The Lies of the "flipped Lyre": Eli Maor and his new Music Science book and how I preemptively debunked his claims

I emailed the below to Professor Emeritus Eli Maor - so I will let people know if I get a response. It did not "bounce back" so I figure his account is still active....

I would like to know what you think of this article and book:
  Music by the Numbers: From Pythagoras to Shoenberg (2018).
https://aeon.co/essays/ringing-the-chords-of-the-universe-how-music-influenced-science?utm_source=pocket&utm_medium=email&utm_campaign=pockethits
 
https://press.princeton.edu/titles/11250.html

The chords of the universe

It’s no surprise that mathematics has influenced music. But did you know that the influence goes both ways?

Just as I predicted and preemptively debunked - it has now happened - the science propaganda machine is now promoting the lies of Archytas and Plato as "music science" via Eli Maor.

Lie Number One - the BIG LIE (see end notes for references):

 Pythagoras also discovered that multiplying two ratios is equivalent to adding their intervals: (2:3) x (3:4) = 1:2, so a fifth plus a fourth equals an octave. In doing so, he unknowingly came up with the first logarithmic law in history.

 No - this is not true. Philolaus and Archytas promoted this and it's the wrong music theory! Specifically to add the ratios as logarithms you can ONLY use 4/3 and not 3/4 - and Archytas did just that. So then 9/8 as the "subtraction" of the logarithm was from Philolaus - his lie of flipping his lyre around - as I have gone into detail about.

Lie Number Two: The Phantom Tonic cover up:

The key thus served as a musical frame of reference, in which every note had a specific relation to the tonic; for example, in the key of C major, the note G (a fifth above C) was the ‘dominant’ note, while the note F below C was the ‘subdominant’.

Ooops! No mention that F as the Perfect Fourth can not be part of the harmonic series because it changes what the tonic is (4/3) and yet if 3/2 is G then 4/3 and not also be G as the ratio for the same octave of 1 to 2. So when Philolaus flipped his Lyre around as his Lie of logarithms - it was so that the root tonic was changed from 0 to 8 for 6/8 to be 4/3 and then from 12 to 6 as the octave so that the 4/3 as Perfect Fourth is now a geometric magnitude as 8/6 of the octave value 2. In other words 2/3 is ALSO the Perfect Fifth as C to F subharmonic. But this empirical truth could not be allowed in order for the logarithms as geometric magnitude, to be created.

So 8 x 9 = 72 (harmonic mean x arithmetic mean = geometric mean squared) and the square root of 72 in simplified radical form is 6 times the square root of 2 – or the equal-tempered logarithmic tritone music interval, the 6th semitone of the 12 note scale aka the Devil’s Interval (called Alogon as Apeiron). So then it was realized even still that if 9/8 is the major second interval and a Perfect Fifth is seven half-steps or minor seconds and a Perfect Fourth is five minor seconds then the Octave contains two Perfect fourths and a major second interval.

“The sound of square roots

Take two strings, one sounding an octave higher than the other, so that their lengths are in the ratio 2:1. Then find the geometric ratio (also called the mean proportional) between these strings, the length x at which 2:x is the same proportion as x:1. This means that 2:x = x:1; cross-multiplying this gives x squared =2. Thus, the “ratio” needed is √2:1 ≈ 1.414, in modern decimals. This is close to the dissonant interval called the tritone, which later was called the “devil in music,” namely the interval composed of three equal whole steps each of ratio 9:8. The tritone is thus 9:8 × 9:8 × 9:8 = 729:512 ≈ 1.424.” 

from “Scandal of the Irrational” M.I.T. Press. pdf link here

"Magnitudes have all the characteristics Plato attributes to Apeiron."

p. 394, Socratic, Platonic and Aristotelian Studies: Essays in Honor of Gerasimos Santas 2011

And so then you have Proclus directly stating if there were no Apeiron there would be no irrational magnitudes.  From this googlebook review link

citing Vassliis Karasmanis, "Continunity and Irrationality in Ancient Greek Philosophy and Mathematics."

Lie Number 3: Logarithmic tuning is "democracy."

 In serial music, complete democracy ruled: no single note held any preferred status over the others.

Did you know that I was told to redo all my past orchestration assignments, after being accepted into the UW-Madison music composition degree program, because my transposition of a Schoenberg piano sonata into a string quartet was called Communist by the music professor! I had already gotten As and Bs on my previous assignments - so this was clearly a political attack on me, since I was always protesting out on the Mall, nearby the music building. haha. As economics professor and music BA, Michael E. Hudson, points out, Archytas lied about the music tuning to present logarithmic distribution of wealth as based on the "harmonic justice" of logarithmic music tuning - and therefore was democratic. And so Plato argued that each citizen is valued at 9/8 which is the major tone in music - but that each citizen must be "compromised" for the good of the state, as music professor Ernest McClain documented and promoted.

