Godfried’s Algebraic Clock Generator

One of Godfrieds track types is being a clock generator thus generate periodic trigger pulses somehow dependant to the master clock. You got it, “Clock Divider” or “Clock Multiplier”

The classic Clock Divider divides a master clock by a given number, mostly a perceived musically usefull. So it generates a trigger every 2, 4, 8…etc master clock beats, some do even weired things like uneven numbers. Similar goes for Clock Multipliers that mostly generate 2, 4, 8… etc evenly spaced triggers for one beat of the master clock.

But what about Polyrhythms, which means uneven or even prime fractions off the classic musical timing, thats based on powers of 2 ( if you don’t to evil things like triplets ) ?

So here is what Godfried does, you might want need to remember some basic algebra from way back in school.

Godfried doesn’t differntiate between Divider and Multiplier, it uses an Algebraic Clock Generator, that calculates the tracks clock in respect to the internal master clock (the one that you set by the Tempo parameter in the Clock Menu).

It generates a Trigger pulse every n counts of a fraction of the master clocks beat by using “Counts” and “Fraction” parameters (numerator and denominator mathematically speaking).

Here are some examples:

Counts = 4, Fraction=1 generates a trigger every 4 beats of the master clock – a classic Clock Divider

Counts = 1, Fraction= 4 generates 4 triggers for every single beat of the master clock – a classic Clock Multiplier

Counts=7, Fraction=2 generates a trigger pulse every 3.5 beats of the master clock – not sooo classic anymore….

Counts=13, Fraction=7 generates a trigger pulse every 13/7 beats of the master clock, that is a 0,4642th note given a 4/4 bar on the master clock which means a trigger every 0,9285s with a master tempo of 120.00 bpm. No sign of classicness anymore, huh? Instead severe Polyrhythmitistm.

Please note, that the Fraction parameter goes all the way up to 32, so it divides a beat of the master clock into 32 slices – thats a 128th note if you consider a 4/4 bar. Please further note, that Counts=4 and Fraction=8 is the same as Counts=1 and Fraction=2. And so on, remember?

Since a digital clock is always quantized rounding errors might occur. And since i know you clever modularists will do self playing patches, that last forever and these tiny weeny fractions will add up after some days rendering your art offbeat – whatever offbeat means in polyrhythms – these are as evenly distributed as possible to the single steps (Counts).