Wilson explanations

>>>Where can I find about the theory of Wilson's combination
>>>product sets? In what manuscript did this theory first appeared?
>
>The first citation I am aware of is Erv's XH12 article,
>"D'Alessandro, Like a Hurricane"...
>http://xh.xentonic.org/tables-of-contents.html>
>The full text of the article can be found here...
>http://anaphoria.com/dal.PDF

Good luck figuring it out!!

I still have no clue what half of the pictures and diagrams in that
article are about.

I actually kind of figured CPS's out for the first time when I read the
bit about them in "Divisions of the Tetrachord" by John Chalmers. Though
sadly, there is an error in his Hexany diagram.

>
>You may find the Tonalsoft encyclopedia entry helpful...
>
>http://tonalsoft.com/enc/cps.htm
>

Someday one of us should re-write this. It's not that useful. There's
no diagrams, pitcures, specific examples of pitch groups or relations,
etc. (let alone sound examples).

hi Chris,

--- In tuning@yahoogroups.com, Christopher Bailey <chris@m...> wrote:
> >
> > You may find the Tonalsoft encyclopedia entry helpful...
> >
> > http://tonalsoft.com/enc/cps.htm
> >
>
> Someday one of us should re-write this. It's not
> that useful. There's no diagrams, pitcures,
> specific examples of pitch groups or relations,
> etc. (let alone sound examples).

did you click on the links at the bottom for
"see further comments by Paul Erlich and Carl Lumma"?
there's quite a bit of explanatory detail on those pages.

as for sound examples ... once the Tonalsoft software
is finished, we plan to be using it to create lots of
visual and audio examples for our Encyclopaedia webpages.

-monz

>>You may find the Tonalsoft encyclopedia entry helpful...
>>
>>http://tonalsoft.com/enc/cps.htm
>
>Someday one of us should re-write this. It's not that useful.
>There's no diagrams, pitcures, specific examples of pitch
>groups or relations, etc. (let alone sound examples).

It links to two tutorials, one by Paul and one by myself, both
of which are excellent IMHO. :) If you can't figure it out after
reading these, please ask any specific questions you may have
here so the tutorials can be improved!!

-Carl

on 25/4/04 20:17, Christopher Bailey at chris@music.columbia.edu wrote:

>>>> Where can I find about the theory of Wilson's combination
>>>> product sets? In what manuscript did this theory first appeared?
>>
>> The first citation I am aware of is Erv's XH12 article,
>> "D'Alessandro, Like a Hurricane"...
>> http://xh.xentonic.org/tables-of-contents.html>
>> The full text of the article can be found here...
>> http://anaphoria.com/dal.PDF
>
> Good luck figuring it out!!
>
> I still have no clue what half of the pictures and diagrams in that
> article are about.
>
> I actually kind of figured CPS's out for the first time when I read the
> bit about them in "Divisions of the Tetrachord" by John Chalmers. Though
> sadly, there is an error in his Hexany diagram.
>
>>
>> You may find the Tonalsoft encyclopedia entry helpful...
>>
>> http://tonalsoft.com/enc/cps.htm
>>
>
> Someday one of us should re-write this. It's not that useful. There's
> no diagrams, pitcures, specific examples of pitch groups or relations,
> etc. (let alone sound examples).
>

Try contacting Kraig Grady off list. He's one of the few people who has
actually made music using CPS structures as opposed to writing explanations
of what they are.

>Try contacting Kraig Grady off list. He's one of the few people who
>has actually made music using CPS structures as opposed to writing
>explanations of what they are.

Kraig has also written explanations of what they are.

