| hi menno -
this is the general formula in csound language. if you have
a) the number of grades: igrades
b) the repeating interval (2 =octave 1.5=fifth): iinterv
c) the basefreq: ibasfq
d) the integer index (usually midi key) for ibasfq: ibaskey
and you want to know the frequency ifreq of a given key ikey, you must
calculate:
ifreq = ibasfq * iinterv^((ikey-ibaskey)/igrades)
for instance:
a) igrades = 24
b) iinterv = 1.5
c) ibasfq = 440
d) ibaskey = 48
and ikey is 72, then
ifreq = 440 * 1.5^((72-48)/24) = 440 * 1.5^1 = 660
of course you could replace all i-variables by k-variables.
all best -
joachim
Am 15.02.2011 21:19, schrieb menno:
>
> Hello,
>
> i was trying to understand the way micro-tuning should work using cpstun and
> i did some reversed engineering to understand the way the multiplication
> values works.
> For the equal temperament scale with the use of: 12th root of 2 =
> 1.05946309, then i made the list of all 12 notes (220*1.05946309 =
> 233.0818*1.05946309=246.9416*1.05946309=261.6255*1.05946309=..........),
> then dividing the octave higher = 440 Hz divided by the frequencies i found,
> i found the values i saw in the example of cpstun:
>
> gitwelf ftgen 2, 0, 64, -2, 12, 2, 261.659, 60, 1.00, \
> 1.059, 1.122, 1.189, 1.260, 1.335, 1.414, \
> 1.498, 1.588, 1.682, 1.782, 1.888, 2.00
>
> That's okay, now i can divide an octave for example in 5 portions following
> the same procedure:
> 5th root of 2 = 1.14869835, then calculating the list with freqs and so on
> blah blah..
> -->
> givife ftgen 1, 0, 16, -2, 5, 2, 261.659, 60, 1.00, \
> 1.1486, 1.3195, 1.5157, 1.7411, 2.00
>
> This all works but surely there is a simpler way to get these values :) ??
> And what would be the formula to get the other example i see in the manual
> "with a 24-grade scale with a base frequency of 440 assigned to the
> key-number 48, and a repetition interval of 1.5"?
> f1 0 64 -2 24 1.5 440 48 1 1.01 1.02 1.03
> ..etc...
>
> http://www.csounds.com/manual/html/cpstun.html
> thanks,
> menno
>
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