Sine
wave
This
is a sound wave with a single frequency. It produces a pure tone
- a tone without harmonics or overtones.
Here's
a Simple Sine Wave:
If a single
wave repeats or oscillates 100 times in a second then the wave has a frequency
of 100 Hertz. The maximum height the wave reaches above and below
zero
is
referred to as the amplitude of the waveform - how loud it
is.
So,
a Sine tone has only the fundamental frequency with no other harmonics.
When you combine two or more Sine tones you get a Complex
tone:
Nearly
all Music consists of Complex
tones
Do
you play the Recorder?
A descant
recorder has a pure quality to its sound and produces notes that are almost
pure tones. It was replaced by the flute in the orchestra mainly because
it was not loud enough.
Why
do Choral Conductors use a tuning fork?
It produces
a pure tone or a sine tone with no harmonics. It is often used to
give a clear pitch to a Choral Conductor because there is no other
'echo' getting in the way of the required note.
Harmonics...
... are
integer multiples (1, 2, 3, 4 etc) of a fundamental note. These
are the overtones we hear when low C (C2) is played.
The
timbre or tone colour of a sound depends on the relative loudness
at any point in time of a series of harmonics, all of which can be thought
of as sine waves. Thus any single sound is essentially a kind of chord
formed from harmonics. The ear integrates the information as a single
'note'.
Odd
harmonics...
...are
the 3rd, 5th, 7th, 9th etc harmonic above a fundamental pitch.
Square
waves
The
Clarinet is a closed pipe and produces odd harmonics only. The sound
waves from a clarinet are Square waves. Here's a diagram of a Square wave:
The fundamental
frequency or pitch is shown at number 1. Numbers 1, 2, 3......9 are
its harmonics. Notice that only the odd harmonics seem to be involved here
and that
the
amplitudes are in inverse proportion to them.
You
can actually see it changing from a Sine wave pattern to a Square wave
pattern
in
the following diagram where the red lines are numbered 1, 3, 5, 7, 9 and
the scale of the vertical line is in fractions of 1:
So,
a Square wave is composed of only odd-numbered harmonics with amplitudes
in the ratio 1/n (f, 3f, 5f, 7f.......with amplitudes of 1, 1/3,
1/5, 1/7........ )
Even
harmonics...
...are
the 2nd, 4th, 6th, 8th etc harmonic above a fundamental pitch.
Sawtooth
waves
An Oboe
looks a bit like a Clarinet and also has a reed in its mouthpiece.
However, it is an open pipe and produces both odd and even harmonics. Sawtooth
waves give a richer sound. Here's a diagram of a Sawtooth wave:
You
can see it changing from a Sine wave into a Sawtooth wave in the following
diagram where the red lines are numbered 1, 2, 3, .... 20 and the
vertical scale is in fractions of 1. The sound is richer than a Square
wave sound because all the harmonics are involved here:
So,
a Sawtooth wave has both odd-numbered and even-numbered harmonics with
amplitudes in the ratio 1/n (f, 2f, 3f, 4f... with amplitudes
of 1, 1/2, 1/3, 1/4...)
What
about a Triangle wave?
It has
odd harmonics with amplitudes in the ratio 1/n² (f, 3f, 5f,
7f......with amplitudes or loudness of 1, 1/9, 1/25, 1/49,
1/81........)
And
a Pulse wave?
It seems
to have a constantly repeating peak of amplitude.
Any
repeating wave... wave... wave..., no matter how complicated, is made up
of simple sine waves.
Frequency...
...
is related to pitch. The number of times a wave repeats per second is described
as its frequency. The note A below middle C
has a frequency of 220 Hertz. The complete waveshape
recurs 220 times each second. The A above middle
C (used by orchestras when tuning up) has a frequency of 440Hz -
its waveshape completes 440 cycles a second.
And guess the frequency of the next A above that? 880Hz... And the
next A..?
Lower
frequencies result in lower pitches, and higher
frequencies in higher pitches. Bigger instruments
have deeper sounds.
Conclusion:
Timbre mainly depends on harmonic structure.
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