-Carl

>>>> may find the Tonalsoft encyclopedia entry helpful...
> > >
> > > http://tonalsoft.com/enc/cps.htm
> > >
> >
> > Someday one of us should re-write this. It's not
> > that useful. There's no diagrams, pitcures,
> > specific examples of pitch groups or relations,
> > etc. (let alone sound examples).
>

> did you click on the links at the bottom for
> "see further comments by Paul Erlich and Carl Lumma"?
> there's quite a bit of explanatory detail on those pages.
>

Yes. Actually, those were e-mails written in response to questions
from either me or Joe PEhrson (can't rmeember which) way back
in '99, I believe. (phew. . . time flies. . . )

> as for sound examples ... once the Tonalsoft software
> is finished, we plan to be using it to create lots of
> visual and audio examples for our Encyclopaedia webpages.
>

That'll be awesome!!!!!!!!!!!!!!!!!11111

> > > > http://tonalsoft.com/enc/cps.htm
>
> > did you click on the links at the bottom for
> > "see further comments by Paul Erlich and Carl Lumma"?
> > there's quite a bit of explanatory detail on those pages.
> >
>
> Yes. Actually, those were e-mails written in response to
questions
> from either me or Joe PEhrson (can't rmeember which) way back
> in '99, I believe. (phew. . . time flies. . . )
>

Actually, between those e-mails, the Chalmers book, and some of
Wilson's diagrams, I learned enough on CPS's to be able to teach
them (the basics) last year in my microtonal music class. (One of m
students wrote a really pretty piece with a hexany, too . . I Was
going to post it but got too lazy . . )

In any case, I think what bugged me about all of the explanations
was there wasn't really any example of how you would go about
composing with them . . . but maybe that's good and open-ended in a
way. (Also I coudl be remembering wrong)

Actually I think Kraig Grady posted something somewhere on how one
of his pieces goes, structurally laying out the CPS, etc. Although
that might have been for another non-CPS piece. though the
processes were similar I'm sure.

anyway, it's late I'm spacing out here. . .

>Actually, between those e-mails, the Chalmers book, and some of
>Wilson's diagrams, I learned enough on CPS's to be able to teach
>them (the basics) last year in my microtonal music class.

Awesome! At Columbia?

>(One of m
>students wrote a really pretty piece with a hexany, too . . I Was
>going to post it but got too lazy . . )

Maybe he/she'd like to post it themselves?

>In any case, I think what bugged me about all of the explanations
>was there wasn't really any example of how you would go about
>composing with them . . . but maybe that's good and open-ended in
>a way. (Also I coudl be remembering wrong)

Thing is, CPS is a method for generating scales, not a method for
generating music. It could be taken that way, and so much the
better I suppose, though I am personally inclined to see such an
approach as a rather desperate manifestation of academic process-
fetishism. Or something. [Maybe this is why mainstream theory
seems to find so little of interest on this list over the last
several years -- they're looking for a process?]

Anyway, the CPS method can generate scales that span the gamut
of what is possible with scales. Any approach to composition, in
the common-practice sense, would have to be based on the actual
scale resulting from the particular CPS used. And the best way
to get into that is to practice composing in the scale (fancy that).

If you stick with the 11-limit Eikosany, as featured in Wilson's
XH12 article, you do get a list of (unsaturated) 11-limit tetrads
that are joined by common dyads (as shown in Wilson's diagrams).
Chord progressions fall out of these diagrams quite readily. He
also shows that you can embed the Eikosany in a chain of fifths,
which presumably gives one a model for drumming out melodies. Is
this non-obvious?

>Actually I think Kraig Grady posted something somewhere on how one
>of his pieces goes, structurally laying out the CPS, etc.

Kraig did a great article on CPSs in XH9, I think. I highly
recommend it.

-Carl

As i was just passing through..........
http://anaphoria.com/cps.PDF
I hope to put up more of my own lattices in the near future which have been
used to various degrees

ZipZapPooZoo wrote:

> Actually I think Kraig Grady posted something somewhere on how one
> of his pieces goes, structurally laying out the CPS, etc. Although
> that might have been for another non-CPS piece. though the
> processes were similar I'm sure.

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

Hope all are well

Carl Lumma wrote:

>
> Thing is, CPS is a method for generating scales, not a method for
> generating music.

