Yahoo Tuning Groups Ultimate Backup tuning-math Extensions of Tripod Notation

--- In tuning-math@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> I've been working on this for the past week:
>
> http://x31eq.com/magic/tripex.pdf
>
> It's about tripod notation, but it also works as a study of
> the Marvel family. It's done but not finished. I'll keep
> tweaking until I'm completely fed up with it.

I've been looking at your original tripod paper, and it seems to be based on the fact that the 3d val, <3 5 7 9|, supports magic. It suggests to me that it could be used for the stuff I've recently done with tablets. I don't know if you'd find that interesting or not, but tablets are a sort of cross between a notation system and a compositional aid.

🔗Mike Battaglia <battaglia01@gmail.com>

On Tue, Oct 18, 2011 at 1:47 PM, genewardsmith
<genewardsmith@sbcglobal.net> wrote:
>
> --- In tuning-math@yahoogroups.com, Graham Breed <gbreed@...> wrote:
> >
> > I've been working on this for the past week:
> >
> > http://x31eq.com/magic/tripex.pdf
> >
> > It's about tripod notation, but it also works as a study of
> > the Marvel family. It's done but not finished. I'll keep
> > tweaking until I'm completely fed up with it.
>
> I've been looking at your original tripod paper, and it seems to be based on the fact that the 3d val, <3 5 7 9|, supports magic. It suggests to me that it could be used for the stuff I've recently done with tablets. I don't know if you'd find that interesting or not, but tablets are a sort of cross between a notation system and a compositional aid.

I still wish I knew what tablets were about. I feel like you've made
some big insight but I can't figure out what it is. Is it a
generalization of phrases like "minor 7th," which implies the <7 11
16| val or something?

I tried to ask you this on Facebook a while ago but never got a
response: the idea is that a tablet is split into two parts: (n, c),
where n is a "note number," and c is an n-tuple that somehow
represents the chord quality. Is that right, and if so, is n defined
with respect to a val?

-Mike

🔗Graham Breed <gbreed@gmail.com>

"genewardsmith" <genewardsmith@sbcglobal.net> wrote:

> I've been looking at your original tripod paper, and it
> seems to be based on the fact that the 3d val, <3 5 7 9|,
> supports magic. It suggests to me that it could be used
> for the stuff I've recently done with tablets. I don't
> know if you'd find that interesting or not, but tablets
> are a sort of cross between a notation system and a
> compositional aid.

Tripod notation is bases on the facts that 3d&19 supports
Magic, I wanted more than 3 and less than 19 staff
positions to the octave, and 3d&9&19 supports Marvel.
Given the 3d&9&19 mapping, the tripod scale, and semitoe
and inch accidentals, you can write any Marvel chord
uniquely. Given some redundant accidentals, you lose that
uniqueness. The same principles would apply to any other
planar notation.

I found tablets here:

http://xenharmonic.wikispaces.com/Tablets

I'm still digesting it. I see it starts with "The 5-limit
3et tablet". That's likely to be useful with tricycle
notation. I lose the thread because I don't know what e3
and e5 are doing there and how they get to be monzos.

Graham

🔗Mike Battaglia <battaglia01@gmail.com>

On Tue, Oct 18, 2011 at 2:58 PM, Graham Breed <gbreed@gmail.com> wrote:
>
> I found tablets here:
>
> http://xenharmonic.wikispaces.com/Tablets
>
> I'm still digesting it. I see it starts with "The 5-limit
> 3et tablet". That's likely to be useful with tricycle
> notation. I lose the thread because I don't know what e3
> and e5 are doing there and how they get to be monzos.
>
> Graham

It has something to do with defining them around vals in a creative
way that's not explicitly written on the page. You can see the
discussion page where I ask Gene more about it.

-Mike

🔗genewardsmith <genewardsmith@sbcglobal.net>

--- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> I still wish I knew what tablets were about. I feel like you've made
> some big insight but I can't figure out what it is.

It's an idea I had before showing up here that I used for a few pieces
such as the Clinton variations and Threnody for the Victims of Wolfgang Amadeus Mozart. So, one thing it is is something you can use to write music with.

> I tried to ask you this on Facebook a while ago but never got a
> response: the idea is that a tablet is split into two parts: (n, c),
> where n is a "note number," and c is an n-tuple that somehow
> represents the chord quality. Is that right, and if so, is n defined
> with respect to a val?

It's best when n is defined via a val, where <val|chord(n, c) = n, since that way things sort themselves out more coherently, but it's not a requirement.

🔗genewardsmith <genewardsmith@sbcglobal.net>

🔗Mike Battaglia <battaglia01@gmail.com>

On Tue, Oct 18, 2011 at 4:00 PM, genewardsmith
<genewardsmith@sbcglobal.net> wrote:
>
> > I tried to ask you this on Facebook a while ago but never got a
> > response: the idea is that a tablet is split into two parts: (n, c),
> > where n is a "note number," and c is an n-tuple that somehow
> > represents the chord quality. Is that right, and if so, is n defined
> > with respect to a val?
>
> It's best when n is defined via a val, where <val|chord(n, c) = n, since that way things sort themselves out more coherently, but it's not a requirement.

What's the chord(n, c) function do? It has to return some kind of
monzo for you to be dot producting it with the val, right?

