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I consider it quite possible that physics cannot be based
on the field concept, i.e., on continuous structures.
In that case, nothing remains of my entire castle in the air,
gravitation theory included, [and of] the rest of modern physics.

Albert Einstein
In a 1954 letter to Michele Besso


Thomas Wagner received a grant from the Richard Lounsbery Foundation to prove the tenets of the Structural Resonance Theories. Mr. Wagner has been relatively inactive in music for some years. This required a 501(c)3 to administer the grant. The Wagner Renaissance Opera Company was reactivated for this purpose.

Now that the opera company is active again it has been decided to use the opera company once again for musical and theatrical ventures.

Tests thus far on the Structural Resonance Theory have been very successful and results will be presented in the near future.

.:The Structual Resonance Project

The Structural Resonance papers contain the development of a matrix and, supported by this matrix, puts forth the idea that all music, and thus by definition, all sound, is discrete. This matrix is comprised entirely of integers and forms the basis for all music and, to a great degree, all sound. Because of the nature of current mathematical methods and procedures virtually all the experimental equipment in use today is analog. Even sampling, which is defined as digital must be changed back into the original analog form in order to be used. These papers propose that analog devices do not show structure; they were not designed to do so.

The dichotomies of our thinking concerning the continuous and the discrete have probably been with us since the beginnings of the species. Our most unique quality as a species is our ability to think abstractly. Nowhere is this ability more manifest than in our mathematics. Most modern mathematicians tell us that the paradox of Zeno concerning the tortoise and the hare is no longer paradoxical as we now know that the sum of an infinite series is 1. This is a contradiction of terms. In some erudite journals it is even stated that this proves that we can go through an infinite number of points in a finite amount of time. We take something that simply doesn't exist and give it a name and that of course gives it a conceptual existence. This is the danger of abstract thinking. It is important to remember that even Euclidean geometry is abstract. Points, lines and planes are not physical realities.

Consider how little energy a violinist uses to excite that string. By the time that energy goes through the various parts of the violin less than two percent actually finds its way into the airborne structure we call sound. This sound will fill a hall and yet, to imitate this function ‘electronically' we must use perhaps a hundred watts or more and the result is still far from sounding real.

Virtually all of the tools and methods we use are designed to produce a linear result. These include the Fourier Transform, the oscilloscope and, unfortunately, tempered tuning. The ancient Greeks, who were closer to a real understanding of the actual physical nature of music than we are today, often stated that, ‘ good comes in through the rational numbers and evil through the irrational' .


This will allow us to build acoustically true halls, halls that will be a delight to audiences and performers alike. One of our aims is to be able to create programmable standing waves of any size. This ability suggests an awesome power. It would give us the ability to create a duplicate of the actual sound of an instrument or a voice with decipherable words in any accent, in fact, a perfect emulation of any sound in the world. This would not be a recording in the usual sense. It would create the sound in precisely the same manner as does the instrument itself. Anyone could recreate the actual sound of the Boston Symphony or an ideal symphony designed by the user in his or her living room. The enharmonic matrix of the Structural Resonance papers is a mathematical absolute. It is irrefutable. No other set of numbers will work. This proposed theory could aid greatly in design and use of cochlear implants. It will be a very fine teaching tool.

Real musical instruments require very little energy and for the most part have very low masses. The facts that we expect to discover should be both pitch and mass independent. They should behave exactly the same in any given range of frequencies and this should occur in any octave, from the ratios of orbiting moons to musical instruments to structures of electromagnetic radiation and even quite likely to the resonances of quantum theory.

Energy input is limited only by the size and mass of the primary resonators. This could provide excellent devices for the military. The potential spin-offs of The Structural Resonance papers are many. There are undoubtedly many other uses that are as yet undiscovered.

A resonance is a very powerful thing. The Tacoma Narrows Bridge was destroyed by a resonance that formed as reaction to wind. This bridge collapsed for primarily the same reason that a trained singer can break a crystal goblet by singing and maintaining the proper pitch. Both the bridge and the goblet will resonate to any frequency. In each case at a certain frequency they will start to oscillate. Helmholtz describes this very well in his metaphor of the playground swing. If we give the swing a gentle push at the proper point in every cycle the swing can be made to go higher and higher.

The amount of energy a singer uses to create a sound is very small and it was a forty-mile an hour wind that undid the Tacoma Narrows Bridge. As with all such occurrences very little of the energy of the singer or the wind actually found its way into the respective resonances. This would mean a colossal result from a very small input. In music a proportionately small energy input creates an amazingly powerful sound. By the same token a proportionately small energy input destroyed the Tacoma Narrows Bridge.


Once the results of the experiments are successful the results will be submitted for publication. Efforts will be made to continue the work begun by this grant. These tests will lay the groundwork for true Virtual Sound. At the same time we will pursue the search for uses of this theory that are not connected with music. One very effective use will be ear prosthetics, such as the now problematical cochlear implant. Another is highly effective weaponry.


Music is mathematically and acoustically totally digital . All acoustic phenomena must be as well. The mathematics of continuous functions has absolutely no place in the study of musical theory, in fact, that is where contemporary musical and acoustic theory goes wrong. Proving the tenets of the Structural Resonance theory should give us the opportunity to use the concepts of music and its inherent mathematics as it was used through much of its history, as a tool to study physical reality. It could prove to be a very valuable tool.


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