In diatonic music, the complement, the tritone transposition of the diatonic hexachord, emerges as the shadow, the unconscious of the diatonic hexachord that is held, that *governs* the surface. This is now an ancient 20th Century habit of thinking. No, older.
There are no limits to what might serve as the shadow of something. The only limit is our imagination in the strong Jamesian sense.
For example, the overtone series is another shadow, on another plane. Zero punning potential (JI) is a shadow of maximal punning potential (XEDO). There is symmetry death and there is specificity death.
And for JI composers, one could consider the house of mirrors (12 EDO) a shadow of the overtone series. That taboos against 12EDO become set in place reinforces the shadow quality.
I’ve seen how the taboos are spread. The anti-EDO partisan points to a piano and says, I hate that thing, teaching a distaste to gather a flock.
The music that could traverse this EDO/JI shadow relationship needs what Johnny Reinhard called for – any tuning system on call within the same work.
Important note:
With regard to XEDO where X≠12. The arguments in favor of such tend to be that intervals will be closer to the overtone series than 12EDO. What’s lost in the conversation is that we have subsets of 12EDO deep in our bones. Those subsets *get their teeth into us*.
This will not stop me from writing microtonal music. I can do it such that subsets of 12EDO (such things that get their teeth in me) are still omnipresent – “0” for Kharkiv Guitar Quaret and Poema armónico II.
Subsets of X≠12EDO are exotic, we don’t know them. And it will take a thousand years to know them. But I don’t want to discourage anyone; I won’t discourage the verloren hoop – the young ones (with brains bent toward danger) first up the wall to storm the castle. And that was me in the 80s and 90s when I was championing improbable music of that time (Babbitt & Wuorinen).
What you hold onto as you scale the wall has a shadow.
The Big Chariot
William Anderson is a guitarist and composer and an advisor to the Roger Shapiro Fund.