back to list

the scaled by P rule

🔗D.Stearns <STEARNS@CAPECOD.NET>

12/3/2000 2:05:34 AM

Let stepsizes be small to large alphabetized variables so that
two-stepsize = [a,b], three-stepsize = [a,b,c] and so forth and so on
where the alphabetized variables are any whole numbers.

Then assign each variable an uppercase fixed size:

A = (LOG(2)-LOG(1))*(1200/LOG(2))
B = (LOG(3)-LOG(1))*(1200/LOG(2))
C = (LOG(4)-LOG(1))*(1200/LOG(2))

etc.,

This will be our fixed interval template, and will allow for an a/b =
log(3)/log(2), c/b = log (4)/log(3), d/c = log(5)/log(4), etc.
distribution of stepsizes amongst any [a,b,...] index.

Next you scale a given [a,b,...] index by a given periodicity (P).
This will give us a percentage (X) to scale the fixed A,B,... interval
template with.

So for a two-stepsize index you'd have (a*A)+(b*B)/P = X.

For a three-stepsize index, (a*A)+(b*B)+(c*C)/P = X.

And so forth and so on...

Now A/X, B/X,... will give a given [a,b,...] index corresponding
stepsizes scaled to P.

--Dan Stearns