[sdiy] Detuning in Digital

[ASSI]

On Monday 02 April 2012, 15:00:35, Matthew Smith wrote:
> 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.

1 cent = 1200th root of 2.

> 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.)

Tuning is generally in logarithmical terms, so you need to multiply or 
divide the base frequency with the appropriate power of the detuning in 
cent.  Or just add/subtract the appropriate multiples of a cent in the 
logarithmic domain and do one exponentiation at the end, whatever seems to 
be more eficient.

> 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? ;-)

The scales-du-jour are based on prime divisions of the octave.  :-)


Regards,
Achim.
-- 
+<[Q+ Matrix-12 WAVE#46+305 Neuron microQkb Andromeda XTk Blofeld]>+

Factory and User Sound Singles for Waldorf Q+, Q and microQ:
http://Synth.Stromeko.net/Downloads.html#WaldorfSounds