John Coltrane illustrates the mathematics of jazz(americanjazzmusicsociety.com) |
John Coltrane illustrates the mathematics of jazz(americanjazzmusicsociety.com) |
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".
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
Maths and math are both used, and the reason I used the plural form is not because I insist on anything but because it is the most commonly used of the two. I personally don't mind either forms.
With that said, linguistically using the plural for either is a bit odd, since that would imply you can pick "a" mathematic out of many, or "a" jazz out of many. But linguistic is not math (nor are lingustics maths), logic doesn't always apply.
https://en.wikipedia.org/wiki/Mass_noun
>In linguistics, a mass noun, uncountable noun, non-count noun, uncount noun, or just uncountable, is a noun with the syntactic property that any part and quantity of it is treated as an undifferentiated unit, rather than as something with discrete elements. Uncountable nouns are distinguished from count nouns.
So "math" is the proper shortening of the mass noun "mathematics". What other mass nouns do you shorten by abbreviate by keeping the "s" ending?
We do not say "phys" for physics or "econs" for economics, so keeping the "s" in "maths" breaks the rule.
DSP uses a lot of actual math for processing and synthesis. But trad music's chords, rhythms, melodies, and forms are linguistic grammars that can be annotated mathematically after they're defined.
The creation process isn't mathematical. Composers are always making choices from possibilities, and the choices rely on subjective taste.
With Coltrane there a lot of similar structures he could have used, and likely experimented with.
But he picked this particular one for subjective creative reasons.
You don't see as much of that mindset in the mainstream of the layman but it's how all industrial processing is done. As an arbitrary example, given a process involving yeast you can construct time vs temp vs moisture vs salt curves to model its behavior.