Yahoo Tuning Groups Ultimate Backup tuning Re: Scales and lattices

Hi Joseph,

Here are a few thoughts following on from your discussion with
Dan Stearns.

I don't think there are good or bad scales, but I think there
are ones that are easy or more tricky to write in.

For example, the hexany is extremely tricky to write in, I find,
though you've written in it with apparent EASE.

The octony is much easier - adding those two notes, for me, turns
it into one that falls easily into nice melodic and harmonic structures.

To make this more concrete, here is the octony piece I posted to
the TL a while back. I wrote it pretty much straight off one
evening, and it was my first attempt in this scale.

"
Here is a little lullaby I did in the 7-limit octony

http://www.robertwalker.f9.co.uk/7-lim_octony_lullaby.mid
Robert
"

Here is the latest of I don't know how many attempts at the
hexany.

http://homepage.ntlworld.com/robertwalker/fts/hexany.mid

1/1 8/7 6/5 48/35 8/5 12/7 2/1

I think perhaps it almost works, but if so, it isn't so
flowing and melodic, and is a much more dissonant, atonal
type of piece. Also, the reason for all those short
broken motifs is that I found I can't get a long
flowing melodic line going at all - not yet anyway.

The octony is much easier - adding those two notes, for me,
turn it into one that falls easily into nice melodic and harmonic
structures.

I wonder if this is just me, or if you also find the hexany
tricky?

Why might the hexany be so tricky? It's a six note subset
of the octony, and usually one thinks of a scale with fewer
notes as easier to use somehow.

Here are some first thoughts towards trying to understand.

The hexany has plenty of pure triads. But it seems to be
rather lacking in the slightly dissonant chords, only having
ones that are very dissonant, leading to a kind of atonal
music.

Maybe its dissonant chords could be used more easily if there
were more in the way of middle ground to get from one
to the other.

To use a rather vague term - it is lacking in "softly dissonant"
chords.

It also has extremely uneven steps. That by itself is okay,
works for the octony, but the way they are distributed is
also extremely awkward under the hands somehow. At least,
that's my experience with it.

Maybe one could make a first step towards a method to measure
the ease of use for a scale by looking for the number of
mildly, somehwat dissonant chords, the number of wonderfully
consonant chords, and the number of ones that are extremely
dissonant.

Perhaps one could also make a similar measure of awkwardness
/ ease of melodic movement.

If one did that, it's perfectly possible that the SCALA 7-limit
19-tone scale might turn out to be a much better scale for
actual composition than some of the ones with beautiful
lattices. One doesn't know, would have to find out.

I like musical lattices as a type of musical geometry, and
I wonder if perhaps Monz's idea of a composition tool based
on lattices may be the way for compoesre to use the rich harmonic
resources of them.

Somehow, when one sees the scale as a linear series of notes,
one can't easily find all those consonant triads, or understand
well how they interact with each other.

Maybe they are best explored with some 3D display of the
scale. Or, maybe some composers can (or will be able to)
naturally see a scale that way and work with it without
3D aids, but others might still need them.

Maybe also one needs a way to find the chords with slightly
detuned j.i. intervals on the lattice, as they too seem
to contribute to the harmonic richness of a scale.

Here is another thought about what could be missing
in some of the lattices (not all I hasten to add).

Perhaps they lack a certain linearity (to coin a word). For
example in the diatonic scale, if you play the chord
with steps 2 2 2, you get a major or minor triad,
wherever you place your hand.

In the hexany, there is no such simple way to find the
consonant triads.

Maybe a search for slightly dissonant / detuned chords, and
for linearity, could help lattice constructors to come up
with scales that both have plenty of consonant triads,
and also are easy to use as a scale structure.

Then maybe also, with methods like Monz's Just Music,
tools may be developed to help composers tackle more
easily some of the highly symmetrical lattices that
lack linearity, or have fewer, or harder to locate,
detuned dissonances.

