[geocentrism] Re: For Martin
- From: "Martin G. Selbrede" <mselbrede@xxxxxxxxxxxxx>
- To: geocentrism@xxxxxxxxxxxxx
- Date: Wed, 19 Sep 2007 18:31:58 -0500
Jack,
I think you mean a 6-line staff, versus the traditional 5-line
staff. Multiple staves are traditional on orchestral scores (one per
instrument) and aren't unusual.
The white keys on the piano represent the unmodified pitches that
would appear on a staff. There are seven per octave, coming full
around to the original pitch (at double the frequency) on the eighth
note (hence "octave"). When you add in the five black keys, seven
plus five provides twelve different pitches, repeating at the 13th.
The black notes are notated with special symbols in front of a
regular unmodified pitch. The unmodified pitches are called
"naturals" while adjustments up are prefixed with a sharp symbol and
adjustments down with a flat symbol. In any event, a full octave can
be written using a staff with only four lines (e.g., treble clef, the
D above middle c to the D one octave higher -- the lower note sits in
the space below the first staff line, the final note -- the 13th --
is the D sitting directly on the fourth line).
The so-called "grand staff" upon which most piano music is written is
the combination of two staffs, the bottom one using bass clef, the
top one using the treble clef. There is a virtual line between the
two (upon which middle C in both staffs is shared), so technically
the grand staff is an 11-line staff, with the middle line being
hidden and only revealed by use of individual leger lines (to reveal
the presence of the virtual line between bass and treble). Leger
lines are used to extend the staff up or down as needed. Excessive
use of leger lines is obviated by use of shorthand markings, such as
8va or 15ma, which, depending on position, indicates the notes are to
be played one or two octaves either higher or lower than notated.
Notation has evolved over time. Four clefs are in common use. The
clefs specify the identity of a specific note on the staff it rests
on. The treble clef is the G clef, showing that G falls on the second
line from the bottom. The bass clef is the F clef, specifying that F
falls on the fourth line of the staff. The alto clef is one of the
so-called C clefs that positions C on a specific line -- in this
case, on the middle line of the staff. Violas use this clef almost
exclusively. The tenor clef is also a C clef, but it positions C on
the fourth line. Cellos, trombones, and bassoons occasionally use
this clef for passages that lie high on the instrument. The appeal of
switching to another clef is in avoiding the need to write lots of
leger lines (which can be hard to read -- music notation is an
intensely practical concern: the easier to read, the easier to play).
Practical considerations show that the human eye can instantly
identify a pitch on a 5-line staff. When you increase the number of
lines, the eye gets lost in the graphical context and can misjudge
the pitch. So the need was to (1) make it readable as is, (2)
providing a suitably large range of notes while (3) minimizing leger
lines where possible (which can also be hard to read in excess).
Martin
On Sep 19, 2007, at 6:02 PM, Jack Lewis wrote:
Dear Steven and Martin,
I have always been puzzled why music wasn't written on 6 staves
since there are 12 notes. Could it be that music has evolved from
the simple tones to the more complex? If 6 staves were used would
it not make playing different keys easier?
Jack
----- Original Message -----
From: Martin G. Selbrede
To: geocentrism@xxxxxxxxxxxxx
Sent: Wednesday, September 19, 2007 9:28 PM
Subject: [geocentrism] Re: For Martin
Dear Steven,
Well, I can say that my piano has drifted off of Western equal
temperament, so compositions for it that I wrote using Western
tonality have jumped the track into the world of microtonality. I
do plan, however, to remedy this with a nice tuning. The biggest
barrier to moving toward, say, the 17-degree scale is I'm not
sufficiently motivated to learn Sanskrit.
However (in the interest of full disclosure), my Opus 16 (which
was, in fact, performed publicly) did include a brief section that
would have made Penderecki proud. I was aware of his works,
particularly Threnody for the Victims of Hiroshima, and so in my
composition the string orchestra indulges in such non-Western
dissonance for nearly a full minute (this occurring in a piece that
lasts about 38 minutes in concert performance). And that's about
it, folks.
I could have sworn that I had mentioned to you the research
conducted by Ernest Ansermet about the geometry of the cochlear
spiral in the inner ear -- that its curvature is based on the log
of 12. Ansermet's conclusion was that the human ear naturally
divides an octave into twelve parts. Since the cochlear spirals of
other mammals are curved differently, such creatures may discern
such music as alien gibberish. If one were to truly test animals
for musical aptitude, the scale should be subdivided based on a
specific animal's cochlear spiral geometry and music then created
within that customized tonal architecture. If the animal responds
to that, and not to music based on other scale divisions, we'd have
some empirical support for Ansermet's theory that would be nearly
unassailable.
Martin
On Sep 19, 2007, at 3:08 PM, Steven Jones wrote:
Dear Martin,
just wondering if you're interested in other tonalities besides
western and whether you've ever explored any of them in your own
compositions?
--
Using Opera's revolutionary e-mail client: http://www.opera.com/mail/
--------
Martin G. Selbrede
Chief Scientist
Uni-Pixel Displays, Inc.
8708 Technology Forest Place, Suite 100
The Woodlands, TX 77381
281-825-4500 main line (281) 825-4507 direct line (281) 825-4599
fax (512) 422-4919 cell
mselbrede@xxxxxxxxxxxxx / martin.selbrede@xxxxxxxxxxxx
--------
Martin G. Selbrede
Chief Scientist
Uni-Pixel Displays, Inc.
8708 Technology Forest Place, Suite 100
The Woodlands, TX 77381
281-825-4500 main line (281) 825-4507 direct line (281) 825-4599
fax (512) 422-4919 cell
mselbrede@xxxxxxxxxxxxx / martin.selbrede@xxxxxxxxxxxx
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