Chromatic Unison Vector

Hate to ask this, but could someone give me a good definition of a
chromatic unison vector? I'm fiddling with matrices and need to know

Thanks

It's just a unison vector in the sense that it defines the
periodicity block in the same way, but it's a different one in
the strict sense because the periodicity block will have
intervals smaller than this chromatic unison vector, which is
normally avoided. So it's always the largest unison vector of
the set, and called "chromatic" because it's not supposed to
"vanish".

Manuel

--- In tuning-math@yahoogroups.com, "Manuel Op de Coul"
<manuel.op.de.coul@e...> wrote:
>
> It's just a unison vector in the sense that it defines the
> periodicity block in the same way, but it's a different one in
> the strict sense because the periodicity block will have
> intervals smaller than this chromatic unison vector, which is
> normally avoided. So it's always the largest unison vector of
> the set, and called "chromatic" because it's not supposed to
> "vanish".
>
> Manuel

Thanks. Can you point me to an example? I am trying to use Graham's
method of calculating generators from unison vector and commas. I'm
pretty close, but don't always know what unison vector to use...

The non-chromatic unison vectors are called commatic unison
vectors. This is a simple example: 64/63 and 50/49 commatic and
36/35 chromatic. The PB is
21/20 8/7 6/5 49/40 4/3 7/5 3/2 8/5 12/7 7/4 28/15 2/1
This be tempered I think with a half-octave period.

Manuel

--- In tuning-math@yahoogroups.com, "Paul G Hjelmstad"
<paul.hjelmstad@u...> wrote:
> Hate to ask this, but could someone give me a good definition of a
> chromatic unison vector? I'm fiddling with matrices and need to know

Have you read these excellent articles by Paul Erlich?

http://sonic-arts.org/td/erlich/intropblock1.htm
http://lumma.org/tuning/erlich/erlich-tFoT.pdf

--- In tuning-math@yahoogroups.com, "Manuel Op de Coul"
<manuel.op.de.coul@e...> wrote:
>
> It's just a unison vector in the sense that it defines the
> periodicity block in the same way, but it's a different one in
> the strict sense because the periodicity block will have
> intervals smaller than this chromatic unison vector, which is
> normally avoided.

That's not accurate. For example, the JI diatonic scale has no
intervals smaller than the chromatic unison vector, whether you
consider the latter to be 25:24, 135:128, or 250:243.

> So it's always the largest unison vector of
> the set,

although its JI pre-image may not the largest.

> and called "chromatic" because it's not supposed to
> "vanish".
>
> Manuel

--- In tuning-math@yahoogroups.com, paul.hjelmstad@u... wrote:
> --- In tuning-math@yahoogroups.com, "Manuel Op de Coul"
> <manuel.op.de.coul@e...> wrote:
> >
> > It's just a unison vector in the sense that it defines the
> > periodicity block in the same way, but it's a different one in
> > the strict sense because the periodicity block will have
> > intervals smaller than this chromatic unison vector, which is
> > normally avoided. So it's always the largest unison vector of
> > the set, and called "chromatic" because it's not supposed to
> > "vanish".
> >
> > Manuel
>
> Thanks. Can you point me to an example? I am trying to use Graham's
> method of calculating generators from unison vector and commas. I'm
> pretty close, but don't always know what unison vector to use...

Graham says "chromatic unison vector" in that method, but doesn't
really mean it. Any non-unison works as well. Try 3/2, since that's
rarely a chromatic unison!

--- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:
> --- In tuning-math@yahoogroups.com, paul.hjelmstad@u... wrote:
> > --- In tuning-math@yahoogroups.com, "Manuel Op de Coul"
> > <manuel.op.de.coul@e...> wrote:
> > >
> > > It's just a unison vector in the sense that it defines the
> > > periodicity block in the same way, but it's a different one in
> > > the strict sense because the periodicity block will have
> > > intervals smaller than this chromatic unison vector, which is
> > > normally avoided. So it's always the largest unison vector of
> > > the set, and called "chromatic" because it's not supposed to
> > > "vanish".
> > >
> > > Manuel
> >
> > Thanks. Can you point me to an example? I am trying to use
Graham's
> > method of calculating generators from unison vector and commas.
I'm
> > pretty close, but don't always know what unison vector to use...
>
> Graham says "chromatic unison vector" in that method, but doesn't
> really mean it. Any non-unison works as well. Try 3/2, since that's
> rarely a chromatic unison!

I meant rarely a *commatic* unison -- the thing you have to avoid for
Graham's method!

--- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:
> --- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
> wrote:
> > --- In tuning-math@yahoogroups.com, paul.hjelmstad@u... wrote:
> > > --- In tuning-math@yahoogroups.com, "Manuel Op de Coul"
> > > <manuel.op.de.coul@e...> wrote:
> > > >
> > > > It's just a unison vector in the sense that it defines the
> > > > periodicity block in the same way, but it's a different one in
> > > > the strict sense because the periodicity block will have
> > > > intervals smaller than this chromatic unison vector, which is
> > > > normally avoided. So it's always the largest unison vector of
> > > > the set, and called "chromatic" because it's not supposed to
> > > > "vanish".
> > > >
> > > > Manuel
> > >
> > > Thanks. Can you point me to an example? I am trying to use
> Graham's
> > > method of calculating generators from unison vector and commas.
> I'm
> > > pretty close, but don't always know what unison vector to use...
> >
> > Graham says "chromatic unison vector" in that method, but doesn't
> > really mean it. Any non-unison works as well. Try 3/2, since
that's
> > rarely a chromatic unison!
>
> I meant rarely a *commatic* unison -- the thing you have to avoid
for
> Graham's method!

Now I am a bit confused. The only way I have gotten this to work is
to take the adjoint of [1 0 0 0 ... and the rest of the matrix as
commas.] That is, if you want the first column of the final matrix
to be a temperment map. I've tried -7 1 1 1 as a non-unison vector
but that doesn't work. (I've tried several calculations).

Paul