RE: 9-limit lattices

>I've been reviewing saturated chords for my website. Although
>Paul Erlich used these as an argument for giving 9 a separate
>direction

Did I really argue that way? I thought my reasons for sometimes giving 9
a separate direction had nothing to do with saturated chords. Although I
may have used a saturated chord as an example of a 9-limit harmony.

>As there are no 7s, we can use a tetrahedral lattice with 9 at
>the apex. The chords then become:
>
> 5 5----15
> / \ \ /
> / 9 \ 9 \ /
> 1-----3 3
>
>Which doesn't look as clear to me.

I would have to disagree with the way you drew those pictures. The
3-limit connection between 3 and 9 is very important, so I would include
an additional 9 to the right of 3 in both chords. As I have said before,
the disadvantage of giving composites their own axes is that certain
notes often have to appear in more than one place in the lattice.


>The reason is that these
>anomalous suspensions work because of the compositeness of 9.

True.

>A lattice that treats 9 as prime can't show that.

Unless you put 9 in two places.

>I can understand why 9 is a separate axis in Erv Wilson's
>diagrams.

In all of his diagrams that I've seen, 9 is NOT a separate axis.


>The way the scales are generated, there's no confusion.

I'm confused.

>For general lattices, though, why? If you want the otonality
>to look like a primary unit, how about a double linkage?

> 5
> / \
> / 7 \
> 1=====3-----9

Something along those lines might be the best solution, although (I'm
assuming you have invisible lines connecting 7 to the other identities)
I would still want to have 9 directly connected to 5 and to 7. The
advantage of giving 9 its own axis is that such connections can be
easily made without a messy tangle of lines.

>Now, a curved
>structure in 5-dimensional space, that might work...

Right, one where the two occurences of 9 would coincide due to the
curvature.