Just a few things to think about,

Robert

🔗jpehrson@rcn.com

--- In tuning@y..., "Robert Walker" <robert_walker@r...> wrote:

/tuning/topicId_19988.html#19988

> Hi Joseph,
>
> Here are a few thoughts following on from your discussion with
> Dan Stearns.
>

> I don't think there are good or bad scales, but I think there
> are ones that are easy or more tricky to write in.
>

Thanks so much, Robert, for your commentary, and you seem to be at
least partially advocating the value of investigating scales
according to certain properties as, possibly, a "pre-compositional"
method.

I wonder what Joe Monzo would say in this regard... Surely all his
"just lattices" must have SOME kind of "pre-compositional"
application.

Of course, I am certainly *NOT* saying that one shouldn't listen to
things!! I was just wondering if, in certain instances, certain
pre-compositional investigations DID have some value. (??)

Dan Stearns says "absolutely not" and YOU seem to be giving a glimmer
of a "maybe..." I'd enjoy hearing from Monzo, who is an accomplished
composer, when he has the time...

I'm just posing some questions... I don't want anyone to think that
my view is set in etched lattice glass!

On the hexany:

> I think perhaps it almost works, but if so, it isn't so
> flowing and melodic, and is a much more dissonant, atonal
> type of piece. Also, the reason for all those short
> broken motifs is that I found I can't get a long
> flowing melodic line going at all - not yet anyway.
>
> The octony is much easier - adding those two notes, for me,
> turn it into one that falls easily into nice melodic and harmonic
> structures.
>
> I wonder if this is just me, or if you also find the hexany
> tricky?
>
> Why might the hexany be so tricky? It's a six note subset
> of the octony, and usually one thinks of a scale with fewer
> notes as easier to use somehow.
>

Quite frankly, I *also* found it tricky. For me, the problem was
getting away from "oriental" associations. Using only 6-notes gave a
kind of "Eastern" flavor that I tried to avoid since the "real"
orientals do it so much better! And, of course, it's been *done.*

Avoiding those associations and relating it to my composing "history"
was the tricky part for me.

I think you are certainly correct about the melodic difficulties. My
OWN solution was to involve melodies that were more akin to jazz. It
was possible, then, to use leaps and more "atonal" associations
without making the piece sound too "contrived" or "academic." THOSE
kinds of melodies seemed to hold together.

Your comments are particularly interesting since these aspects of the
hexany were DEFINITELY things I encountered when I composed my HEXY.

(Which people seem to like... three separate public performances
coming soon!)

Of course, these "solutions" were not something I consciously thought
about BEFORE composing, but were evolving as I experimented and
worked with the scale... (I'm lending more credence to the Dan
Stearns' opinion here...!)

Thanks for the interesting commentary!

_______ _____ _____ ___
Joseph Pehrson

🔗David J. Finnamore <daeron@bellsouth.net>

Robert Walker wrote:

> For example, the hexany is extremely tricky to write in, I find,
> though you've written in it with apparent EASE.
>
> The octony is much easier - adding those two notes, for me, turns
> it into one that falls easily into nice melodic and harmonic structures.

> I wonder if this is just me, or if you also find the hexany
> tricky?
>
> Why might the hexany be so tricky? It's a six note subset
> of the octony, and usually one thinks of a scale with fewer
> notes as easier to use somehow.

Robert,

It's not just you, you'll be happy to know. A few months ago I got interested in x-anies, tried
for days to conquer the basic 1-3-5-7 hexany, and finally gave up. It seemed that there was no
feeling of "homeness" to be found no matter how I approached it. I felt like I was driving a car
with the steering wheel stuck turned all the way one way, just going around in endless circles
getting no where harmonically or melodically. I figured if I couldn't get used to the simplest of
hexanies than x-anies in general were not for me. Maybe I'll try an octany or dekany sometime.
Thanks for the heads up.

--
David J. Finnamore
Nashville, TN, USA
http://personal.bna.bellsouth.net/bna/d/f/dfin/index.html
--

🔗MONZ@JUNO.COM

--- In tuning@y..., jpehrson@r... wrote:

/tuning/topicId_19988.html#19995

> Thanks so much, Robert, for your commentary, and you seem to
> be at least partially advocating the value of investigating
> scales according to certain properties as, possibly, a
> "pre-compositional" method.
>
> I wonder what Joe Monzo would say in this regard...
> Surely all his "just lattices" must have SOME kind of
> "pre-compositional" application.
>
> Of course, I am certainly *NOT* saying that one shouldn't
> listen to things!! I was just wondering if, in certain
> instances, certain pre-compositional investigations DID
> have some value. (??)
>
> Dan Stearns says "absolutely not" and YOU seem to be giving
> a glimmer of a "maybe..." I'd enjoy hearing from Monzo, who
> is an accomplished composer, when he has the time...

