Download 6/26/06 Introduction We all have a mental/aural image of “music

6/26/06
Introduction
We all have a mental/aural image of “music.” But is the mental image the same for
everyone? Probably not. The idea of “what” music “is” is not the same around the
world. Different cultures divide aural space differently. Likewise, different cultures
have different conventions of musical practice.
In Western music, aural space is divided into 7 diatonic pitches. How did we arrive at the
fixed number of pitches in Western musical practice? We define pitches in the aural
continuum in terms of proportions—the relationships among pitches are mathematically
derived from Nature. The basis for Western tonal music is the natural division of the
monochord:
Remember the rope demonstration?
The rope represents a vibrating column of air, a string, or the monochord. When the
vibrating string of the monochord sounds at full wavelength, a tone is produced. This
sound is the fundamental. When the wavelength is progressively divided into 2, 3, etc.,
new tones are produced. Each new tone has a specific mathematical relationship
(proportion) to the fundamental. The proportions between wavelengths (and thus
frequencies) of tones produced by a single string are the same as those among pitches in
the diatonic scale, beginning on a pitch, arbitrarily chosen and named:
C
D
E
F
G
A
B
C (octave)
Like words in language, pitches’ names are arbitrary. Again, it is the relationships among
them that are fixed in a tonal system. On a piano keyboard, these note names correspond
to the white keys.
Notation
The treble clef is often called the “G” clef because it articulates the position of the note
G (the second line from the bottom of the staff). Its swirly shape is even derived from a
fancy letter “G.”
The bass clef, or “F” clef articulates the position of the tone F on the staff. It shows that
the pitch F is located on the second line from the top of the staff.
If we know where these pitches are in the given clef, the rest all fall into place. For
example, since the treble clef tells us that the pitch G is the second line from the bottom,
we know that the names of the pitches ascending (moving higher on the staff “stepwise”
to the space, line, space, line, etc.) are A, B, C, D, E, F, G (on top of the clef), etc.
Similarly, the notes below the original G are F, E, D (below the staff), etc.