The Kyma Language for Sound Design, Version 4.5

every 256 samples, it outputs the spectrum for the next frame. We are trying to make a synthetic set of
pitches for the spectrum. Since we know they should be evenly spaced in log frequency, we have set the
SyntheticSpectrumFromSounds to LogScale, and we are using a ramp wave (i.e. a linear function from
zero to one) that repeats every 256 samples to specify the pitches — assuming that the first partial is the
lowest, then the next partial, and so on linearly until reaching the highest pitch when the ramp reaches its
highest value. Why did we use a Sample with loop rather than an Oscillator? Because the Sample, unlike
the Oscillator, does not interpolate between the last value before the loop and the beginning of the loop.
For waveform generation, the Oscillator would be better, but for this specific application, we want
something that drops immediately from one back to zero, without interpolation.
OK, so far, with a 256 sample period of repetition, we have a static spectrum that does not change from
frame to frame and that gives us components whose frequencies are evenly spaced in pitch space.
What is the effect of increasing or decreasing the frequency of the Ramp wave?
Increasing the frequency of the ramp wave effectively increases its slope. So each corresponding point
along the line is a little larger than it would have been at the original repetition rate. The effect is that the
pitches of all the components go up.
Decreasing the repetition rate gives the ramp a shallower slope. So corresponding points are smaller than
they were in the original ramp wave, and the pitches of all components are correspondingly lower.
So far, so good. But we don’t have just a single ramp wave, we have a repeating ramp wave controlling the
pitches of the components. A change in the repetition rate of the ramp means that it no longer lines up
with the 256 sample-long frames. If we increase the repetition rate, the ramp will wrap around to zero
before the end of each frame. In a sense, the repeating ramp is “rolling” with respect to the frame rate.
Think of two identical tapes being played at very slightly different rates; they slowly move out of synchronization
until they are so far out of synchronization that they line back up again. Or think of two sine
waves that are 2 or 3 hertz apart in frequency; they gradually move out of phase with one another until
they are fully 180 degrees out of phase at which point they line back up (causing a beating effect as they
reinforce or cancel each other during the “roll”).
It turns out that this “roll” is exactly what we want to get the circular pitch effect. Think of one point on
the ramp wave. If we increase the slope of the ramp, then on each frame, this point is higher than it was
on the last. This is true until it reaches the maximum value. Then on the next frame, it returns to the lowest
value again. This is the result we are after: that each component increase in pitch until reaching the
highest frequency and then that it wrap around and sneak back in at a subaudio frequency.
The Gain called 256 scales the ramp so that its range is (0,256). The Attenuator called interval density
reduces that range to achieve the actual pitch interval that you specify with !Int. The log frequencies are
set up so that one is the half sample rate and each decrease of 1/15 is a decrease of one octave from that
maximum frequency. The Attenuator turns your interval into a fraction of an octave and uses that to
scale the range of the ramp function.
Now for the really cool part! How to specify a spectral envelope? It would be tempting to just take an Oscillator
on the Hann wavetable and use that as the Amplitude input to the SyntheticSpectrum-
FromSounds. But it would be wrong! Actually for a static spectrum, it would be OK. But each amplitude
is matched with its corresponding partial number, not necessarily with any particular pitch. And we have
partials that are changing frequency on each frame. So we need some way to associate specific amplitude
values with specific pitches. One way to do this would be to have a table of values that list the amplitude
value for each possible frequency, and use the current frequency value to look into the table for the correct
amplitude value to use.
This concept — that of a table where you can use one value as an index into the table and output the
value found at that index — immediately suggests the Waveshaper.
The Waveshaper is a nonlinear transfer function that maps values between -1 and 1 to arbitrary values
stored in an arbitrary-sized table. So the first task is to get our all-positive frequencies to lie between -1
and 1. This is accomplished by the ScaleAndOffset called -1 to 1. It simply multiplies by two and subtracts
one.
This scaled value is then used as an index into a Hann function (forced to zero on the first and last entries
of the table) by means of the Waveshaper called pch->amp.
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