Music notation is descriptive. There is no single absolutely correct way of transcribing any piece of music any more than there is a single absolutely correct way to express particular fractions. 1/2 is 2/4 is 4/8 is 8/16. Not a single one of these is incorrect.
However, it behooves us to transcribe music in such a manner that it is readily understandable and indicates the correct feel of the music. A person reading and playing from the score, assuming they are reasonably capable on their instrument, should be able to reproduce the music accurately. With respect to this particular goal, certain ways of transcribing a piece of music are obviously better than certain others.
There have been inordinate measures of discussion concerning Radiohead's "Pyramid Song" from their album Amnesiac. It's an excellent song, definitely worthy of analysis, and given that the rhythm is relatively unusual for a piece of music written by a rock group, the amount of discussion is perhaps understandable. In fact, for as long as I've been aware of Radiohead, my opinion has been that, in spite of all the talk of their purported innovation and weirdness, the best things they have going for them are: first and most importantly, a firm sense of effective melodic and harmonic content; and secondly and slightly less importantly, a special talent for arrangement and production that lends their work a certain uniqueness and importance within the music world. They matter in a musico-historical sense, but not because they are weird or innovative (they aren't especially weird or innovative, in fact). They matter because of compositional prowess.
Having said that, "Pyramid Song" is a special example of a piece of music that uses nonstandard rhythms in an effective way that benefits the music significantly, rather than using them for the sake of being unusual. Melodically and harmonically, it is very well written. Rhythmically, it is also very well written, and unusual rhythms are definitely my compositional specialty. So to me, it is not surprising that it has generated so much discussion so consistently. The discussion apparently goes on even today.
In the March 2013 issue of Music Theory Online, Nathan D. Hesselink offers his thorough take on the song, compiling a comprehensive list of analyses of the song's rhythm. Unfortunately, the simplest and clearest interpretation in my estimation receives relatively little coverage. Two of the comments made under the mixed meter subheading hit the mark exactly, but none of the example images highlight these, though some are close.
In my opinion, the best way to write it is as follows:
Consistent cycles of 3/4, 2/4, and 3/4 throughout the entire song. The lengths of the five chords in each cycle are two dotted quarters, a half, followed by two more dotted quarters. It is swung, so that odd numbered eighth notes are twice as long as even numbered eighths, as though we were dealing with triplets. Thus, in terms of the feel of the music, the 3/4 bars have 9 atomic note lengths, while the 2/4 bars have 6. What I mean is that if you divide the 3/4 bars into 9 equal pieces and the 2/4 bars into 6 equal pieces, this is sufficient to depict every note in exact detail. The first chord is 5 atoms long, the second is 4, the third is 6, the fourth is 5, and the fifth is 4.
Thus, you could theoretically describe the music as cycles of 9/8, 6/8, and 9/8 as some have suggested. However, this requires tying notes together just about everywhere and needlessly complicating the score. It is far simpler to use 3/4, 2/4, and 3/4 and then plainly indicate the feel of the swing at the top of the score. This requires absolutely no ties, and correctly indicates what's going on.
Compare and decide for yourself. This...
...is technically equivalent to this...
Which do you prefer?
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