Gtaylor@rtqe.net at 16:12, 6 July 2012

2012-07-06T16:12:05Z

Gtaylor@rtqe.net at 16:08, 6 July 2012

2012-07-06T16:08:14Z

Gtaylor@rtqe.net at 15:53, 28 June 2012

2012-06-28T15:53:32Z

Admin: Created page with "Click here to open the tutorial patch: 05sWaveshapingSynthesis.maxpat In this tutorial, we'll look at a latent (but very useful) attribute of samples, which is that they ..."

2012-06-25T16:51:07Z

Created page with "Click here to open the tutorial patch: 05sWaveshapingSynthesis.maxpat In this tutorial, we'll look at a latent (but very useful) attribute of samples, which is that they ..."

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Click here to open the tutorial patch: [[05sWaveshapingSynthesis.maxpat]]

In this tutorial, we'll look at a latent (but very useful)
attribute of samples, which is that they can be used as lookup
tables to transform the shape of other waveforms. This process
is called ''waveshaping'', and is used in synthesis to generate
complex spectra from a sinusoidal input. It's also the basic signal
processing technique behind many types of amplitude-dependent distortion,
and can be used to model the non-linearities of different kinds of
amplifier.

===Using a stored wavetable as a transfer function===

Take a look at the tutorial patcher. The basic sound-generating
circuit in the upper-left of the patcher should look familiar, with
one new object ({{maxword|name=lookup~}}) inserted into the chain. We have
a {{maxword|name=cycle~}} object going through an amplifier ({{maxword|name=*~}}) to
the {{maxword|name=ezdac~}}.

* Turn on the {{maxword|name=ezdac~}} object and adjust the {{maxword|name=number}} box
labeled <code>amplitude</code>. You should hear a sine wave at <code>220</code> Hz.

The new object in this signal chain at first seems to be doing
nothing, and in terms of what we hear, it isn't... yet.
The {{maxword|name=lookup~}} object interprets a piece of sample memory
stored in a {{maxword|name=buffer~}} object as a ''transfer function'',
with the beginning of the sample used representing input values
of <code>-1</code> and the end of the sample used representing values
of <code>1.</code> Incoming values are scaled across this ''X'' axis,
and the resulting audio comes from the corresponding values along
the ''Y'' axis.

In our patch, the {{maxword|name=buffer~}} named <code>waveform</code> is serving as
a ''lookup table'' (or transfer function) for the incoming sine
wave. When the {{maxword|name=cycle~}} object generates a <code>-1</code>, for
example, ''whatever sample value'' is at the beginning of
the {{maxword|name=buffer~}} comes out of the {{maxword|name=lookup~}} object. When
our {{maxword|name=cycle~}} hits <code>1</code>, the {{maxword|name=lookup~}} object reads
from the end of the {{maxword|name=buffer~}} to find its outgoing sample.

* Double-click the {{maxword|name=buffer~}} object at the bottom of the tutorial
patcher. Notice that the waveform loaded in is a simple ramp. Because
our waveshape (the sample in the {{maxword|name=buffer~}} is a linear ramp with
the beginning of the sample at <code>-1</code> and the end at <code>1</code>,
our {{maxword|name=cycle~}} object sounds unchanged.

The {{maxword|name=lookup~}} object takes three possible arguments: the first
is the name of the {{maxword|name=buffer~}} to use as its waveshape; the second
and third are the start and end points (in ''samples'' to use
within the {{maxword|name=buffer~}} as the boundaries of the transfer function.
Because we want our {{maxword|name=buffer~}} to be exactly <code>512</code> samples
long in our patcher, we created it with the argument of <code>10.66667</code>
milliseconds. How did we get this number. At the right of the patcher,
you can see the {{maxword|name=sampstoms~}} object, which allows us to convert
from samples to milliseconds.

