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Author Topic: List of 351 Just intervals (.pdf file)  (Read 2211 times)

Mat

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List of 351 Just intervals (.pdf file)
« on: January 25, 2012, 04:08:52 PM »

Feel free to download, copy, distribute. See attachment. There are larger lists on the web, but mine has the powers (exponents) of the prime factors for each interval. For example, an 11-limit interval has a zero in the 13 column, a 7-limit interval has zeros in the 11 and 13 columns, and so on.
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Gedankenwelt

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Re: List of 351 Just intervals (.pdf file)
« Reply #1 on: January 27, 2012, 06:13:27 PM »

Thanks for sharing your list! I like the idea how you split the dimensions (7-limit except octave in 3d, embedded in a 2d plane for 13-limit extension).

I realized that the list often contains adjacent intervals with a difference of ~ 0.42 Cent. I suppose this is related to the fact that 9/8 * 5/4 * 7/4 * 13/8 is only ~ 0.42 Cent lower than 2 octaves (this might be interesting when searching for tunings that approximate 13-limit well).

On a slightly unrelated note: I was a little stunned when I saw the number 351, because that's exactly the number of scale systems in 12-EDO that contain all possible 2048 scales (e.g. the 7 scales built from each degree of the major scale constitute a scale system).
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