I am not sure you can call CPS a scale, it is a structure and that
structure have very musical useful properties. Most of the time you have
to add tones to really make it a scale to fill in the gaps so to speak.
The Diamond is this way also, not a scale but a structure, and more than
one has likewise filled in the gaps to make it a scale. Notice Partch
used the diamond but a 43 tone scale.

It does influence the way the music can be generated for instance no
matter what you do, hexanies or pulling out a tetrachordal scale, the
inversion of this will always be found on the most remote place within
the tuning. Inversion implies you are at most remote point. It is a
feature that judging from my own experience is learn rather easily and
somewhat unconsciously without much effort. There is allot of acoustical
cues that let you know where you are in the structure and what is within
you easy grasp.

I know i have promised to put up some of my lattices in the past but
i really will try to put them up soon. Most were used in one way or
another.

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >Actually, between those e-mails, the Chalmers book, and some of
> >Wilson's diagrams, I learned enough on CPS's to be able to teach
> >them (the basics) last year in my microtonal music class.
>
> Awesome! At Columbia?
>

No, at Cincinnati Conservatory. 'twas a fun class, but probably a
little too jam-packed. But people tried a lot of different
approaches.

> >(One of m
> >students wrote a really pretty piece with a hexany, too . . I Was
> >going to post it but got too lazy . . )
>
> Maybe he/she'd like to post it themselves?

I'm working on it. . .

>
> >In any case, I think what bugged me about all of the explanations
> >was there wasn't really any example of how you would go about
> >composing with them . . . but maybe that's good and open-ended in
> >a way. (Also I coudl be remembering wrong)
>
> Thing is, CPS is a method for generating scales, not a method for
> generating music.

OK . . .but different scales have different properties, which might
affect the way one would approach writing music with them. Like
kinds of melodies one would write, or kinds of harmonies, etc.

> It could be taken that way, and so much the
> better I suppose, though I am personally inclined to see such an
> approach as a rather desperate manifestation of academic process-
> fetishism. Or something. [Maybe this is why mainstream theory
> seems to find so little of interest on this list over the last
> several years -- they're looking for a process?]

huh? what are you reffering to? Most mainstream theory is not
concerned with composition at all. Rather with analysis.

>
> Anyway, the CPS method can generate scales that span the gamut
> of what is possible with scales. Any approach to composition, in
> the common-practice sense, would have to be based on the actual
> scale resulting from the particular CPS used. And the best way
> to get into that is to practice composing in the scale (fancy
> that).
>

Well, sure. And maybe it's better to just dive in, rather than
someone saying "Try this. . . or this. . . . "

> If you stick with the 11-limit Eikosany, as featured in Wilson's
> XH12 article, you do get a list of (unsaturated) 11-limit tetrads
> that are joined by common dyads (as shown in Wilson's diagrams).
> Chord progressions fall out of these diagrams quite readily. He
> also shows that you can embed the Eikosany in a chain of fifths,
> which presumably gives one a model for drumming out melodies. Is
> this non-obvious?

"a chain of fifths,
which presumably gives one a model for drumming out melodies."

What? Why? how?

--- In tuning@yahoogroups.com, kraig grady <kraiggrady@a...> wrote:
> As i was just passing through..........
> http://anaphoria.com/cps.PDF
> I hope to put up more of my own lattices in the near future which
have been
> used to various degrees
>
> -- -Kraig Grady
> North American Embassy of Anaphoria Island
> http://www.anaphoria.com
> The Wandering Medicine Show
> KXLU 88.9 FM WED 8-9PM PST

Yep, this was the one.

> somewhat unconsciously without much effort. There is allot of
acoustical
> cues that let you know where you are in the structure and what is
within
> you easy grasp.
>
>

Hmmmmm . . . in my limited experience with them, I haven't found
this yet. . . .but it may come with time. Right now they still just
sound like. . . .floaty quasi-atonal harmonies.

