in beats is that the two sounds are reinforcing and partly cancelling each other at the beat rate.</p>


          (BTW, when I say that the two sounds are of similar amplitude, I mean at the point of entry into the ear canal. Thus a very loud but distant sound could beat with a close but soft sound. If the pitch and amplitudes of the two sounds are EXACTLY the same to the ear, but 180 degrees out of phase, then the ear would hear no sound at all. But the fact that we have two ears would make this hard to test, without blocking one of our ears!)</p>


          It should be clear that our ear is not detecting a "new sound" of pitch 1 Hz. Our hearing does not go that far down. But we are certainly hearing the beats.</p>


          I think one of our problems in this discussion is that we are confusing "sounds perceived" with "sounds in the real world". Because of the nonlinearity of the human ear, the two things are not the same.</p>


          John Reimer</p>

          [/quote]</p>

          OK, fair point about the tuning of fifths.</p>

          As I have said before, I am only a student of acoustics, not a master, and so I asked my lecturer at University about this. He said that theoretically, beating does not exist, but that in practice if the beating is strong enough, it can then cause a vibration of it's own, and therefore in that situation it can be said to exist in the real world.</p>

          In the end, this doesn't answer the question of whether or not resultant basses are always a function of the ear or not, but perhaps some approach the problem in this way by trying to produce the vibration through very strong beating, and perhaps others try to acheive the effect through other means.
          </p>

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          • #50
            Re: 64' resultants



            I have been doing some reading on this subject, and I think I can now understand the objections some have to my statement that the sum and difference frequencies exist. It is probably true that a Fourier analysis would not discern the difference frequency, because the phenomenon we perceive as the difference frequency (which is just a beat frequency at a higher rate) is actually an amplitude modulation of the composite signal, the result of the reinforcement and cancellation effects of the two freqencies interacting. Fourier analysis is not designed to react to AM signals, which have to be transformed by rectification (the non-linear process that has been mentioned) before they can be perceived as a new frequency. Persons trained in the use of carriers and AM circuitry will be familiar with this process. So, in a sense, the difference frequency does exist, but it is in a different form, being a periodic pulsation in the amplitude of the signal, which can be discerned due to the non-linearity of the ear.</P>


            David</P>

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            • #51
              Re: 64' resultants



              [quote user="cosmicpanda"] In the end, this doesn't answer the question of whether or not resultant basses are always a function of the ear or not . . . [/quote]</P>


              You don't actually 'hear'resultants in the range of 8 Hz - 16 Hz, since human hearing only goes down to about 20 Hz. The resultant is perceived via your hands and feet, and particularly in the seat of your pants.</P>
              2008: Phoenix III/44

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              • #52
                Re: 64' resultants



                Yes, that is just as you say.</p>

                But I hope that you can agree that typing 'hear' is much easier than 'quivers your hands and feet and causes vibrations in your buttocks.'
                </p>

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                • #53
                  Re: 64' resultants



                  Well, "feel" works for me. "Perceive" would, also.</P>


                  David</P>

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