Question for Kraig Grady

Kraig, Dave Keenan brought up the interesting issue of how many CPSs that
use composite factors other than 1 have "extra" consonant intervals --
intervals that are not considered consonant by the CPS formalism but are
exactly equal to others that are -- for example, 3*7/1*9. Don't these
intervals "destroy" the structural integrity of the CPSs in much the same
way as when you claimed tempering the CPSs to add more consonances would
"destroy" the structural integrity of the CPSs?

Paul!
Well if you use the 3*7 /1*9 as a 7/6 yes you would weakening the structural relationship.
If used as opposite points in a 1-3-7-9 hexany this 7/6 becomes a dissonant in the same way a
B Major chord, although consonant to itself, could be heard as a dissonant in the key of C.
Especially when you complete each triad to a tetrad does it become clear that a 9 is a 9 and
not a 3. One can you the structure as nothing more than a set of very closely related pitches,
but to highlight the structural element offer one new resources. A context where 7/6 could be
a consonance in one place and a dissonance in another. I have to state that Erv has pointed
out points where and how things can be tempered. Like I pointed out in a recent post, It is
hard to tell if Erv was checking out my thoughts or he consider this a good idea. In certain
cases he will be more free (allowing maybe a cent) and in other cases where something relies
on difference tones, absolutely no tolerance at all.

BTW I want to point out how sometimes that which is under our nose gets overlooked. When Kris
Peck was recently in L.A., he showed me how two 1-3-5-7 hexanies a 3/2 apart are a 10 tone
constant structure. How did we missed that!!!!!!!!!!!

"Paul H. Erlich" wrote:

> Kraig, Dave Keenan brought up the interesting issue of how many CPSs that
> use composite factors other than 1 have "extra" consonant intervals --
> intervals that are not considered consonant by the CPS formalism but are
> exactly equal to others that are -- for example, 3*7/1*9. Don't these
> intervals "destroy" the structural integrity of the CPSs in much the same
> way as when you claimed tempering the CPSs to add more consonances would
> "destroy" the structural integrity of the CPSs?
>

-- Kraig Grady
North American Embassy of Anaphoria island
www.anaphoria.com

Kraig wrote,

>Well if you use the 3*7 /1*9 as a 7/6 yes you would weakening the
structural relationship.
>If used as opposite points in a 1-3-7-9 hexany this 7/6 becomes a dissonant
in the same way a
>B Major chord, although consonant to itself, could be heard as a dissonant
in the key of C.

umm . . . what is acting as the analogue to the "key of C" in this analogy?

>Especially when you complete each triad to a tetrad does it become clear
that a 9 is a 9 and
>not a 3.

You're speaking of stellation, right?

>One can you the structure as nothing more than a set of very closely
related pitches,
>but to highlight the structural element offer one new resources. A context
where 7/6 could be
>a consonance in one place and a dissonance in another. I have to state that
Erv has pointed
>out points where and how things can be tempered.

I'm sure we'd all love to hear more about Erv's views on this.

>BTW I want to point out how sometimes that which is under our nose gets
overlooked. When Kris
>Peck was recently in L.A., he showed me how two 1-3-5-7 hexanies a 3/2
apart are a 10 tone
>constant structure. How did we missed that!!!!!!!!!!!

That's interesting! Maybe you missed it because you weren't specifically
focusing on 10-tone scales.

If you look at
http://www.uq.net.au/~zzdkeena/Music/ErlichPentDec7Lattice.gif, you'll see
that my pentachordal decatonic scale has one hexany in it, which (using
Dave's notation) is

Eb
,'/ \`.
F--/---\--C
|\/ \/|
|/\ /\|
B\--------F#\
`.\ /,'
G#\

If you look a 3/2 above _or_ a 3/2 below, you'll see another hexany, only
missing one note, e.g., a 3/2 above, you see:

Bb
,'/ \`.
C--/---\--G
| / \ |
|/ \|
F#\-------C#\

The note required to complete that hexany would be D#\, while the only
remaining note in the decatonic scale is an E. That's pretty close, so I'm
not surprised that the resulting scale is CS.