Tuesday, October 28, 2008

Nonogonal Music


While others have noticed that Pelog fourths form a good cycle at 9 tones, it was Wilson’s work along these lines that seem to represent it the best. There were three forms that he found had been used historically as the basis of pentatonics, made by rotating around the cycle 5 at a time. Since 2 tones are not tuned they skip to the next tone which gives us 3 different forms. These can be seen in the three rings in this diagram. If one uses all 9 tones one can characterize these as 5 fourths in a row, 4 in a row and skipping two, or the last can be seen as 3 in a row skipping two and then two more or these last 2 first. While 12 ET is a bad way to represent pelog, one can form a 9 tone cycle by using tritones in 3 places, in stead of perfect fourths for those who refuse to concede to mesotones. One will have to figure these out for oneself, and the same idea can be transferred to any other scale, of equal steps or not. I have even applied in use to the meta Slendro I use. A larger form of this diagram can be downloaded here. While not as precise geometrically as one could do, I still find it visually interesting.

3 comments:

  1. Kraig- i need to hear you play again.. when are you going to play?

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  2. the number 9 is a pretty interesting one geometrically and esoterically.

    i don't really know how exactly these things could be used in conjunction with your diagram, but i've done a bit of study on the enneagram personality typology, which is supposedly based on gurdjieff's enneagram, though other divisions are also available. there's also a passing reference to the kabbalistic tree of life in the article on gurdjieff's fourth way enneagram. interestingly, 9 could also be taken as the number of sephira preceding malkuth.

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  3. Tagged you are, here.

    What's more, you're number 8 out of 7. That must be just a little bit numerologically significant.

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