Lie Number 4: Einstein has now been disproven about Localism

In 1905, Einstein gave the ether its coup de grâce: there is no ether, no single universal frame of reference at absolute rest; rather, every observer has his or her own reference system, related only to its infinitesimally close neighbouring system in spacetime. One cannot fail to note the similarity to Schoenberg’s atonal music, in which each note is related only to its immediate predecessor in the series.

yes Einstein could never accept the "ghost waves" that he realized would have to be real for quantum physics to work - which it did - and Max Born agreed that these "ghost waves" or a ghost field - an ether - or what de Broglie called the pilot wave - must be the foundation of reality. This was of course covered up but is now being accepted as EPR=ER for quantum teleportation satellite signals, for example.

To be honest - this topic is very abstract. I would have to review all the mathematical - music details again because I have not studied it in detail for the past four months. haha. But I have posted all my research on this blog - so I can just go back and review my blog posts - just as anyone else can.

But the truth is not a popularity contest - and yet "music" as the metaphor for science truly is the Big Lie as the great popularity contest of why we should all worship science. Certainly science is the great mythology of our times and it would be stupid for us not to believe in it - as it provides so many reality changing techno-gadgets, foisted upon us to be sure. And yet, as math professor Luigi Borzacchini stated, the wrong music theory that was covered up, as the origin of science, is a "deep, pre-established disharmony" that is the "guiding evolutive principle" of science.

Borazzhini wrote: “The ‘demusicalization’ of the theory of proportions by Plato is shocking.” (Borzacchini, p. 281 of his academic article on the topic, “Incommensurability, Music and Continuum: A Cognitive Approach”)…. “…this ‘removal’ seems really astonishing!”... .“we can maybe reveal the deep ‘preestablished disharmony’ of the link between human knowledge and reality.”

 To quote Borzacchini again:

“Hence Arithmetic is the source of that preestablished harmony between reality and language that we can not not believe after almost four centuries of astonishing achievements, but we must even say that, neither tendentially, syntactic representation can thoroughly mirror reality, become someway iconic. And this because it is marked in its basic principles with a preestablished disharmony, that is even its hidden evolutive principle.”

So Eli Maor's book is just a reiteration of a long tradition of Platonic music-math propaganda that disregards the truth - one that Fields Medal math professor Alain Connes has discovered - the noncommutative phase origin of reality as 2, 3, infinity. So we can go back and show how Plato and Archytas and Philolaus lied - by flipping the Lyre around - and covering up the subharmonic or subdominant or the subcontrary mean - as the new "harmonic mean" to create symmetric math logarithmic logic.

Really there is no going back now. We've had 2500 years of this "science" that has destroyed over 80% of mammals on Earth, wiping out 50% of vertebrates on Earth just in the past 40 years! Ah but that is progress right? Yes the global warming crisis is much more "abrupt" than science is willing to admit since then entropy would have to be redefined. So what science neglects to focus on - is the true disharmony of music that science created from the wrong music theory.

END NOTES

1) THE BIG LIE ABOUT PYTHAGORAS:

“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.

3/2 squared = 9/4 halved into octave as 9/8. 3/2 x 4/3 = 2 (geometric mean squared). log(3:2×4:3)=log(2:1) and  log(3:2)+log(4:3)=log(2:1) and so to "subtract" the Perfect Fifth from the Perfect Fourth with 9/8 as the result means to multiply the inverse as geometric magnitude (not frequency x wavelength inversion of Orthodox Pythagorean teachings). Archytas used the equation "arithmetic mean (3/2) x harmonic mean (4/3) = geometric mean squared (2)" in order to construct logarithms.

Conclusion: Since Orthodox Pythgoreanism did not use 9/8 therefore Orthodox Early Pythagoreanism did not invent the logarithm as Eli Maor incorrectly claims. Boethius tells that "the fifth hammer [9/8] which was dissonant with all, was rejected."

 “The Minor Sixth (8:5) in Early Greek Harmonic Science,” The American Journal of Philology, 1978)

“Any who doubt that the musical ratios are all of greater inequality, i.e., that the antecedent or first term in each is greater than the consequent or second term, should consult Archytas DK 47 B 2. This Fragment requires that the ratios be of this form if the assertions about the three means [arithmetic, harmonic and geometric] are to be true. Accordingly, the ratios assigned to the octave, fifth, fourth and minor sixth, must be 2:1, 3:2, 4:3 and 8:5, and not 1:2, 2:3, 3:4 and 5:8, respectively, as Mosshammer and others would have them.”

