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| The New Millennium: Scanned Synthesis
As you can see, Csound brings the old and the new together. It has preserved a historical approach to computer music and more importantly preserved a library of instruments that represent the accumulated knowledge and understanding that grew from a unique and symbiotic relationship between performers, composers and engineers. Csound is what happened when science met art. But it is also the language of research and the future. New directions are being explored and new discoveries shared every day. In this master class, I'll introduce you to an exciting new synthesis technique - Scanned Synthesis.
Scanned synthesis represents a powerful and efficient technique for animating wavetables and controlling them in real-time. It was developed by Bill Verplank, Rob Shaw, and Max Mathews, (the "father of computer music"), between 1998 and 1999 at Interval Research. Scanned synthesis is based on the psychoacoustics of how we hear and appreciate certain timbres and on our motor control (haptic) abilities to manipulate them during live performance. Scanned Synthesis involves a slow dynamic system whose frequencies of vibration are below about 15 Hz. The ear cannot hear the low frequencies of the dynamic system. So, to make audible frequencies, the "shape" of the dynamic system, along a closed path, is scanned periodically. The "shape" is converted to a sound wave whose pitch is determined by the speed of the scanning function. As shown in figure 25, pitch control (2) is completely separate from the dynamic system control (1). Thus timbre and pitch are independent. This system can be looked upon as a dynamic wavetable. The model can be compared to a slowly vibrating string, or a two dimensional surface obeying the wave equation.
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Verplank, Shaw and Mathews studied scanned synthesis chiefly with a finite element model of a generalized string - a collection of masses connected by springs and dampers that can be analyzed with Newton's laws. From there, they generalized a traditional string by adding dampers and springs to each mass as shown in figure 26.
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All parameters - mass, damping, earth-spring strength, and string tension can vary along the "string." The model is manipulated by pushing or hitting different masses (the individual samples in a very short wavetable) with simple or complex "hammers" (as shown in figure 27), and by manipulating parameters. What is unique here is that the wavetable itself is a dynamic model whose "natural" evolution is based on the initial conditions and the properties of the model.
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So, you are manipulating this "mechanical" model at haptic rates 0-10 Hz, and independent to this, you are scanning out the wavetable at the pitch frequency. The wavetable itself (the "string") has its own dynamics, but there are no discontinuities because the model is implemented as a "circular string" (as shown in figure 28) What you end up with is a 128 point looping oscillator with a constantly evolving loop! In scanned synthesis, extremely short samples are animated and harmonically rich because of the complex interactive nature of the elements in the underlying system - the mechanics of the model.
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In fact, even enveloping can come directly from the model. It turns out that the specific setting of the centering springs can affect the damping of the system - low values allowing the rich timbre to ring, high values causing the tone to die away quickly.
In June of 1999, a graduate student from the MIT Media Lab, Paris Smaragdis, further generalized the model by added two Scanned Synthesis opcodes to Csound. The first is an opcode that defines the mass/spring network and sets it in motion (scanu); and the second is an opcode that follows a predefined path (trajectory) around the network and outputs the dynamic waveform at a user specified frequency and amplitude (scans).
The syntax for scanu is:
What is unique about the Csound implementation of Scanned Synthesis is the fact that Smaragdis added support for both a scanning trajectory and a scanning matrix. The matrix offers the possibility of reconnecting the samples (masses/dots) in different orders (not necessarily to their direct neighbors) causing the signal to propagate quite differently. Essentially, the matrix has the effect of "molding" this surface/mesh into radically different shapes. The trajectory allows one to scan the "string" in any direction, at variable rates, or even randomly. Figure 29 shows a basic scanned synthesis instrument with uniform masses (f2). However, the non-uniform centering force applied to them (f4) results in a timbre quite similar to a slow "filter-sweep" (without filters of course).
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scanu init, irate, ifnvel, ifnmass, ifnstif, ifncentr, ifndamp, kmass, \
kstif, kcentr, kdamp, ileft, iright, kx, ky, ain, idisp, id
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| -init: |
The initial position of the masses. If this is a negative number, then the absolute of init signifies the table to use as a hammer shape. If init > 0, the length of it should be the same as the number of masses (128), otherwise it can be anything.
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| -irate: |
The amount of time between successive updates of the mass state. Kind of like the sample period of the system. If the number is big, the string will update at a slow rate showing little timbral variability; otherwise it will change rapidly resulting in a more dynamic sound.
