Re: list archives from last August

[Paul Hahn:]
>Search the list archives from last August. Look for the word
"nonatonic".

How exactly would I go about this? Where are the pre `99 digests archived?

Dan

On Wed, 16 Jun 1999, D. Stearns wrote:
> [Paul Hahn:]
>> Search the list archives from last August. Look for the word
>> "nonatonic".
>
> How exactly would I go about this? Where are the pre `99 digests archived?

Y'know, that's a better question than I realized. The mills archive
apparently doesn't go past '95 or '96, for some reason. I had thought
that somebody else was taking up the slack and archiving them on a
website, but I could be wrong--Joe Monzo only has a select few digests,
and the Xenharmonikon website, where I had thought Jon Pusey was
collecting them, doesn't seem to have them after all.

In the meantime, I've appended a few relevant messages of mine.

--pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
O
/\ "Hey--do you think I need to lose some weight?"
-\-\-- o
NOTE: dehyphenate node to remove spamblock. <*>

*** BEGIN APPENDIX(-AGE? 8-)> ) ***

>From manynote@library.wustl.edu Thu Jun 17 10:38:05 1999
Date: Thu, 6 Aug 1998 06:39:19 -0500 (CDT)
From: Paul Hahn <manynote@library.wustl.edu>
To: tuning@eartha.mills.edu
Bcc: Rosemary Hahn <hahn@wulaw>
Subject: RE: Scales and Numerology

On Wed, 5 Aug 1998, Paul H. Erlich wrote:
> Paul Hahn wrote,
> >Interesting. I've lately been toying with a 9-out-of-31 scale.
>
> Care to let us in on it?

Well, I'm still working out the details, plus I lack a means at the
moment to tune it up and listen to how it sounds so my toying at the
moment just means working out theoretical quirks, but the basic scale is
4-4-2-5-3-3-4-3-3. In the 3, 5, 7 lattice it looks like this:

6/5 --- 3/2 ---15/8
/ \ / \ /
/ \ / \ /
/ 7/5 \ / 7/4 \ / 35/32
8/5 --- 1/1 --- 5/3

28/15

The pivotal pitch of the scale is pitch 28 out of 31, represented twice
by 15/8 and 28/15 (separated by 225/224), this scale's equivalent of the
supertonic in that it relates the "dominant" and "subdominant" harmonic
regions to each other. There are only two complete Otonal 4:5:6:7
tetrads, but a nice distribution of (Otonal and Utonal) 4:5:6 and 4:5:7
triads.

Eventually I plan to generalize the nonatonic framework by fixing the
1/1, 5/4, and 8/5 as the boundaries of three tetrachords, within which
the other scale degrees can vary as long as they form 8/7s, 7/6s or 6/5s
with those three "framework" pitches--but first I have to find a new
instrument, or figure out how to get one of my existing ones to work for
microtonality. Frankly, my theorizing has never made it to this stage
before.

Oh, John and Daniel--I know full well numerology is a bunch of hooey.
My father is a mathematician, after all. But in this case it's kind of
fun to speculate on what subconscious or cultural influences may have
been at work. F'rinstance, cats have nine lives and I love cats, and as
I mentioned before nine is significant in Norse mythology, which I have
been interested in for a long time. Here's a quote from _The Norse
Myths_, by Kevin Crossley-Holland:

Nine worlds encompassed by the tree (which so becomes a symbol
of universality known to mythologists as the World Tree); nine
nights hanging on the tree; the number nine recurs again and
again in Norse mythology. Odin learns nine magic songs from a
giant that enable him to win the mead of poetry for the gods;
Heimdall has nine mothers; Hermod, Odin's son, journeys for nine
nights in his attempt to win back the god Balder from Hel; the
great religious ceremonies at the temple of Uppsala lasted for
nine days in every ninth year, and required the sacrifice of
nine human beings and nine animals of every kind. Why nine was
the most significant number in Norse mythology has not been
satisfactorily explained, but belief in the magical properties
of the number is not restricted to Scandinavia. In _The Golden
Bough_, J.G. Frazer records ceremonies involving the number nine
in countries as widely separated as Wales, Lithuania, Siam and
the island of Nias in the Mentawai chain. Nine is, of course,
the end of the series of single numbers, and this may be the
reason why it symbolises death and rebirth in a number of
mythologies; hence it also stands for the whole.

No luck yet on 31 though. 8-)>

--pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
O
/\ "Churchill? Can he run a hundred balls?"
-\-\-- o
NOTE: dehyphenate node to remove spamblock. <*>

>From manynote@library.wustl.edu Thu Jun 17 10:38:05 1999
Date: Thu, 6 Aug 1998 08:54:09 -0500 (CDT)
From: Paul Hahn <manynote@library.wustl.edu>
To: tuning@eartha.mills.edu
Bcc: Rosemary Hahn <hahn@wulaw>
Subject: RE: Scales and Numerology

On Thu, 6 Aug 1998, Paul Hahn wrote:
> 6/5 --- 3/2 ---15/8
> / \ / \ /
> / \ / \ /
> / 7/5 \ / 7/4 \ /35/32
> 8/5 --- 1/1 --- 5/3
>
>
> 28/15

D'oh! That 5/3 should be a 5/4, of course. I guess my finger slipped.

--pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
O
/\ "Churchill? Can he run a hundred balls?"
-\-\-- o
NOTE: dehyphenate node to remove spamblock. <*>

>From manynote@library.wustl.edu Thu Jun 17 10:38:05 1999
Date: Fri, 7 Aug 1998 14:42:24 -0500 (CDT)
From: Paul Hahn <manynote@library.wustl.edu>
To: tuning@eartha.mills.edu
Bcc: Rosemary Hahn <hahn@wulaw>
Subject: Re: Numbers, cont.

On Thu, 6 Aug 1998, John Chalmers wrote:
> As for 9-tone scales in 31-tet, David Rothenberg and Connie Chan studied
> this one: 5 3 3 3 3 5 3 3 3, generated by a chain of 14 degrees of 31-tet.
> This scale is an MOS, is strictly proper,

Call me a heretic, but I'm beginning to wonder if these properties
aren't as important as I'd once thought they were. Look at the success
of the minor pentatonic in Japan, for example.

> has "stability" of 1.0 and
> "efficiency" of .7407.

Shame on me, but I don't even know what these measure signify. Help,
please.

--pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
O
/\ "Churchill? Can he run a hundred balls?"
-\-\-- o
NOTE: dehyphenate node to remove spamblock. <*>

>From manynote@library.wustl.edu Thu Jun 17 10:38:05 1999
Date: Sun, 9 Aug 1998 01:34:40 -0500 (CDT)
From: Paul Hahn <manynote@library.wustl.edu>
To: tuning@eartha.mills.edu
Bcc: Rosemary Hahn <hahn@wulaw>
Subject: More nonatonic maunderings

On Thu, 6 Aug 1998, Paul Hahn wrote:
[the basic 9-out-of-31 scale is]
> 4-4-2-5-3-3-4-3-3. [snip]
>
> There are only two complete Otonal 4:5:6:7
> tetrads, but a nice distribution of (Otonal and Utonal) 4:5:6 and 4:5:7
> triads.

Hey, I just realized that if you change the first two steps to 3-5
instead of 4-4, you just lose one 5/4 but gain a 3/2, a 7/5, and another
(Utonal) 4:5:6:7 tetrad. Hmm . . .

--pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
O
/\ "Churchill? Can he run a hundred balls?"
-\-\-- o
NOTE: dehyphenate node to remove spamblock. <*>

From manynote@library.wustl.edu Thu Jun 17 10:40:56 1999
Date: Wed, 12 Aug 1998 09:08:56 -0500 (CDT)
From: Paul Hahn <manynote@library.wustl.edu>
To: John Chalmers <non12@deltanet.com>
Subject: Re: 9-toners again

On Tue, 11 Aug 1998, John Chalmers wrote:
> I've been so
> busy recently that I haven't been reading the tuning list very carefully
> and must have missed your post on 3-tetrachord enneatonics. Sorry, when
> was it?

Last Thursday. Basically, you fix 1/1, 5/4, and 8/5 as the boundaries
of three tetrachords (pitches 1, 4, 7 of the nonatonic scale), then the
others can vary within those bounds as long as they form a 8/7, 7/6, or
6/5 with one of those pitches. Nine tones is a little too few to have
very many complete tetrads, but this technique practically guarantees
you a reasonable number of triads. So far the interesting ones I have
are:

4-3-3-5-3-3-4-3-3

The most regular melodically. Harmonically there are only two consonant
tetrads, one Otonal and one Utonal, both most consonant with the 1/1 of
the scale as the root. For these reasons I think of it as being
somewhat analogous to the major pentatonic (12TET 2-2-3-2-3). Looking
for interesting scales I generally start with this one and then start
varying pitches by 36/35s and 49/48s.

4-4-2-5-3-3-4-3-3

The most regular harmonically, as it can be derived from three 4:6:7
triads rooted on 1/1, 5/4, and 8/5. Possibly the best nonatonic
equivalent of the major diatonic scale. Two Otonal tetrads on 1/1 and
8/5.

3-5-2-5-3-3-4-3-3

The one with the most (7-limit) consonances. Also it has three tetrads
instead of two; the same two the above scale has, plus a Utonal one.
Sort of analogous to Mixolydian.

3-4-3-5-3-3-4-3-3
3-4-3-3-5-3-4-3-3
3-5-2-3-5-3-4-3-3

Other variants with three tetrads, but the way they relate to each other
harmonically is a little stranger. Still figuring these out.

> I haven't spent much time looking
> for harmonic derivations as things like 3 triads without common tones or
> 3 tetrads with tend not to be very good scales melodically in my
> experience.

This is where Fokker's method really helps me out; it assures me of a
relatively even distribution of pitches, as pairs of pitches separated
by one of the "vanishing" intervals are disallowed. Surprisingly, I
find it sort of ends up paralleling Ben Johnston's method of intervallic
subdivision.

--pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
O
/\ "Churchill? Can he run a hundred balls?"
-\-\-- o
NOTE: dehyphenate node to remove spamblock. <*>