[sdiy] Detuning in Digital

[Matthew Smith]

Wondering if anyone can give me the Magic Formula for calculating a 
de-tuned frequency. I understand (rightly or wrongly!) that a cent above 
a note is one hundredth of one twelfth of twice that original frequency 
and ditto with half the original frequency for one cent down.

My mathematical ability, unfortunately, does not stretch to getting this 
into a simple formula where I plug in a frequency and detune value and 
come out with a new frequency. (Or even one formula for up and one for 
down, so I don't have to muck around with signed numbers.)

Ideally, I'd like to do this with the simplest of operations (shift, 
add, subtract, *possibly* multiply,) and avoid use of floating points, 
if possible. I'm not after precision, only something that sounds right 
to the average ear. Or sounds right to an ear that is happy with 
acoustic instruments, where perfect tuning is an impossibility. (Saw 
something about Lionel Ritchie on the news last night - his piano was 
WAY out of tune!)

If the math is too onerous for simple operations, what increment of 
cents detune is clearly audible? Quite happy to use a frequency lookup 
table, but don't see any point in creating a 14,400-entry LUT for a 72 
note range, if only eight divisions per semitone are readily 
distinguishable.

Oh, and whilst we're at it, can we dump the 12-semitone octave in favour 
of 16, and have 128 cents to the semitone (hey, no more stupid than the 
Imperial measurement system) so we're working only in powers of 2? ;-)

Cheers

M

-- 
Matthew Smith

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