Sunday, December 19, 2021

More Incorrect Pythagorean Propaganda goes Viral on the Interwebs!! (Oh when will the masses learn the truth?)!!

 This vid is "well produced" but lacks any true depth of analysis. Here is your glaring logical error:

 "I'm going to ignore the shifting up or down by octaves, so things are a bit clearer, but as we established octaves don't change the character of a note much, so everything I say here will apply whatever octave you're in." 

Then you try to correct this with another error: 

"My version of Pythagorean tuning starts with a base note at the lowest frequency and works up. In reality, some Pythagorean systems start with a base in the middle and create equal numbers of fifths above and below. The harmonic relationships in these systems are functionally identical."

 I recommend you read Professor Richard McKirahan's essay, "On Philolaus." The Perfect Fifth "below" the root tonic is a Perfect Fourth "above" the root tonic as I'm sure you know. You neglect to point out this crucial fact - and the reason it is "crucial" is because it signifies the truth of Orthodox Pythagorean philosophy - namely the "noncommutative time-frequency" or noncommutative geometry.

I urge you to watch Fields Medal Math Professor Alain Connes lectures on music theory, kindly posted on youtube. His 2012 lecture, "Music of Shapes" given in conjunction for the Fields Institute. I have written a recent paper on this - that I would be happy to email to you. You can just post a comment on my youtube channel and I'll give you my email address.
 
Let me explain your error in more detail. 
 
Philolaus had to FLIP his lyre around in order to CREATE the "irrational magnitude" of the 9/8 ratio. So in other words the root tonic was originally a 12 string with the lowest note toward the body. Then it was flipped with the six string as the lowest and the 8th string was then used as a NEW root tonic. This enabled creating 8/6 as the Perfect Fourth from the previous 8/12 as the Perfect Fifth. So then the newly established "logarithmic" equation of the Perfect Fifth (or 8/12) PLUS the Perfect Fourth (8/6) could equal the Octave. 
 
The Perfect Fourth is "never" a natural overtone of the root tonic and thus the Perfect Fourth is also called the "Phantom Tonic." The fact that it IS a noncommutative time-frequency phase has much deeper implications that you (and everyone) has ignored. Please see Alain Connes again for the details.
 
So that was the first Greek use of the word "magnitude" to refer to numbers - and it was done in music theory by Philolaus - and therefore music was the basis to create what is called "incommensurability" in mathematics. You can read math professor Luigi Borzacchini's 2007 published article, "music theory, incommensurability and the continuum." He is retired but I contacted him in 2001 - and he was discussing this in 1999 - and he still is publishing on "academia.edu" in case you want to discuss this further.
 
Sorry to burst your bubble about not really knowing about Pythagorean philosophy. That's OK because Boethius also could not figure out Philolaus. But Alain Connes is really the ONLY person to have cracked the secret of Pythagorean music-math philosophy as noncommutative geometry and if you want to know the true meaning of it then check out his work. He has a Fields Medal for a reason. haha. Until you check out his videos then you'll have no idea what I'm talking about and neither will anyone reading this comment. So please spare any flippant responses and just go study Alain Connes already. 
 
thanks very much.
 
 
Here's a well-documented overview of Pythagorean philosophy.
 
aikifab
"We hear equal temperament all the time" : not totally true. A brass instrument uses the harmonics of its base note to make the different notes. For a given fingering or slide position, you'll have the fundamental, an octave, a pytagorean fifth, an ocatve, a pythagorean major third, a pythagorean fifth, an horrible in-between note, and an octave. An please don't mix tritone with wolf's fifth. But apart from that, great video !
1
This is also why in voicing there is not supposed to be a Perfect Fourth in the bass note because it's never a natural overtone and so thus establishes a new root tonic. If you have heard of this please elaborate. thanks

Tanner Eanes
I honestly think the slight dissonance equal temperment gives sounds better than the squeeky clean music tuned by key,
the Pythagorean tuning is not by key - there is another secret to it. Consider Blues music - the tuning is based on the natural overtones and so that's why the notes are "bent" - not squeeky clean at all! Rather the notes are "smashed." There is a physics lecture about blues tuning as natural tuning if you are interested.
 
