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.
That's an excellent comparison and it raises an interesting question. When cooking a basic understanding of chemistry techniques will generally prove quite useful but when it comes to music I'm not so sure about math. Maybe some electronic artists who write their own tools?
There are features described with math, but if you try to approach music purely as math it evaporates.
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.
I'm certainly no chef, and am only somewhat familiar with one particular side of chemistry (physical chemistry) but I don't see how it would be useful in cooking. Unless you count boiling water as chemistry.
The logic behind organic extractions, the temperatures at which different things oxidize or otherwise degrade, the temperature dependence of reaction kinetics (it's nonlinear which is incredibly important when you want one thing but not another), the thermal transfer characteristics of different materials and configurations, all sorts of stuff. The actual "doing" in cooking and baking is figuratively 95% chemistry (and 5% biology) even if the goal is different.
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.
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".
>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.
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.
Original article should be the link (2017 btw):
https://www.openculture.com/2017/04/the-tone-circle-john-col...
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!
Actually appears to be 2 concentric whole-tone rings, not chromatic.
Proto-supersaw! https://static1.squarespace.com/static/519a384ee4b0079d49c8a...
I don't remember much about music theory but I know enough about symmetry to know that there's a mistake in the diagram at 9 o'clock.
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.
Odd to mention Einstein and not Slonimsky, whose work he studied a lot and built upon.
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.
Why not maths and jazzes? If you insist on making math plural, then what's so singular about Jazz?
Same. If this counts as math, anything and everything is connected to math. Everything has patterns or structure that can be described.
You are so close to enlightenment. Now say it again without the sarcasm.
Ah, so it's the cooking of chemistry.
That's an excellent comparison and it raises an interesting question. When cooking a basic understanding of chemistry techniques will generally prove quite useful but when it comes to music I'm not so sure about math. Maybe some electronic artists who write their own tools?
There are features described with math, but if you try to approach music purely as math it evaporates.
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.
I'm certainly no chef, and am only somewhat familiar with one particular side of chemistry (physical chemistry) but I don't see how it would be useful in cooking. Unless you count boiling water as chemistry.
The logic behind organic extractions, the temperatures at which different things oxidize or otherwise degrade, the temperature dependence of reaction kinetics (it's nonlinear which is incredibly important when you want one thing but not another), the thermal transfer characteristics of different materials and configurations, all sorts of stuff. The actual "doing" in cooking and baking is figuratively 95% chemistry (and 5% biology) even if the goal is different.
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.
> “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
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".
It's just a shortening of "mathematics". You don't call it "mathematic" do you?
"Mathematics" is a mass noun that happens to look plural (ends in -s) but behaves singular: "Mathematics is hard" not "Mathematics are hard".
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.
I have heard both used before.
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