===The waveform~ object===

Look at the graphical object at the top of the tutorial patcher.
Notice that it contains the same shape that is loaded into our {{maxword|name=buffer~}}.
The {{maxword|name=waveform~}} object allows us to view, select regions of, and
directly modify the contents of a {{maxword|name=buffer~}} with a drawing tool.

* Using your mouse, doodle in the {{maxword|name=waveform~}} object's display.
Notice how different shapes affect the output sound. Try drawing
smooth curves, then jagged ones, then ones with lots of plateaus
(straight horizontal lines). Notice that even slight variations
in the shape have tremendous impact on the spectrum generated by
the {{maxword|name=lookup~}} object.

The {{maxword|name=waveform~}} object is operating in <code>draw</code> mode, where
you can literally modify a sample loaded into a {{maxword|name=buffer~}} with
your mouse. Other modes allow you to select regions, the boundaries
of which can be used as Max messages for other objects.

===Setting sample values with Max messages: peek~===

* Click on the {{maxword|name=button}} labeled <code>A</code> in the tutorial patcher.
Our waveshape (and our sound) should return to normal.

The way we got the default waveshape in our tutorial patcher is through
the logic controlled by the {{maxword|name=uzi}} below the {{maxword|name=button}}
labeled <code>A</code>. The {{maxword|name=uzi}} object, you may recall, generates a
lot of data instantly depending on its argument... the right outlet
of the object generates a numeric ramp from <code>1</code> to its argument.
We've subtracted <code>1</code> from that value to generate a stream of Max
numbers from <code>0</code> to <code>511</code> when you click the {{maxword|name=button}}.
These numbers are then sent to the middle and left inlets of a {{maxword|name=peek~}} object...
the left inlet receives the numbers unchanged; the middle inlet
receives them after they have been scaled into the range of <code>-1</code>
to <code>1</code> (via the {{maxword|name=scale}} object).

The {{maxword|name=peek~}} object allows us to manually set the sample values within
a {{maxword|name=buffer~}} via Max messages. The left inlet (which is "hot",
and actually performs the operation) sets ''which'' sample we're
changing; the middle inlet sets the value to change that sample to.
In our case, the {{maxword|name=uzi}} object generates a stream of numbers
that our entire {{maxword|name=buffer~}} to an ascending ramp, e.g.

Sample Value

0 -1.

1 -0.996086

2 -0.992172

3 -0.988258

4 -0.984344

5 -0.980431

...

508 0.988258

509 0.992172

510 0.996086

511 1.

===For the math geeks in the room===

* Click on the other {{maxword|name=button}} objects in the patcher
(labeled <code>B</code>, <code>C</code>, and <code>D</code>). Notice how the
waveshape in the {{maxword|name=buffer~}} changes, and note how it affects
the sound. Each waveshape seems to ''multiply'' the frequency
of the sound generated by the {{maxword|name=cycle~}} object. The logic
at <code>B</code> makes our <code>220</code> Hz wave sound at <code>440</code>,
<code>C</code> at <code>660</code>, and <code>D</code> at <code>880</code>.

The equations that the {{maxword|name=expr}} objects are doing in these parts
of the patch generate special types of transfer functions
called ''Chebyshev polynomials''. These functions are interesting
in that they have the ability to transform sinusoidal input to
different harmonic multiples. The four Chebyshev polynomials in our
tutorial are:

y = x ({{maxword|name=uzi}} object <code>A</code>, leaves the input unchanged)

y = 2*x^2-1 ({{maxword|name=uzi}} object <code>B</code>, doubles the frequency)

y = 4*x^3-3*x ({{maxword|name=uzi}} object <code>C</code>, triples the frequency)

y = 8*x^4-8*x^3+1 ({{maxword|name=uzi}} object <code>D</code>, quadruples the frequency)

In practice, what they do looks like this:

[[Image:Samplingchapter05a.png|border]]
''Our four Chebyshev polynomials and their effect on a cosine input''

* Click on the <code>read</code> messages in patcher area <code>E</code>. These will
load 512-sample audio files into our waveshape {{maxword|name=buffer~}}. Notice
their effect on the sound:

[[Image:Samplingchapter05b.png|border]]
''Waveshaping through gtr512.aiff and blp512.aiff, respectively.''

