Callisto : a 21-tone poly-microtonal system

Hey All !

Long time, eh ? I was out of it for a little while, mainly due to
a hard drive crash :-( that lost all my data except for a back-up of my
music, hail Zeus !...

The aluminium fingerboard fretless guitar did get done & turned out really
nice considering the old acoustic I used could double as a canoe. Musically
will take a while to get the hang of, especially to really use non-12EDO*
notes, those being so ingrained, it's (almost) easy to play in that tuning.
Of course the fact that this guitar has a neck thick as a tree doesn't help.
One annoying thing is the fingers tending to get a bit black from the
aluminium. Hope there's no health risk. Gotta be safer than dining in
Belgium, eh ? ;-)

I also spent some time conjuring up a flexible microtonal fretting system,
which, while I won't be doing any refretting anytime soon, did yield an
interesting result in my quest for a nice set of notes that I could wring a
lot out of.

Among my favourite tunings are 7 & 5 EDO, with JI embellishments. So, I
thought what if I were to put both those on a guitar. After plotting the
position of the frets for 5 & 7 EDO, it turned out there was lots of room
left for more frets, which I decided to fill in with JI intervals. Half an
inch appears to be a reasonable minimum spacing of frets.

What I wound up with is a very interesting set of 21 tones that incorporate
3 distinctive systems, while integrating into a 4th, poly-microtonal scheme.
I call the tuning "Callisto", after the scary-crazy woman in Xena.

Here it is :
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Tone ----------- Pitch as Ratio --------- Approximate ---- Notation
# or ET division & Pitch in Cents Scheme
ratio approximation (n = neutral)
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0 ----------- 1/1 ---------------- 0 ------ C
1 ----------- 143/140 ---------------- 36.7 ------ C+
2 ----------- 24/23 ---------------- 73.7 ------ C#-
3 ----------- 16/15 ---------------- 111.7 ------ C#
4 ----------- (191/173) 2 of 7edo ------ 171.4 ------ D
5 ----------- (85/74) 2 of 5edo ------ 240 ------ D+
6 ----------- 32/27 ---------------- 294.1 ------ Eb
7 ----------- (128/105) 3 of 7edo ------ 342.9 ------ En
8 ----------- 5/4 ---------------- 386.3 ------ E
9 ----------- 9/7 ---------------- 435.1 ------ E#
10 ----------- (95/72) 3 of 5edo ------ 480 ------ F-
11 ----------- (179/133) 4 of 7edo ------ 514.3 ------ F+
12 ----------- 7/5 ---------------- 582.5 ------ Gb
13 ----------- 36/25 ---------------- 631.3 ------ Gn
14 ----------- (159/107) 5 of 7edo ------ 685.7 ------ G
15 ----------- (144/95) 4 of 5edo ------ 720 ------ G+
16 ----------- 11/7 ---------------- 782.5 ------ G#
17 ----------- (105/64) 6 of 7edo ------ 857.1 ------ A-
18 ----------- (148/85) 5 of 5edo ------ 960 ------ Bb
19 ----------- (221/122) 7 of 7edo ------ 1028.6 ------ Bn
20 ----------- 15/8 ---------------- 1088.3 ------ B
21 ----------- 2/1 ---------------- 1200 ------ C

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Notation scheme : "n" = neutral, "-" = a little flat, "+" = a little sharp
(very scientific, n'est pas ?)

It's got 12 JI tones in there. And with relation to some popular JI
tunings, it offers a variety of 2nds, 3rds, 4ths, 5ths, & 7ths, though
the only tone close to a Maj 6 is @ 27 cents flat.

After pondering over Dante's & David Canright's pages about their
approach to tuning the open strings, something similar might work :

Tune the strings as two sets of 3 strings tuned an octave apart from
each other, effectively the open strings are :

1/1 2/1 4/1 1/1 2/1 4/1

Can you hear the drones yet ?

This might work nicely on an electric running through a pitch shifter,
transposing the entire instrument for modulating between "keys". Also,
some variation on the above scheme such as tuning the 2 sets to different
pitches/tones could work to give at least 2 "keys".

I've begun exploring by sequencing things, having managed to tune the
12-note XG tables in my Yamaha keyboard by dedicating 3 channels to get it
right. However, Csound is the poor person's secret weapon.

Any comments are welcome, especially ones that point out any boo-boos. Also,
I've not yet quite figured out those pretty little lattice thingies some of
u do, so if anyone out there cares to make a little triangular lattice, I'd
really appreciate it. I did one of my own, but I'm not sure I have it right,
duh, I'll show you mine if u show me yours...

*EDO = Equal Divisions of the Octave, after Dan Stearns.
(It was u Dan, wasn't it ???)

- Drew

--
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Drew Skyfyre email : drew_skyfyre@yahoo.com

web : http://www.geocities.com/Paris/Palais/8151
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