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Though it might seem counterintuitive at first, it turns out that you can notate 22-tone equal temperament using regular standard western notation. The intervals of each system simply correlate to the movements along the circle of fifths in either tuning. (For example, a minor third is found by going down three fifths and up two octaves. This is true using 12-tone equal temperament's fifth, or 22-tone equal temperament's fifth.) The fifth is different enough in size in 22 from standard western tuning's fifth, however, that, after going even a short distance in the circle of fifths, the tuning of the intervals derived therefrom shifts pretty dramatically. One crazy repercussion of that is how the augmented second is actually more "in tune" than the major third is, and so the purer C "major chord" is spelled C-D#-G!

You could, of course, just treat that D# as a more in tune "kind of E" but, especially melodically, that can lead to funky unintended consequences. When actually treated melodically like an augmented second, however, I found that it worked exceedingly well.

I wrote and notated a round (like "row row row your boat", where you can sing the song on top of itself) that I think demonstrates that feature of 22: 

https://www.youtube.com/watch?v=xONo-1OxSAw

What do you think? Are you able to pick up the melody and sing/read along, with or without knowing how the notation lines up with 22 exactly?

Any other composers interested in writing in 22-tone equal temperament can use the same free plugin for Sibelius that I did, from offtonic, here:

http://offtonic.com/sib/plugins.html#ntet

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