MSP Filter Tutorial 3: Analog-Style Synthesis - Revision history

Gtaylor@rtqe.net at 15:31, 28 June 2012

2012-06-28T15:31:35Z

Admin: /* The many aliases of digital oscillators */

2012-06-25T21:18:38Z

‎The many aliases of digital oscillators

Admin at 21:16, 25 June 2012

2012-06-25T21:16:03Z

Show changes

Admin: /* {{maxword|name=scope~}}ing things out */

2012-06-25T20:42:46Z

‎{{maxword|name=scope~}}ing things out

Admin: /* Waveforms */

2012-06-25T20:40:30Z

‎Waveforms

Admin at 21:32, 22 June 2012

2012-06-22T21:32:50Z

Admin: Created page with "Click here to open the tutorial patch: 03fAnalogStyleSynthesis.maxpat Now that we are familiar with some basic types of filters, we can think about different sounds to us..."

2012-06-22T21:26:43Z

Created page with "Click here to open the tutorial patch: 03fAnalogStyleSynthesis.maxpat Now that we are familiar with some basic types of filters, we can think about different sounds to us..."

New page

Click here to open the tutorial patch: [[03fAnalogStyleSynthesis.maxpat]]

Now that we are familiar with some basic types of filters, we can think about
different sounds to use with them. Most of the synthesis work we've looked at thus
far has involved working with sinusoidal oscillators (the {{maxword|name=cycle~}}) object,
creating complex spectra through different types of modulation synthesis (e.g. FM)
or waveshaping. MSP has a number of oscillators that create more complex sounds
on their own, and they are quite useful for creating richer sounds that can be shaped
by filters. We'll introduce these oscillators here. briefly looking at a couple of
objects that allow you to plot signal data along the way.

===Waveforms===

Look at the tutorial patcher. It consists of a {{maxword|name=kslider}} object
controlling the frequencies of four different MSP objects: {{maxword|name=cycle~}},
{{maxword|name=tri~}}, {{maxword|name=saw~}}, and {{maxword|name=rect~}}. These oscillators each have their
own volume control (a {{maxword|name=*~}} object) that feeds them through a
{{maxword|name=lores~}} object to the {{maxword|name=dac~}} and to a pair of graphical objects at the
bottom. Some additional logic in the patcher exposes some other features of these
oscillators.

* Turn on the audio in the patcher by clicking on the {{maxword|name=ezdac~}} object and pick a note on the
{{maxword|name=kslider}}. One-by-one, turn up and listen to the different oscillators by
adjusting the <link type="refpage" name="number">number box</link> objects below each one. Listen to the sound, and look
at the images that appear in the objects at the bottom of the patcher.

Our tutorial features four oscillators that are commonly used in analog
sound generation and, as a result, are very common in digital synthesizers that are
modeled on analog-style synthesizers from the 1960s and 1970s.

The {{maxword|name=cycle~}} object, as we already know, generates a cosine wave
which, when discussed in the context of a basic synthesizer setup, is
indistinguishable from a '''sine''' wave. It generates a roller-coaster shaped
waveform that is generated by solving a sine (or cosine) function on the angle of a
line tracing a circle. The property of a sine wave that is of sonic interest is it's
''spectrum''; it contains only one frequency, and is the purest tone we can
generate:

[[Image:Filterchapter03a.png|border]]
''How to make a sine wave, the Max way.''

The {{maxword|name=tri~}} object generates a triangular waveform. This triangle can
be equilateral (i.e. the rising part of the ramp is the same percentage of the entire
wave as the falling part), or it can be unequal. This proportion of rising versus
falling is called the ''duty cycle'' of the waveform. In an equal triangle wave,
the spectrum contains only ''odd'' harmonics, at a power of 1/n<sup>2</sup>,
where ''n'' is the harmonic number. In other words, for a triangle wave at 100
Hz, we hear, in addition to the fundamental, a 300 Hz tone at 1/9th the volume of
the fundamental, a 500 Hz tone at 1/25 the volume, a 700 Hz tone at 1/49th the
volume, and so on:

[[Image:Filterchapter03b.png|border]]
''Generating a triangle wave in Max.''

The {{maxword|name=saw~}} object generates a sawtooth waveform. This waveform is
simply a rising ramp from <code>-1</code> to <code>1</code> that repeats at a set
frequency. It contains all the harmonics of the fundamental at a power equal to 1/n.
Thus a 100 Hz sawtooth wave contains a 200 Hz tone at 1/2 volume, a 300 Hz tone
at 1/3 volume, continuing on upwards:

[[Image:Filterchapter03c.png|border]]
''A sawtooth (rising ramp) generator in Max.''