Thanks for the compliment, Joe. I really do wish I'd heed
Brian McLaren's (admittedly quite abrasive) frequent
exhortations to "stop wasting so much valuable composition
time on theory". My productivity has indeed dropped off
quite drastically over the last few years, as I've become
more and more interested in theoretical research.

Anyway, I've stated here, before, the whole background on
my lattices and approach to theory. But I'll do it again,
hopefully in a way that will try to specifically answer
your question.

The whole reason I started diagramming tuning systems on
lattices was simply to compare different ones.

I found while reading Partch's book that I had a lot of
difficulty internalizing the "essence" of a tuning from a
list of ratios.

It was much easier for me to understand these scales by
reducing all the harmonic relationships to their "lowest
common denominator" (quite literally) and graphing them.

Now, why would it be important to compare different tunings?

For me, here's the quick answer:

I don't have "absolute (A.K.A. perfect) pitch", but do have
very good "relative pitch".

I had gone thru a heavy musical training which enabled me to
"see" the music I composed in my mind as it would appear in
score, so that I could easily write it down without having to
play it on an instrument (most likely, a piano) first. I was
able to sit in the park or on the subway and notate the music
in my head.

Of course, I'm talking about 12-tET tuning here.

Then, when I learned about microtonality, I quite rapidly
became mentally overwhelmed by the vast universe of new pitches
that I realized were available.

As I became more and more familiar with the sound of rational
tunings, the dilemma which unfolded was that now I could no
longer "see" in my mind the music I could "hear" in my mind.

My home-grown solution to that was a new personal ear-training
course. But the key to understanding the differences between
all those small intervals that were audibly more-or-less similar,
was to see *on a lattice diagram* how their mathematics differed.

Of course, the regulars on this list know that as I've dug
more and more deeply into historical tunings, I've quite lost
the ability to climb out of that hole by now...

But my goal 15 years ago was, and today still is, to grasp enough
of the variety in these various tuning schemes that I will
eventually be able to sit down with pen and paper (and nothing
else) and compose that great microtonal opera that's swimming
around in my brain.

Along the way, I'd have to say that, yes, a diagram of a tuning
does often suggest ways of manipulating pitches that I probably
wouldn't have thought of otherwise. (A good example of this
is the meditative middle section of _A Noiseless Patient Spider_,
where I sort of hop-scotch around a 5-limit lattice.)

But there's also a bit of a difference between hearing a piece
unfold silently, entirely in one's mind, and composing by
actually playing an instrument, which is really more a form
of improvisation.

I'm not knocking either approach - I use both; more often the
latter. I'd have to say that the combination of my imagination
and my ears provides most of the stimulus in composing a new
piece.

If I do spend time studying the lattice of a tuning, then
certainly it does have *some* influence on the piece which
results. But it's usually a kind of slow "osmosis" effect
which comes out in the final act of composition in a more
subliminal way. It's less often that I actually use a lattice
in a direct sort of way, as I did in _Spider_.

Hope that helps shed some light on your query.

-monz
http://www.monz.org
"All roads lead to n^0"

🔗jpehrson@rcn.com

🔗Joe Monzo, monz <MONZ@JUNO.COM>

--- In tuning@y..., jpehrson@r... wrote:

/tuning/topicId_19988.html#20039

> --- In tuning@y..., MONZ@J... wrote:
>
> /tuning/topicId_19988.html#20030
>
> >
> > If I do spend time studying the lattice of a tuning, then
> > certainly it does have *some* influence on the piece which
> > results. But it's usually a kind of slow "osmosis" effect
> > which comes out in the final act of composition in a more
> > subliminal way. It's less often that I actually use a lattice
> > in a direct sort of way, as I did in _Spider_.
> >
> > Hope that helps shed some light on your query.
> >
>
> Thanks, Monz... it *does." Thanks for the description of your
> process...

