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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

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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

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    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

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        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

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        Hi Tom,

        Probably the system that I would like to describe to explain the mass of the carrier of information and therefore the gauge symmetry breaking that we observe at LHC is more similar to the air chamber of a instrument rather than of a Chapel...but this are just hits that I am trying to work out.

        I keep Reyleight's book close to my desk and I am sure that there I will find help for my hints...actually in that fundamental book about sound theory it is possible to see how an apparently abstract mathematical tool such as the Hilbert space has a very simple description and application in describing the harmonics of a sound source.

        regards,

        Donatello

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        I do know very much about moonquakes during the lunar missions. Your description could be interesting to study that phenomenon, though this is not something questioning the foundations of physics, it could be something questioning the foundations of the moon ;)

        Regards,

        Donatello

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        Ben

        I don't know if there is sufficient material to warrant writing a book but I have written several comprehensive papers about the subject. I have been trying to get to be able to upgrade my Webpage but I have it so messed up I think I will have to make an entire new Web page.

        Meanwhile if you wish to read the papers, titled Structural Resonance I will be glad to send you the Preface and Parts 1 and 2.

        If you wish to read them send me an email. That will provide me with your URL.

        Thanks for your very nice reply.

        Tom Wagner

        Tom,

        I would be quite interested in reading them... I don't see your email address on your essay, and I'd prefer not to put mine on the open thread, but it's on the first page of my essay here. Or you could give me your webpage URL. Take care,

        Ben

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        Ben

        Go to my Webpage - wropera.com. You will find the webpage is rather sparse and incomplete. I created it some years ago simply because the corporations and institutions that I deal with expect you to have a Web page. I am now in the process of remaking the Web page. Then it will be much more interesting.

        Go to the 'contact us' page and send an email with the Contact Button. That way both our URLs will not be shown.

        Tom

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        Dear Thomas Wagner,

        Isn't my argument compelling? Future music cannot be heard for sure in advance ;).

        Eckard

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        Joel

        I found your thoughts both interesting quite original. I have a somewhat different view of gravity - which follows:

        Einstein, who, more than anyone else gave us our current view of the nature of gravity, said that gravity is not a force and yet in most of contemporary physics gravity is treated as if it were. It appears that the presently held view of gravity is that it does not pull you into the chair in which you are sitting but rather, because of the curvature of space-time, it pushes you into the chair. This is a bit absurd; Gravity is either a force or it isn't, it simply can't be both.

        Einstein used the example of a man jumping from a building. The man would feel no force pushing or pulling him. The only way he would know he is moving is by the motion of the building that seems to be moving up and the friction of the wind. While nobody challenges this it seems to be almost universally ignored. The example of the man falling is a good one but gravity can be proved to not be a force by use of a very simple, basic physical law.

        Suppose I hold a ball of a given weight stationary in the air. The understanding of vectors tells us that a force equal to the force I am supplying must be pushing down on the ball. Vector analysis also tells us that a resulting vector will appear in a direction opposite the acute angle formed by the two vectors. The acceleration of the resultant vector, if the forces are constant, is dependent upon the sine of the acute angle formed by the two vectors. In the case of my holding the ball the angle formed by my pushing up and the alleged force of gravity pushing down is 180°. The sine of 180° is zero so the resultant vector is zero. It is important to remember that the force and acceleration of both vectors is still very real.

        Newton's second law of motion says that Force is equal to Mass times Acceleration - F=ma. If I hold a ball ten times heavier the force I supply must be ten times stronger as well. In order to the stationary position of the ball I must also increase the downward force ten times. Herein lies the problem.

        Acceleration is dependent on force and mass. The only way acceleration can be changed is to alter either the force or the mass. We know that acceleration in a gravitational field is a constant. On the earth it is 32 feet per second squared. If the gravity of the earth is a force and created by the curvature of space-time then this force too must be constant. The only thing that is a variable is the mass however, if we change the mass we change either the force or the acceleration. Thus either heavier objects fall more slowly than lighter objects or the acceleration changes as a result of the change in mass. We know empirically that this cannot be true as both force and acceleration are constant. Therefore gravity cannot be a force.

        The ball is now ten times heavier and thus the gravitational field (if indeed that is the correct term) is ten times as strong. The curvature of the space-time created by the ball is greater and so, if gravity is a force, the ball is pulling the earth with a stronger force. Actually the acceleration of the earth toward the ball has increased and so the earth is falling toward the ball at a greater velocity. We can see this in Newton's other formula: While this does not exactly hold in GR it is sufficient for this argument. The increase in the apparent attraction of the earth and the ten pound ball is so small as to be virtually immeasurable.

