ah irrationality.  possibly my favorite aspect of the human condition...

consider equal temperament.  the geometric series that coincides with an n -tone equal temperament scale is highly irrational, with ratios based on the nth root of 2.  since 2 is the lowest prime, all equal tempered gamuts are based on irrational numbers.  for a while now, people have been arguing over this compromise in music, specifically in the context of tuning.  for reference, i direct the interested reader to google.  i would say this is one of the great controversies in the field of music.  personally, i tend to use just intonation in my work, because i love how it sounds.  often, a piece written in just intonation simply pulls on my emotions in ways that equal temperament just doesn't.  as a piano player, i also love the tuning system that grand pianos use, which contrary to popular belief is not equal temperament.  generally a well tuned grand piano uses a stretched octave due to the weird overtone structure of piano strings.

another reason i often use just intonation in my music is that i have the tendency to re-apply ideas from one domain, such as tuning, to another, such as rhythm.  harmonies are determined by whole number ratios in just intonation; the parallel in rhythm is the polyrhythm.  but ever since a year or so ago, i started playing with massive sets of equal tempered sines.  the result is an infinitely expanding wavefront, made up of many smaller waves, who start out perfectly aligned and march inexorably into entropy.

click here to look at the code.  (apparently from some kind of tutorial i was writing at some point)

click here to listen to the mp3.

so i've been thinking recently about massive, irrational, rhythmic structures.  this has led me to the following patch:

click here to look at the code.

click here to listen to the mp3.

it's made up of a set of 100 irrational relationships, each one mapping to a different place in a soundfile, and a different rate of occurrence.  since these rates begin completely in phase and theoretically will never line up again (remember computers can offer only finite representations of values...), we get the same richness, but in a different domain.  more on this in the next hackpact entry...

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