Tonal Hierarchies

Musical Tone Organization as Particle/Atomic Energy Organization

By Sandborn, M.T.

Abstract:

There is one fundamental system of energy organization that is defined by the basic harmonic properties of electromagnetic waves1,2,3,4,5,6,7,8. These basic properties define sub-particle organization resulting in the particles, and particle organization resulting in the elements, as well as all other natural energy systems. The natural system of musical tone organization, as defined through the experiments of Krumhansl, C.L., Bharucha, J.J., & Kessler, E.J.9, is such a system and thus should correspond to particle and atomic organization. The basic process is to identify the relativity of tone relationships and then compare the hierarchy of relativity to the hierarchy of energy positions defined in the particles and atoms.

Relevant Information:

Sandborn and Sandborn have related pending patents; own percentages in a partnership and a corporation that are in the process of utilizing the pending patents and other related materials.

Main:

The order of harmonics within the harmonic particle structure is based on overtone harmonics: 1-2, 3-6, 9- 18, 27: 5-10, 15-30, 45-90, 135: 25-50, 75-150, 225-450, 675; and undertone harmonics 1-2, 3-6, 9- 18, 27: 5-10, 15-30, 45-90, 135: 25-50, 75-150, 225-450, 675 (undertone harmonics being fractions such as 1-1, 2-5, 8, and the starting undertone energy position being related to the starting overtone position by ¸/128). Diagram 1 shows a simplified view of the harmonic energy arrangement including the organization into quarks which defined a charge/gravity symmetry center for each quark. Harmonic positions from 25 to 675 are active only half of the time due to the existence of neutral wave positions, and are negatively charged compared to the positive charge of the two dominant quarks. The quark is further divided by perception. If one perceives the positive side of the particle composed of the two positive quarks, then one cannot simul-taneously perceive the negative side of the particle composed of the one negative quark.

The next step is to assign the various tone names (Western tone names) to the 12 alpha wave positions of the proton particle and view the results. The reference overtone alpha wave is identified through symmetry to be the tone A (433 cps). The remaining tones are then referenced to this tone.

FIG. 2 shows the orientation of the 12 tones within the proton quark structure. The tones E, G#, and C form the symmetry centers. The tones A, E, B, F#, C#, G# and D# form the perceived key of the proton (E Major). The tones A#, F, C, G and D form the unperceived non-key tones. In between the tone positions are directional arrows that show the relative charge and gravity relationships around the symmetry centers. For example, around the E tone symmetry center the A tone is perceived to be of lesser symmetry value as is the B tone. Even further removed are the tones D and F# which means they will have a more reduced symmetry influence. Overall, the E symmetry center is the dominant symmetry center followed by the G# symmetry center and then the C symmetry center. It is expected that perception of tone organization relative to key will form this same pattern of symmetry relationships.

The tonal hierarchy results found by Krumhansl, C.L., Bharucha, J.J., & Kessler, E.J are the same for each key tested so that the results of all keys can be represented by one key. For the purposes of this presentation the key ofE Major is used in order to directly relate the results to the proton. The results presented by Krumhansl and Kessler (1982) are converted to values from 0 to 1, ordered by strength of association, and then given a number reflecting their hierarchical order (Table 1).

If the tones are organized according to vector sets, and relative intensity arrows are used to show decreases in tonal hierarchy, then the same pattern shown in FIG. 2 is produced (FIG. 3). Note: intensities are shown relative to the reference 1.

Figure 4 shows the results of the probe tone tests place in the context of the proton structure and then compares it to the expected pattern of FIG. 2.

The only probe tone result that does not correspond with the expected results is the relationship between F and A#. Several observations can be made about A# based on the harmonic particle structure and other test results. A# is the complementary tone to E which is defined musically as the tri-tone. Test show that perception of the tri-tone is skewed by what is called the tri-tone effect10. Thus it may be difficult to accurately assess the correct value of A#. FIGs. 2 and 4 suggest that there may be two perceived values of A# which would not necessarily disagree with tests of the tri-tone effect.

Commentary

The correspondence between the particle and atomic wave structures proposed by Sandborn and the probe tone studies conducted by Krumhansl and Kessler is just one of many examples of correspondence. From a musical perspective the results are useful in proving the direct connection between the particle and atomic organizations and the sensory structure. And since the intellectual development is dependent upon the natural sensory organization, it will also be defined by the particle ant atomic organization. This observation results in a clear path between the science of harmonics that produce the particle and atomic organization and music theory, thus giving music a strong scientific foundation on par with other sciences.

Krumhansl and Kessler also tested tone relationships for the Minor key. At the time of this essay early comparisons show that the minor key is a resultant of spin changes in the proton in which the energy is made to flow backward through the harmonic structure. It is noted that the minor chord is a reversed undertone major chord.

Bibliography

1) Sandborn, M.T., Sandborn, M.D. An Hypothesis for Undertones as Amplitude Modulation, unpublished paper

2) Sandborn, M.T., Sandborn, M.D. The Harmonic Energy Transformation Octave Wave, unpublished paper

3) Sandborn, M.T., Sandborn, M.D. Harmonic Color, Numbers, and the Electromagnetic Wave, unpublished paper

4) Sandborn, M.T., Sandborn, M.D. The Formation of the Particle Alpha Wave, unpublished paper

4) Sandborn, M.T., Sandborn, M.D. The Harmonic Formation of the Proton, Electron and Neutron, unpublished paper

6) Sandborn, M.T., Sandborn, M.D. The Harmonic Energy Structure Identification of Quarks and the Assessment of Quark Charge, unpublished paper

7) Sandborn, M.T., Sandborn, M.D. The Unified Wave Theory, Undertone 1st Edition, Atlanta: MS Squared, 2001

8) Sandborn, M.T., Sandborn, M.D. The Origin of Understanding, Atlanta: MS Squared, 2002

9) Krumhansl, C. L. Cognitive Foundations of Musical Pitch. Oxford Psychology Series No. 17. New York: Oxford: Oxford University Press, 1990, p. 30 (Krumhansl, C.L., Bharucha, J.J., & Kessler, E.J. Perceived harmonic structure of chords in three related musical keys. Journal of Experimental Psychology. Human Perception and Performances. 1982)

10) Structure and Perception of Electroacoustic Sound and Music, proceedings of the Marcus Wallenberg symposium held in Lund. Sweden, on 21-28 August 1988, Editors: Soren Nielzen, Olle Olsson, (1989). Excerpta Medica, New York, pp 63-78.

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