He Talks in Maths: Why Geeks Love Radiohead(davidpcheng.com)
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He Talks in Maths: Why Geeks Love Radiohead
http://www.davidpcheng.com/post/20910078637/he-talks-in-maths-why-geeks-love-radiohead
28 comments
I don't know what "music theory" is, and I agree that I wouldn't listen to Radiohead if I didn't like the melodies (there are other mathy/geeky bands out there I don't listen to, an extreme case being Information Society giving you instructions on how to configure a modem to translate their "song" into ASCII, no. 1 listed here: http://www.cracked.com/article_18896_10-mind-blowing-easter-...).
But some theories about music are very mathematical. We probably are just beginning to understand how to think about music in terms of math, because music is complex and (at least much of Western music) discrete. An article in Science in 2008 defines equivalence relations and uses n-dimensional symmetries to describe sequences of pitches in time. See here: http://www.sciencemag.org/content/320/5874/346 and here: http://www.sciencemag.org/content/320/5874/328.full)
I think there is some truth in a Leibniz quote: "The pleasure we obtain from music comes from counting, but counting unconsciously. Music is nothing but unconscious arithmetic." (http://www-history.mcs.st-and.ac.uk/Quotations/Leibniz.html)
It's hard to say why I like Radiohead. At first I really didn't like them; I found Kid A (album) especially discomforting. I had to let go of a lot of pre- (mis?) conceptions about what makes music good before I could come to like it. I probably had to let go of a lot of pre- (mis?) conceptions about myself and my worldview at the same time to appreciate the lyrics. But now it's one of my favorite works of art.
But some theories about music are very mathematical. We probably are just beginning to understand how to think about music in terms of math, because music is complex and (at least much of Western music) discrete. An article in Science in 2008 defines equivalence relations and uses n-dimensional symmetries to describe sequences of pitches in time. See here: http://www.sciencemag.org/content/320/5874/346 and here: http://www.sciencemag.org/content/320/5874/328.full)
I think there is some truth in a Leibniz quote: "The pleasure we obtain from music comes from counting, but counting unconsciously. Music is nothing but unconscious arithmetic." (http://www-history.mcs.st-and.ac.uk/Quotations/Leibniz.html)
It's hard to say why I like Radiohead. At first I really didn't like them; I found Kid A (album) especially discomforting. I had to let go of a lot of pre- (mis?) conceptions about what makes music good before I could come to like it. I probably had to let go of a lot of pre- (mis?) conceptions about myself and my worldview at the same time to appreciate the lyrics. But now it's one of my favorite works of art.
I don't know if there is really any specific relationship between Radiohead and mathematics more than any other musician or composer, and I agree with you-- mathematics doesn't play into my feelings towards radiohead, they're a great band. But you point out "music theory isn't much rooted in math." I think the sentiment is true, music theory is generally taught and practiced without much thought to mathematics.
However, the fundamental concepts music theory are based on are all analogous to mathematical statements. You can see what I'm talking about here.
http://en.wikipedia.org/wiki/Music_and_mathematics#Frequency...
You'll notice that a fundamental frequency is picked, and we give names to several related frequencies (octave, third, fifth etc). All of these labels are analogous to various multiplications of the fundamental frequency. We learn to recognize some of the simpler relationships, as they are easily identifiable (different chords are an example of this).
Any one who can count can recognize a number on the number line and compare it to another number and tell if it's smaller or larger. Those who have begin to understand arithmetic can identify the difference between those numbers, and if they are multiples of each other. Advanced mathematicians can tell us about more complicated relationships.
In music we have tones that can be ordered, and musicians learn through experience to make these same judgments about tones without even knowing it. Any amateur musician can hear a pair of tones side by side and recognize which is higher or lower in pitch. The more advanced ear can identify notes that are the same or they can tell you a harmonic relationship between them. This is a different way of experiencing mathematical relationships within an ordered set.
