Overtones, harmonics and Additive synthesis


Uploaded by SynthSchool on 30.03.2010

Transcript:
this is a sine wave
a sine wave is the basic building block of sound
any sound can be constructed by combining several sine waves in
different frequencies
the sine wave gets its name from the sinusoid function which describes a
circle in two dimentions
since sound only exists on one dimension -
the time dimension, the graph cannot go back on itself to create a real
circle
so basically a sine wave is audio's circle
just as you can create a complete drawing from small dots
you can also create any sound conceivable by mixing together several
sine oscillators
let's listen to the sine oscillator
the graph you're looking at is an oscilloscope
the y_ axis represents the amplitude
this is the zero point this is
the maximum and this is the minimum
and the x-axis represents time
the y_ axis that's exactly as your speaker would
when the graph is on top
their speaker is pushed forward towards you
when it's down
the speaker is pulled away from you
when it's on zero the new speakers driver is centered on an ideal state
when i play high notes
more wave cycles are compressed into the view
this is because high frequencies are shorter an our graph has a set time
window
if we play low notes,we can see that there are less cycles in our view
this is because there are slower and they take more time to evolve let's
look at the sine in our frequency analyzer
as you can see the sine only has one peak
and has no frequency content on any sides of the spectrum
this is why a wine wave is often referred as a pure tone as it is the
only sound that consists of a single basic frequency
this basic frequency is called the fundamental frequency
if we look at other wave shapes such as the saw or square
now we're looking at a saw wave on an oscilloscope
if we look at the frequency analysis of the sound
we can see that it
has many spikes
those spikes are extra high frequencies that construct the sound's timber
these also called overtones
overtones construct each sound that we hear each day
overtones can be harmonic
or non harmonic
non harmonic overtones result in noise or sounds with ambiguous pitch
while harmonic overtones
support the fundamental frequency
and keep its tonality intact so as you can already guesse
we can make a saw oscillator out of many sine oscilltors
the lowest frequency of the sound is the basis
on which the sound is built and is called the fundamental frequency the
rest of the spikes here are called overtones
harmonic overtones will always be the fundamental frequency multiplied
by a whole number
let's take for example the note A 110hz
it as a fundamental frequency of one hundred and ten hertz
and its first harmonic is it's fundamental frequency
one hundred and ten hertz
its second harmonic would be
the frequency times two which means 220Hz
the third one will be 330Hz
times four
times five
and so on
the idea behind the system
is to keep our wave cycle repetitive and the only way to do that
is to have the overtones
start
and finish it at the same phase over the fundamental frequency
as you can see here and we have a green blue we have small sine waves here
that
represent the harmonics of the sound
the first harmonic would be the fundamental frequency the second
harmonic has two cycles per one cycle of the
fundamental frequency
and because of that it starts
and it's ends and the same point
and it's the same with the third harmonic which has three cycles per one
or here we have four cycles per one and it actually follow it it's pretty
accurate
and so on to infinity
let's listen to those harmonics
does it sound musically familiar
of course it does this is the building block of all music
it occurs naturally in nature
and it exists in all human music
personality for me it sounds like an indian flute indian flute or something like this
let's see how a saw is constructed from many sine oscillators by adding them
one by one
let's start with the fundamental frequency
and now we add the second harmonic
third harmonic, as you can see there are
three slides here
and its starting to resemble a saw shape
we are going to add this harmonic here
and i could go on forever but but my cpu does not have enough horse power
and sixteen is enough too demonstrate the idea
this saw wave has all of the harmonics but not all waves have to have all of the harmonics
for instance the square
does not have any even harmonics
it skips the two four six
and so on
of the harmonics adding only the odd harmonics
so, one is the odd harmonic
as you can see two,
we're not mixing inside
we're skipping it
str8 to twtree
and voilla it starts to look like a square
we skip the fourth harmonic,
fifth we add in
we skip the sixth
we add the seventh and so on...
let's look at the same thing on the frequency analyzer
here is a saw wave
this is our fundamental frequency and now we're going to add the overtones
let's look at our square wave
the first one
the second one we skip
third, fifth, seventhи
let's look at the relations between frequencies
i have selected to 220hz as my fundamental frequency
and my next overtone will be an octave higher,
the fundamental frequency times two
thats 440hz
the next overtone will be
a fifth higher than the second overtone
or and octave and a fifth higher than the fundamental
the fourth one will be two octaves higher than the fundamental
and a perfect fourth higher than the previous overtone
and as you can see, as i go up the overtones
the interval
with the previous overtones gets smaller and smaller and smaller
as i go up it reaches microtones
the recipe for making a classic saw oscillator is having heath overtone's
amplitude divided by its harmonic count.
so for instance
the first overtone would be on maximum volume
the second one
would be half the volume
third one, would be thirthd the volume you can see it here also
and so on
so theoretically a saw wave should have infinite overtones
that's it for this lesson i hope you got a little bit wiser if you want to
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