Casio CZ-5000 - Basic Waves and Harmonics

‘/
Basic
Waves
and
Harmonics—Shaping
the
Timbre
Ses
lc
ine
ac
ae
eae
tals
=
ilk
elas
dceshis
Now
you
would
probably
like
to
know
how
you
can
determine
the
shape
of
a
wave
(=
timbre)
in
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
combining
two
sine
waves
to
form
a
saw-tooth
wave.
B
is
the
basic
sine
wave
while
C
has
twice
the
fre-
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,
but
it
will
infinitely
approach
a
perfect
saw-tooth
shape
if
sine
waves
with
triple
(3x),
quadrupie
(4x},
quintuple
(5x)
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
sine
waves
to
a
basic
sine
wave.
Waves
such
as
C
with
frequencies
that
are
integral
multiples
of
the
frequency
of
the
basic
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.
A=B
mC
@
Saw-tooth
wave
PA Are Harmonic
components
lal=ibl— ic]
\ A | | | | | Harmonic
components >
*Graphs such as the ones above which show the har-
monic components of a wave form are calied ‘har-
monic spectrums”.
conrnocuvcoca -
“NW yma m oo
IN\
oOoooaoOoOaGn -
“NW kU wee
@ Music and nojse
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.
oN
_«
*
rae
SS
Besides
importa
it is the
in time
increase
mines ti
Out dec.
time ar
envelop
Envelor
Volume
|
4
ae
ar)
(z)
|
Koes
¢)
aan)
When
have h
too co;
Analog
sound
e VC
THis. :¢:
to crea
e VC
This c
by the