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.
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.
Not only does it cycle through a ton of keys, but wind instruments like the sax require unique fingerings and embouchure changes in each key. It’s not nearly as hard on a guitar.
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:
Thanks for sharing! I've been playing music for 30 years but my theory knowledge is pretty bare bones. That video was really accessible but still got the point across in enough detail.
On the bandstand, there's usually a ton of highly aware counting going on. 24 bars of rest! followed by 8 bars of rest! and then 16 bars of latin feel! now back to 8 of swing!
On top of that there is definitely some feel and intuition going on. But for a band to play non-trivial music, everyone is counting unless they know the material cold, and even then they are probably counting at times.
Indeed, as a long time fan of prog metal and tech death I'm quite aware of the importance of counting (and the existence of people whose counting abilities far surpass my own)!
But I think the quote is also referring to casual enjoyment of music where the counting might not be deliberate.
Right, I should have spelled that out - the listener gets to count subconsciously only because the players are counting very consciously.
Playing music has changed my listening, and not necessarily for the better. I'm sometimes counting or listening for structural and composition elements in a way that can be distracting from just enjoying the sound/vibe.
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).
Just finished listening to it yesterday! My first time with it, excellent stuff, but not topping Mingus Ah Um! I've been on a Jazz kick since listening to an episode of Kirk Hamilton's Strong Songs podcast about John Williams[1]—which was an excellent listen and I learned tons—that touched on Jazz and Mingus in particular.
A Love Supreme is a wonderful album, but Ascension and his later avant-garde work marked a new direction in jazz. Listening to Coltrane play his later work, feels to me like he had unshackled himself from the past, from the changes, and was his most pure expression of self.
Without more prominent melody or harmony I could not find what is finer about it than conventional approaches to jazz. Could you please elaborate on what its quality is?
To be honest, I am not a jazz musician or even a jazz fan. When I do record music I have better progress when holding myself to a standard or a set of limitations to work within. It gets the brain going to find new solutions to fit within a self-imposed framework.
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!
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.
Absolutely, exquisitely, undeniable. I didn't get a lot of what it was until I was relistening to Al Davis in reverse chronological order. I also in a fit of recognition saw how Vernon Reed played homage to him. ( And that took a few decades )
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.
Deification of artists in theory writing is commonplace, as is aspiring to be seen as an authority. The subject matter could have been Mozart, or Picasso — you'd see the same phenomena.
I agree that we have some distance to go in ensuring that wealth moves to the communities that created the art and the value, but absent evidence that this author has been "treating their descendants like dangerous parasites", I think they're catching strays from you.
GP is describing a well-known phenomenon that spans countries, cultures and history: majority culture having a love/hate relationship with minorities, with extraordinary individuals on one side and diffuse fear and hatred on the other. Go read Othello's speeches.
Not every instance of white people liking or consuming black culture is that of a racist parasite trying to bleed the culture dry though. Sometimes white people just like stuff, and their interests overlap (as in this case with esotericism and music.) Culture works that way for everyone. The author doesn't seem to be trying to redefine anything or whitewash John Coltrane or what have you.
> Nothing upper-middle class people love more than worshiping dead black Americans, while treating their descendants like dangerous parasites.
I know, right? It's those Dutch folks living in Bulgaria hating black American descendants again, eh? /s
So, to be serious, do you have evidence that Roelant Hollanderr is treating black American descendants as "dangerous parasites"? Those are pretty hefty accusations. I haven't found anything on their website, but I am sure you have some solid evidence somewhere.
While the critique of this author seems unjustified, I think we do well to grapple with issues like this and not dismiss them outright. The problem is real, even if this may not be a good example.
Grapple with what, though? Abstract Whitey loves Coltrane and Satchmo and hates every Black person born since? It's not a coherent theory to begin with.
Also, if the current regime is in a position to fully eradicate all the blacks and browns, the statues will all be of Confederate generals and Trump family members, not black people.
Financial exploitation of oppressed culture by the dominant culture. Fetishization of minority figures as exotic and mystical. Crowding out minority voices when establishing critical narratives around minority art and culture.
These sorts of things happen in music industry, music criticism and music journalism. As I said, I don't think this is a good example, but as someone who has benefited greatly from Black American culture, I see bearing these issues in mind as one way to pay back my benefactors.
I chuckled, but at the risk of getting slapped with thatsthejoke.gif, Tommy Flanagan falls back to playing chords at the end of his piano solo. Comping on Giant Steps is easier than soloing.
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.
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
Not only does it cycle through a ton of keys, but wind instruments like the sax require unique fingerings and embouchure changes in each key. It’s not nearly as hard on a guitar.
“Quantity has a quality of its own.” — Karl Marx, or maybe Coltrane.
Absolutely. And Central Park West is a good example of the same concept but slowed down.
Ah yes the best welcome for people joining a jam session: "OK, let's do Giant Steps. One, one two three..."
Hehe, that had me laughing out loud and I haven't touched a sax in two decades :)
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:
https://www.youtube.com/watch?v=62tIvfP9A2w
Thanks for sharing! I've been playing music for 30 years but my theory knowledge is pretty bare bones. That video was really accessible but still got the point across in enough detail.
> 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.”
On the bandstand, there's usually a ton of highly aware counting going on. 24 bars of rest! followed by 8 bars of rest! and then 16 bars of latin feel! now back to 8 of swing!
On top of that there is definitely some feel and intuition going on. But for a band to play non-trivial music, everyone is counting unless they know the material cold, and even then they are probably counting at times.
Indeed, as a long time fan of prog metal and tech death I'm quite aware of the importance of counting (and the existence of people whose counting abilities far surpass my own)!
But I think the quote is also referring to casual enjoyment of music where the counting might not be deliberate.