>> >In any case, I think what bugged me about all of the explanations
>> >was there wasn't really any example of how you would go about
>> >composing with them . . . but maybe that's good and open-ended in
>> >a way. (Also I coudl be remembering wrong)
>>
>> Thing is, CPS is a method for generating scales, not a method for
>> generating music.
>
>OK . . .but different scales have different properties, which might
>affect the way one would approach writing music with them. Like
>kinds of melodies one would write, or kinds of harmonies, etc.

Unfortunately, the theory just isn't anywhere near being able to do
things like, 'scale is x? try composing like y...', in my opinion.
Even for common-practice music, which has focused on the same few
scales for generations, musical progress seems to happen slowly,
through musicians hearing and playing one another's music.

There are things to try. Looking for fifths, or lack thereof.
Looking for chords, as I did this morning in Mark Gould's scale.
Comparing modes for things like leading tones, "characteristic
dissonances" and other features that might allow tonal progressions.
Looking at how equally-spaced the scale degrees are (culminating,
people like me would say, in Rothenberg's "propriety"). These
things are interesting for those who are interested in them, and
there's been plenty of discussion here and on tuning-math about
them (though tuning-math is has been mostly about generating scales).
But for composers, I recommend *composing*. Daily, if possible.
If you're looking to do common-practice-ish music in alternate
tunings, the stuff that's been cooking over at tuning-math will
give you some great scales to work with (drop by and have Gene
cook one up for you!). There's some extremely interesting stuff
in that department, no question. As far as what to do with them,
the picture is less clear.

>> It could be taken that way, and so much the
>> better I suppose, though I am personally inclined to see such an
>> approach as a rather desperate manifestation of academic process-
>> fetishism. Or something. [Maybe this is why mainstream theory
>> seems to find so little of interest on this list over the last
>> several years -- they're looking for a process?]
>
>huh? what are you reffering to?

It was just a cheap shot at serialists. Please disregard.
(Especially if you're a serialist! :)

>Most mainstream theory is not
>concerned with composition at all. Rather with analysis.

That's fine, but then you wind up with the 'prescriptive
vs. descriptive' conundrum. Analytical theory, as I've
experienced it, has a miserable record of predicting
breakthroughs like Beethoven and the jazz.

>>Anyway, the CPS method can generate scales that span the gamut
>>of what is possible with scales. Any approach to composition, in
>>the common-practice sense, would have to be based on the actual
>>scale resulting from the particular CPS used. And the best way
>>to get into that is to practice composing in the scale (fancy
>>that).
>
>Well, sure. And maybe it's better to just dive in, rather than
>someone saying "Try this. . . or this. . . . "

It depends on how you work best, I guess. You can get a hold of
Scala and turn out CPSs by the dozens, and lay down a track in
each. Or you could try a more staid approach.... if you're into
Partch, you might first check out the tonality diamond, via
Partch's own advice on that.* After, the 11-limit Eikosany will
probably seem like Christmas (hint, hint, Prent Rodgers...).

* Via _Genesis of a Music_, and also check out the audio lecture
on *Enclosure 2*.

>> If you stick with the 11-limit Eikosany, as featured in Wilson's
>> XH12 article, you do get a list of (unsaturated) 11-limit tetrads
>> that are joined by common dyads (as shown in Wilson's diagrams).
>> Chord progressions fall out of these diagrams quite readily. He
>> also shows that you can embed the Eikosany in a chain of fifths,
>> which presumably gives one a model for drumming out melodies. Is
>> this non-obvious?
>
>"a chain of fifths,
>which presumably gives one a model for drumming out melodies."
>
>What? Why? how?

Nobody really knows, but chains of fifths seem to work well (in
one but certainly not all senses) melodically.

-Carl

Well then if they are just simple ratios, why would they sound like
that if it wasn't a part of the structural framework. It would be harder to
get such an effect with simple ratios on the diamond.
My article in retrospect was written long before there was a list like
this. It was never meant to be an introduction to the subject. Those
reading Xenharmonikon at the time were for the most part pretty familiar
with the territory. The purpose was to show one counterpuntal cycle (which
was latter used in the Creation of the Worlds).
Right now i have finished tuning another set of Jenco Vibes adding it
to the 22 eikosany which will give me the full Dallensandro tuning. A
keyboard base layout has been picked and hope to get to the last
resonators and the frame by the end of the year. It is interesting to
possibly finish an instrument started in 1963 (by Paul Beaver) which is one
of the reasons to do so. Maybe it will inspire me to write in the is tuning
again.

