The Scientific Spirit In Acoustics

 The ratios of the fourth and the fifth are inverse opposites of the octave overtone ( both ratios cause a pull to resolve at the fundamental (and octave). When the ratios are explored at depth, the relation of their overtones is in dissonance. As Rothstein describes, "These two consonant tones (fifth and fundamental) have strongly dissonant overtones...[and] are the poles of tonal musical drama."251 It is this paradox of the poles that defines the description of thesis and antithesis in the dialectics of music theory. Erno Lendvai states,

By taking a V-I cadence the essential notes in the five chord bear an equal tritonic relationship according to their overtones. These essential notes are what cause the strong feeling to I. By inverting these notes the same tritone relationship is formed...The tritones' overtones act as subdominants [fourths] and as dominants [fifths] at the same time. These two positions neutralize and again, the tritone's relationship to the tonic [fundamental] is found, the two are acoustically interchangeable.252

Jeans provides the following on the topic: "In the case of wider intervals such as C and F# [the tritone] there are no beats to be heard, either pleasant or unpleasant, but Helmholtz asserted that C and F# sound badly together because certain of their harmonics (e.g. g' and f'#) make unpleasant beats."253

The dialectical process is demonstrated through sound-current nondualism by the splitting of nothing (the zero beats root of the fundamental) into two parts: the fundamental and the octave, that freely resonate into the next multiple of the fifth, forming complimentary opposites to the fundamental. The fifth splits the octave and fundamental in half but also pulls to or, resolves to, the octave and fundamental.

As described by Lendvai and Rothstein, the free vibration of the fifth and its overtone become extreme opposites to the fundamental, via the overtone forming tritonic relations to the tonic. The tritone has traditionally been known as "the unutterable" or "diabulus in musica" and for Pythagoras it was the secret transcendental ratio from which the Pythagorean theorem was derived.254 Lendvai points out that the tritone overtones act as both the fourth and the fifth, the yin and yang, thereby unifying and neutralizing and modeling the dialectical reversal. In the scale the tritone (F#) is in between the subdominant or fourth (F) and the dominant or fifth (G).

Certainly neither Pribram and Schmidt or the global green movement that Wilber also supports, are advocating a "regressive" return to pre-industrial society as the immediate dominant fear arises, but instead the societal model of an open multidimensional process that continually reaffirms the universal common ground of the void. From systems theory music analysis, Leonard Meyer calls this societal model "fluctuating stasis" based on "steady-state" systems theory, a prediction of the same recommendation from radical ecologist open systems theorist Fritoj Capra.276

In Noise: The Political Economy of Music Jacques Attali presents a similar societal vision-predicted by and achieved through profound music practices that challenge the hegemony of linearly repressed symbolic abstraction of the western knowledge system.277 John E. Peck documents how in fact indigenous cultures already enact concepts of sophisticated open systems theory:

Given its sensitivity to time and place, indigenous knowledge would seem to be better situated to successfully adopt and apply a nonequilibrium perspective to ecosystem management than conventional scientific thinking, particularly in settings unfamiliar to western policy makers. Ecosystemic trajectories are so contextually contingent that an observer can hardly afford to entertain a theoretical framework

219 Peter Gorman, Pythagoras: A Life (London: Routledge and Kegan Paul, 1979), p. 137. For the latest biography see John Strohmeier, Peter Westbrook, John Scrohmeier, Divine Harmony: The Life and Teachings of Pythagoras (CA: Berkeley Hills Books, 1999).

220 The latest analysis that assumes Pythagoras did not know about the transcendental or "irrational" only approaches the problem from arithmetic or geometry and leaves out the actual music proportional approach that Pythagoras used. Philip Hugly; Charles Sayward, "Did the Greeks discover the irrationals?" Philosophy 74 (April 1999): 169.

221 For the connection between the Taoist and Pythagorean use of initiation and the transcendental see, "A. Volkov, "Zhao Youqin and his calculation of pi," Historia Mathematic 24 (Aug. 1997): 301-331. Zhao Youqin was a Taoist Master.

222 Leibniz, the founder of calculus and binary logic, was bent on creating a "characteristica universalis" or universal method of reasoning enabling direct communication. His motivation was the complete destruction of the great thirty year religious war from which a desire for dogmatic abstract certainty or the modern paradigm arose. Leibniz though was already transcending the linear materialistic religion of technology suffering of his day, by using the I Ching as a parallel basis for his multidimensional approach, unlike Descartes.

250 Zizek, Tarrying with the Negative, pp. 122-123. Just like the derivative for Weierstrass, for Zizek, the linear symbolic limit is the never-ending goal, still repressing the transcendental consequences of analysis. The focus of Zizek's latest book The Fragile Absolute: Or, Why the Christian Legacy is Worth Fighting For (NY: Verso, 2000) is an overt attack on the growing recognition of "the sacred" and is literally a full embrace of linear symbolic logic reflected by the materialistic western religion of technology.

251 Rothstein, Emblems of Mind, p. 28.

252 Lendvai, Bela Bartok, p. 24. The intervals, although found in the chords, are dependant on the chord inversions as well.

253 Jeans, Science and Music, p. 157.

254 Rothstein, Emblems of Mind, p. 29. For tritone as source of the infinite transcendental (or "irrational" [Ã2] in the modern paradigm) see "Music's Discipline of the Means: An Interview with Ernest McClain." Parabola 16 (Winter, 1991): 85.

255 On the void as the source of the dyad see O'Meara, Pythagoras Revived, pp. 67-68.

256 Although I have never seen the multidimensional spiral fifths used to demonstrate the dialectical process before, Ernst Levy did perceive the relationship when he described the cadence of the dominants of dominants of tonics (the cycle of fifths) as a "dialectical process." Levy, A Theory of Harmony, p. 98 citing Moritz Hauptman, The Nature of Harmony and Metre (London: Swan Sonnenschien, 1888).

Elisabet Sahtouris, Ph.D, "The Survival Path: Cooperation between Indigenous and Industrial Humanity" at http://www.ratical.org/LifeWeb/ A balanced overview can also be found in the books on the topic by anthropologist Jack Weatherford.

276 Meyer, Music, the Arts, and Ideas, p. 172. See also former World Bank senior economist Herman Daly, Beyond Growth: The Economics of Sustainable Development (Boston: Beacon Press, 1997) and his earlier work, Steady-State Economics (San Francisco: Island Press, 1991). Daly works with John B. Cobb an advocate of Alfred Whitehead's Pythagorean process theology also studied by David Griffin. Herman E. Daly, John B. Cobb, For the Common Good: Redirecting the Economy Toward Community, the Environment, and a Sustainable Future (Boston: Beacon Press, 1994). Polkinghorne notes the Cobb process theology in Belief in God in an Age of Science, p. 55. For the evidence of Pythagoras' continued social systems influence on "organizational behavior:" James Bedfore-Roberts, "Concepts from Pythagoras," Hewleet-Packard technical report; HPL-91-22, 1991.

277 Jacques Attali, Noise: The Political Economy of Music (Theory and History of Literature, Vol 16) (Minneapolis, MN: University of Minnesota Press, 1985).

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