# [PD] phasor time scaling

Frank Barknecht fbar at footils.org
Sun Dec 9 18:53:24 CET 2007

```Hallo,
Jamie Bullock hat gesagt: // Jamie Bullock wrote:

> Hi Frank,
>
> On Sat, 2007-12-08 at 14:24 +0100, Frank Barknecht wrote:
> > Hallo,
> > Jamie Bullock hat gesagt: // Jamie Bullock wrote:
> >
> > > Has anyone implemented 'phasor time scaling' as an abstraction (or
> > > external)? I know it is relatively easy scale a phasor where the
> > > frequency of the scaled phasor is an integer multiple of the master
> > > phasor:
> > >
> > > [phasor~]
> > > |
> > > [*~ 2]
> > > |
> > > [wrap~]
> > >
> > > ...but what about non-integer multiples, and fractional scaling?
> >
> > A full phasor~ whose frequency is a non-integer multiple of the freq
> > of another phasor~ will not start again at zero everytime, when the
> > first phasor~ starts at zero. For example a phasor with 1.5 times the
> > frequency of the first phasor~ would be in sync only every 3 cycles.
> > So you cannot sync the second phasor with the first phasor on *every*
> > jump of the first phasor with wrap~ ... without keeping track of where
> > the second phasor is.
>
> Sure. I think you might have misunderstood the question.

That may well be. ;)

So to clarify:

Suppose I have a phasor with period p1 (and thus freq=1/p1) and I want
to generate a signal with p2 = 1.5 * p1. Then I have (at least) two
ways to do this ("|" should indicate the jumps):

p1:  |.....|.....|.....|.....|.....|

p2a: |........|........|........|....
p2b: ......|........|........|........|....

Turn p1 and p2 around and you get a similar situation for trying to
generate a phasor with a frequency of 1.5 times the original
frequency:

p2:   |........|........|........|....

p1a:  |.....|.....|.....|.....|.....|
p1b:  ...|.....|.....|.....|.....|.....|

I suppose, you don't really care which sync point to use, only that
both phasors sync at the least common multiple of their periods,
right? That's where I suggested to use an additional phasor with a
period of the LCM of the phasor signals you'd like to achieve in the
end, and sync to that. (As the LCM of two numbers generally is larger
than the single numbers, that phasor~ would be slower.)

Anyway, otherwise "something" would need to discern between jumps in
the driving phasor that should and those jumps that should not trigger
a jump in the resulting phasor signal. I think that's tricky: Where to
get the needed info for "something"?

Ciao
--
Frank Barknecht                                     _ ______footils.org__

```