He Talks in Maths: Why Geeks Love Radiohead
davidpcheng.com
davidpcheng.com
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).
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.
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.
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.
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.
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. :)
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.
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.
I do love math rock though.
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
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).
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.
They just make damn good music.
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.