At it's core, I think music theory is absolutely the study of finding which combinations of tones create the numerical relationships we find most appealing in sound.
However, the fundamental concepts music theory are based on are all analogous to mathematical statements. You can see what I'm talking about here.
http://en.wikipedia.org/wiki/Music_and_mathematics#Frequency...
You'll notice that a fundamental frequency is picked, and we give names to several related frequencies (octave, third, fifth etc). All of these labels are analogous to various multiplications of the fundamental frequency. We learn to recognize some of the simpler relationships, as they are easily identifiable (different chords are an example of this).
Any one who can count can recognize a number on the number line and compare it to another number and tell if it's smaller or larger. Those who have begin to understand arithmetic can identify the difference between those numbers, and if they are multiples of each other. Advanced mathematicians can tell us about more complicated relationships.
In music we have tones that can be ordered, and musicians learn through experience to make these same judgments about tones without even knowing it. Any amateur musician can hear a pair of tones side by side and recognize which is higher or lower in pitch. The more advanced ear can identify notes that are the same or they can tell you a harmonic relationship between them. This is a different way of experiencing mathematical relationships within an ordered set.
At it's core, I think music theory is absolutely the study of finding which combinations of tones create the numerical relationships we find most appealing in sound.
This isn't much different from what I'm saying, I think -- you mention frequencies, which don't come up much in most study of music theory beyond more or less what you have in your comment.
Beyond that, well, I suppose you could say it's "math", but that's a bit like saying price comparing at the grocery store (calculate the per-kilo price!) is math -- it won't have math geeks drooling.
I can recognize intervals by ear, but it's just practice. You start out by "cheating" (twinkle twinkle starts with a leap of a perfect fifth, the NBC call sign with a major sixth, etc.), then you just learn it. I'll bet you could get the gist of it using the reference melodies pretty quickly.
You can refer to the relations using basic math terminology, or just the music theory technology, but regardless it doesn't feel like anything beyond elementary math -- it goes much quicker into psychology territory.
Beyond that, well, I suppose you could say it's "math", but that's a bit like saying price comparing at the grocery store (calculate the per-kilo price!) is math -- it won't have math geeks drooling.
I can recognize intervals by ear, but it's just practice. You start out by "cheating" (twinkle twinkle starts with a leap of a perfect fifth, the NBC call sign with a major sixth, etc.), then you just learn it. I'll bet you could get the gist of it using the reference melodies pretty quickly.
You can refer to the relations using basic math terminology, or just the music theory technology, but regardless it doesn't feel like anything beyond elementary math -- it goes much quicker into psychology territory.
I agree that the math connection is pretty... loose, although it always impresses me when a good musician (like my guitar instructor) can transpose on the fly. "Oh, I wonder what this would sound like in A Major instead of C Minor?"
The same guitar instructor re-introduced me to Radiohead, and some of the most joy I've ever had as an aspiring musician was hearing some of those chords come together in unexpected and beautiful ways.
The same guitar instructor re-introduced me to Radiohead, and some of the most joy I've ever had as an aspiring musician was hearing some of those chords come together in unexpected and beautiful ways.
Transposing on a guitar is trivial, it's not like piano where changing keys changes fingering. On a guitar, you can just move to a new position and play the same fingerings, bam new key.
Guitar or piano, it's still just patterns that are generally well burned-in.
Study any instrument seriously and you'll play scales enough that they're quite natural "forms" that you just lay on the keyboard/fretboard in your imagination. Playing a melody through a different scale pattern (as long as they have the same number of notes... whole tone etc. are off-limits here) is fairly easy.
Something with chords, or multiple melodies, and especially if it doesn't stick to its starting key, takes a little more planning ahead (assuming you can't just move up/down the guitar neck, or add a capo... that's of course trivial), but is still mostly applying the same technique - laying the same notes into a slightly different (but very familiar) pattern.
