Wikipedia "pitch space" page

While we're on the subject of Wikipedia pages about tuning ...

I find it plain wrong that the page on "pitch space"
makes no mention of Fokker, Ben Johnston, Erv Wilson,
me, or Paul Erlich.

http://en.wikipedia.org/wiki/Pitch_space

Geometrical modeling of pitch space is certainly the
most important aspect of my own work, and i would say
the same is true of Fokker and Wilson, and probably
Johnston and Erlich too ... and perhaps Graham Breed.

It would be nice if someone would add the appropriate
info, and perhaps include the appropriate citations
and links to my, Erlich's, and Kraig Grady's (and
Graham's?) webpages.

(I know, Carl, that you are the one hosting Paul's papers.)

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

--- In tuning@yahoogroups.com, "monz" <joemonz@...> wrote:
>
> While we're on the subject of Wikipedia pages about tuning ...
>
> I find it plain wrong that the page on "pitch space"
> makes no mention of Fokker, Ben Johnston, Erv Wilson,
> me, or Paul Erlich.
>
> http://en.wikipedia.org/wiki/Pitch_space

What have you contributed to the topic?

> Geometrical modeling of pitch space is certainly the
> most important aspect of my own work,

Does the Monzo lattice exist in a space? If so, what kind?

-Carl

Hi Carl,

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "monz" <joemonz@> wrote:
> >
> > While we're on the subject of Wikipedia pages about tuning ...
> >
> > I find it plain wrong that the page on "pitch space"
> > makes no mention of Fokker, Ben Johnston, Erv Wilson,
> > me, or Paul Erlich.
> >
> > http://en.wikipedia.org/wiki/Pitch_space
>
> What have you contributed to the topic?

Umm ... how about this: i created the only software
in existence (AFAIK) which *directly* uses geometrical
pitch-space as a compositional tool.

> > Geometrical modeling of pitch space is certainly the
> > most important aspect of my own work,
>
> Does the Monzo lattice exist in a space? If so, what kind?

The type of lattice which i refer to as a "Monzo lattice"
is based on JI, recognizes 2:1 (octave) equivalence, and
has a unique axis for each prime-factor of the tuning.
There is an imaginary circle around each lattice point
to represent the 2:1, and the logarithmic pitch-height
of each prime-factor determines the angle from which
that prime's axis protrudes from each lattice point.

Probably the nicest example of this "Monzo lattice" is
one that i made of Partch's 43-tone 11-limit JI tuning
-- the last lattice on this page:

http://tonalsoft.com/monzo/partch/scale/partch43-lattice.aspx

The fullest explanation of the Monzo lattice formula is here:

http://tonalsoft.com/monzo/lattices/lattices.htm

And then there's the applet that Ming Sun Ho made
where you can see the Monzo lattice grow as you
increase the prime-limit:

http://tonalsoft.com/monzo/lattices/ming/ming.htm

I've been taking math courses in hope of being able to
explain all this better, but i haven't reached that
level of mathematics yet. So i can't explain what kind
of space this is, beyond what i've already said about
JI, prime-factors, and 2:1 equivalence. I'm sure the
less math-challenged here can figure out a good way
to explain it.

I'm disappointed that my Monzo lattice formula was
not implemented in Tonescape before the project ran
out of money. The lattices Tonescape makes are great,
but of course i'm partial to my own lattice formula.
(no pun intended)

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

Hi Monz,

In my opinion, tonescape does deserve an external link on the
pitch space entry. Chris probably deserves some credit too,
don'tcha think?

As I think you already know, I do not believe your style of
"lattice" has any theoretical merit whatsoever. In a decade
on these lists, I've never seen anyone present a cogent
argument why they do. The best argument for them that I know
of is that you think they're 'a great way to display the
information'. But feel free to enlighten us.

