question about period-less-than-an-octave calculation

Hi all,

I'm making Tonescape files of all of the TOP temperaments
described by Paul Erlich in his "Middle Path" paper
(_Xenharmonikon_ 18).

The calculation for the temperaments with period of
~octave is straightforward: my procedure is to use
Paul's formula for finding the tempered approximations
of prime-factors 2, 3, and 5, then create a Tonespace
lattice and look for the interval which is obviously
very close to the cents-value which Paul gives as the
generator. Then i simply multiply the generator by
positive and negative integers modulo the period.
Paul starts at zero and then goes thru the generators
either +1, -1, +2, -2, ... etc. or vice versa.
I'm using Open Office Calc, and the formula is like this:

=MOD(GeneratorCents*GeneratorNumber;Period)

But i cannot figure out how to calculate the cases
(augmented, for example) where the equivalence-interval
(or "formal octave") is a multiple of the period.

I would really appreciate it if someone could give
me the exact formula i would have to use in Calc.
Please use TOP augmented as the example -- the
cents-values for the primes are thus:

"2" = 1197.060039195180
"3" = 1901.955000865390 (untempered)
"5" = 2793.140091455420

The period for TOP augmented is 1/3 of the approximation
for "2" = ~399.02001306506 cents, and the generator is
~93.1450644599108 cents.

If you use Excel, the formula works the same way except
that commas separate arguments instead of semicolons.
Thanks.

-monz
http://tonalsoft.com
Tonescape microtonal music software

monz wrote:

> =MOD(GeneratorCents*GeneratorNumber;Period)
> > But i cannot figure out how to calculate the cases
> (augmented, for example) where the equivalence-interval
> (or "formal octave") is a multiple of the period.

I think you need to make the period mapping explicit. Maybe

GeneratorCents*GeneratorNumber + Period*PeriodNumber

if I understand the original formula correctly.

Graham

Hi Graham,

--- In tuning-math@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> monz wrote:
>
> > =MOD(GeneratorCents*GeneratorNumber;Period)
> >
> > But i cannot figure out how to calculate the cases
> > (augmented, for example) where the equivalence-interval
> > (or "formal octave") is a multiple of the period.
>
> I think you need to make the period mapping explicit. Maybe
>
> GeneratorCents*GeneratorNumber + Period*PeriodNumber
>
> if I understand the original formula correctly.

Thanks! Works perfectly!

-monz
http://tonalsoft.com
Tonescape microtonal music software