cylindrical meantone diatonic lattice, flat projection

[sorry all ... sent this with the wrong subject line before]

Since I've never drawn one of these before, and I just
made one for a private email to Paul, I'd like to share...

Here's a cylindrical meantone diatonic lattice, flat projection:

,,--B
,,--E--'' / \
,,--A--'' / \ / \
..D-''.../..\..../....\../..,,--D..
\ / \ / ,,--G--''
\ / ,,--C--''
F--''

-monz

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--- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> [sorry all ... sent this with the wrong subject line before]
>
>
> Since I've never drawn one of these before, and I just
> made one for a private email to Paul, I'd like to share...
>
>
> Here's a cylindrical meantone diatonic lattice, flat projection:
>
>
> ,,--B
> ,,--E--'' / \
> ,,--A--'' / \ / \
> ..D-''.../..\..../....\../..,,--D..
> \ / \ / ,,--G--''
> \ / ,,--C--''
> F--''

That's very nice -- for those who are confused, the dotted line is
actually rolled into a circle so that the two Ds meet at a point.

Also, if viewing this on the website, you'll need to click
on "Message Index" and then "Expand Messages" to view this properly.

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
> >
> > [sorry all ... sent this with the wrong subject line before]
> >
> >
> > Since I've never drawn one of these before, and I just
> > made one for a private email to Paul, I'd like to share...
> >
> >
> > Here's a cylindrical meantone diatonic lattice, flat projection:
> >
> >
> > ,,--B
> > ,,--E--'' / \
> > ,,--A--'' / \ / \
> > ..D-''.../..\..../....\../..,,--D..
> > \ / \ / ,,--G--''
> > \ / ,,--C--''
> > F--''
>
> That's very nice -- for those who are confused, the dotted line is
> actually rolled into a circle so that the two Ds meet at a point.
>
> Also, if viewing this on the website, you'll need to click
> on "Message Index" and then "Expand Messages" to view this properly.

Monz, let me say that it's so nice to finally see you making lattices
which really reflect most of the music you're interested in :)

A meantone pentatonic scale would look like this:

> > ,,--E
> > ,,--A--'' / \
> > ..D-''......\..../....\.....,,--D..
> > \ / ,,--G--''
> > C--''

Anyway, here's a lattice which reflects my recent observation that
tempering out 135:128 (instead of 81:80) gives you a Pelog scale. I
use the notation on the third page (p. 38) of
http://www.anaphoria.com/mcphee.PDF :

> > I--,,
> > / \ ''--U--,,
> > ..O,,......./....\..../.....''--O..
> > ''--A--,, \ /
> > ''--E

You know what to do to view this properly. Note that both scales are
5 notes in a chain of fifths, with major and minor triads formed
where the chain is broken -- but one has a major triad where the
other has a minor triad, and vice versa!

> From: paulerlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, January 27, 2002 10:56 PM
> Subject: [tuning] Re: cylindrical meantone diatonic lattice, flat
projection
>
>
> A meantone pentatonic scale would look like this:
>
> > > ,,--E
> > > ,,--A--'' / \
> > > ..D-''......\..../....\.....,,--D..
> > > \ / ,,--G--''
> > > C--''
>
> Anyway, here's a lattice which reflects my recent observation that
> tempering out 135:128 (instead of 81:80) gives you a Pelog scale. I
> use the notation on the third page (p. 38) of
> http://www.anaphoria.com/mcphee.PDF :
>
> > > I--,,
> > > / \ ''--U--,,
> > > ..O,,......./....\..../.....''--O..
> > > ''--A--,, \ /
> > > ''--E
>
> You know what to do to view this properly. Note that both scales are
> 5 notes in a chain of fifths, with major and minor triads formed
> where the chain is broken -- but one has a major triad where the
> other has a minor triad, and vice versa!

Hmmm... that's an interesting symmetrical relationship.

-monz

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--- In tuning@y..., "monz" <joemonz@y...> wrote:

> Hmmm... that's an interesting symmetrical relationship.

It arises from the fact that 81:80 is three fifths "plus" a minor
third, while 135:128 is three fifths "plus" a major third.