This is a really fun singing exercise, BTW, that many people can try (with minimal music training, though you'll need to know how to sing a minor scale first): take a really simple melody in a major key (most children's songs), and sing it in a minor key. Start with something like Row row row your boat or twinkle twinkle, then something like Happy Birthday -- which doesn't start on the first note of the scale -- is more challenging. :)
Study any instrument seriously and you'll play scales enough that they're quite natural "forms" that you just lay on the keyboard/fretboard in your imagination. Playing a melody through a different scale pattern (as long as they have the same number of notes... whole tone etc. are off-limits here) is fairly easy.
Something with chords, or multiple melodies, and especially if it doesn't stick to its starting key, takes a little more planning ahead (assuming you can't just move up/down the guitar neck, or add a capo... that's of course trivial), but is still mostly applying the same technique - laying the same notes into a slightly different (but very familiar) pattern.
This is a really fun singing exercise, BTW, that many people can try (with minimal music training, though you'll need to know how to sing a minor scale first): take a really simple melody in a major key (most children's songs), and sing it in a minor key. Start with something like Row row row your boat or twinkle twinkle, then something like Happy Birthday -- which doesn't start on the first note of the scale -- is more challenging. :)
> Guitar or piano, it's still just patterns that are generally well burned-in.
Sure, but it takes much less effort to play something in different keys on a guitar than on a piano because the fingers don't change just because the key did. It takes more practice on a piano to play a song you already know in another key, not really so for the guitar if you're using movable forms.
Sure, but it takes much less effort to play something in different keys on a guitar than on a piano because the fingers don't change just because the key did. It takes more practice on a piano to play a song you already know in another key, not really so for the guitar if you're using movable forms.
Yup, I agreed with that already, I think, though it's a special case. If you're switching major/minor, for example, it's about equal... for some pieces slightly easier on piano because the scales are horizontally laid out more obviously, whereas some guitar fingerings won't easily convert by just shifting over a few notes of the scale -- you're limited by the way your fingers can bend.
Agreed.
That doesn't work if you're going to do a minor/major change, though, and it also doesn't work if any of your chords have open strings in them. Not all chords are "moveable" chords.
Not all chord phrasings are movable, but all chords are. Name any chord, there's a movable version of it.
OK Computer came out at the peak of the electronica period, so the use of text to speech and dub production wasn't really novel. Plus the album was more about urban alienation rather than just technology. I don't think they appeal specifically to geeks though, they are widely critically acclaimed.
I personally believe when an artist or group starts being taken seriously by the Jazz world, that's a sign that they're doing something right. Highly recommend Jonny Greenwood's recent other work: http://www.npr.org/2012/03/04/147668709/first-listen-krzyszt...
See also Brad Mehldau's treatment of Radiohead: http://www.youtube.com/results?search_query=brad+mehldau+rad...
It's probably from the better part of modern orchestration but it's not something you'll enjoy listening to when sitting in a bus driving to work in the morning, at least that's my opinion.
Re: the reference to Fibonacci numbers. Five years ago I stumbled upon a video that connected Fibonacci to a song off of Tool's Lateralus album:
http://www.ilamont.com/2007/09/tool-math-rock-and-fibonacci-...
FWIW, Lateralus and 10,000 Days (also by Tool) are among the few rock albums I can listen to while working at night. It's very methodical. I love OK Computer (and Radiohead's "Airbag/How Am I Driving" EP, released around the same time) but it's hard for me to concentrate while listening to them -- too many hooks.
http://www.ilamont.com/2007/09/tool-math-rock-and-fibonacci-...
FWIW, Lateralus and 10,000 Days (also by Tool) are among the few rock albums I can listen to while working at night. It's very methodical. I love OK Computer (and Radiohead's "Airbag/How Am I Driving" EP, released around the same time) but it's hard for me to concentrate while listening to them -- too many hooks.
