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series within a generalized periodicity

🔗D.Stearns <STEARNS@CAPECOD.NET>

11/2/2000 1:16:24 PM

I've just started working on a new piece that uses a group of scales,
or series, that are derived from a method I don't believe I've
encountered before.

The idea is simply to generalize the "P" in (LOG(N)-LOG(D))*(P/LOG(2))
so that alternate -- or "generalized" -- over and under series can be
derived within a given P (i.e., a given non 1:2 periodicity).

As an example of this, here's two of the "scales" that figure
prominently in the piece I'm currently working on:

0 270 511 729 928 1111 1281 1439 1586

0 199 382 552 710 858 996 1127 1251 1368 1480 1586

These eight and eleven note "scales" are actually just an 8 - 16 and
11 - 22 over series where P = 2:5.

The possibilities are endless, extremely xenharmonic, and so far as
I've gone into them, interesting as well.

--Dan Stearns

🔗Paul Erlich <PERLICH@ACADIAN-ASSET.COM>

11/3/2000 10:19:59 AM

--- In tuning@egroups.com, "D.Stearns" <STEARNS@C...> wrote:
> I've just started working on a new piece that uses a group of
scales,
> or series, that are derived from a method I don't believe I've
> encountered before.
>
> The idea is simply to generalize the "P" in (LOG(N)-LOG(D))*(P/LOG
(2))
> so that alternate -- or "generalized" -- over and under series can
be
> derived within a given P (i.e., a given non 1:2 periodicity).
>
> As an example of this, here's two of the "scales" that figure
> prominently in the piece I'm currently working on:
>
> 0 270 511 729 928 1111 1281 1439 1586
>
> 0 199 382 552 710 858 996 1127 1251 1368 1480 1586
>
> These eight and eleven note "scales" are actually just an 8 - 16 and
> 11 - 22 over series where P = 2:5.

I'm having trouble reproducing your results using the formula above.
Could you check the formula you're using?