The Twenty-First Century
2005 Rising World Entertainment
Three: The Overtone Series
German musicologist Wilfried Kruger discovered that the eight
electrons of the oxygen atom shell and the eight protons of the
nucleus of the oxygen atom generate a major scale with the spins
of the particles delineating the half tones and whole tones.
According to the work of the famous astronomer, Johannes Kepler,
certain proportions of the elliptical orbits of the planets
correspond beautifully to the simpler relationships naturally
found in the overtone series. These same harmonic relationships
are found not only throughout nature but also at the basis of
the most successful human constructs such as classical Greek
The Overtone Series
overtone series, also called the harmonic series, is a
naturally occurring phenomenon that reflects the inner laws of
creation and is the
very essence of music. It is a series of notes that looks like
first note in overtone series (the lowest one) is called the
fundamental. The remaining notes are the partials (also
called harmonics, or overtones).
this drawing, I assigned a low C note to the fundamental;
series can begin with any note, however. The next
note is another C, but this C is one octave higher than the
fundamental. Following that
is G, then another C that is two
octaves above the fundamental. Next in the series is E, then another G, a Bb,
a scale from C up to the next C with an F# and
two Bs: Bb and B natural, but these notes aren't tuned exactly
as they would be on a piano.
overtone series is the
audible example of natural law, the law of our solar system, and
the basis for the science of acoustics. Because it defines the very nature of sound,
it has always been the basis for all of our scales and chords.
- The overtone series is inherent
to the nature of the vibrating strings of musical
2 - The overtone series is the basis of sound that is produced by woodwind and brass
3 - The overtone series is what defines timbre.
A simple instrument
called a monochord, said to be invented by Pythagoras somewhere
around 550 BC, was used by theorists
for centuries to demonstrate the relationship
between string length and the notes produced by a vibrating string. The monochord is extremely simple in design. A string, such as a guitar or violin string,
is attached at both ends and pulled taunt over a resonating body
with a moveable bridge underneath. When the string
is plucked, it vibrates at a rate that is directly
proportional to the length of the string. However,
it simultaneously vibrates in particular proportional divisions of its length.
In other words, an additional vibration occurs at 1/2 the
length, another at 1/3 the length, another at 1/4, 1/5, 1/6, and so on: proportional distances. Each of these
vibrations produces a harmonic, or overtone that
has a frequency that is inversely proportional
(2x, 3x, 4x, 5x, 6x, etc.) to each division of
These are the members of the overtone
series, the partials, harmonics, or overtones. Starting at the fundamental, the loudness of each harmonic gets
softer and thus, the higher overtones are so soft that they are
difficult to hear. When we pluck the string, our ears hear the
resultant sound as a collection of the fundamental and
its overtones: this is what makes the sound of that particular
string different that, say, a pure sine wave that only contains
the fundamental. The
order, tuning, and volume of the overtones are what make the notes
played by, say, a brass instrument sound different
than those of, say, a flute, or a violin.
This is called timbre.
fundamental can be dampened out when the performer applies a light
pressure at one of the proportional locations on the string,
thus revealing the rest of the sound that was vibrating as part of
the pitch, and thus creating a sound at a higher frequency.
To get a sound an octave higher, the musician lightly touches the string at its
midpoint. This same light fingering can be applied
at 1/3, 1/4, etc. of the string length to create higher and
higher overtones. Simply pressing the string to the fingerboard at these positions
wouldn't create the same note, nor the same sound, as the
overtone, or harmonic (as it is usually called in this
This technique is called for in 20th century and late romantic
orchestral scores for strings and harp, and is also one of the
acoustic guitarist's favorite tricks.
On the monochord, or any string instrument, the fundamental
note is determined by the length of the string. For brass and
woodwind instruments, the pitch of the fundamental depends upon the
length of the tube that comprises the instrument itself. The player
overblows (by tightening the embouchure and blowing air
faster) to produce
overtones. Woodwind instruments have keys that open up holes in
the tube, thus changing its length, and hence, the note. Before valves
were invented (which mechanically
change the length
of the tube on brass instruments), trumpet, and horn players could only play
the lower overtones (and in the case of the clarion, or clarino
trumpets of Torelli, Perti, Cazzati, and the
composers at San Petronio in Bologna the full 'upper
scale'), and sometimes
the fundamental, so these brass parts
had to be written that way, playing simple chord notes.
Trombonists change the length of the tube by means of a slide.
A brass instrument with no valves, like the bugle and the post horn, can create only the notes of the harmonic series,
and that is why bugle and post horn melodies are use only the three
or four notes lower overtone notes.
ears tend to blend the fundamental and its overtones into a single
sound that we call pitch.
Rather than perceiving the many individual
harmonics of a musical tone, we perceive a tone color, or
timbre, with a pitch that is of the fundamental.
is the amplitude (loudness) and placement of the overtones that determines
what the timbre, or sound quality will be. For
example, clarinets sound only the odd
numbered overtones, creating notes that have a purer timbre
than those produced by a stringed or brass instrument. The strength
the brass instrument's
higher overtones makes the sound "brassy": a sound
that is rich, but slightly dissonant. Additionally, not all musical instruments have
that exactly match the pure harmonic partials. The piano's
overtones, for example are increasingly sharper than perfect
harmonics because stiffness of the metal strings.