Frequency Math

[Tony Hardie-Bick]

Matt Picone wrote:
> James R. Coplin wrote:
>> Matt Picone wrote:
>>> If A440 is flattened 32 cents, what is the resulting frequency?
>>>
>>> -m@
> 
> Anyone? Is this right:
> 
> 32 cents flat is 32/100ths down along the way from A440 to Ab 415.305?
> Would it be (440 - 415.305) = 24.695Hz
> 
> 24.695/100 * 32 cents = 7.9024 Hz = The resulting tone is 432.0976Hz?

Nope, it's non-linear.

To flatten by an octave you do:

	440 * 0.5

To flatten by any number of semitones you do:

	440 * 2 ^ ((-n)/12)

To check this:

	  2 ^ ((-12)/12)

	= 2 ^ (-1)

	= 1/2

	= 0.5

So, to answer your question:

32 cents is 0.32 semitones. To flatten by this amount:

440 * 2^((-0.32)/12)

gives 431.94 Hz

:)

Tony (HB)