ZipZapPooZoo wrote:

> Hmmmmm . . . in my limited experience with them, I haven't found
> this yet. . . .but it may come with time. Right now they still just
> sound like. . . .floaty quasi-atonal harmonies.

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >>You may find the Tonalsoft encyclopedia entry helpful...
> >>
> >>http://tonalsoft.com/enc/cps.htm
> >
> >Someday one of us should re-write this. It's not that useful.
> >There's no diagrams, pitcures, specific examples of pitch
> >groups or relations, etc. (let alone sound examples).
>
> It links to two tutorials, one by Paul and one by myself, both
> of which are excellent IMHO. :) If you can't figure it out after
> reading these, please ask any specific questions you may have
> here so the tutorials can be improved!!
>
> -Carl

Yes, please do, I'd be happy to help answer any such questions.
Better yet, come visit me in Boston . . . as Monz can attest, I'm
better at explaining CPS structures in person than in writing.

I'm posting because I was just directed, on another list, to a
website about water. It appears that the familiar form of
ice, "hexagonal ice" (talking molecular structure here), has a
counterpart called "cubic ice" which exists at colder temperatures:

http://www.lsbu.ac.uk/water/ice1c.html

The website states that a portion of this structure, consisting of 10
water atoms and shown in red, was found recently in a supramolecular
structure (ref: L. J. Barbour, G. W. Orr and J. L. Atwood, An
intermolecular (H2O)10 cluster in a solid-state supramolecular
complex, Nature 393 (1998) 671-673.)

Now if you look at figures 32 and 33, showing dekanies, in Wilson's
classic CPS article:

http://www.anaphoria.com/dal.PDF (p.33)

you'll see that exact same structure! (someone tell erv)

The thing though that it is possible to only show one facet of the
symmetry in 3D. To adequately show it you should be able to rotate all the
factors and it still look the same. since there is no way to equally space
5 factors in 3d (i might be wrong about this) this is probably the best we
can do. Working with the actual tones though, one can get a handle on just
how tightly packed these figures are. Same with the 10 sided Eikosany
figure, 240 ways to permutate the factors that generate the figure,
although I have written out only 120 as the other 120 are a mirror and
don't involve much practical use beyond the other. Counterpoint in any one
figure will transform perfectly into 240 variations. To adequately to
comprehend the Eikosany we can say we look at it from 240 different
directions and it would look the same.

wallyesterpaulrus wrote:

> Now if you look at figures 32 and 33, showing dekanies, in Wilson's
> classic CPS article:
>
> http://www.anaphoria.com/dal.PDF (p.33)
>
> you'll see that exact same structure! (someone tell erv)

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

--- In tuning@yahoogroups.com, kraig grady <kraiggrady@a...> wrote:
> The thing though that it is possible to only show one facet of
the
> symmetry in 3D. To adequately show it you should be able to rotate
all the
> factors and it still look the same. since there is no way to
equally space
> 5 factors in 3d (i might be wrong about this) this is probably the
best we
> can do.

For these diagrams, Wilson put one of the five factors in the center,
and the other four at the vertices, of a regular tetrahedron. In
other diagrams he arranges them in a regular pentagon. See, for
example, the second row up from the bottom of Figure 19 (page 21) of

http://www.anaphoria.com/dal.PDF

In both of these arrangements, there are only two possible distances
from one factor to another. So they seem about equally good to me.

But yes, a 4D simplex (or hyper-tetrahedron) would be the ideal way
to geometrically depict the five factors.

