Notation for Fibonacci tuning (Wilson's horogram #22)?

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herman.miller
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Notation for Fibonacci tuning (Wilson's horogram #22)?

Postby herman.miller » Sat Dec 10, 2016 1:10 pm

http://www.elvenminstrel.com/music/tuni ... gram01.htm

I'm wondering about the best way to notate this tuning. It looks the Spartan level is sufficient for smaller subsets of the tuning, and Athenian should be good for almost anything. Promethean gets you an extra level, but many of the symbols are different. Here's what I've got for different sizes of accidentals (in cents):

108.20 :(||~:
82.66 :||): or :)||~:
66.87 :(|\:
51.09 :/|):
41.33 :/ /|:
25.52 :|):
15.79 :~|(:
9.76 :)|(:
6.03 :|(:
3.73 :)|:

The similarity of :~|(: and :)|(: is a bit confusing, so the Promethean :|~: could perhaps be substituted in place of :~|(:. How does this look?

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Dave Keenan
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Re: Notation for Fibonacci tuning (Wilson's horogram #22)?

Postby Dave Keenan » Sat Dec 10, 2016 1:39 pm

Hi Herman. That's a tough one! Not intended to approximate JI. 12 generators before you get a decent fifth.

Can you tell me how many generators each alteration in your list corresponds to? And what mapping you have assumed, if any?

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herman.miller
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Re: Notation for Fibonacci tuning (Wilson's horogram #22)?

Postby herman.miller » Sun Dec 11, 2016 3:16 am

I'm not assuming any mapping for now, just trying to find accidentals of approximately the right size. You could either use +10 generators or -11 generators for the 7th harmonic, for instance.

And I think I got the 108c one wrong, it should be :/||): .

Here's the list with a few more additions sorted by generators. Many of these will only be needed if you're using large subsets of the tuning or if you're using the chain of fifths every +12 generators to notate the unmarked nominals. (E.g. a chain of generators starting with C would be C F:\ \!: A:~|(: D:!): G:(!/: B:)!(:, etc.)

-5 (108.2039) :/||):
+8 (66.8737) :(|\:
-13 (41.3302) :/ /|:
+21 (25.5435) :|):
-26 (82.6604) :||): or :)||~:
+29 (92.4172) :||\:
-34 (15.7867) :~|(: or :|~:
+42 (51.0870) :/|):
-47 (57.1170) :(|):
+55 (9.7567) :)|(:
-60 (98.4472) :(||(:
+63 (76.6305) :~||(:
-68 (31.5735) :(|:
+76 (35.3002) :(|(:
-81 (72.9037) :)||(:
-89 (6.0300) :|(:


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