Commission Music

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Monday, 25 April 2005

Just Intonation and Meditation

While I was working on my political works, I became concerned that my music was too negative. I was pointing out error, but I was not offering counter-proposals. I used pitch, especially just intoned pieces, to give friendly experiencers breaks between Text Sound pieces. Proponents of just music note the lack of meditative music in western culture. They blame this on the tuning system. Kyle Gann writes, “Most cultures use music for meditation, and ours may be the only culture that doesn't. With our tuning, we can't.” (Gann) I hoped the meditative qualities of my tuning pieces would help serve as an antidote to any angst incurred by listening to political Text Sound. During my concert, I routed all of my just pieces through the architectural speakers, to give them greater authority than voices coming through the smaller speakers on stage.

Many of my tuning pieces use a set of algorithms taught to me by Ellen Fullman, who I studied with during breaks. These are expressed most easily mathematically. Just tuning uses whole number ratios. The fractions values are between 1 – 2. To keep fractions in this range, they can either be multiplied by 2 or divided by 2. Remember that a doubling of halving of a frequency changes the octave, but not the note. 220 and 440 are both A.

If we call the numerator x and the denominator y, both those numbers may be 2 or an odd number greater than 2. Just tuning systems are typically described by the largest odd number that the use. My tunings are usually 21 limit tuning, so in my pieces x and y can be 2, 3, 5, 7, 9, 11, . . . 21. Tunings that are next to each other in a tuning table from a chord. A chord may be otonal or utonal. In an otonal chord, all the ratios have the same denominator, however, the numerators are adjacent values of x. For example: 3/2, 5/,4, 7/4. In a utonal chord, all the ratios have the same numerator, but the denominator changes. For example: 11/12, 11/10, 11/7. When a proposed chord involves a number greater than the limit, the chord wraps around back to 2. For example: 19/16, 21/16, 2/2 is a valid otonal chord.

21 is an unusually high number to use as a limit. Often tunings have a 5 or a 7 limit. The high limit allows combinations with large relatively prime numbers that have a greater amount of beating. That is, it sounds less in tune. This makes my just pieces microtonal and gives them a certain harmonic logic without necessarily making them overly relaxing.

I just want to be doooone

I think I need a conclusion. I'm quoting Marx. This is not a good sign.

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