(The effect in question was, in Chris's words, "sound
like. . . .floaty quasi-atonal harmonies")

--- In tuning@yahoogroups.com, kraig grady <kraiggrady@a...> wrote:

> Well then if they are just simple ratios, why would they sound
>like
> that if it wasn't a part of the structural framework. It would be
>harder to
> get such an effect with simple ratios on the diamond.

Maybe so, but there are plenty of less-symmetrical structures,
equally compact in the simple-ratio lattice, where it would probably
be just as easy.

(Similarly, you don't need serialism to get atonality in 12-equal.)

The 22-tone scale you mention, which contains the 20-tone eikosany,
as well as the 41-tone scale that contains 27 tones of the 29-tone
diamond (Partch's 43 includes two more and thus the whole diamond),
are only two possible periodicity blocks (or Constant Structures)
with 22 or 41 notes. Not to mention other numbers of notes.

Most of the others will only (but necessarily) contain *parts* of
both structures (diamond & eikosany).

I'd be happy to review examples or create new ones.

Thus most such scales could employ portions of various eikosany
progressions, combined with movements to and from the diamond that
don't imply tonality around the diamond's center. Thus, floaty
atonality.

The necessity above comes about because the two structures (diamond &
eikosany) themselves overlap and contain many notes, dyads, triads,
and even a couple of consonant tetrads in common -- see figure 15
(page 17) of

http://www.anaphoria.com/dal.PDF

Even the diamond itself, or a part of it, could be used in an atonal
way. The eikosany is typically harmonized with consonant tetrads but
the diamond with consonant hexads -- and in the latter case all the
hexads have a note in common (Partch's version of "tonality") -- the
1/1. But what if we harmonized the diamond with consonant tetrads
too? Then one could move around from one tetrad to another, using one
(or even three, when moving between subsets of a utonal hexad) common
tones that were rarely, if ever, the 1/1 -- or no common tones
whatsoever. Floaty quasi-atonal harmonies? Probably. And what if one
didn't stick to pure "consonant" chords? Plenty of potential for
floaty atonality.

> My article in retrospect was written long before there was a
list like
> this. It was never meant to be an introduction to the subject. Those
> reading Xenharmonikon at the time were for the most part pretty
familiar
> with the territory. The purpose was to show one counterpuntal cycle
(which
> was latter used in the Creation of the Worlds).
> Right now i have finished tuning another set of Jenco Vibes
adding it
> to the 22 eikosany which will give me the full Dallensandro tuning.
A
> keyboard base layout has been picked and hope to get to the last
> resonators and the frame by the end of the year. It is interesting
to
> possibly finish an instrument started in 1963 (by Paul Beaver)
which is one
> of the reasons to do so. Maybe it will inspire me to write in the
is tuning
> again.

Best Wishes!

The purposes of the different diagrams is to highlight a different
substructure such as hexany or tetrad.

wallyesterpaulrus wrote:

>
> For these diagrams, Wilson put one of the five factors in the center,
> and the other four at the vertices, of a regular tetrahedron. In
> other diagrams he arranges them in a regular pentagon. See, for
> example, the second row up from the bottom of Figure 19 (page 21) of
>
> http://www.anaphoria.com/dal.PDF
>
> In both of these arrangements, there are only two possible distances
> from one factor to another. So they seem about equally good to me.
>
> But yes, a 4D simplex (or hyper-tetrahedron) would be the ideal way
> to geometrically depict the five factors.
>

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

on 4/28/04 1:22 PM, wallyesterpaulrus <paul@stretch-music.com> wrote:

>

Welcome back!

If you're going to stick around for a while, 10-to-1 the volume of this list
increases by a factor of 5 to 10 within a couple of weeks. (My private
theory of why list volume has been low is that it was due to your absense.)
Of course I don't mean *only* because of the volume of your own messages.

-Kurt

--- In tuning@yahoogroups.com, kraig grady <kraiggrady@a...> wrote:

> The purposes of the different diagrams is to highlight a different
> substructure such as hexany or tetrad.

That's the great thing about them.

