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Scale ramblings.
The harmonic series (1:2:3:4:5:6:7:8 etc.) does occur in nature and is
often cited as the naturalist explanation for numerous music-theoretical
constructions (scales, triads, intervals, harmonic-progressions etc.) The
naturalist explanation of the "major pentatonic" goes as follows: The
perfect 5th (the frequency ratio produced by notes C G) is the first
instance of a "pure" two-note relationship that can be derived from the
harmonic series (the 2:3 ratio). The pentatonic scale CDEGA is produced
by projecting this ratio above C four times and then transposing the
resulting pitches down by octave until they all fit within the octave
occupied by C - G. The minor pentatonic (ACDEG) cannot be produced be
produced in this manner. It is merely an artifact of rotation, putting the
A (the 5th step) below the C (the 1st step) in the above "naturalistic"
example. In the end, interval-projection theories and the rotational
theories are after-the-fact "constructions" of theorists who are attempting
to explain the subjective process that began way back in history when the
"minor pentatonic" first made its appearance on the world's stage as the
result of someone experimenting with pleasant sounds. Nelson you are sooo
right. You need a flute to make the scale. Build the flute. Allow a
flute-playing culture to emerge that finds those sounds to be interesting,
and I'll guarantee that in a few hundred years someone will claim that the
scale it plays is derived form and explained by chaos theory or the
Mandelbrot set!
On half steps:
My theory....the 2:3 ratio in the harmonic spectrum produces axial tones
(RE RO), and whether you're playing In-sempo, Major, or melodic minor,
you'll find that the half steps are used as auxiliary embellishments to
these tones, and that there will be subjective differences in the
performance practices of expert players (Western or Eastern) as to how they
should be "tuned" --- meaning that no systematic method of temperament
accounts for the frequencies that actually occur in practice. The musical
"stream" (ryu), the culture, and its interpretation of the musical context,
more than anything else, accounts for how half-steps, quarter-steps, meri,
or keri, are "tuned".
Dan
Shakuhachi Links by Category -
http://www.wm.edu/CAS/music/gutwein/Shakuhachi/links.htm
Zen Flute for Beginners -
http://www.wm.edu/CAS/music/gutwein/Shakuhachi/WMshakuhachi.htm
My home page - http://www.wm.edu/CAS/music/Gutwein/
Family page - http://pages.prodigy.net/dfgutw/family/
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: Mon Feb 03 2003 - 09:09:52 PST
Scale ramblings.<br><br>
The harmonic series (1:2:3:4:5:6:7:8 etc.) does occur in nature and is
often cited as the naturalist explanation for numerous music-theoretical
constructions (scales, triads, intervals, harmonic-progressions etc.) The
naturalist explanation of the "major pentatonic" goes as
follows: The perfect 5th (the frequency ratio produced by notes C
G) is the first instance of a "pure" two-note relationship that
can be derived from the harmonic series (the 2:3 ratio). The
pentatonic scale CDEGA is produced by projecting this ratio above C four
times and then transposing the resulting pitches down by octave until
they all fit within the octave occupied by C - G. The minor
pentatonic (ACDEG) cannot be produced be produced in this manner.
It is merely an artifact of rotation, putting the A (the 5th step) below
the C (the 1st step) in the above "naturalistic" example.
In the end, interval-projection theories and the rotational
theories are after-the-fact "constructions" of theorists who
are attempting to explain the subjective process that began way back in
history when the "minor pentatonic" first made its appearance
on the world's stage as the result of someone experimenting with pleasant
sounds. Nelson you are sooo right. You need a flute to make
the scale. Build the flute. Allow a flute-playing culture to emerge
that finds those sounds to be interesting, and I'll guarantee that in a
few hundred years someone will claim that the scale it plays is derived
form and explained by chaos theory or the Mandelbrot set!<br><br>
On half steps:<br>
My theory....the 2:3 ratio in the harmonic spectrum produces axial tones
(RE RO), and whether you're playing In-sempo, Major, or melodic minor,
you'll find that the half steps are used as auxiliary embellishments to
these tones, and that there will be subjective differences in the
performance practices of expert players (Western or Eastern) as to how
they should be "tuned" --- meaning that no systematic method of
temperament accounts for the frequencies that actually occur in
practice. The musical "stream" (ryu), the culture, and
its interpretation of the musical context, more than anything else,
accounts for how half-steps, quarter-steps, meri, or keri, are
"tuned".<br><br>
<x-sigsep><p></x-sigsep>
<i>Dan <br>
<font face=3D"Times New Roman, Times">Shakuhachi Links by Category</i> -
<a href=3D"http://www.wm.edu/CAS/music/gutwein/Shakuhachi/links.htm"=
eudora=3D"autourl">http://www.wm.edu/CAS/music/gutwein/Shakuhachi/links.htm=
</a></font><font face=3D"Times New Roman, Times" size=3D2><b><i>
<br>
Zen Flute for Beginners</b> - </i></font><a=
href=3D"http://www.wm.edu/CAS/music/gutwein/Shakuhachi/WMshakuhachi.htm"=
eudora=3D"autourl"><font face=3D"Times New Roman,=
Times">http://www.wm.edu/CAS/music/gutwein/Shakuhachi/WMshakuhachi.htm><=
br>
<i>My home page </i>- <a href=3D"http://www.wm.edu/CAS/music/Gutwein/"=
eudora=3D"autourl">http://www.wm.edu/CAS/music/Gutwein/></font> <br>
<font face=3D"Times New Roman, Times"><i>Family page - <a=
href=3D"http://pages.prodigy.net/dfgutw/family/"=
eudora=3D"autourl">http://pages.prodigy.net/dfgutw/family/></i></font>=
<br><br>
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