-Carl

--- In tuning@yahoogroups.com, "monz" <joemonz@...> wrote:
>
> Hi Carl,
>
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> >
> > --- In tuning@yahoogroups.com, "monz" <joemonz@> wrote:
> > >
> > > While we're on the subject of Wikipedia pages about tuning ...
> > >
> > > I find it plain wrong that the page on "pitch space"
> > > makes no mention of Fokker, Ben Johnston, Erv Wilson,
> > > me, or Paul Erlich.
> > >
> > > http://en.wikipedia.org/wiki/Pitch_space
> >
> > What have you contributed to the topic?
>
>
> Umm ... how about this: i created the only software
> in existence (AFAIK) which *directly* uses geometrical
> pitch-space as a compositional tool.
>
>
> > > Geometrical modeling of pitch space is certainly the
> > > most important aspect of my own work,
> >
> > Does the Monzo lattice exist in a space? If so, what kind?
>
>
> The type of lattice which i refer to as a "Monzo lattice"
> is based on JI, recognizes 2:1 (octave) equivalence, and
> has a unique axis for each prime-factor of the tuning.
> There is an imaginary circle around each lattice point
> to represent the 2:1, and the logarithmic pitch-height
> of each prime-factor determines the angle from which
> that prime's axis protrudes from each lattice point.
>
>
> Probably the nicest example of this "Monzo lattice" is
> one that i made of Partch's 43-tone 11-limit JI tuning
> -- the last lattice on this page:
>
> http://tonalsoft.com/monzo/partch/scale/partch43-lattice.aspx
>
>
> The fullest explanation of the Monzo lattice formula is here:
>
> http://tonalsoft.com/monzo/lattices/lattices.htm
>
>
> And then there's the applet that Ming Sun Ho made
> where you can see the Monzo lattice grow as you
> increase the prime-limit:
>
> http://tonalsoft.com/monzo/lattices/ming/ming.htm
>
>
> I've been taking math courses in hope of being able to
> explain all this better, but i haven't reached that
> level of mathematics yet. So i can't explain what kind
> of space this is, beyond what i've already said about
> JI, prime-factors, and 2:1 equivalence. I'm sure the
> less math-challenged here can figure out a good way
> to explain it.
>
>
> I'm disappointed that my Monzo lattice formula was
> not implemented in Tonescape before the project ran
> out of money. The lattices Tonescape makes are great,
> but of course i'm partial to my own lattice formula.
> (no pun intended)
>
>
> -monz
> http://tonalsoft.com/tonescape.aspx
> Tonescape microtonal music software
>

Hi Carl,

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Hi Monz,
>
> In my opinion, tonescape does deserve an external link
> on the pitch space entry. Chris probably deserves some
> credit too, don'tcha think?

Sure, i'd have to agree with that. Chris has done a
fantastic job of implementing my ideas about what the
best lattice-drawing music composition software should be.

For about a year, Wikipedia did have a page about Tonescape,
and at one point i edited it to include more information,
and i mentioned Chris.

Unfortunately, the project has been stalled for two full
years now, because we need investment capital to continue.
But fortunately, Chris has already put the "hooks" in
Tonescape on which we can easily hang further code to
implement the features we know we want but which are
still missing. The source code has become too large for
him to continue coding by himself, and with an infusion
of investment money, we would hire a team of programmers
to work under him.

But anyway, making the current version of Tonescape
available for free has not resulted in the amount of
use we had hoped for, because too many potential users
have had problems installing it or getting it running.
So we would like to migrate the graphics engine from
Windows DirectX to OpenGL, but again, that requires
time and programming work which we cannot do now.

> As I think you already know, I do not believe your style of
> "lattice" has any theoretical merit whatsoever. In a decade
> on these lists, I've never seen anyone present a cogent
> argument why they do. The best argument for them that I know
> of is that you think they're 'a great way to display the
> information'. But feel free to enlighten us.

Yes, well, obviously Chris felt the same way, because
he didn't implement my lattice formula in Tonescape either.
Instead, he used a formula which makes all axis angles
as orthogonal as possible. It's obvious that for 2-d
this creates a plane divided into squares, and for 3-d
it creates a space divided into cubes. For higher dimensions,
i can't explain what's going on, because they are ultimately
still projections of >3-d space down into 3-d. But Tonescape
will allow the user to create Tonespaces with up to
7 dimensions. For example, with a 2:1 equivalence-interval
using one dimension, you could let the other six dimensions
represent prime-factors 3, 5, 7, 11, 13, and 17, giving
you the full 17-limit JI with octave-equivalence.

But you aren't required to use tunings with an equivalence
interval. I've created Tonescape Tuning files for ancient
Greek genera which illustrate this: they occupy the 2-octave
pitch-space described by all ancient Greek theorists, without
an equivalence interval.

And of course, the axes of a Tonespace don't have to
represent prime-factors -- they can be anything. For
example, i have Tonescape Tuning files of Brink's
"Pyramid of Mars" tuning, which uses phi as a generator:

http://tonalsoft.com/enc/m/mars-pyramid.aspx

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