Going back to that water-molecule (not atom, d'oh) dekany,

You were right that it's the superior depiction, because taking
advantage of a visual "third dimension" frees one to rotate and
eliminate overlaps in the depiction.

It turns out that that dekany-containing cube that forms the
molecular structure of "cubic ice" is also present in that of a
special form of carbon:

http://cst-www.nrl.navy.mil/lattice/struk.picts/a4.s.png

And of course, an even better depiction, if we could wrap our brains
around it, would be a four-dimensional ones, such as Dave's which
rotates around five planes while stimulating your sound card.

I'd enter the factors 4,5,7,11,15, or 7,8,10,11,15, or
16:15:14:11:10, or etc., so as to hear the 2)5 [1.5.7.11.15] dekany
Erv was depicting, choose a good JI-friendly patch, and transpose
down several notches. Turn up the "Distance at which volume goes to
zero" to 180 or so. Strap on your 3-d goggles, hit "go", and enjoy
the ride.

wallyesterpaulrus wrote:

>
> http://cst-www.nrl.navy.mil/lattice/struk.picts/a4.s.png
>

I will show this to Erv tomorrow as along with Stephan taylor, we will
tagging along to his lecture at Harvey Mudd College (c/o Bill Alves). Video
in Hand

>
> And of course, an even better depiction, if we could wrap our brains
> around it, would be a four-dimensional ones, such as Dave's which
> rotates around five planes while stimulating your sound card.

Setting up automatic playing of such figures would be nice.

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

--- In tuning@yahoogroups.com, kraig grady <kraiggrady@a...> wrote:
>
>
> wallyesterpaulrus wrote:
>
> >
> > http://cst-www.nrl.navy.mil/lattice/struk.picts/a4.s.png
> >
>
> I will show this to Erv tomorrow as along with Stephan taylor, we
will
> tagging along to his lecture at Harvey Mudd College (c/o Bill
Alves). Video
> in Hand
>
> >
> > And of course, an even better depiction, if we could wrap our
brains
> > around it, would be a four-dimensional ones, such as Dave's which
> > rotates around five planes while stimulating your sound card.
>
> Setting up automatic playing of such figures would be nice.

It's pretty automatic already. What further automation did you have
in mind? Perhaps Dave and Andy could accomodate you.

can't remember if this was sent or not

wallyesterpaulrus wrote:

>
>
> The necessity above comes about because the two structures (diamond &
> eikosany) themselves overlap and contain many notes, dyads, triads,
> and even a couple of consonant tetrads in common -- see figure 15
> (page 17) of
>
> http://www.anaphoria.com/dal.PDF
>

the interesting thing is that if you put 2 diamonds on any of the
complementary factor pairs an eikosany will be formed in-between the two.
One of my favorite features of the eikosany is that each tone will
function as one of the factors in some way either harmonically or sub
harmonically. In example the 1-3-11 will function in tetrads as either the
1 , the 3 or the 11 but will function in other tetrads sub harmonically as
the sub 5, sub 7 and sub 9. Each tone thus is equal on the level yet
unique, something Socrates would have enjoyed or frown upon. The political
implications are interested but don't know one could translate this over.
Years working with it i could hear a single tone and would recognize its
'personality'.
When i started i thought it was beyond my capacity to grasp it all,
after 15 years it seemed as easy as the Major scale. i imagine PArtch and
others who have used the diamond have similar experiences.
It is for this reason i advocate picking the absolute best tuning one can
get a hold of for ones purposes and really live with it.

>
> Even the diamond itself, or a part of it, could be used in an atonal
> way. The eikosany is typically harmonized with consonant tetrads but
> the diamond with consonant hexads -- and in the latter case all the
> hexads have a note in common (Partch's version of "tonality") -- the
> 1/1. But what if we harmonized the diamond with consonant tetrads
> too? Then one could move around from one tetrad to another, using one
> (or even three, when moving between subsets of a utonal hexad) common
> tones that were rarely, if ever, the 1/1 -- or no common tones
> whatsoever. Floaty quasi-atonal harmonies? Probably. And what if one
> didn't stick to pure "consonant" chords? Plenty of potential for
> floaty atonality.

