tlhIngan-Hol Archive: Fri Jun 10 12:04:48 1994

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Re: solfeggio (was Re: Bad To The Bone)

According to James Jones:
.. 
> Anyone out there familiar with temperaments know whether nine or twenty-
> seven is a particularly useful number of pieces to chop the "octave" up
> into?
> 
> 	James Jones
> 
> No organization with which I'm associated has any opinion on Guido d'Arezzo,
> as far as I know.

Either would produce what humans would consider very dissonant
tones, since it would include intervals very near, but not
quite fourths and fifths, which occur naturally as overtones of
any fundamental tone (fundamental, then an octave higher, then
a fifth higher, then a fourth higher... this is the progression
you get when you first play a string at full length, then hold
it still in the middle so it vibrates as two equal strings half
as long, then three equal lengths, then four...).

When intervals approach this near to being natural overtones,
but miss slightly, you get "beats", the kind of warbling you
probably know most in the sound of a piano that badly needs
tuning.

Hmm. Thinking on it more, it becomes obvious that a lot of
arbitrary decisions need to be made about the math of the
music. For example, we divide an octave into THIRTEEN distinct
tones, with one of them being a "duplicate" of the first.
Twelve unique tones from C to B.

If we decided that Klingons used octaves at all, and split
things up like we do, using nine tones the way we use twelve,
you'd get a scale like: C, something sharper than C#, something
flatter than D#, E, Something flatter than F#, something
flatter than G#, A, Something sharper than A#, and then you'd
be ready to repeat the C.

On the other hand, it might be more logical to conclude that
Klingons might build their structure around dividing a string's
lenth into three parts instead of two, so instead of an octave,
the unit of repetition would be our octave and an additional
fifth: From C to the next C and on to the next G.

This would make the fingering of a clarinet very natural for a
Klingon, since, unlike other wind instruments which tend to
repeat (with minor variations) their fingering once you cross
an octave boundary, the clarinet does this at an octave and a
fifth. It acts like a closed tube instead of an open tube, and
overblowing to every second overtone instead of to every
overtone is a trait of a closed tube.

Consider also that an octave and a fifth is only slightly wider
than an average untrained singing voice (typically an octave
and a third; whereas an average trained voice can achieve about
two octaves), this would mean that an average song could have
unique note names for every tone in the singing range without
repeating names at the high and low end of the scale.

And we could do all of this without retuning any of our
instruments...

charghwI'
-- 
muneH "Paramount", 'ach wej Sov chaH

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