calculating cents for ratios

John writes:
> Of course, if one is using JI, then simply memorizing the
cent values ofa small set of key intervals such as 3/2,
5/4, 7/4, 11/8, 13/8, etc. would be sufficient.

I don't read this list all the time so forgive me if someone has
already written about this.......

Since cents are logarithmic, for JI, one perform division by
subtracting cents. Thus one need only keep a table
of the cent values for the prime integers. To calculate
the cents value for a ratio, just subtract the cents for the
denominator from the numerator.

1 -- 0
2 -- 1200
3 -- 1902
4 -- 2400
5 -- 2786

So for cents for 3/2 = 1902 - 1200 = 702

The same principle applies for pitch bend because it is
also logarithmic. I use this trick in a relative intonation
score entry system in HMSL to rapidly calculate pitch bend
values for ratios without using transcendentals.

Phil Burk

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