Adam Neely here. The reason why I said that the 4:3 perfect fourth doesn't exist in the harmonic series *as measured from the root* is because I was looking to explain why perfect fourths are considered "dissonant" in certain contexts, even though they are a simpler ratio than major 3rds. Some of it's context, of course.
16level 1· 3y · edited 3yyes, it's P4 as harmonic from the root he means.
overtones have to be related to 1... kinda by definition. but you are not wrong in saying that a P4 exists between overtones... but never directly to the fundamental.
that it doesnt exist as an overtone of the fundamental doesn't matter. it's an undertone.
So it's nice to see the corroboration that the Perfect Fourth is not part of the Harmonic Series and that it IS the undertone...
the thing about a fourth is it's inherently an inverted fifth. if you play C-F, it harmonically sounds it wants to be F-C or F-C-F... F owns C yet is above it so it feels unstable just like any inverted chord.
And so again this is great that the person Acknowledges that the PErfect Fourth is HEARD or listened to as the new root tonic from below as a Perfect Fifth.
F is the daddy of Cmaj/Amin (at P4 and m6). F owns every note in the scale directly as an overtone ie: intervals all with a power of 2 in the denominator.
So this is VERY CLOSE but not quite understanding the truth of Noncommutative Phase.
To be honest I'm not sure WHY these musicians didn't figure out the secret of the Infinite Spiral of Fifths as noncommutative phase ALCHEMY?! I'm thinking it's because they did NOT read Sir James Jeans book, "Science and Music" - a book that I read when I was in high school doing my private music training.
So after reading this thread I can now HONE in on that Sir James Jeans book being the definitive "crystallization" of the alchemical concept for me.... when I was around 17 years old.
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