Australia's film & video rating board rated the first volume of Azumanga Daioh MA15+: mature audiences 15 and over. Volume 2 was rated G. Okayy...

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February 14th, 2005 - Trapped on a Strange Planet

The sublime is ridiculous

14 February 2005 @ 10:59 am

Australia's film & video rating board rated the first volume of Azumanga Daioh MA15+: mature audiences 15 and over. Volume 2 was rated G. Okayy...

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14 February 2005 @ 10:54 pm

Instead of using pitch, defined as frequency, I'm using tone, defined as number of scale steps above any reference pitch. So a motive doesn't actually define a series of absolute pitches, but a series of relative intervals. The reference pitch must be defined for performance (for example, modern Western tuning uses A above middle C = 440Hz, but this hasn't always been the case) but it's irrelevant for the algebra, where it corresponds to a tone of 0. This is in line with pitch set theory as well.

I forgot to address timing in multiplication last time too. Here's how multiplication works now: the product of two notes is a note with timing equal to the product of its factors' timings, duration equal to the product of its factors' durations, and tone equal to the

I should note that what I call vertical inversion is typically just called inversion, and what I call horizontal inversion is typically called retrograde.

Another operation is concatenation: following one motive by another. A concat B would be the sum of A, and B times a note with tone 0, duration of 1 beat, and timing that is the sum of the timing and duration of the final note in A.