You're welcome. I've thought of a few more things about it.

I'm glad you singled out this paragraph for your quote, because
a few posts before mine Johnny Reinhard wrote that bit about
messing around with a tuning long enough so that intuition
takes over in the compositional process. I think what Johnny
said there is very similiar to what I was trying to get across
here. So he and I are in total agreement on that one.

Our methods differ in that Johnny chooses to think in terms
of a virtual pitch continuum quantized into 1200-tET (which I
agree works just fine from an audible/practical standpoint,
and which therefore works better for Johnny's purposes), while
mine is quantized by prime-factorization (which works better
for my purposes).

As far as the influence the lattice diagrams have on
pre-composition, I'm interested in someday exploring
methodical ways of manipulating the diagrams... things
such as game theory.

The _Solar System_ piece will hopefully someday evolve
into something of this sort: a constantly moving and changing
(and audible) lattice diagram of the harmonic relationships in
our local cosmic environment.

I'd also wondered in a post a couple of years ago if there
was any way to study a possible relationship between tonal
lattice diagrams and neural networks. (Sarn Ursell was
particularly taken by this idea.)

I'm certain that the compositional and performance choices we
make in selecting certain pitches has something to do with the
way electric signals travel thru our nervous system, and vice
versa. I wonder if there is or can be any direct corellation
between the modeling of these two domains.

Just a few more ideas to get the old wheels turning...

As always, if anyone out there is really interested in working
on any of these projects, I'm happy to try collaborating over
the internet.

-monz
http://www.monz.org
"All roads lead to n^0"

🔗Haresh BAKSHI <hareshbakshi@hotmail.com>

> > --- In tuning@y..., MONZ@J... wrote:
> >
> > /tuning/topicId_19988.html#20030
> >
> > >
> > > If I do spend time studying the lattice of a tuning, then
> > > certainly it does have *some* influence on the piece which
> > > results. But it's usually a kind of slow "osmosis" effect
> > > which comes out in the final act of composition in a more
> > > subliminal way. It's less often that I actually use a lattice
> > > in a direct sort of way, as I did in _Spider_.
> > >
> > > Hope that helps shed some light on your query.
> > >
> >
> > Thanks, Monz... it *does." Thanks for the description of your
> > process...
>
> You're welcome. I've thought of a few more things about it.
>
> I'm glad you singled out this paragraph for your quote, because
> a few posts before mine Johnny Reinhard wrote that bit about
> messing around with a tuning long enough so that intuition
> takes over in the compositional process. I think what Johnny
> said there is very similiar to what I was trying to get across
> here. So he and I are in total agreement on that one.

I think you and Johnny Reinhard have, perhaps, referred to the
creative process in general. When a raga is being improvised,
something similar happens: the performer starts, as if by drawing
from the "prototype" of the raga which "resides" in the third
component of the 3-part world of Popper, the philosopher. Then he
gets hold of a thread that he has thus developed. Now he developes
it further by deliberately and consciously using permissible, raw
raga material that he has acquired through learning, intuition and
gharana (school) practices.

Good to hear from you, Monz.

Regards,
Haresh.

🔗Robert Walker <robert_walker@rcwalker.freeserve.co.uk>

Hi David,

> It's not just you, you'll be happy to know. A few months ago I got interested
in x-anies, tried
> for days to conquer the basic 1-3-5-7 hexany, and finally gave up. It seemed
> that there was no
> feeling of "homeness" to be found no matter how I approached it. I felt like I
> was driving a car
> with the steering wheel stuck turned all the way one way, just going around in
> endless circles
> getting no where harmonically or melodically. I figured if I couldn't get used
> to the simplest of
> hexanies than x-anies in general were not for me. Maybe I'll try an octany or
> dekany sometime.
> Thanks for the heads up.

Thanks,. Exactly my experience with it too.

I wonder how many others get put off x-anies in the same way!

Perhaps one should add a note when describing the hexany to the effect that
though a small scale, it is pretty tricky to use in music?

