f/
Basic
Waves
and
Harmonics-Shapi~g
th~
Timbre
Now
you
would
probably
like
to
know
how
you
ca~
determine the
shape
of a'
wa
?e (d
tim
b
re
)"i
n order
to
create the
kind
of sound
you
want.
Have
a look at the
diagram
on
the
lower
left first. It illustrates the
process
of eombining
two
sine
waves
to foup a saw-tooth
wave.
, B
is
the
basic
sine
,
wave
whjle
C
has
i
twice
the
fre
r
quency of B (it
is
thus one octave higher
in
pitch)
and
only half
its
amplitude (volume).
When
B
and
C
are
combined, the result
is
the
waveform
A.
A
is
still
not a perfect saw-tooth
wave,
b.ut
it
will
infinitely,
appr0ach
a perfect saw-tooth
shape
if
sine
waves
with
triple (3x), quadruple (4x), quintuple
(Sx)
etc. frequencies
are
added.
If,
on
the other hand, only
sine
waves
with
odd
numbered frequency multiples
are
added,
the
basic
sine
wave
will
gradually approach a square
wave.
In
this manner,
any
waveform
can
be
created
by
adding
a number
of-si
~e
waves
to
a
ba
sfo
sine
wave.
Waves
such
as
C
with
frequencies that
are
integral
multiples of
the
frequency of
the
-
ba
~
ic
wave
(in
our'
case
B)
are
called
harmonics.
In
other
words,
the
waveform
and
thus the timbre
are
determined
by
the
kind
of
harmonics
added to the
basic
sine
wave.
Put
differently, almost
all
sounds
with
their different timbres that
reach
our
ears
include a variety of different
harmonics,
and
it
is
these
harmonics
which
are
responsible for the
count-
less
characteristic timbres.
•
Music
and
noise
Saw,toqth wave
,.,
Harmonic
1J
,.,
, · '
components
t:
,.,
,.,
'·'
,.,
...
Harmonic
l:!
,.,
,~9111ponents
:::
,.,
,.,
I,
I •
- ,.
\:'
J
_J
' 7 +
lf
Jr
"
Sf
,,
71
81
' ' ' ' /,<. (I)
......
,,-'
*Graphs 'su'ch as the o·nes above which , show
the
har-
mon!c
components
of
a wave form are ~alled
"har-
·
monic spectr,ums~.
Depending
on
its
main
kind
of vibrations,
sound
is
divided
into "musical"
and
"noise".
Sounds
with
regular
vibrations
(i.e.
sounds
in
which
components other
than
harmonics
are
very
few)
are
considered
to
be
musical,
while
sounds
caused
by
complicated
irregular
vibrations
(i.e
.
sounds
with
many
compo-
nents that
are
not
harmonics)
whose
pitch
can
therefore not
be
measured
are
noise.
Most
of the sounds
used
in
music
are
of
course
musical
sounds,
but
various
kinds
of
noise
such
as
that
produced
by
percussion
instruments
are
also
used
to
highten
the
musical
effect.
•
Pure
Tones
Sounds
which
have
no
other components
such
as
harmonics
at
all
and
consist of only
one
simple
fre-
quency
are
called
pure
tone.
The
wave
form
of a
pure
tone
is
always
a perfect
sine
wave.
The
timbre
of a tuning
fork
or the telephone
time
tone
are
almost
pure
tones
(perfect
sine
waves),
but a
truly
pure
tone
does
not exist
in
the
natural
world.
Pure
tones, therefore,
can
only
be
created artificially
(e.g.
electronically).
Remember
)--------------------------------,
• Frequencies
which
are
integral
multiples of a
basic
wave
with
a certain frequency
are
called
har-
monics.
•
The
timbre
(waveform)
is
determined
by
the
harmonic
components.
-66-
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