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varispeed in terms of pitch

Hello forum.

I have a question regarding varispeed. Hope you can help me.

If a tape machine is running at 50 cycles and then I tweak the varispeed knob all the way down to 42 cycles, how much would this affect a sound in terms of pitch (semitones or cents).

The reason I'm asking is because I'd like to recreate that same effect using a pitch shifting plugin... but I don't know how to set it up properly. Is there any sort of formula in order to determine the cycles to cents conversion?

Thank you.


Boswell Mon, 09/11/2006 - 08:16
A cent is one hundredth of a semitone. A semitone (in equal temperament) is a fequency ratio equal to the twelfth root of two (1.059463), or a difference of roughly 6%. Cents can't really be used to express pitch differences of more than half a semitone up or down (+/-50cents), because you are then nearer to the next named semitone.

Now take your example of adjusting the speed of a tape machine. If you recorded an A (440Hz) at the 50 cps speed and then wound the machine down to 42 cps, the 440Hz would now be at 369.6Hz, which is about an F#, i.e. 3 semitones lower. You could arrive at this by ratioing the frequencies (440 x 42 / 50) and then looking up the result in a pitch table. So your speed adjustment in that direction shifts everything down by 3 semitones, and stretches the time by about 19%.

A useful pitch to frequency table is to be found at