Lastly, the {{maxword|name=rect~}} object generates a square wave. This waveform is
''binary'', consisting only of values <code>-1</code> or <code>1</code>. The duty cycle
of a square wave controls the proportion of the wave that is negative versus
positive. Like triangle waves, square waves only contain odd harmonics, but at a
power of 1/n, resulting in stronger harmonic content than a triangle. A 100 Hz
square wave contains a 300 Hz tone at 1/3 volume, a 500 Hz tone at 1/5 volume,
etc.:

[[Image:Filterchapter03d.png|border]]
''A square wave in Max with an even (0.5) duty cycle.''

These waveforms are popular in synthesis design because they contain well-
understood timbral properties that are easy to predict and, as a result, to
manipulate through filtering. Mixing and matching these waveforms (often with
slight detuning) allows us to create fairly rich synthesizer sounds reminiscent of
classic analog synthesizers.

* Turn up one or more of our oscillators. At the right of the patcher, adjust
the controls for the {{maxword|name=lores~}} object, adjusting the {{maxword|name=dial}} and
{{maxword|name=number}} box controlling the cutoff frequency and resonance of the filter.
Listen to the result, and also look at its effect on the visuals at the bottom of the
patcher.

==={{maxword|name=scope~}}ing things out===

At the bottom of the tutorial patcher are two MSP user-interface objects that
allow us to plot and view a signal. The top one is called the {{maxword|name=scope~}} object,
and it functions much like an analog oscilloscope, tracing the incoming signal across
the ''X'' at a regular speed, with the amplitude of the waveform corresponding
to the height (''Y'' axis) of the line. Two <link type="refpage" name="number">number box</link> objects attached to the
{{maxword|name=scope~}} control how many samples of audio it chunks into small buffers
which it draws as pixels in the object. Adjusting those numbers allows us to get a
more or less detailed view of the signal entering the object.

The second (lower) user interface object is called a {{maxword|name=spectroscope~}}:
it provides a different view of our signal: that of a spectrogram (or spectrum plot).
The ''X'' axis of the graph corresponds not to time, but to ''frequency'',
with the ''Y'' axis showing the amplitude of the signal at that corresponding
frequency.

* One by one, turn up our waveforms and see how they 'look' in the
{{maxword|name=scope~}} and {{maxword|name=spectroscope~}} objects. If the waveform in the
{{maxword|name=scope~}} seems to go by too quickly or slowly, adjust the {{maxword|name=number}}
boxes attached to the object to see if you can 'tune in' a good setting for the
waveform.

* Using the controls for the {{maxword|name=lores~}} object, change the amount of high
frequencies filtered out in the sound, and see how that impacts on the waveform.
Notice that the {{maxword|name=cycle~}} object is largely immune to the effects of the
{{maxword|name=lores~}} object unless the cutoff frequency falls below its fundamental; this is
because the sine wave only generates one frequency to begin with.

* When listening to the {{maxword|name=tri~}} and {{maxword|name=rect~}} objects, adjust the
{{maxword|name=number}} box labeled 'Duty cycle'. Lowering it towards <code>0</code> or
raising it towards <code>1</code> changes the balance of the harmonics in those two
waveforms.

===The many aliases of digital oscillators===

The waveforms described above are discussed as optimal shapes: when
viewed, a triangle wave should look like a triangle, a sawtooth should resemble its
namesake, and a square should look, well, square. Because of the implementation of
these oscillators in a ''digital'' system, however, some changes are made to
their shapes or, more accurately, the algorithms that generate their shapes. This is
to avoid the higher harmonics of the mathematically accurate waveforms exceeding
the Nyquist frequency of your audio hardware and ''folding over'' creating
unpleasant artifacts. The upshot of this is that {{maxword|name=tri~}}, {{maxword|name=saw~}}, and
{{maxword|name=rect~}} are all ''anti-aliased'' (or ''band-limited'') oscillators, and
have slightly different shapes than the ideal, even though their generated spectra
look (and sound) correct:

[[Image:Filterchapter03e.gif|border]]
[[Image:Filterchapter03f.png|border]]
[[Image:Filterchapter03g.gif|border]]
[[Image:Filterchapter03h.png|border]]
''The waveforms and spectra of antialiased oscillators.

Top-left: sine. top-right: triangle, bottom-left: sawtooth, bottom-right:
square.''