2) The "subdominant" F as the Perfect Fourth, is actually the Perfect Fifth as the noncommutative phase subharmonic!

 Pythagoreans taught that ALL IS NUMBER AND HARMONY - not that all is geometric magnitude so that 12:8 (3/2) plus 8:6 (4/3) = 2/1 as geometric magnitude from the double octave. This has to use 0 to 8 as one "root tonic" for 6/8 wavelength as 4/3 frequency and then 0 to 12 as the other root tonic for 12/8 frequency as 3/2 with 8/12 wavelength. This is called the "ghost tonic" in music theory since the Perfect Fourth can not be created from the harmonic series as 3 does not go into 2 from 1 as the root tonic denominator. In other words the root tonic changes due to complementary opposites.

"Not a fourth above, but a fifth below: the phantom tonic." https://nmbx.newmusicusa.org/IV-The-Phantom-Tonic/

 Professor Richard McKirahan, "On Philolaus and Number":

So instead of taking 12:9, which is 3/4 of 12, we take 8:6, which is 3/4 of 8. And so by adding the length 12 to 8 [as geometric magnitude not wavelength!!] with the length 8 to 6, [as geometric magnitude, not wavelength!!] we get the length 12 to 6, which corresponds to the ratio 2:1.

 3) Democracy is Logarithmic Tuning! The great Lie of science as political freedom:
Professor Michael Hudson’s essay, “Music as an Analogy for Economic Order in Classical Antiquity” in Jürgen Backhaus (ed.), Karl Bücher. Theory, History, Anthropology, Non-Market Economies (Marburg:Metropolis Verlag, 2000): pp. 113-35:

“Pythagoras became the patron saint of the most anti-democratic clubs. They used the principles of musical harmony as a patina of pseudo-science to give intellectual legitimacy to a movement whose worldly consequences were anything but harmonious. The Pythagorean clubs became a network of civic cults rising above the local sphere to which most clubs related. There seems to have been some connection with the Delphi temple (the name Pythagoras means “voice of Pythia,” the snake-goddess of Delphi and its oracle). They have been likened to the Free Masons, in that they served as a kind of Council of Foreign Relations or New World Order…. Archytas developed the musical scale into a political metaphor for the scales of justice. What gave music this imagery of social balance and just proportion was the ability of its mathematics of harmonic (“geometric”) proportions to serve as an analogy for how inequities of wealth and status rendered truly superior men equal in proportion to their virtue — which tended to reflect their wealth. By this circular logic the wealthy were enabled to rationalize their hereditary dominance over the rest of the population.”

 4) Einstein's Localism from geometric magnitude is not quantum nonlocality, the foundation of reality, from the correct music theory tuning!

a “universal scaling system”, ... this discrete scaling manifests itself in acoustic systems, as is well known in western classical music, where the two scalings correspond, respectively, to passing to the octave (frequency ratio of 2) and transposition (the perfect fifth is the frequency ratio 3/2), with the approximate value log(3)/ log(2) ∼ 19/12 responsible for the difference between the “circulating temperament” of the Well Tempered Clavier and the “equal temperament” of XIX century music. It is precisely the irrationality of log(3)/ log(2) which is responsible for the noncommutative [complementary opposites as yin/yang] nature of the quotient corresponding to the three places {2, 3,∞}. 

-Alain Connes

 a "universal scaling system," manifests itself in acoustic systems....They are the same [frequency] spectrum but they are not the same chord. There are three types of notes.... The point [zero in space] makes a chord between two notes. When the value of the two eigenfunctions [2, 3, infinity] will be non-zero. ... Musical shape has geometric dimension zero....There is a fine structure in spacetime, exactly as there is a fine structure in spectrals [frequencies]...Our brain is an incredible .... receives moments of space... of the photons we receive and manufactures a mental picture. Which is geometric. But what I am telling you is that I think ...that the fundamental thing is spectral [frequency]....And somehow in order to think we have to do an enormous Fourier Transform...on geometry. By talking about the "music of shapes" is really a fourier transform of shape and the fact that we have to do it in reverse....It is precisely the irrationality of log(3)/ log(2) which is responsible for the noncommutative [complementary opposites as yin/yang] nature of the quotient corresponding to the three places {2, 3,∞}.  .it's related to mathematics and related to the fact that there is behind the scene, when I talk about the Dirac Operator, there is a square root, and this square root, when you take a square root there is an ambiguity. And the ambiguity that is there is coming from the spin structure. 

Alain Connes, 2012