* Now that you know a bit more about the expected behavior of the
waveshaping distortion, return to drawing in the {{maxword|name=waveform~}} object
to see what kind of results you can achieve.

===Summary===

The {{maxword|name=lookup~}} object allows you to use a {{maxword|name=buffer~}} as a
transfer function to perform a process called ''waveshaping''
on an input sound. Different shapes cause different distortions
of the spectra and can create very complex timbres. The {{maxword|name=waveform~}}
object allows you to directly view and modify the contents of an
MSP {{maxword|name=buffer~}} using your mouse, and the {{maxword|name=peek~}} object
allows you to set sample values programmatically with Max messages.
Some transfer functions (such as Chebyshev polynomials) have special
properties when used as a waveshaping function on a sinusoidal input.

===See Also===

{{maxword|name=lookup~}} - Transfer function lookup table

{{maxword|name=waveform~}} - buffer~ viewer and editor

{{maxword|name=peek~}} - Read and write sample values

{{maxword|name=sampstoms}} - Convert time from samples to milliseconds

[[Category:Teaching Material]]

← Older revision		Revision as of 16:12, 6 July 2012
Line 1:		Line 1:
−	Click here to open the tutorial patch: [[Media:05sWaveshapingSynth.zip]]	+	Click here to open the tutorial patch and files: [[Media:05sWaveshapingSynth.zip]]

	In this tutorial, we'll look at a latent (but very useful) attribute of samples, which is that they can be used as lookup tables to transform the shape of other waveforms. This process is called ''waveshaping'', and is used in synthesis to generate complex spectra from a sinusoidal input. It's also the basic signal processing technique behind many types of amplitude-dependent distortion, and can be used to model the non-linearities of different kinds of amplifier.		In this tutorial, we'll look at a latent (but very useful) attribute of samples, which is that they can be used as lookup tables to transform the shape of other waveforms. This process is called ''waveshaping'', and is used in synthesis to generate complex spectra from a sinusoidal input. It's also the basic signal processing technique behind many types of amplitude-dependent distortion, and can be used to model the non-linearities of different kinds of amplifier.

← Older revision		Revision as of 16:08, 6 July 2012
Line 1:		Line 1:
−	Click here to open the tutorial patch: [[Media:~~05sWaveshapingSynthesis~~.~~maxpat~~]]	+	Click here to open the tutorial patch: [[Media:05sWaveshapingSynth.zip]]

	In this tutorial, we'll look at a latent (but very useful) attribute of samples, which is that they can be used as lookup tables to transform the shape of other waveforms. This process is called ''waveshaping'', and is used in synthesis to generate complex spectra from a sinusoidal input. It's also the basic signal processing technique behind many types of amplitude-dependent distortion, and can be used to model the non-linearities of different kinds of amplifier.		In this tutorial, we'll look at a latent (but very useful) attribute of samples, which is that they can be used as lookup tables to transform the shape of other waveforms. This process is called ''waveshaping'', and is used in synthesis to generate complex spectra from a sinusoidal input. It's also the basic signal processing technique behind many types of amplitude-dependent distortion, and can be used to model the non-linearities of different kinds of amplifier.

MSP Sampling Tutorial 5: Waveshaping - Revision history

Gtaylor@rtqe.net at 16:12, 6 July 2012

Gtaylor@rtqe.net at 16:08, 6 July 2012

Gtaylor@rtqe.net at 15:53, 28 June 2012

Admin: Created page with "Click here to open the tutorial patch: 05sWaveshapingSynthesis.maxpat In this tutorial, we'll look at a latent (but very useful) attribute of samples, which is that they ..."