Love Radiohead, they're an intellectual group. They're also competitive bridge players too, cool piece on them: http://www.followmearound.com/presscuttings.php?year=1993...
Flip side of the proposition: many geeks don't love Radiohead. No disrespect those who do, because everyone certainly has their own set of tastes. But the statement is just as false as claiming that geeks love Bach (I do, but you may not).
I don't like radiohead hardly at all. I think, besides a few songs, they are boring. Same with My Bloody Valentine.
I do love math rock though.
I do love math rock though.
Why Geeks Love Radiohead? because they're not very big music fans.
Radiohead has a song called "Palo Alto"? Well here's an album called Chip-Meditation by a group called Software: http://www.discogs.com/viewimages?release=132407
Radiohead uses a mathematical basis for composition? Try an album by Autechre and try and let your brain parse the mathematical precision and complexity of the music.
That's not to say that Radiohead aren't a decent pop group: they have proven that they are. I'm just sayin that based upon the points brought up by the author, Radiohead are pretty entry-level
Radiohead has a song called "Palo Alto"? Well here's an album called Chip-Meditation by a group called Software: http://www.discogs.com/viewimages?release=132407
Radiohead uses a mathematical basis for composition? Try an album by Autechre and try and let your brain parse the mathematical precision and complexity of the music.
That's not to say that Radiohead aren't a decent pop group: they have proven that they are. I'm just sayin that based upon the points brought up by the author, Radiohead are pretty entry-level
I don't agree at all with this article, imo loving music has nothing to do with the things in the article.
But to claim Radiohead fans aren't big music fans is massively closed-minded. You might not like them, and that's fine. However, Radiohead are highly acclaimed by music lovers (OK computer topping lots of respected 'best of the 90's' lists etc).
But to claim Radiohead fans aren't big music fans is massively closed-minded. You might not like them, and that's fine. However, Radiohead are highly acclaimed by music lovers (OK computer topping lots of respected 'best of the 90's' lists etc).
I got the impression that arrakeen is saying, if the article were correct, then that would mean geeks don't know much music.
Because if they went searching for music that ticked off all of the boxes listed in the article, they'd fine other stuff that did it far more.
But the article isn't really on the mark (I don't think so either), so the conclusion about geeks doesn't hold water either.
Because if they went searching for music that ticked off all of the boxes listed in the article, they'd fine other stuff that did it far more.
But the article isn't really on the mark (I don't think so either), so the conclusion about geeks doesn't hold water either.
Radiohead is my favorite band, but it has nothing to do with math or pop geek references or their distribution methods.
They just make damn good music.
They just make damn good music.
Same here. I would argue that most of their songs that I like have a certain melancholy to them. They invoke a mood that is like the feeling I get after reading the bipolar lisp programmer:
http://www.lambdassociates.org/blog/bipolar.htm
> OK Computer and In Rainbows are 10 years apart and are intended to be listened together, a binary joke on the rest of us.
This is just a myth, and it's wrong. And none of these things have anything to do with why anyone likes Radiohead or not.
This is just a myth, and it's wrong. And none of these things have anything to do with why anyone likes Radiohead or not.
Knuth has written (and talked) about interesting mathematical/algorithmic takes on music.
But music theory isn't much rooted in math -- I mean, sure, there's a bit of math involved, there are composers (mostly within the last 60 years) who've decided to build lots of math into their music (but much of it is aggressively unlistenable, OR they did lots of extra work dressing up the mathematical stuff in "kind on the ear & brain" regular old music to make it sound nice...), and if you dig into the acoustics of music, or DSP, there's math there.
But music theory itself is mostly the somewhat-arbitrary documentation of what music is doing (not in mathematical terms), and sadly even the terms that involve numbers don't even do it consistently.
The easter eggs are cool -- but I wouldn't listen to the music regardless if I didn't like the melodies, orchestration, "feel" and so on in most of it. (Radiohead is quite melodic, on the whole).