Zebra Rate Calculator by Andre Loker

Manual

This tool calculates how the "Rate" knob found on the LFOs and global LFOs affects the frequency/duration^[1] of the LFO cycles in U-HE's magnificent Zebra software synthesizer. The idea came to me when I read this thread at kvraudio.com.

Note: the Rate knob scales the speed of the LFO relative to the value set for the "Sync" parameter. E.g. if you set the "Sync" value to 10s (10 seconds), a Rate value of 100 - the neutral setting - means that one cycle of the LFO takes 10 seconds. A Rate value of 200 (the maximum, which is a speed scaling factor of 8.0) will cause the LFO to run 8 times faster (that is, each cycle takes only 1.25 seconds). A Rate value of 50 corresponds to a speed scaling factor of 0.125, ie. each cycles takes eight times as long (80 seconds).

Basically, this tool answers three questions:

What is the speed/duration scaling factor for a given knob value?: Use the slider on the left hand side to set the knob value or enter the value directly in the text box next to "Knob value". The text boxes on the left now show how much the speed and the duration of the cycle respectively affect the base value (the "Sync" parameter).
Example: you want to know what the speed/duration scaling factor is for the knob value "150". Set the knob value to "150". The "Speed scaling factor" value is 3.375, that is, the frequency is actually 3.375 times faster than the "Sync" value. Likewise, the duration of one LFO cycle is scaled by 0.296, ie. each LFO cycle takes only 29.6% of the time of the base value.
Whats is the knob value for a given speed relative to the base value?: Use the slider on the right side to set the "Speed scaling factor" value or enter the value directly in the corresponding text box. The "Knob value" text box on the left hand side now shows the value you need the "Rate" knob to.
Example: you want the LFO to go 50% faster than the "Sync" value. Set "Speed scaling factor" to 1.5 (1.5 times faster than sync value). The "Knob value" shows 114.471, so set the Rate knob to 114.47 to achieve a (roughly) 50% speed up.
Whats is the knob value for a given duration relative to the base value?: Use the slider on the right side to set the "Duration scaling factor" value or enter the value directly in the corresponding text box. The "Knob value" text box on the left hand side now shows the value you need to set the "Rate" knob to.
Example: you want the LFO to take 3/4 of the time of the sync value. Set "Duration scaling factor" to 0.75. The "Knob value" shows 110.064, so set the Rate knob to 110.064 to make one LFO cycle last roughly 3/4 of the time of the base value.

The formula

The relationship between the knob value and the actual speed scaling factor is as follows:

SpeedScale = (KnobValue/100) ^ 3 (ie. the cube of a hundredth of the knob value)

-- or respectively --

KnobValue = 100 * SpeedScale ^ (1/3) (ie. 100 times the cube root of the speed scaling factor)

Where KnobValue is the value of the Rate knob and SpeedScale is the scaling factor of the LFO frequency.

NB: SpeedScale can be replaced by (1/DurationScale) (where DurationScale is the duration scaling factor applied to the duration of the cycles of the LFO) if necessary.

Credits and Licence

This tool was originally developed by Andre Loker and is provided as-is without any express or implied warranties. Use at own risk. You may copy the code of this website and use it for your own purposes in its original or in modified form. Attribution of the original author (Andre Loker) is highly appreciated but not strictly necessary.

^[1] We use the term "speed" for an LFO's frequency (cycles per second) and the term "duration" for its period (duration of one cycle) in this text. Frequency and period of a wave are closely related. The frequency is the inverse of the period (and vice versa): if the frequency is F, the period is 1/F.