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From: PAULE
To: Steven Rezsutek
Subject: Post: Guitars
Date: Mon, 28 Apr 1997 13:28:12 -0500 (EST)


It's great to hear about all the re-fretted guitar work that is going on. I
am still waiting for my 22-tET guitar neck to be completed, but hopefully
I'll "catch up" with Steven and his band once it's done. Lucy's meantone
guitar is a great idea; you can start with 19 frets and then add more once
you're comfortable. Meantone means no pseudocommas, which is nice if you're
into diatonic triadic music. Lucy's tuning is close enough to optimal
meantone that it's not worth arguing with its silly derivation from pi.
However, 31-tET would be just as good and would have the advantage that you
could use any of the open and slack-key tunings Lucy described and never
have more than 31 pitches per octave. Plus it's a closed system, so you can
modulate as much as you like with no problems.
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please, someone, give me a hand. I don't understand thee fraction
representaions. (e.g. 3/2 G ? why ? etc)

however, I am in the most advanced class in math around :(


help, thanks

______
Boris Krivulin

"Today is gonna be the day,
That it gonna throw it back to you,
By now, you should have somehow,
Realize what you got to do..."

OASIS, Wonderwall


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>please, someone, give me a hand. I don't understand thee fraction
>representaions. (e.g. 3/2 G ? why ? etc)
>however, I am in the most advanced class in math around :(

Fortunately, the math involved isn't terribly complicated. Also 3/2
(same as 3:2) doesn't really necessarily imply a G. It does only in the
key of C.

This harkens back to the age-old, venerable, and still pretty much
accepted, observation attributed to Pythagoras, that our ears are
exceptionally sensitive to simple ratios of vibrational frequency. This is
the basis behind just intonation - tunings built around precise renderings
of these simple ratios, rather than approximations to them like our usual
tuning (12-Tone-per-octave Equal-Temperament, often abbreviated "12-equal",
"12TET", "12tET", or "12ET").

The simple ratio for an octave is 2:1, meaning that the vibrational
frequency of the higher note is twice the frequency of the lower one. The
ratio for the perfect fifth (G being a P5 above C), is 3:2. Here are some
others:

Perfect Fourth P4 4:3
Major Third M3 5:4
Minor Third m3 6:5
Major Sixth M6 5:3
Minor Sixth m6 8:5
Major Second M2 either 9:8 or 10:9, the difference between the two being a
"syntonic comma", or Paul R. would presumably call it a Just Syntonic Comma
or perhaps a 5-limit Just Syntonic Comma.
Major Seventh M7 15:8

And heading into nontraditional harmonies:
Septimal subminor third Septimal minor third 7:6
Septimal subminor seventh Septimal minor seventh 7:4
Neutral third 11:9 (11:9 is the most commonly-discussed neutral third, but
there are others.)
And there are many many others in this comparatively unexplored realm.



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