If you don’t have the time (or the musical background) for the full article, this short YouTube video touches on some of the same ideas in a much more condensed and accessible version:
> Thelonious Monk once said “All musicians are subconsciously mathematicians“.
I haven’t heard that one. I think I prefer this one, attributed to Leibniz:
“Music is the pleasure the human mind experiences from counting without being aware that it is counting.”
As a musician I wanted to hear the notes on the diagram so I made a little tool to do so: https://coltrane.sven.zone
Mathy look at the topology and some stuff about Yusef Lateef: https://medium.com/@lucas_gonze/coltrane-pitch-diagrams-e25b...
I want to consider the higher-level claims in the article. In between the historical context helpfully provided by the article there is also some speculation about Merkaba, Platonic solids, Flower of Life and other sacred geometry.
There is a premise hidden in those speculations that there is some strong connection between the structure of the universe itself and the structures humans find pleasing when listening to music. And I detect a suggestion that studying the output of our most genius musicians might reveal some kind of hidden information about the universe, specifically related to some kind of "spirituality".
This was a sentiment shared, in some sense, by the deists of the enlightenment. They rejected the scriptures and instead believed that studying the physical universe might reveal the "mind of God".
If we are looking for correspondences between these things - why limit ourselves to Euclidean geometry? Modern physics leans on Riemannian geometry, symmetry, and topology. It appears the topology of the universe, under a wide array of experiments, is way more complicated than the old geometric ideas. Most physicists talk about Lie Groups, fiber bundles, etc.
If you take "as above, so below" seriously and you want to find connections between cosmology and music, I believe you have to use modern mathematical tools. I think we need to expand beyond geometry and embrace topology. Can we think of the chromatic scale tones as a Group? What operators would we need? etc.
It's interesting to try to get into the head of a guy like Coltrane and his mathematical approach, but perhaps we could be pushing new boundaries based on new understanding.
Fascinating, well-written piece. Thanks for sharing! I plan to revisit it more closely when I free up (probably while listening to A Love Supreme -- arguably the greatest jazz album of all time).
This is a good intro to Giant Steps, which has this concept in there.
Nice site but we're at the point in "Show an In Depth Thing on Hacker News" where circles like these need to be presented with a live GUI that includes sound and colors as you spin the circles around to play different chords.
towards my craving for instant gratification with sound and lights I found a well produced video by Vox on the subject: https://www.youtube.com/watch?v=62tIvfP9A2w
Nothing upper-middle class people love more than worshiping dead black Americans, while treating their descendants like dangerous parasites. They were so cool, such genius! I can't wait to be the authority on them, and make more on redefining them than they ever saw in their lives, or to buy the new product that no black American makes a dime from.
One day, every black American will be gone, and all that will be left of them are statues that everybody holds in very high regard.
As you follow the circle around, as if a sprite, there is a butterfly flapping its wings.
Listen to Giant Steps. The man was a genius https://www.youtube.com/watch?v=xy_fxxj1mMY
Although the author puts a disclaimer up front ("no expert") it is still astounding how wrong one can be (taking all his honest effort into account). It's not that he´s wrong "by choice", but if your priors are wrong there's just no other possible outcome.
He is using the right "words" or "concepts" (tetrachord, hexachord) but these words have been mutilated by "musicology" and "music theory" to the point that they don't have any "useful" meaning at all anymore. The tetrachords and hexachords he mentions just are no tetra-/hexachords. If this fundamental building block is wrong, everything else down the line has to be, too.
How do I know?
Well, a colleague of mine (fellow professor) has found the Bach manuscript and I have found the Coltrane manuscript where BOTH of them lay out the whole of "music theory" in half a page.
If the two greatest masters of music used the SAME system, it should be ok for you and me. Just stay away from all the crap coming out of "music theory" or "musicology" or YouTube videos or websites made by "experts" or "non-experts". They just don't know.
Instead take any piece of classical music (e.g. WTK 1) or any Coltrane improvisation (from 1960 on) and look for the smallest "building block" - WITHOUT any priors!
That's difficult, I know, but that separates the men from the boys. These priors are "scales" (there is no C-C seven-note scale), or "harmonies" (there is no "dominant", Bach wouldn't know what you were talking about, and Coltrane just used it to be able to communicate with the rest of the world), or wrong tetra- and hexachords.
So just LOOK at the page or transcription! No priors! Then it will become obvious to you, too, especially in Coltrane's later improvisations, e.g. Live at the Half Note, and Bach made it abundantly clear in the first two fugues of the WTK 1.
That's why he wrote it in the first place (read the title page).
It's there for all of us to see and understand and - much more importantly - to use!
Is it the cacophony that adapts to the theory, or the theory that adapts to the cacophony?
See also: Arcana V. Music, Magic & Mysticism. Ed: John Zorn, Hips Road 2010
https://archive.org/details/zorn-john-ed.-arcana-v.-musician...
Coltrane wrote that song because he didn't have to play the harmony... he played the easy part. /s
A few months ago, I was studying Giant Steps and I came across the “Giant Steps is actually very simple (yes, really)” video by Dave Pollack. https://www.youtube.com/watch?v=Xd75Mwo4JNo
Pollack argues that the main reason that Giant Steps is such a high mountain is because it is traditionally played at such a ferocious tempo. Slow it down, and the Coltrane Changes become fairly ordinary ii-V-I substitution progressions.
I’m persuaded. I love Coltrane, and I’ve listened to the Giant Steps album countless times. The Coltrane Changes are very nice, but in the line of other jazz theory such as tritone substitution, the deceptive cadence, and so on.
The main thing with Giant Steps is that to play it like Coltrane does you have to practice it to death, accumulate a vocabulary of riffs, and gain facility at improvising over sophisticated changes moving at a speed that other tunes won’t have prepared you for.
EDIT: I originally posted the wrong link, to Giant Steps slowed down 30%. https://www.youtube.com/watch?v=ilbrDJy9-98