A novice finds toothless wolves and so delves into theory

With a little help from Reaktor* I have have been playing with
various tunings. I particular, I have been having a lot of fun with
the Centaur tuning described at Anaphoria (www.anaphoria.com/centaur.html).
It has a lot of interesting resources and I find manageable for a
beginner to start with. I find the collection of major, minor and
septimal minor triads particularly intriguing.

While playing around with this tuning I noticed that I was
doing something that should have made my toes curl, at least by all
reports: I was playing this as a chord: 9/8 7/5 5/3. This looks like
DF#A using the mapping from the web page. My fingers were thinking
"major." Overtone series: 84:100:135. The interval from 9/8 to 5/3
is the much maligned wolf fifth, 40:27. The 40:27 interval sounded
like a fine member of the Major family to me combined with the 7/5,
though the beating from just the 40:27 is not quite nice.

Now this is no surprise that the addition of the 7/5 would
improve the overall sensation of consonance, I thought, until I
checked the intervocalic ratios: 56:45, 25:21. Now, 25:21 is only two
cents off (301.85) a tempered minor third, but 56:45 is well away from
anything at 378.6 cents (5/4 is 386.31). I've checked the tuning of
the synth several times in desperation.

Why in the world didn't this chord shriek at me?

I don't have an answer to that. I listen to a lot of
obnoxious electronic music with a fondness for fairly brilliant - not
to say discordant - timbres, which may have left me with an
appreciation, somehow, for a chord like 84:100:135. However, I did
start to wonder about ways of characterizing a chords "distance" from
some other chord, such that one can say "nope, these are too far apart
to be misconstrued for each other?" I grabbed "Divisions of the
Tetrachord" and read through chapter 5 a few times. There are lots of
interesting tables there, but I'm not quite sure comparing tetrachords
and comparing chords are the same thing. Has anyone done any work on
this? I'd rather not rediscover work already done. :)

* Reaktor. At the risk of sounding like a marketing person for
www.native-instruments.de, I must say that Reaktor is one of the most
wonderful software synthesizers I have ever seen. It is in fact a
system for *building* synths and samplers. This flexibility has
allowed me to add a bunch of retuning knobs to every "ensemble" (a
working collection of sound modules) I find I like. It makes playing
with tuning a joy, though my neighbors may not agree. :)

--
William S. Annis wsannis@execpc.com
inorganic name - http://www.mp3.com/inorganicname
Mi parolas Esperanton - La Internacian Lingvon www.esperanto.org