-Mike

🔗Graham Breed <gbreed@gmail.com>

"genewardsmith" <genewardsmith@sbcglobal.net> wrote:
>
>
> --- In tuning-math@yahoogroups.com, Graham Breed
> <gbreed@...> wrote: I lose the thread because I don't
> know what e3
> > and e5 are doing there and how they get to be monzos.
>
> A 5-limit monzo for 2^e2 3^e3 5^e5 is |e2 e3 e5>.

Yes, so what's <* e3 e5|? If it's written in terms of
monzos, it means e3 and e5 must be monzos. If it's a typo
for |* e3 e5>, along with the |r e3 e5>, why haven't you
fixed it yet? I have to assume it really should be <r e3
e5|, in which case I don't understand it. That's a big
obstacle to get over in the first example.

Graham

🔗Graham Breed <gbreed@gmail.com>

"genewardsmith" <genewardsmith@sbcglobal.net> wrote:

Tablets, then, seem to be chords used as scales. You
define the scale, and then define a pitch as a degree of
the scale. Except the scale can change, so a pitch is a
pair of {degree, specification of the scale it's a degree
of}. And you call the scale a chord.

It's an interesting idea. I wrote the musical examples in
this new paper (which still doesn't exist on paper) by
getting a single chord worked out, transposing it to
different degrees, and deleting the ones Lilypond gave an
error for. I can see that same approach working for real
music. So, for an example so dumbed down it isn't useful,
you could have a tune in C major

c d e d e f c

and decided you want to move it to C minor. For some
reason, you don't know how to write accidentals. But you
can move it to A minor

a b c' b c' d' a

and then transpose that to C

\transpose a c {a b c' b c' d' a}

In a piece with big chords and no static scale, where you
want the melody to follow the chords, this kind of thing
would make more sense.

There are ways of specifying chords/scales as functions in
Lilypond as well. You can do almost anything given that
it's really a Scheme dialect. So we can imagine

\tablet #0 c4 \major
\tablet #1 c \major
\tablet #2 c \major
\tablet #1 c \major
\tablet #2 c \major
\tablet #3 c \major
\tablet #0 c \major

but I don't find that particularly readable. There is a
limitation of the syntax that stops you writing pitches as
numbers, so the rhythm has to be part of the chord
specification.

Graham

🔗genewardsmith <genewardsmith@sbcglobal.net>

--- In tuning-math@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> "genewardsmith" <genewardsmith@...> wrote:
> >
> >
> > --- In tuning-math@yahoogroups.com, Graham Breed
> > <gbreed@> wrote: I lose the thread because I don't
> > know what e3
> > > and e5 are doing there and how they get to be monzos.
> >
> > A 5-limit monzo for 2^e2 3^e3 5^e5 is |e2 e3 e5>.
>
> Yes, so what's <* e3 e5|?

A typo, which I've now fixed.

🔗Mike Battaglia <battaglia01@gmail.com>

🔗genewardsmith <genewardsmith@sbcglobal.net>

🔗Mike Battaglia <battaglia01@gmail.com>

On Wed, Oct 19, 2011 at 4:44 PM, genewardsmith
<genewardsmith@sbcglobal.net> wrote:
>
> --- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > On Tue, Oct 18, 2011 at 4:04 PM, Mike Battaglia <battaglia01@...> wrote:
> > >
> > > What's the chord(n, c) function do? It has to return some kind of
> > > monzo for you to be dot producting it with the val, right?
> >
> > I'd still like a response to this when Gene has a second...
>
> I responded yesterday.

Doesn't seem like it went through, it's neither in my inbox nor on tuning-math.

-Mike

🔗genewardsmith <genewardsmith@sbcglobal.net>

--- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> > It's best when n is defined via a val, where <val|chord(n, c) = n, since that way things sort themselves out more coherently, but it's not a requirement.
>
> What's the chord(n, c) function do? It has to return some kind of
> monzo for you to be dot producting it with the val, right?

I really meant to say note(n, c), which returns a monzo which the val maps to n, and which designates a note in the chord c.

🔗Mike Battaglia <battaglia01@gmail.com>

On Tue, Oct 18, 2011 at 4:10 PM, genewardsmith
<genewardsmith@sbcglobal.net> wrote:
>
> --- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > > It's best when n is defined via a val, where <val|chord(n, c) = n, since that way things sort themselves out more coherently, but it's not a requirement.
> >
> > What's the chord(n, c) function do? It has to return some kind of
> > monzo for you to be dot producting it with the val, right?
>
> I really meant to say note(n, c), which returns a monzo which the val maps to n, and which designates a note in the chord c.

Oh ho ho, there it is. I was going to send another message about this
soon. Only 12 days late Yahoo, good work.

So note(n,c) returns the nth note in ascending pitch order from the
bottom of the chord? For example, note(0,4:5:6) would return the note
I just called "4", and note(1,4:5:6) would return "5"?

If so, you're saying that tablets work best with respect to the val <1
2 3 4 5 ...| in the basis of note(n)/note(0), or intervals over the
root, right? For example, the basis of intervals over the root for
4:5:6:7:8 would be [5/4, 3/2, 7/4, 2/1], and in that basis you want
the val <1 2 3 4|, which when changed to [2/1, 3/1, 5/1, 7/1] yields
the val <4 6 9 11|.

-Mike