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| -ifnvel: |
The number of the ftable that contains the initial velocity for each mass. It should have the same size as the number of masses (128).
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| -ifnmass: |
The number of the ftable that contains the mass of each mass. It should have the same size as the number of masses (128).
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| -ifnstif: |
The number of the ftable that contains the spring stiffness of each connection. It should have the same size as the square of the number of masses (16384). The data ordering is a row after row dump of the connection matrix of the system.
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| -ifncentr: |
The number of the ftable that contains the centering force of each mass. It should have the same size as the number of masses (128).
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| -ifndamp: |
The number of the ftable that contains the damping factor of each mass. It should have the same size as the number of masses (128).
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| -kmass: |
Scales the masses.
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| -kstif: |
Scales the spring stiffness.
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| -kcentr: |
Scales the centering force.
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| -kdamp: |
Scales the damping.
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| -ileft: |
If init < 0, the position of the left hammer (ileft = 0 is hit at leftmost, ileft = 1 is hit at rightmost).
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| -iright: |
If init < 0, the position of the right hammer (iright = 0 is hit at leftmost, iright = 1 is hit at rightmost).
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| -kx: |
The position of an active hammer along the string (0 leftmost, 1 rightmost). The shape of the hammer is determined by init. The power it pushes with is ky.
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| -ky: |
The power that the active hammer uses.
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| -ain: |
The audio input that adds to the velocity of the masses.
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| -idisp: |
If 0, no display. If 1, display of the dynamic evolution of the masses.
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| -id: |
The ID of the scanu opcode. This will be used to point the scanning opcode (scans) to the proper waveform maker. If this value is negative, it indicates the wavetable on which to write the waveshape. That wavetable can be used later from another opcode to generate sound. Note: The initial contents of this table will be destroyed, so don't rely on them being there.
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The syntax for scans is:ar scans kamp, kfreq, ifntraj, id[, korder] |
| -kamp: |
The output amplitude. Note that the resulting amplitude is also dependent to the state of the wavetable.
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| -kfreq: |
The frequency of the scan rate.
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| -ifntraj: |
The number of the ftable that contains the scanning trajectory. This is a series of numbers that contain addresses of masses - the order of these addresses is used as the scan path. It should not contain more values than the number of masses (128), and it should not contain negative numbers.
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| -id: |
The ID number of the scanu waveform to use.
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| -korder: |
The order of interpolation used internally. It can take any value in the range 1 to 4, and defaults to 4, which is quartic interpolation. The setting of 2 is quadratic and 1 is linear. The higher numbers are slower, but not necessarily better.
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What is unique about the Csound implementation of Scanned Synthesis is the fact that Smaragdis added support for both a scanning trajectory and a scanning matrix. The matrix offers the possibility of reconnecting the samples (masses/dots) in different orders (not necessarily to their direct neighbors) causing the signal to propagate quite differently. Essentially, the matrix has the effect of "molding" this surface/mesh into radically different shapes. The trajectory allows one to scan the "string" in any direction, at variable rates, or even randomly. Figure 29 shows a basic scanned synthesis instrument with uniform masses (f2). However, the non-uniform centering force applied to them (f4) results in a timbre quite similar to a slow "filter-sweep" (without filters of course).
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Furthermore, by providing a means to update the velocity of the masses with real-time audio, one has a means of "injecting" natural energy (and randomness) into the system resulting in wonderful resonator and vocoder effects. We could also use audio input as a complex hammer to continuously inject energy into the system as shown in figure 30. In addition to using this physical model as a resonator, the instrument shown in figure 30 has dual scan paths by virtue of the two scans opcodes with unique trajectories (f7 & f77).
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Finally, because Smaragdis separated the opcode that scans the wavetable from the one that computes and updates the wavetable it is possible to apply the scanning system to other "classic" synthesis techniques and dynamically animate them. Imagine if you can, the sound of scanned FM, scanned granular, or scanned subtractive. Since many of Csound signal generators use wavetables, they can practically all be scanned - and thus "animated" in a new, vivid and controllable way!
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Charting and discovering these new worlds of sound will be up to you. And for now anyway, the only place to experience and experiment with Scanned Synthesis is in Csound.
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[next] Csound for Dummies
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