Obviously one can find the corners around any tuning to do what one wishes.
There are those who hear the G in the diamond even if it isn't play ,it is
implied is some fashion.

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

--- In tuning@yahoogroups.com, kraig grady <kraiggrady@a...> wrote:

>
> >
> > Even the diamond itself, or a part of it, could be used in an
atonal
> > way. The eikosany is typically harmonized with consonant tetrads
but
> > the diamond with consonant hexads -- and in the latter case all
the
> > hexads have a note in common (Partch's version of "tonality") --
the
> > 1/1. But what if we harmonized the diamond with consonant tetrads
> > too? Then one could move around from one tetrad to another, using
one
> > (or even three, when moving between subsets of a utonal hexad)
common
> > tones that were rarely, if ever, the 1/1 -- or no common tones
> > whatsoever. Floaty quasi-atonal harmonies? Probably. And what if
one
> > didn't stick to pure "consonant" chords? Plenty of potential for
> > floaty atonality.
>
> Obviously one can find the corners around any tuning to do what one
wishes.
> There are those who hear the G in the diamond even if it isn't
play ,it is
> implied is some fashion.

If you avoided the note G and avoided chords which were subsets of
the otonal hexad on G, I doubt you'd hear the G.

If one treated it like a 41 tone scale with two variables i am sure you
could use some of the near simple just chords to create other tonics. With
the Eikosany you needn't avoid anything to create non tonal music, it just
exudes such animals. The 'effect' as i may use the term is not like what
gets with a row it is more feeling that everywhere you are sitting sounds
like your tonic and then you move to a different one, and get the same
feeling, yet it all somehow makes sense in relationship to what sounded
before.

wallyesterpaulrus wrote:

> If you avoided the note G and avoided chords which were subsets of
> the otonal hexad on G, I doubt you'd hear the G.

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

--- In tuning@yahoogroups.com, kraig grady <kraiggrady@a...> wrote:

> If one treated it like a 41 tone scale with two variables

Whoa! That's a lot more than I was thinking about. The diamond only
has 29, the eikosany 20.

> i am sure you
> could use some of the near simple just chords to create other
>tonics.

Yes, even the diamond itself has six otonal tetrads, only one of
which is rooted on G (1/1).

> With
> the Eikosany you needn't avoid anything to create non tonal music,
it just
> exudes such animals.

Well, at least by Partch's definitions of tonality and consonance, it
would certainly be a minimum of the former and a maximum number of
the latter (for structures with about that many notes).

Thing is, I don't quite agree with Partch's definition of tonality --
even on which notes are the roots of utonal chords or of the 5-limit
diamond -- while you yourself have repeatedly spoken up against some
parts of his definition of consonance, such as 'limits'. They still
make for some fun theory, at least.

The funny thing is that a musical theory to be useful requires consistency
more than an absolute truth to make it work. We can take 12 Et and treat
the thirds as either consonances or dissonances and create extensive music
which sounds right to our ears. the human musical ear picks up on these
predetermined patterns that appear as a result of such theories and adjust
to them.
Composers such as Xenakis seem to also elicit a recognition of such an
ordered world. even Feldman who used no system beyond his intuition, makes
us perceive an order. I believe our ears have gotten to a point where we
can recognize such structural processes (resulting from the theory) quite
quickly.
Of course to base a system on say whole tones as consonances and fifths
as disonances with 12 ET would not work i don't think. In such a case
though we can learn this 'language' which might come off comic. Perception
has it hierarchy, but that doesn't mean these relationships are static

wallyesterpaulrus wrote:

> Thing is, I don't quite agree with Partch's definition of tonality --
> even on which notes are the roots of utonal chords or of the 5-limit
> diamond -- while you yourself have repeatedly spoken up against some
> parts of his definition of consonance, such as 'limits'. They still
> make for some fun theory, at least.

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST