Essay Abstract

Up until quite recent time music has been taught as and considered to be a science. The analog approach to synthesis and the linear approach to scale construction have virtually destroyed the use of music as an analytic tool. Acoustics is an area where wrong assumptions are rife. This essay deals with the errors present in contemporary understanding of music, acoustics, vibration and resonance.

Author Bio

Originally a professional composer who wrote everything from Nightclub acts to film score to piano concertos and four and a half operas. Founded and led The Wagner Renaissance Opera Company, Inc. and wrote and directed most of its repertoire. (http://wropera.com). Wrote the Structural Resonance papers and received a grant to pursue development of this theory from the Richard Lounsbery Foundation. Designed a novel medical billing program. Designed an automatic prescription filling program. Co-developed a music engraving program that received the first patent in that field in150 years. Developed a novel and virtually unbreakable hardware encryption program. Designed a new cochlear implant. Designed a method to duplicate ort better the sound of a Stradivarius. Designed a method to acoustically condition any hall or listening area.

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  • [deleted]

Thomas,

I am not a musician, but your article was very interesting and I have forwarded it to an engineer that has a passion for flutes and a mechanical engineer turned archeologist.

Your statement, "Hearing music inside a standing wave is an experience that is incredible and is never forgotten.", reminded me of an article where an electrical engineering student at MIT had identified an electromagnetic resonant mode of the large EE lecture hall, a metal sheeted building. He built a transmitter tuned to the lecture hall mode, then walked around with an antenna coupled to a meter identifying the positions of the standing waves peaks and nulls.

    Hello Thomas,

    Various points in your paper resonate with me, after only a quick read through. Unlike Frank I AM a musician and singer, plus a recording engineer... I have experienced singing in places so live that a quartet sounded like a chorus and every singer could hear the others effortlessly, but such venues are rare.

    The discussion in your paper is meaningful and I apply some of your insights. When I use equalization in mixdown, I like to tune the EQs to the key of the song - so as to preserve harmonic relationships of natural tonality. But sometimes; one must tune out the boominess or other defect in the acoustics of a hall. So one must be mindful of those considerations too.

    You can find examples of both approaches on "At 89" by Pete Seeger, which won me a Grammy award.

    I have MP3s showing the contrast in sound of harmonic and tempered chords and scales (computer generated tones), which I will locate. In Barbershop style, singers will attempt to make some chords 'ring' - by adjusting intonation to the harmonic tuning. And of course; Classical Indian music is all based on harmonic tunings.

    But I wanted you to know I found your paper both meaningful and fun. My essay is Cherished Assumptions and the Progress of Physics. Good luck in the contest.

    All the Best,

    Jonathan

      • [deleted]

      The Structural Resonance papers will appear on my Web page (wropera.com) in a day or so. Sorry for the minor delay.

      Tom Wagner

        Dear Thomas Wagner,

        Structural acoustics is indeed perhaps manifold enough as to possibly inspire those who are trying to understand the structure of elementary waves. Having thoroughly dealt with the physiology of hearing and participating in the cochlear amplifier list maintained by Flatmax, I would like to slightly complete what you wrote on auditory function. Acoustics is not just standing waves. My first main insight from study of hearing is as trivial as important for physics: Signal processing in the ear does not correspond to Fourier analysis but to the simpler cosine transformation because the input is restricted to the past.

        An other contribution of acoustics to physics relates to an experiment by Norbert Feist. See Fig. 5 of my essay. If I am correct - and so far nobody objected although I am urgently asking for objections - then the never measured length contraction / time dilution according to Lorentz covariance has no justification. While I am not the first one to suspect that the infamous expectation of a non-null result for the famous experiment by Michelson and Morley was wrong, I consider my reasoning easily understandable for everybody.

        I often attended the annual meetings of the German Society of Acoustics (DAGA), and I will not forget an impressive demonstration of ultrasound that was audibly directed at will to any spot of reflection like a spotlight. This and the light spots to be seen on clouds or flying targets inspired me to understand the experiments by Feist and by Michelson.

        I hope your essay will get the due attention.

        Best,

        Eckard

        Dear Thomas Sanford Wagner,

        The phenomenon of resonance may be well described by defining matters as strings, in that a generic wave mechanics to be defined for both acoustic and EM waves.

        With best wishes,

        Jayakar

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        Jonathon

        Thanks for the nice thoughts. You are quite right about the rarity of really fine listening areas. When my opera company was still active we were located in the basement of a lovely old church on West End Avenue in New York City. The acoustics of that basement were excellent. When we once performed upstairs in the main church the acoustics there were dreadful.

        The air chamber in any musical instrument will resonate to any frequency fed to it. I am thinking that a listening area should do so as well so one project I am presently involved with is to see if I can force a resonance into a concert hall. It presents some unique problems.

        Tom Wagner

        It's weird,

        One of my favorite places to sing is this one hallway in a mall, where the singers can hear each other, the listeners can hear all the singers in balance, and there is a lovely natural reverb and tonal evenness.

        As you say; sometimes the meeting rooms used for practice in those old churches are much finer listening spaces than the sanctuary. And these days; the natural acoustics are often deadened or flattened in halls - rather than being allowed to resonate at all - because the thought is that there will always be electronic amplification where needed.

        But I loved the tuned urns in your description of the halls of ancient times. Maybe instead of trying to deaden the wild frequencies, acoustic designers should be looking for ways to make dead frequencies resonate more, or be filtered out less. That would be a whole different approach to acoustic design from what is prevalent today. Sounds cool.

        Regards,

        Jonathan

        • [deleted]

        Jonathan

        In a truly resonant hall the absolutely last thing we would want to do is deaden or remove any sound at all. When a true resonance forms all of the ambient sound in the hall becomes part of the resonance and it behaves as a marvelous natural amplifier. In such a hall amplification is totally unnecessary. There are no echoes in a properly tuned hall. All of the sound present supports the music being performed. The singers and instrumentalist in the opera company were seasoned veterans who performed in many halls around the world and yet not one had ever experienced anything like the acoustics of the Chapel of the Resurrection.

        The primary reason good halls are so rare is because of our rigid adherence to the concert pitch. 440A is considered to be as immutable as the atomic weight of hydrogen. If we were to use the pitch of the hall instead of 440A we would find many more good halls. We could of course build halls with the proper ratios of dimensions as defined by Vitruvius and then the hall would be tuned to 440A. This is not likely to happen as architects seemed to be totally locked into absorptive materials and reflective panels and Sabine's ray analysis and so good halls remain lucky accidents.

        The theater of Epidaurus in Greece is remarkably in tact and might be a place to test the wither or not the ancient Greek theaters were tuned.

        Tom

        • [deleted]

        Eckard

        We had a fascinating exchange of comments in the last contest and I welcome your idea in the present one. I cannot, however, find your essay. Can you supply the URL for it?

        Tom

        • [deleted]

        Frank

        Thank you for your post.

        I think the nodes and anti-nodes the engineering student found were different from the structure of a standing wave in a properly tuned hall. The nodes would not be so evident if they appear at all in such a condition.

        This particular phenomenon has never really been studied.

        Tom Wagner

        • [deleted]

        Dear Thomas,

        nice essay, I'll give you a good rate. 聽Sound it is the link between physics, mathematics, figurative 聽arts and music. Pease, read my essay ElementaryTime Cycles, where I describe how is possible to describe mathematically elementary particles as the relativistic generalization of sound source. In fact sound also is at the base of quantum formalism, see Reyleigh. However I have not considered the difference between vibration and resonance. Is it correct to say that a sound source vibrates and the air of the hall, or the hall itself, resonates? In this case matter field are vibrations of the space-time whereas the mediators of interactions are resonances.聽

        best regards,聽

        Donatello

        • [deleted]

        Donatello

        Music and sound are fundamental to the concepts of Quantum Mechanics but this is useless without a proper understanding of the physics of music and sound. You are absolutely correct in you statement that the sound source vibrates and the air in the hall resonates.

        Musical instruments provide the best example. The sound of any musical instrument begins with a vibration and this is the only vibration that can exists in the instrument. In woodwind and brass instruments the vibration forms in the mouthpiece and, like the example of the tuning fork, this vibration elicits a resonance which forms in the sides of the tube which in turn creates the internal structure in the air within the body of the instrument.

        A vibration can only occur if the frequency is at or near one of the partials of the basic nodal structure of the vibrating object. A resonance on the other hand will accept any frequency. This is the most significant difference between vibration and resonance.

        I am in the process of reading your paper which so far is terrific. I will write about the behavior of the air in listening areas such as concert hall in my reply to paper on your Web page.

        Tom Wagner

          • [deleted]

          Donatello

          Thank you for that essay. I have been hoping to find one such as this. It also opens the door to connections with others who are realizing that music has much to do with physics, especially quantum physics.

          In your essay you mention:

          In physics the most groundbreaking ideas are the simple ones.

          This is a principle held by many, including Einstein. However, the mathematics used to define such things as quantum mechanics is horrendous. When we consider fields as continuous in nature and mass as composed of infinitesimal points it follows that the mathematics will be very complex.

          Musical mathematics, although it can become quite complex, can be reduced to very simple precepts. The structures of music are defined by the Enharmonic System. If you look up enharmonic in a dictionary it will define enharmonic as - notes that sound the same but are written differently. This is the exact opposite of what enharmonic actually means. In an enharmonic system we are dealing with notes that are written the same but sound differently.

          Even a simple scale, called a diatonic scale in music, has intervallic problems. It actually takes three diatonic scales to create perfect harmony. It takes 38 scales to allow for proper tuning of the chromatic system. Most musicians do not understand the enharmonic system. If they did we certainly would not have the tonometric system. I described the tonometric system in the essay.

          Not only can everything in music be defined by positive integers the entire enharmonic system is comprised of the powers and multiples of just three numbers; 2, 3 and 5.

          I cannot help wondering that if so much of quantum mechanics appears to be musical in nature how much could it be simplified if we really used musical principles.

            Donatello

            While in many ways the interior of a concert hall behaves like the interior of an instrument such as, say a trombone there is a difference that bothered me for a long time. That remarkable standing wave that was created when we performed in the Chapel of the Resurrection in Valparaiso Indiana was created by the resonances of the voices and instruments of the performers.

            In a voice or an instrument the air chambers that contain the resonances are small and the wave would form virtually instantaneously. In an area the size of the Chapel there should have been a delay. The delay in that area should have been greater than a tenth of a second and would have easily be sensed but the lovely sound started immediately.

            Then I remembered the first moon landing where they crashed the LEM into the surface of the moon. This caused a resonance (NASA called it resonance which is to their credit). According to NASA the moon rang like a bell for a considerable time. If the resonance was progressive the size of the moon should possibly have made the resonance impossible but apparently the resonance was instantaneous, just as with the interior of the Chapel.

            The only explanation is that the resonance was already sounding. There is plenty of ambient energy in just about anything, solids, air, whatever.

            On the moon it was an impulse function, much like clapping to elicit a resonance. This is usually what is done in places like Stonehenge and the old Greek theaters (not the best method) but it words to a degree. The chapel had such a dramatic response because the pitch of our performance was at or very near the fundamental frequency of the already existing resonance of the chapel.

            I cannot help wondering about the resonance of an elementary particle and is it a simple as the resonance of macroscopic body.

            This could be a great over-simplification or perhaps it could be something worth thinking about.

            Thanks again for that great article.

            Tom

            The problem with speculative thinking is that it is too easy to overlook a basic premise. While I think I am correct about the existence of a natural resonance in the moon I overlooked the fact that a resonance is not self-sustaining. There has to be an initial vibration if a resonance or a cascade of resonances if the resonance is sustainable. There must be a vibration and a feedback occurring in the moon and I will leave the argument there as I am not sure we have enough data about the internal structure of the moon.

            My apologies for this but it does in no way challenge my basic argument.

            Dear Thomas,

            I don't know if you have considered writing a book about this, but if not, you should. I know other music people besides myself who would be interested in it. A lot of physicists and mathematicians are interested in music, but few seem to have detailed or precise knowledge about it. For instance, I play and compose (mostly classical piano), but didn't know much of the material in your essay. Anyway, I appreciate it. Take care,

            Ben Dribus

              • [deleted]

              Hi Thomas,

              Thank you for your detailed reply. What you say is really fascinating. Though I cannot see your attachments, I can figure out what you say. But I would rather say that if the structure of music is defined by the Enharmonic system, the structure of sound is described by the harmonic system of a vibrating string for example. That is to say on Pythagoras studies. According to my mathematical results the axiomatic (and not intuitive) structure at the base of our description of QM can be elegantly and simply derived from the physics of a harmonic system...after all this idea is also behind orthodox string theory, though this theory is absolutely not simple from a mathematical point of view.

              This also means that the other aspects of music or sound that you describe, if correctly generalized to 4D, can be used to describe important quantum phenomena in a very elegant way, an resolve some of the quantum paradoxes that we have.

              Please give a look to the caption of the pictures in my web page: http://www.ph.unimelb.edu.au/~ddolce/

              regards,

              Donatello