I'm sure it will be worth it if one does manage to write something in it, but
I think that would be a later stage, rather than the first one to try, as one
would expect. I think when one does master the hexany eventually, it may well
be rather rewarding.

From my experience, the octony does seem a pretty good one to begin with, and
wonder what other lattices people have tried and found easy ones, to recommend
to those who are attempting them for the first time?

Anyone on the TL got good recommendations for geometrical musical lattices that are
especially welcoming to write music in? Or maybe that
should be a kind of newbies question (i.e. newbie to composing using lattices)
- what are good lattices to try, to get into the way of using them in music?

Robert

🔗Kraig Grady <kraiggrady@anaphoria.com>

Robert and David!
It was always this weightlessness that attracted myself and caused me to use the eikosany for
over 20 years. To the point where a single tetrad tells me everything about where I am. Even with
a hexany, one gets use to where everything is!
I still hold to the view that it takes a good year at least to learn a tuning and remain
skeptical of those who use tuning after tuning. The result of this is the same music transferred
from scale to scale with the unique qualities of each barely explored!

Robert Walker wrote:

> Hi David,
>
> > It's not just you, you'll be happy to know. A few months ago I got interested
> in x-anies, tried
> > for days to conquer the basic 1-3-5-7 hexany, and finally gave up. It seemed
> > that there was no
> > feeling of "homeness" to be found no matter how I approached it. I felt like I
> > was driving a car
> > with the steering wheel stuck turned all the way one way, just going around in
> > endless circles
> > getting no where harmonically or melodically. I figured if I couldn't get used
> > to the simplest of
> > hexanies than x-anies in general were not for me. Maybe I'll try an octany or
> > dekany sometime.
> > Thanks for the heads up.
>
> Thanks,. Exactly my experience with it too.
>
> I wonder how many others get put off x-anies in the same way!
>
> Perhaps one should add a note when describing the hexany to the effect that
> though a small scale, it is pretty tricky to use in music?
>
> I'm sure it will be worth it if one does manage to write something in it, but
> I think that would be a later stage, rather than the first one to try, as one
> would expect. I think when one does master the hexany eventually, it may well
> be rather rewarding.
>
> >From my experience, the octony does seem a pretty good one to begin with, and
> wonder what other lattices people have tried and found easy ones, to recommend
> to those who are attempting them for the first time?
>
> Anyone on the TL got good recommendations for geometrical musical lattices that are
> especially welcoming to write music in? Or maybe that
> should be a kind of newbies question (i.e. newbie to composing using lattices)
> - what are good lattices to try, to get into the way of using them in music?
>
> Robert
>

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

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

🔗David J. Finnamore <daeron@bellsouth.net>

Kraig Grady wrote:

> Robert and David!
> It was always this weightlessness that attracted myself and caused me to use the eikosany for
> over 20 years. To the point where a single tetrad tells me everything about where I am. Even with
> a hexany, one gets use to where everything is!
> I still hold to the view that it takes a good year at least to learn a tuning and remain
> skeptical of those who use tuning after tuning. The result of this is the same music transferred
> from scale to scale with the unique qualities of each barely explored!

Thanks, Kraig. I'm sure you're right about that. It's just that it can sometimes take a lot of
stumbling from tuning to tuning to find something you know will be worth pursuing, in terms of your own
musical tastes and goals. There really is no such thing as a good or bad tuning, considered in
isolation. If your music requires simple, precise consonances, then JI is good, low number ET is bad.
If you need smooth melodic motion, Myhill's property is good, JI is most likely not so good. The
eikosany is well suited for those who value permanent weightlessness but maybe not for those who prefer
to feel our feet planted firmly on the ground at certain points.

The main benefit I got out of exploring x-anies was that it lead me "accidentally" to the discovery of
Wilson's Horagrams of the Scale Tree. :-) It was love at first hearing.

--
David J. Finnamore
Nashville, TN, USA
http://personal.bna.bellsouth.net/bna/d/f/dfin/index.html
--

🔗jpehrson@rcn.com

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:

/tuning/topicId_19988.html#20371

> Robert and David!
> It was always this weightlessness that attracted myself and
caused me to use the eikosany for over 20 years. To the point where a
single tetrad tells me everything about where I am. Even with a
hexany, one gets use to where everything is!
> I still hold to the view that it takes a good year at least to
learn a tuning and remain skeptical of those who use tuning after
tuning. The result of this is the same music transferred
> from scale to scale with the unique qualities of each barely
explored!

