im reading charles dodge computer music book and ive come across a mathematical expression to calculate the basic equal tempered division
the book says

"(i is equal to the interval I raised to the 1/N power). For the 12-tone equal tempered system, the basic division of the octave is the semitone (I = 2), and so i is equal to 2 raised to the 1/12 power. Thus two adjacent tones in this system tuned a semitone apart have a frequency ratio of 1:2 raised to the 1/12 power or 1:1.05946..."

id like to know exactly what is the procedure to get the number 1.05946

ive attached a patch in PD that multiplies this number to a given frequency and the result is a frequency a semitone apart

help please!

http://www.pdpatchrepo.info/hurleur/math_expr_for_semitones.pd

I think... the ratio 1:2 describes 2 notes an octave apart - the frequency is doubled. Between those 2 notes are 12 divisions (western music puts 12 equal divisions between them) - so each of those steps can be calculated as being 2pow(1/12) greater than the previous one. 2pow(1/12) = 1.05946 - try it. If this is right then a frequency * 2pow(2/12) should be 2 semi-tones higher. The formula should be [expr $f1*(pow(2, ($f2/12))] with $f1 being the original frequency and $f2 being the number of semitones. There could be a mistake in there somewhere, but try it out.
Simon

its right simon thanks!

what i dont understand is how you raise to the 1/12 power... i know raising to power of 2 or 3 but in fractions?... 1/12 = 0.083333
how do i raise 2 to 0.08333

sorry if it seems like a stupid question but ive never done that and if in the future i plan to do some sort of microtonal piece i feel understanding this will help me a lot.

Raising a number to a power is the same as finding the inverse root of the number...? Yeah, I can't think of a good way to actually say that, so let me just give examples:

Raising to the 1/2 power is the same as finding the square root. Raising to the 1/3 power is the same as finding the cube root. So, raising to the 1/12th power is the same thing as finding the 12th root.

If you are asking what does it mean to raise something to the 1/12 power ... 1/12 power of a number is 1 * the 12th root of that number
2/12 power is 2*12th root
more simply to raise a number to the 1/2 power is the same as 1* the square root of that number so 4^(1/2) = 2
... check out the attachment in the next post

try this out...

http://www.pdpatchrepo.info/hurleur/fractional_powers.pd

good timing

I love it when that happens.

it took a while but eventually got it right
thank you so much for your time!