 Scratch
I think the equal tuning works because every note is relative to every other note, you can be as "Out of tune" as you want, just as long as the notes are relative to one another within the octave, the ratio between the notes in any major chord will always be the same no matter which note you pick, a perfectly irrational ratio
yes only if you read Sir James Jeans book, "Science and Music" he points out that the "out of tuning" builds up so that it is a quarter tone out of tune over the octave. Then he points out that if you stick to the empirically true natural number Perfect Fifth then it is an infinite spiral and "then all simplicity disappears." There is a deeper truth to this called "noncommutative time-frequency" or noncommtuative geometry. You can watch Fields Medal math professor Alain Connes youtube lecture, "Music of Shapes" for details. thanks
 
 Elvin Aurelius Yamin
Wait, if it's Pythagoras calc made it bad, why don't we flip it around. Cuz i believe that "bad = good, good = bad". So like yin and yang kind of thing So what happens instead of 2/1, we do 1/2 as a reverse octave
You got it! Yang is the Perfect Fifth and yin is the Perfect Fourth as 4/3. He never mentions that the Perfect Fourth is constructed from the Perfect Fifth as the undertone or 2/3 - in music theory as C to F pitch undertone. Oops.
 
 https://en.wikipedia.org/wiki/Iatromantis

Iatromantis[1] is a Greek word whose literal meaning is most simply rendered "physician-seer," or "medicine-man". The iatromantis, a form of Greek "shaman", is related to other semimythical figures such as Abaris, Aristeas, Epimenides, and Hermotimus.[2] In the classical period, Aeschylus uses the word to refer to Apollo[3] and to Asclepius, Apollo's son.[4]

According to Peter Kingsley, iatromantis figures belonged to a wider Greek and Asian shamanic tradition with origins in Central Asia.[5] A main ecstatic, meditative practice of these healer-prophets was incubation (ἐγκοίμησις, enkoimesis). More than just a medical technique, incubation reportedly allowed a human being to experience a fourth state of consciousness different from sleeping, dreaming, or ordinary waking: a state that Kingsley describes as “consciousness itself” and likens to the turiya or samādhi of the Indian yogic traditions. Kingsley identifies the Greek pre-Socratic philosopher Parmenides as an iatromantis. This identification has been described by Oxford academic Mitchell Miller as "fascinating" but also as "very difficult to assess as a truth claim".[6]

 Scott from Baltimore

the Perfect Fourth is actually also called the Phantom Tonic because it is noncommutative to the Fifth. He doesn't understand this. I recommend watching Fields Medal math professor Alain Connes youtube lectures on "music of shapes", etc. thanks

 ffggddss

With a strong background in math, and a lifelong interest in music (as an amateur), I've been familiar with this problem for many years. Once you realize that small-integer frequency ratios are the most pleasing, the problem of devising a system of notes, boils down to finding a good rational approximation of the irrational ratio log3/log2. [3:2 being the simplest non-trivial, integer frequency ratio.] This can be done by the method of continued fractions, and the first "really good" fraction that pops out, is 19/12. Which then leads to division of the octave (2nd harmonic) into 12 steps, of which the 3rd harmonic is 19. Other, better approximations, with bigger terms, can and have been used. The next one is 84/53. After that, they get ridiculous. They make some fascinating music, but like you say, the octave quickly gets too crowded to be practical, or for that matter, for the steps to be discernible to the ear. I really found your video maybe the clearest, simplest, well-thought-out presentation I've seen. One of the things I've used to explain why we have 12 steps in our chromatic scale, is that 2^19 is close to 3^12. I.e., 524288 ≈ 531441. This is what makes 12 perfect fifths close to 19–12 = 7 octaves. And stopping at 11, pairing that note with the exact 7th octave, is what gives what you call the "wolf fifth." 2^18/3^11 = 262144/177147 ≈ 1.48 which makes it noticeably (& annoyingly) flat. Thanks for introducing me to that name; it's useful to know. Fred
Only you've missed the crucial math concept that only Fields Medal math professor Alain Connes has noticed. You correctly state it is 2 to the 19th against 3 to the 12th but it is also 2 to the 1/12 against 3 to the 1/19th as the logarithm such that the discrete integers are actually noncommutative time-frequency. For what this means please see Alain Connes youtube lectures on music theory - his 2012 "Music of Shapes" talk has been given numerous times - recently as well.

 Wow - the transgressions of Sharing the Pythagorean Secrets - in this book - are fascinating!! 

 

 

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