===Sync or swim===

* In the upper-right of the tutorial patcher, open the {{maxword|name=gate~}} object by
checking the {{maxword|name=toggle}} box. Set the frequency of the {{maxword|name=phasor~}} to
<code>1</code> by typing into the {{maxword|name=number}} box connected to its inlet. Turn up
the {{maxword|name=tri~}} object, and turn down everything else. You should hear a 'jump' in
the waveform once per second. Raise the frequency of the {{maxword|name=phasor~}} by
dragging in the {{maxword|name=number}} box. Once you get into the audible frequency range
(around <code>20</code> Hz) you should notice the frequency of the {{maxword|name=phasor~}}
dominate over the frequency of the {{maxword|name=tri~}} object. Try turning down the
{{maxword|name=tri~}} wave and turning up the {{maxword|name=saw~}} and {{maxword|name=rect~}}. Notice
that audible-range settings for the {{maxword|name=phasor~}} seem to eliminate the audio
from the square wave generator.

The three complex oscillators have an additional inlet that allows them to be
''synchronized'' by another oscillator. Every time the {{maxword|name=phasor~}} object
resets its phase (i.e. repeats its waveform), the oscillator receiving the 'sync' resets
itself, i.e. starts drawing its shape over again. This technique of ''oscillator
sync'' is useful for using one oscillator as a source of timbre ringing at the
frequency of a second (master) oscillator. In this way, we could have a 200 Hz
{{maxword|name=phasor~}} signal controlling triangle, sawtooth, and square waves at
different frequencies of their own, applying richness to the sound from the
interaction of the two waveforms.

===Summary===

In addition to the {{maxword|name=cycle~}} object, which produces a cosine wave, MSP
has three other 'analog-style' antialiased oscillators: {{maxword|name=tri~}}, which produces a
triangle wave, {{maxword|name=saw~}}, which generates a sawtooth wave, and {{maxword|name=rect~}},
which creates a square wave. Both {{maxword|name=tri~}} and {{maxword|name=rect~}} can have their
duty cycles modified, and all three can receive 'sync' from another oscillator. The
{{maxword|name=scope~}} and {{maxword|name=spectroscope~}} objects are very useful for viewing
signal data, either unfolding in the time domain ({{maxword|name=scope~}}) or in the
frequency domain ({{maxword|name=spectroscope~}}).

===See Also===

{{maxword|name=tri~}} - Antialiased triangular oscillator

{{maxword|name=rect~}} - >Antialiased sawtooth oscillator

{{maxword|name=saw~}} - Antialiased rectangular (pulse) oscillator

{{maxword|name=scope~}} - Signal oscilloscope

{{maxword|name=spectroscope~}} - Signal spectrogram or sonogram

[[Category:Teaching Material]]

← Older revision		Revision as of 15:31, 28 June 2012
Line 1:		Line 1:
−	Click here to open the tutorial patch: [[03fAnalogStyleSynthesis.maxpat]]	+	Click here to open the tutorial patch: [[Media:03fAnalogStyleSynthesis.maxpat]]

	Now that we are familiar with some basic types of filters, we can think about different sounds to use with them. Most of the synthesis work we've looked at thus far has involved working with sinusoidal oscillators (the {{maxword\|name=cycle~}}) object, creating complex spectra through different types of modulation synthesis (e.g. FM) or waveshaping. MSP has a number of oscillators that create more complex sounds on their own, and they are quite useful for creating richer sounds that can be shaped by filters. We'll introduce these oscillators here. briefly looking at a couple of objects that allow you to plot signal data along the way.		Now that we are familiar with some basic types of filters, we can think about different sounds to use with them. Most of the synthesis work we've looked at thus far has involved working with sinusoidal oscillators (the {{maxword\|name=cycle~}}) object, creating complex spectra through different types of modulation synthesis (e.g. FM) or waveshaping. MSP has a number of oscillators that create more complex sounds on their own, and they are quite useful for creating richer sounds that can be shaped by filters. We'll introduce these oscillators here. briefly looking at a couple of objects that allow you to plot signal data along the way.

