The Coltrane changes are great, but on the scale of other harmonic innovations over the years inside Jazz and other traditions. They aren't analogous to Einstein.
What makes Giant Steps so amazing is the sheer speed at which those changes go past — if you slow it down, it's not that different from other Jazz tunes. It took took years of practice for Coltrane to acquire the specialized skillset for improvising over Giant Steps.
I notice it's a double ring, not a single circle. Two concentric chromatic rings, offset. That's not decoration: the outer ring and inner ring are the same field read at a phase offset (looks like a tritone / minor-third rotation). Fault tolerance!
Yeah but only in the heart shaped circles. The middle of the hearts are the classic circle of fifths. In this circle they show where the half steps in the scales are.
As someone who's really into music theory, I am always annoyed by what I perceive as a patronizing faux exaltation of it supposedly being mathematically based. It's not math; it's cyclical patterns. Yes, it can all be represented mathematically, and it is surprising to some people how something with feeling can map to these interesting cycles of discrete values in unexpectedly regular ways, and there are very interesting mathematical ratios involved, but that doesn't make it math. I don't think we need to pat John Coltrane on the head and talk about how he's actually kind of smart because he's doing math.
Actually I think that maths and jazz have something in common in the general public peception that you have to be smart to "get it".
Nobody will try to perform a deep intellectual analysis of Lady Gaga's or Ed Sheeran's work the way they analyse Coltrane or Miles Davis (or Mozart, or Stravinsky). Those musicians are intellectuals of the sort Einstein is, unlike Lady Gaga or Ed Sheeran (in the collective perception). Jazz is intellectual music.
And when they analyse something, "smart" people use maths.
I am putting scare quotes around "smart" here to insist that this is largely a social perception and expected behaviour. However, maths can sensibly be used to analyse art, just like it's used elsewhere. This is not patronising, it is more that maths provides a useful language to talk about patterns.
Number theory is all about cyclical patterns, and its theorems fetishize finding cycles of discrete values with suspiciously regular behavior. Last I heard, number theory, group theory, and Fourier analysis are all math.
And yes, I will die on this singular hill: it's all one math, not a bunch of "maths". Math is one interconnected cathedral with music flowing through it, not a drawer full of unrelated trinkets. The British habit of calling it "maths" is oddly reductionist -- it makes it sound like you've got separate jars labeled "algebra", "geometry", and "spicy numbers".
24 comments
What makes Giant Steps so amazing is the sheer speed at which those changes go past — if you slow it down, it's not that different from other Jazz tunes. It took took years of practice for Coltrane to acquire the specialized skillset for improvising over Giant Steps.
https://www.openculture.com/2017/04/the-tone-circle-john-col...
Nobody will try to perform a deep intellectual analysis of Lady Gaga's or Ed Sheeran's work the way they analyse Coltrane or Miles Davis (or Mozart, or Stravinsky). Those musicians are intellectuals of the sort Einstein is, unlike Lady Gaga or Ed Sheeran (in the collective perception). Jazz is intellectual music.
And when they analyse something, "smart" people use maths.
I am putting scare quotes around "smart" here to insist that this is largely a social perception and expected behaviour. However, maths can sensibly be used to analyse art, just like it's used elsewhere. This is not patronising, it is more that maths provides a useful language to talk about patterns.
And yes, I will die on this singular hill: it's all one math, not a bunch of "maths". Math is one interconnected cathedral with music flowing through it, not a drawer full of unrelated trinkets. The British habit of calling it "maths" is oddly reductionist -- it makes it sound like you've got separate jars labeled "algebra", "geometry", and "spicy numbers".
> “Thelonious Monk once said ‘All musicians are subconsciously mathematicians.’
I mean, we also don’t need to see something that’s not there. Also, I see you OP. https://news.ycombinator.com/item?id=47645844