guitars, slides & harmonics - simple help wanted

In-Reply-To: <199511091619.IAA05972@eartha.mills.edu>
Dear All,

I have just returned from gigging in Istanbul, home of the
multi-fretted long-necked lute (saz et al.), still coughing the
cigarette-smog of 15million chain-smoking Turks out of my poor
old lungs, but happy and bearing fine spoils. I can report that
micro-tonalism is alive and well; I told my Gypsy friends about
you all and they said to send greetings. But Lachio!

This + the many recent wild and whacky postings has inspired me
to take down my good old occidental 5-string open-tuned
acoustic guitar and play about with an old slide thing I found
some years back.

Seeing as how there be less mathematically-challenged folk out
there than myself, I was hoping one such kind person might be
able to help me with a couple of problems that have been
nagging at me for the last decade or so.

1.
Firstly, does anyone have an idea of the mathematical
expression (algorithm?) for the following:

* Get acoustic guitar and slide.
* Place slide at the octave, i.e. half-way point of the string,
strike both sides. Result = same note.
* If you then move the slide up (or down) and continue to
strike both sides of the string, certain "nodes" emerge in
which with each side of the string harmonises, according to the
relationship - i.e. "perfect" third, fourth, fifth etc...
For example: if the string in question is a G, then going up
the neck towards the nut you will pass from:

unison (g) | (g) - at the half-way length of the string, to:
octave (d') | (d) - at the third-way length of the string.

Although many of these nodes are the expected ones, plenty are
"out" of the standard "g" harmonic series. For example, the
minor 3rd is near enough a quarter-tone and the 7th is
decidedly skew.

Questions:
Maybe people have been going on abut this under some other
name, if so what is this sort of harmonic collection called?
What is the mathematics of this as a whole series? Are there
any proper big compositions & works in this field of, I suppose
I'd call it "bifurcative-JI"? Is it possible to play this in
yet another plane (i.e have not 2 but 3 floating sliding points
in the frequencu spectrum)? Is this a bit like what Brian
McLaren is talking about with rhythm?

2.
My second request is of a similar nature, but more practical
and applies to anyone who is interested in the visualisation of
fretless finger-stopping (as opposed to diagrams of music!),
who has a computer and means op generating waving nice wavy
patterns (sine, cosine will do).

I have this thing called a c�mb�s (that's pronounced jumbush
with puckered lips for the u umlauts). It's about the hardest
animal I ever encountered but essentially it is a 12-string
fretless banjo. The neck is bolt-on and the fingerboard is made
of (if you please) a formica strip. Cheap & cheerful and the
best friend the hard-working 7-days-a-week, 5-hours-a-night
Istanbul Gypsy twangers have. Louder than an Ud, less of a loss
if drunken revellers are sick on it, have to be controlled etc.
Also good for cooking up some rice in.

If I can provide the exact dimensions of the fingerboard,
tuning of strings, string scale length etc... can anyone knock
me up a nice wavy pattern that approximates the "tree of life"
design found on all the nice old bouzoukis? This is a
traditional sinuous curvy thing with vine leaf bits coming off
it. I have PC running MS things and access to Quark and other
bigger apps.

Essentially I am looking for a visual aid to a fretless
fingerboard that I can cut into the fingerboard so I can
encourage myself to play other forms of tuning. I imagine
something a bit more modern than vine-leaves, lots of
super-imposed sine and cosine waves that produce nice, moire
patterns, super-imposed over standard, or JI or 14ET fretting
marks etc...

Hoping this is of interest or at least germane to the current
(wonderful high level) of postings & discussion, and apologies
if not. All responses gratefully received.

Lu
aka: chad@cix.compulink.co.uk
London, UK


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