@@ Line 56: / Line 56: @@
 [[Image:Filterchapter03e.png|border]]
 [[Image:Filterchapter03f.png|border]]
 [[Image:Filterchapter03g.png|border]]
 [[Image:Filterchapter03h.png|border]]
-''The waveforms and spectra of antialiased oscillators. Top-left: sine. top-right: triangle, bottom-left: sawtooth, bottom-right: square.''
+''The waveforms and spectra of square antialiased oscillators''
 ===Sync or swim===

@@ Line 82: / Line 82: @@
 * Turn up one or more of our oscillators. At the right of the patcher, adjust the controls for the {{maxword|name=lores~}} object, adjusting the {{maxword|name=dial}} and {{maxword|name=number}} box controlling the cutoff frequency and resonance of the filter. Listen to the result, and also look at its effect on the visuals at the bottom of the patcher.
-==={{maxword|name=scope~}}ing things out===
+===scope~ing things out===
-At the bottom of the tutorial patcher are two MSP user-interface objects that
+At the bottom of the tutorial patcher are two MSP user-interface objects that allow us to plot and view a signal. The top one is called the {{maxword|name=scope~}} object, and it functions much like an analog oscilloscope, tracing the incoming signal across the ''X'' at a regular speed, with the amplitude of the waveform corresponding to the height (''Y'' axis) of the line. Two <link type="refpage" name="number">number box</link> objects attached to the {{maxword|name=scope~}} control how many samples of audio it chunks into small buffers which it draws as pixels in the object. Adjusting those numbers allows us to get a more or less detailed view of the signal entering the object.
 allow us to plot and view a signal. The top one is called the {{maxword|name=scope~}} object,
 and it functions much like an analog oscilloscope, tracing the incoming signal across
 the ''X'' at a regular speed, with the amplitude of the waveform corresponding
 to the height (''Y'' axis) of the line. Two <link type="refpage" name="number">number box</link> objects attached to the
 {{maxword|name=scope~}} control how many samples of audio it chunks into small buffers
 which it draws as pixels in the object. Adjusting those numbers allows us to get a
 more or less detailed view of the signal entering the object.
-The second (lower) user interface object is called a {{maxword|name=spectroscope~}}:
+The second (lower) user interface object is called a {{maxword|name=spectroscope~}}: it provides a different view of our signal: that of a spectrogram (or spectrum plot). The ''X'' axis of the graph corresponds not to time, but to ''frequency'', with the ''Y'' axis showing the amplitude of the signal at that corresponding frequency.
 it provides a different view of our signal: that of a spectrogram (or spectrum plot).
 The ''X'' axis of the graph corresponds not to time, but to ''frequency'',
 with the ''Y'' axis showing the amplitude of the signal at that corresponding
 frequency.
-* One by one, turn up our waveforms and see how they 'look' in the
+* One by one, turn up our waveforms and see how they 'look' in the {{maxword|name=scope~}} and {{maxword|name=spectroscope~}} objects. If the waveform in the {{maxword|name=scope~}} seems to go by too quickly or slowly, adjust the {{maxword|name=number}} boxes attached to the object to see if you can 'tune in' a good setting for the waveform.
 {{maxword|name=scope~}} and {{maxword|name=spectroscope~}} objects. If the waveform in the
 {{maxword|name=scope~}} seems to go by too quickly or slowly, adjust the {{maxword|name=number}}
 boxes attached to the object to see if you can 'tune in' a good setting for the
 waveform.
-* Using the controls for the {{maxword|name=lores~}} object, change the amount of high
+* Using the controls for the {{maxword|name=lores~}} object, change the amount of high frequencies filtered out in the sound, and see how that impacts on the waveform. Notice that the {{maxword|name=cycle~}} object is largely immune to the effects of the {{maxword|name=lores~}} object unless the cutoff frequency falls below its fundamental; this is because the sine wave only generates one frequency to begin with.
 frequencies filtered out in the sound, and see how that impacts on the waveform.
 Notice that the {{maxword|name=cycle~}} object is largely immune to the effects of the
 {{maxword|name=lores~}} object unless the cutoff frequency falls below its fundamental; this is
 because the sine wave only generates one frequency to begin with.
-* When listening to the {{maxword|name=tri~}} and {{maxword|name=rect~}} objects, adjust the
+* When listening to the {{maxword|name=tri~}} and {{maxword|name=rect~}} objects, adjust the {{maxword|name=number}} box labeled 'Duty cycle'. Lowering it towards <code>0</code> or raising it towards <code>1</code> changes the balance of the harmonics in those two waveforms.
 {{maxword|name=number}} box labeled 'Duty cycle'. Lowering it towards <code>0</code> or
 raising it towards <code>1</code> changes the balance of the harmonics in those two
 waveforms.
 ===The many aliases of digital oscillators===

@@ Line 37: / Line 37: @@
 generate:
-[[Image:Filterchapter03a.png|border]]
+[[image: Filterchapter03a.png|border]]
 ''How to make a sine wave, the Max way.''