JIP

http://66.98.148.43/~xenharmo/top.htm

If the JIP is not a point in the original space it operates on, then
it probably shouldn't be referred to as a point. Rather, it seems to
measure pitch, so why not refer to it as PITCH or something? (You
probably asked me if I preferred that already but I had even less
idea what it meant then.)

--- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:
> http://66.98.148.43/~xenharmo/top.htm
>
> If the JIP is not a point in the original space it operates on,
then
> it probably shouldn't be referred to as a point.

It's a vector in a normed vector space, and these are sometimes
called points if you are thinking of the geometry involved.

Rather, it seems to
> measure pitch, so why not refer to it as PITCH or something?

I did call it SIZE, which I recall you didn't like. Anyway, I don't
think your remark makes much sense--it's just as much a point as
something in the Tenney space.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
> wrote:
> > http://66.98.148.43/~xenharmo/top.htm
> >
> > If the JIP is not a point in the original space it operates on,
> then
> > it probably shouldn't be referred to as a point.
>
> It's a vector in a normed vector space, and these are sometimes
> called points if you are thinking of the geometry involved.

Thinking about the geometry involved, I understand that for any given
value returned by JIP, there is an n-1 dimensional hyperplane in
Tenney space.

> > Rather, it seems to
> > measure pitch, so why not refer to it as PITCH or something?
>
> I did call it SIZE, which I recall you didn't like. Anyway, I don't
> think your remark makes much sense--it's just as much a point as
> something in the Tenney space.

I'm smiling, but I don't think there's any hope of us ever writing a
paper together.

So does it measure pitch or not?

--- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:

> So does it measure pitch or not?

It maps monzos to pitches.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
> wrote:
>
> > So does it measure pitch or not?
>
> It maps monzos to pitches.

So when it operates on monzos (which would seem to be the understood
role of a functional in Tenney space), it returns the pitch. This
seems like a basic thing you'd want to inform the reader of . . .