triangular trivalance, and other dissonant decorative delights...

You know those Christmas tree lights, the strings with the tiny
colored bulbs that flash off and on in a pattern? Well I had an
idea... How about a microtonal Christmas decorative tree type thing
that uses triangular number patterns as a template for flashing
sounds... ?

Oh, I want one!

Well, I probably want several actually...

I don't think that the usual 4:5:6, 1/(6:5:4) triangular lattice
expansion, or even a centered 4:5:6:7, 1/(7:6:5:4) expansion, would be
quite resplendent and sparkly enough for my decorative tastes
though...

I'd much rather have an expansion based on say overtones, or
undertones... yeah, that'd be much better! Here's a little example --
perhaps a tree ornament -- using a 6-over expansion (the idea being
that the "triads" light up individually in a sequential firing
pattern; perhaps left to right, bottom to top):

4/3
/ \
/ \
7/6---5/3
/ \ / \
/ \ / \
1/1---3/2--11/6

Here's a bit larger -- perhaps a door hanging decoration -- example
using a 15-under expansion:

15/13
/ \
/ \
10/9--15/11
/ \ / \
/ \ / \
15/14-30/23-30/19
/ \ / \ / \
/ \ / \ / \
30/29--5/4---3/2--30/17
/ \ / \ / \ / \
/ \ / \ / \ / \
1/1---6/5--10/7---5/3--15/8

Weird, sparkly little light on ice triads that gleam ever brighter in
a left to right, bottom to top array.

I guess if you wanted to fly this same idea over to a centered
triangular expansion you'd have something along the lines of this
10-over rotating tabletop centerpiece... ?

6/5
/|\
/ | \
/17/10\
/ ,/|\. \
11/10/-+-\`7/5
/|\/`.|,'\/|\
/ |/,19/10/\| \
/ 8/5-\-+-/`9/5 \
/ ,' `. \|/ ,' `. \
1/1'-----13/10-----`3/2

How about a triangulated [2,2,2] tribonacci expansion in 18-tET...

6
/ \
/ \
3----12
/ \ / \
/ \ / \
0----10----16

Or a triangulated [5,4,1] tribonacci in 16-tET...

5
/ \
/ \
3----10
/ \ / \
/ \ / \
2-----9----14
/ \ / \ / \
/ \ / \ / \
0-----7----11----15

I'm sure others will see some firing patterns more to their liking
(not quite so discordant perhaps), but in the spirit of Carl Ruggles'
"dissonant chords have talismanic ecstasy" I like 'em just as they
are...

wishing happy holidays to all,

--Danta Claus