        If gravity is not a force why do we feel our weight when sitting in a chair? Consider a situation where two opposing vectors are both forces, such as two cue sticks pushing on a billiard ball at two points in direct opposition.

        The change in the position of the ball is zero and we can state that this is the resultant force of the two primary vectors. We have the mass of the cue ball and the force applied by the cue sticks. This means that there is in both cases an acceleration. An object can have any number of independent motions and in this case the ball is moving in two directly opposite directions but the ball is moving. The second law of motion states that force and mass will produce an acceleration. These two opposing accelerations do not 'cancel each other'. They create a vector with zero acceleration. Perhaps it may be more correct to say that they produce no vector.

        Since gravity behaves much like a force, we feel our weight in a chair because we are still falling. Just because the chair stops a change in position does not mean we are not still falling. Our feeling of weight comes from momentum. A falling body has a certain momentum even if it does not actually change its position. It is this momentum we feel when sitting in a chair.

        Since gravity is not in any way a force it has none of the properties of a force. It does not propagate. It would only propagate if it were a force. Contemporary physics not only thinks of gravity as a force but appears to think of it as an electromagnetic force. Many, many hours have been spent by really brilliant people trying to reconcile the 'force' of gravity with such forces as magnetism. The mass of an atom does not create the curvature of space-time any more than the nucleus creates the electron. The curvature is an integral part of the atom that was created when the atom was created. It cannot be modified nor removed.

        Newton, when he worked out his gravitation theories, was concerned with action at a distance. Even though gravity is ubiquitous through the universe there is no action at a distance because there is no action. Gravity does not do anything, it simply is. It is not one of the elementary forces as it is not a force. There is no need for energy mediating bosons to mediate the force ergo, thus there is no graviton. I seriously doubt that the Large Hadron Collider will find any evidence of a massless, spin-2 boson.

        It has been said that if the sun were to suddenly disappear we would not be aware of it for eight and a half minutes. That is true but has nothing to with the curvature of space-time and thus gravity. If the sun were to disappear instantly the curvature would disappear instantly as well. We would not sense this in any way, since the path of earth around the sun is a geodesic nothing would have changed; we would still be traveling in a straight line. Eight and a half minutes later everything would become instantly dark and start to quickly become very cold. That we would certainly sense and then we would know that the sun had disappeared.

        The extent of a gravitational field appears to be limitless. It diminishes as described by the inverse square law but never completely disappears. Thus the entire universe is one large structure formed of a myriad of space-time curvatures.

        Finally; since gravity is not a force why it is considered along with magnetism, the strong nuclear force and the weak nuclear force to be one of the primary force interactions of physical reality? Gravity is not a force, it is a condition.

        If indeed gravity is not a force, are we correct is thinking that gravity functions at the quantum level? Does an elementary particle warp the space-time or is the concept of space even valid at the quantum level. It seems quite possible that gravity at quantum level may be a mathematical concept that would only be valid if gravity is a force.

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        Loel

        Once the program dropped my formula. The missing formula is : F = G(m1m2/r2)

        It is not particulately important to the post but just to keep everything tidy.

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        Jonathon

        A thought about your mention of harmonic tunings. Apart from such dada-esque or musique concrete-like musical forms such as Chinese Opera of the Japanese GaGaKu virtually all the world's music conforms to the same mathematical structure. Just about every culture we discover has one common musical element, the pentatonic scale. From this basic scale all of the various music systems develop.

        There is only one pentatonic scale and it is defined by the overtone numbers that comprise it. These are 1, 9, 5, 3, 27.

        The difference between the East Indian scale and the western scale is the major sixth. The western scale is a reciprocal scale (I explain this in my Structural Resonance papers) and the major sixth is the ratio is 5/3. The Eat Indian scale which is not reciprocal and usually sounds over a drone requires the major sixth ratio to be 27/16. Apart from that the scales are identical but their functions are quite different.

        Tom

        Tom,

        I sent you an email... please let me know if you don't receive it. Take care,

        Ben

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        Hi Thomas,

        Thanks for leaving a comment on my page, and thanks for sharing your essay. I think that your essay is quite awesome, because I do love music a lot and the essay taught me some things.

        I was reading a bit about your work called The Legend of the Rood, and that got me reading about a whole lot of other related things, so thanks for that too. It's not really related, but I have to ask: have you read the books in the series A Song of Ice and Fire by GRR Martin? Aside from the light dusting of fantasy, it's a pretty fascinating interpretation of what medieval life might have been like. As a bonus for me, his universe also includes songs and music. :)

        - Shawn