I really enjoy how you connect AI with music theory. It is fascinating to me that we force the circle of fifths to close. It shows that the octave scale is not really a circle at all but a logarithmic spiral—an open system (I wonder to what degree this reflects the geometry of the cochlea, and to what degree it reflects the physics of sound that the cochlea evolved to align with). It almost seems as though closure is forced to make it more “rational”instead of natural. Forcing the whole system out of tune in order to preserve an internal consistency. The map taking over the territory. I like where you are going with the corpus AI is trained on. And perhaps the geometry of the AI architecture itself. I wonder how flattening of the natural geometry might be related to hallucination.
Glad you enjoyed the read. Good catch: the circle of fifths comes from repeatedly moving by perfect fifths, a relationship closely tied to the harmonic series through the 3:2 ratio.
That’s part of why equal temperament was such a challenge. If you stack pure fifths, they don’t close perfectly into 12 equally usable keys—the tuning drifts. Equal temperament solves this by slightly adjusting each fifth so all 12 keys can work together well enough within the same composition.
In the citations, this link talks in much more detail about the “wolf” that existed before equal temperament, and why the WTC is considered to be so important in history.
Lovely article. I have always enjoyed explaining to hobby musicians that F-sharp is not the same as G-flat and that violinists actually play in tune, unlike pianists! The colour and overtones of just intonation are so valuable. And I love that F minor Prelude and Fugue, too. Fun fact, my mother taught one of Irving Berlin's granddaughters the piano for a few years! I think you're absolutely right about us getting used to AI in the same way that we now unthinkingly accept equal temperament as the norm.
Music is an odd one. 100 years after the radio and recording technology got invented, we have seen Music Education and Classical Music traditions essentially disappear.
There is real science to how instruments and music works, but it is downplayed to mere entertainment in the 21st century. Tuning is one that people get all mixed up about. Same with notation, a fast disappearing language.
Glad you enjoyed the read. Irving Berlin was definitely an amazing composer.
I really enjoy how you connect AI with music theory. It is fascinating to me that we force the circle of fifths to close. It shows that the octave scale is not really a circle at all but a logarithmic spiral—an open system (I wonder to what degree this reflects the geometry of the cochlea, and to what degree it reflects the physics of sound that the cochlea evolved to align with). It almost seems as though closure is forced to make it more “rational”instead of natural. Forcing the whole system out of tune in order to preserve an internal consistency. The map taking over the territory. I like where you are going with the corpus AI is trained on. And perhaps the geometry of the AI architecture itself. I wonder how flattening of the natural geometry might be related to hallucination.
Glad you enjoyed the read. Good catch: the circle of fifths comes from repeatedly moving by perfect fifths, a relationship closely tied to the harmonic series through the 3:2 ratio.
That’s part of why equal temperament was such a challenge. If you stack pure fifths, they don’t close perfectly into 12 equally usable keys—the tuning drifts. Equal temperament solves this by slightly adjusting each fifth so all 12 keys can work together well enough within the same composition.
In the citations, this link talks in much more detail about the “wolf” that existed before equal temperament, and why the WTC is considered to be so important in history.
Thanks.
https://www.slate.com/articles/arts/music_box/2010/04/the_wolf_at_our_heels.html
Lovely article. I have always enjoyed explaining to hobby musicians that F-sharp is not the same as G-flat and that violinists actually play in tune, unlike pianists! The colour and overtones of just intonation are so valuable. And I love that F minor Prelude and Fugue, too. Fun fact, my mother taught one of Irving Berlin's granddaughters the piano for a few years! I think you're absolutely right about us getting used to AI in the same way that we now unthinkingly accept equal temperament as the norm.
Music is an odd one. 100 years after the radio and recording technology got invented, we have seen Music Education and Classical Music traditions essentially disappear.
There is real science to how instruments and music works, but it is downplayed to mere entertainment in the 21st century. Tuning is one that people get all mixed up about. Same with notation, a fast disappearing language.
Glad you enjoyed the read. Irving Berlin was definitely an amazing composer.