Right, I should have spelled that out - the listener gets to count subconsciously only because the players are counting very consciously.
Playing music has changed my listening, and not necessarily for the better. I'm sometimes counting or listening for structural and composition elements in a way that can be distracting from just enjoying the sound/vibe.
"Music is math for people that don't like numbers"
-- some movie I don't recall
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...
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).
Just finished listening to it yesterday! My first time with it, excellent stuff, but not topping Mingus Ah Um! I've been on a Jazz kick since listening to an episode of Kirk Hamilton's Strong Songs podcast about John Williams[1]—which was an excellent listen and I learned tons—that touched on Jazz and Mingus in particular.
1: https://strongsongspodcast.com/blogs/episodes/s05e05-john-wi...
A Love Supreme is a wonderful album, but Ascension and his later avant-garde work marked a new direction in jazz. Listening to Coltrane play his later work, feels to me like he had unshackled himself from the past, from the changes, and was his most pure expression of self.
You meant to say "Kind of Blue", I'm sure.
Else: Deringers at noon. Bring your second.
The Davis / Coltrane collaboration Kind Of Blue significantly influenced Coltrane's later works like the OP's Giant Steps and parent's A Love Supreme.
Of which you're undoubtedly aware; I'm just explaining the inside joke in your second line to others.
P.S. Kind of Blue is also my favorite.
My favorite music podcast, You’ll Hear It, uses “is it better than KOB” as one of their album review metrics!
I think you wrote "On The Corner" a bit weird there.
I did qualify it with "arguably". Kind of Blue is, IMHO, the other viable candidate.
This is pretty solid, I try to use this method all the time.
In my opinion the underrated "Get Your Greasy Head Off The Sham" by Breastfed Yak is jazz at it's finest.
Without more prominent melody or harmony I could not find what is finer about it than conventional approaches to jazz. Could you please elaborate on what its quality is?
To be honest, I am not a jazz musician or even a jazz fan. When I do record music I have better progress when holding myself to a standard or a set of limitations to work within. It gets the brain going to find new solutions to fit within a self-imposed framework.
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!
Can you give an example of what you are talking about?
Also what are the manuscripts that lay out their approach to music theory in half a page?
Genuinely curious. I personally think I probably agree and music theory is often misunderstood as prescriptive rather than descriptive.
As you follow the circle around, as if a sprite, there is a butterfly flapping its wings.
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
See also: Arcana V. Music, Magic & Mysticism. Ed: John Zorn, Hips Road 2010
https://archive.org/details/zorn-john-ed.-arcana-v.-musician...
Any particular chapter in this issue of Arcana?
The following chapter includes Coltrane's diagram, briefly comparing it to a North Indian Tai Chakra drawing.
Chapter 25 - Music and Mysticism, Rhythm and Form: A Blues Romance in 12 Parts - Adam Rudolph
This is a better scanned copy: https://archive.org/download/zorn-john-ed.-arcana-v.-musicia... (PDF)
Listen to Giant Steps. The man was a genius https://www.youtube.com/watch?v=xy_fxxj1mMY
Absolutely, exquisitely, undeniable. I didn't get a lot of what it was until I was relistening to Al Davis in reverse chronological order. I also in a fit of recognition saw how Vernon Reed played homage to him. ( And that took a few decades )
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.
Deification of artists in theory writing is commonplace, as is aspiring to be seen as an authority. The subject matter could have been Mozart, or Picasso — you'd see the same phenomena.
I agree that we have some distance to go in ensuring that wealth moves to the communities that created the art and the value, but absent evidence that this author has been "treating their descendants like dangerous parasites", I think they're catching strays from you.
You ok man? Having a bad day?
GP is describing a well-known phenomenon that spans countries, cultures and history: majority culture having a love/hate relationship with minorities, with extraordinary individuals on one side and diffuse fear and hatred on the other. Go read Othello's speeches.
So I know what they're saying. Do you not?
Not every instance of white people liking or consuming black culture is that of a racist parasite trying to bleed the culture dry though. Sometimes white people just like stuff, and their interests overlap (as in this case with esotericism and music.) Culture works that way for everyone. The author doesn't seem to be trying to redefine anything or whitewash John Coltrane or what have you.
> Nothing upper-middle class people love more than worshiping dead black Americans, while treating their descendants like dangerous parasites.
I know, right? It's those Dutch folks living in Bulgaria hating black American descendants again, eh? /s
So, to be serious, do you have evidence that Roelant Hollanderr is treating black American descendants as "dangerous parasites"? Those are pretty hefty accusations. I haven't found anything on their website, but I am sure you have some solid evidence somewhere.
While the critique of this author seems unjustified, I think we do well to grapple with issues like this and not dismiss them outright. The problem is real, even if this may not be a good example.
Grapple with what, though? Abstract Whitey loves Coltrane and Satchmo and hates every Black person born since? It's not a coherent theory to begin with.
Also, if the current regime is in a position to fully eradicate all the blacks and browns, the statues will all be of Confederate generals and Trump family members, not black people.
Financial exploitation of oppressed culture by the dominant culture. Fetishization of minority figures as exotic and mystical. Crowding out minority voices when establishing critical narratives around minority art and culture.
These sorts of things happen in music industry, music criticism and music journalism. As I said, I don't think this is a good example, but as someone who has benefited greatly from Black American culture, I see bearing these issues in mind as one way to pay back my benefactors.
Not to detract from your point but he's been back in NL for a while I believe.
Coltrane wrote that song because he didn't have to play the harmony... he played the easy part. /s
I chuckled, but at the risk of getting slapped with thatsthejoke.gif, Tommy Flanagan falls back to playing chords at the end of his piano solo. Comping on Giant Steps is easier than soloing.