A formula module for VCV Rack, by Frank Buss, based on BokontepByteBeatMachine.
This module provides 4 inputs: w, x, y and z. In the text field you can write a
formula for the output. For example x+y would be a simple adder.
Some functions take 2 arguments. For example you could use the max function, to
get either the input x or the input y, depending on which voltage is higher:
max(x, y).
The red LED is blinking if there is a parsing error. If it is on, the formula is running.
The integrated knob is available as the variable k. The integrated -1 / 0 / +1
radio buttons are available as the variable b.
The frequency field is another formula, all variables can be used for it. The
result of this formula is used as the frequency for an integrated sawtooth
oscillator, available as the variable p (phase). It starts at 0 and wraps
around at 1.
It works with CV and audio signals. The output is clamped to -5V/+5V, if the clamp toggle button is pressed. Some more examples for what you can use it:
You can also use functions, see later for a list of all available functions, and
you can use the variable pi. In combination with the integrated sawtooth, this
can be used as a mathematically wave generator. The sawtooth has to be a simple
generator, with no anti-aliasing algorithms, because the falling edge of the
ramp needs to be with no smoothing in one sample. Otherwise there would be
samples from the rising part created, which results in distortions. The
integrated oscillator has this property.
So a sine wave with the usual 10Vpp can be generated with sin(2*pi*p/5)*5. In
the freq field you can enter the frequency formula, which could be a simple
number as well, like 440 for 440 Hz.
More complex formulas are possible as well, you can enter multiple lines. For example this approximates the square wave function with additive synthesis with the base frequency and the first 3 harmonics of the square wave:
4*(
sin(2*pi*p)+
sin(6*pi*p)/3+
sin(10*pi*p)/5+
sin(14*pi*p)/7
)
The variable k in the frequency field allows to use the integrated knob to
adjust the frequency. You could use any of the inputs as well to modify it and
to build a full featured VCO.
Another wider range of applications is parameter adjustment. For example the VCO-1 in Fundamental has a V/OCT input. This means when you create a new instance with the initial frequency for C4 (261.626 Hz) and apply 1 V, the frequency will be increased by one octave to C5 (523.252 Hz).
But what if you have a linear V/Hz CV signal and want to convert it in a way
that it can be used with a V/OCT input? Then you need to calculate the log to
base 2 of the input level, which is the function log2. So for x=1.5 it would
be exactly 1.5 * 261.626 Hz = 392.439 Hz.
The relational operators (<, >, <= and >=) allow other interesting applications.
For example if you want to select one of two signals, based on the CV level of
another signal (a multiplexer), then you could use the formula
((w<=5)*x+(w>5)*y)*b. This would output x, if the level at the w input is
5V or less, otherwise it outputs y. It works because if w<=5 is valid, the
term evaluates to 1, otherwise to 0. Additionally the multiplication with the
variable b allows to mute the signal, if the 0 radio button is selected.
Finally there are the boolean operators & for logical-and, | for logical-or
and !for not. This can be useful, if you want to test two signals with the
relational operators, like if x and y has some minimum value at the same time,
only then output the value of z. Or you could even use it to implement a 10 step
sequencer with chromatic scale:
((p>=0.0&p<0.1)*1+(p>=0.1&p<0.2)*5+
(p>=0.2&p<0.3)*8+(p>=0.3&p<0.4)*9+
(p>=0.4&p<0.5)*10+(p>=0.5&p<0.6)*12+
(p>=0.6&p<0.7)*10+(p>=0.7&p<0.8)*9+
(p>=0.8&p<0.9)*8+(p>=0.9&p<1.0)*5)
/12
The knob can be used to change the frequency. Try it and listen to it, then change the factors interactively. Unlike a normal step sequencer, you can adjust the length of the indivual steps as well by changing the p time windows, lots of fun :-)
You can use the floor function to implement a simple quantizer. This function
rounds the value down to the next integer value. For example floor(1.8)=1. For
a chromatic quantizer, only the voltages 0, 1/12, 2/12 etc. are allowed. This
can be enforced with this formula: floor(k*12)/12. With the variable k you
can use the integrated knob to adjust the output in the range from -1 to 1
octave, using a chromatic scale. Of course you can use the inputs as well
instead of the knob, or add both, like floor(x)+k, which would quantize the
input x, but would allow a fine adjustment with the knob.
Some more examples of a simple sawtooth generator with adjustable frequency and simple waveform transformations. Works with 0-5V CV and might be useful for example to shape ADSR curves. But works with audio as well, just shift and scale the input to 0-5V and then back again to the desired output level and offset.
The following functions are implemented:
acos, asin, atan, atan2, cos, cosh, exp, abs, mod, log, log2, log10, pow, sin, sinh, tan, tanh, sqrt, ceil, floor, max, and min. See here for a detailed description of each function: http://www.cplusplus.com/reference/cmath/
The full BNF grammar for the parser looks like this:
expression = and-expression [or-operator and-expression]
and-expression = equal-expression [and-operator equal-expression]
equal-expression = relational-expression [equal-operator relational-expression]
relational-expression = sum [relational-operator sum]
sum = [sign] term {additive-operator term}
term = factor {multiplicative-operator factor}
factor = power {power-operator power}
power = power_operand {power-operator power_operand}
power_operand = unsigned-real | variable | (expression) | function-call
or-operator = |
and-operator = &
equal-operator = == | !=
relational-operator = < | > | <= | >=
additive-operator = + | -
multiplicative-operator = * | / | %
power-operator = ^
not-operator = !
variable = [a-z, A-Z, _]+ [a-z, A-Z, 0-9, _]*
unsigned-real = [0-9]* [.] [0-9]* [real-exponent]
real-exponent = [e|E] [+|-] [0-9]+
I wrote the formula library in 2001, here is the original page with a function plotter as another example: http://www.frank-buss.de/formula/index.html
If you have a patch file which uses the old FrankBussFormula plugin, you have to rename the internal name. Open your vcv file in an editor and search for these lines:
"plugin": "FrankBussFormula",
"model": "FrankBussFormula",
and replace it with these lines:
"plugin": "FrankBuss",
"model": "Formula",
If you have Perl installed (free for all operating systems), you can enter these 2 lines from a console to convert all your .vcv files in the current directoy:
perl -i -pe 's/"plugin": "FrankBussFormula"/"plugin": "FrankBuss"/g' *.vcv
perl -i -pe 's/"model": "FrankBussFormula"/"model": "Formula"/g' *.vcv