Music and the Making of Modern Science: Dear Peter Pesic

Dear Peter Pesic: Thank you for your fascinating Music and the Making of Modern Science book, (use Scribd to pdf converter below in footnotes) as I had a citation that you corroborated with your quote of Boethius about Pythagoreans finding 9/8 as unacceptably dissonant.      “Orthodox Pythagorean theory recognizes five consonances: fourth, fifth, octave, twelfth, and double octave; and these are represented by the multiple and superparticular ratios [n + 1 : n] from the tetrad. The number 8 obviously does not belong to the tetrad.”

André Barbera, "The Consonant Eleventh and the Expansion of the Musical Tetractys: A Study of Ancient Pythagoreanism," Journal of Music Theory, 1984.

and

R. P. Winnington-Ingram's, “Aristoxenos and the Intervals of Greek Music,” (1932) as an article “admits that the pre-Platonic theorists used the tone 8:9 to construct a scale, but for some reason is reluctant to attribute this construction to the Pythagoreans.”

And so you interpret this as the Pythagoreans needed to confront and accept dissonance but I disagree with you. I agree with Alain Connes that the secret of music theory is that 2, 3, infinity is noncommutative and so the infinite spiral of fifths is because of the subharmonic C to F, Perfect Fifth, that Archytas covered up by changing the subcontrary mean to harmonic mean for his "arithmetic mean x harmonic mean = geometric mean squared" logarithmic source of Perfect Fifth plus Perfect Fourth = Octave.

The Orthodox Pythagoreans allowed the subcontrary mean, just as the "three gunas" of India are based on the secret of noncommutative phase of Sattva as the octave, rajas as the Perfect Fifth and tamas as the PErfect Fourth and in China the same secret is the origin of the Tai Chi - octave is emptiness, yang is perfect fifth and yin is perfect fourth.

Orthodox Pythagorean, Kriya Yoga and Daoist alchemy all practice a cycle of energy as an infinite spiral of 12 harmonic notes for mind body transformation - a yogic meditation.

This is now being confirmed by biophysics and quantum biology based on de Broglie's Law of Phase Harmony. So Schroedinger, by repressing the relativistic secret of the superluminal phase wave, then did not understand the origin of the light emissions as subharmonic beats.

Your book corroborates my 2000 master's thesis that also did a Helmholtz harmonic analysis of quantum physics - I did not know that both Planck and Schroedinger relied on Helmholtz beat harmonics as well. But I also did not know the noncommutative phase secret - until I continued studying science on my own for 10 plus years, after my master's thesis.

But I did do the intensive meditation to test to see if the Orthodox Pythagorean philosophy was correct, based on the same Daoist harmonics, as taught by qigong master Chunyi Lin who trained at Mt. Qingcheng, doing one month full lotus meditation, no sleep, no food. http://springforestqigong.com and his healing ability was corroborated by Dr. Ann Vincent of Mayo Clinic, doing randomized controlled testing of his "external qi" healing of chronic pain, that she called "especially impressive" since the clients had suffered for 5 years, with pain not treatable by Western medicine.

My blog has more details of my research - I just did an article with lots of images - that blends the quantum biology de Broglie analysis with the Pythagorean critique of Archtyas harmonics.

http://ecoechoinvasives.blogspot.com/2018/02/the-blue-light-of-blues-music-ii.html

Please let me know any comments, criticisms or questions and thanks again for your insightful research.

drew hempel