Archive for the ‘math’ Category

Samurai Stoner Rock – Tool’s Lateralus On Koto

December 16th, 2010 by frankie23

Man, even my jaded soul fucking loves this. YouTube user radialaxis went and arranged Lateralus by Tool for an eight-piece koto group; this video is from their first performance. He also shares with us something I did not know; the song is actually partially based on the Fibonacci sequence, which means it’s related to the Golden Mean, which means that it is mathematically beautiful. See, now even if you don’t like Tool, you can blame liking this song on nature! Here’s a chunk of his very verbose write-up for the song, from the YouTube page:

The first 6 steps and the 15th step (6=1+5) of the Fibonacci sequence for the numbers 0 and 1 feature prominently in the structure of this piece:

(0-1) -1-2-3-5-8-13-21-34-55-89-144-233-377-61­0-987

This is reflected, for example, in the rhythm of the second section, 9/8-8/8-7/8, 987 being the 15th step of the sequence, as well as in the structure of the 3rd section. While the underlying rhythm of this section is 5/8 (the 6th step of the sequence is 5+8=13), the lead melody progresses back and forth through a series of phrases of length 0 to 13, again the first 6 steps of the sequence plus the root numbers, separated by pauses of length 1 to 5, the 1st 4 steps of the sequence. Together the melody phrases and rests form the image of 2 interlocking spirals. The lyrics of the song at this point also reflect the mathematical structure, the first words being ‘black then white,’ i.e. 0 and 1. The lyrics later in the song make use of extensive spiral imagery.

In my arrangement I tried to incorporate this element of the original composition as much as possible. There are 8 instruments in the group, 6 koto and 2 bass koto. The 6th step in the sequence is 13, which is the number of strings on a koto. The 2 bass kotos together have 34 strings, 34 being the 8th step of the sequence. In the first 9/8-8/8-7/8 section the 8 players are subdivided into 2 groups, one of 5 and one of 3. The groups play the 9/8/7 figure 3 times, with a variation in the 3rd iteration subdividing it into 3=2+1. The 2nd time through the 9-8-7 figure the groups themselves subdivide into smaller groups of 3+2 and 2+1 for 2 iterations before subdividing again in the 3rd iteration (3=2+1 again).

I just must say, thank you sir; this really made my god-damn week. Cheers!

Tool – Lateralus – Japanese Version – ラテララス [YouTube]