23edo: Difference between revisions

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I would argue that the most significant modes of 23 edo are those of the 2 2 2 3 2 2 3 2 2 3 scale;

This is derived from extending the ~1/3 comma tempered 13th harmonic, two of which add up to the h21

and three add up to the h17 almost perfectly (I discovered the temperament before I even realised 23 tone fits)

The chord 8:13:21 is a fragment of the fibonacci sequence, and 16:21:26 is harmonically symmetrical

(The chord 26:29:32 is also symmetric, but only 20 and 43 edo approximate the h29 as well)

13:17:21 is symmetrical, and 17:21:26:32 has an interesting linear widening pattern, but more importantly,

the h13 and h17 are both dual primes like 3&5 and 7&11

Thus I have named these 10 modes according to the Sephiroth as follows:

2 2 2 3 2 2 3 2 2 3 - Mode Keter

2 2 3 2 2 3 2 2 3 2 - Chesed

2 3 2 2 3 2 2 3 2 2 - Netzach

3 2 2 3 2 2 3 2 2 2 - Malkuth

2 2 3 2 2 3 2 2 2 3 - Binah

2 3 2 2 3 2 2 2 3 2 - Tiferet

3 2 2 3 2 2 2 3 2 2 - Yesod

2 2 3 2 2 2 3 2 2 3 - Chokmah

2 3 2 2 2 3 2 2 3 2 - Gevurah

3 2 2 2 3 2 2 3 2 2 - Keter

-- Kosmorsky

=Books=

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