Hi Kraig!

You know, this is VERY interesting, and it got even MORE interesting
the more I thought about it. It's quite possible that, for my OWN
music, I really AM just writing the same music, MY music, and
adapting it to different tunings. Perhaps, though, that is the way
that I go about things...??

HOWEVER, your suggestion of getting INSIDE tunings and going the
OTHER WAY... from INSIDE the tuning to determine the music is a
fascinating one... Maybe I'll try to write pieces with that approach.

Anyway, it's an important thing to think about, and I want to thank
you for bringing it to my attention...

________ _____ ____ _
Joseph Pehrson

🔗Robert Walker <robert_walker@rcwalker.freeserve.co.uk>

Hi Joseph,

Yes, I have been trying leaps with the hexany, and it does help.

Here are some ideas about why it is:
Here is the 1 3 5 7 hexany
1/1 8/7 6/5 48/35 8/5 12/7 2/1

As steps:
8/7 21/20 8/7 7/6 15/14 7/6

It is superparticular, but the 21/20
and 15/14 don't seem to work well with
the other steps in melodic movement.

These are the intervals between
opposite vertices of the hexany (with the
last of the three pairs being the 1/1 and 48/35).

When one tries to get from one note
to another via a scale passage, with the
others as passing notes, those steps
really stand out, and can sound awful.

I'm sure they'd sound okay in another context,
as it is just in the context of this scale that they
sound bad. I don't think it is just the difference
in size either as the ratio of the semitone to the
tone of the 17-tet major scale is about the same,
and that sounds great.

Also prob. one can exploit the contrast, even in melodic movement,
but that's perhaps not for complete beginners at the scale.

While with many six note scales, just
playing an ascending or descending scale of all the notes
sounds great melodically.

So here is an idea, to define four modes of the
hexany:

Steps:
2 1 2 1 = 6/5 8/7 5/4 7/6

1 2 2 1 = 8/7 6/5 5/4 7/6

2 1 1 2 = 6/5 8/7 7/6 5/4

1 2 1 2 = 8/7 6/5 7/6 5/4

I.e. all the possible ways of leaving out
one each of the 8/7 6/ and 8/5 12/7 pairs.

They aren't meant to be used in the normal way
as modes that one stays in for any length of time,
just that if you want a scale passage to get
from A to B, you use one of these modes
to do it.

Could be helpful for hexany newbies.

However, I haven't had a chance to try them out
so this is just theoretical right now - I'm without
sound for a few days on my computer as the speaker
is in for repairs, and for one reason and another
can't use the tiny speakers that came with the
computer either right now, nor can i use earphones
as they also plug into the speaker amp.

May give someone some ideas though,...

May be more to it than that too. Glad you like
the opening phrase, and it is very leapy I agree.

Robert

🔗jpehrson@rcn.com

--- In tuning@y..., "Robert Walker" <robert_walker@r...> wrote:

/tuning/topicId_19988.html#20599

>
> However, I haven't had a chance to try them out
> so this is just theoretical right now - I'm without
> sound for a few days on my computer as the speaker
> is in for repairs, and for one reason and another
> can't use the tiny speakers that came with the
> computer either right now, nor can i use earphones
> as they also plug into the speaker amp.
>
> May give someone some ideas though,...
>
> May be more to it than that too. Glad you like
> the opening phrase, and it is very leapy I agree.
>
> Robert

Hi Robert...

I think when you get your speakers and listen to what Kraig Grady has
been doing with these structures, you'll probably get another view.
Kraig, who has been working with this stuff a LOT, seems to use the
pitches as a kind of gestalt... with frequent wide leaps in fairly
inharmonic timbres with his acoustical instruments.

So this should sound disjointed, yes? Well, it DOESN'T, it all comes
together nicely, which leads me to conclude that the INTEGRATION of
the hexany can only be appreciated through such a GESTALT approach,
and not by playing it in a typically scalar fashion...

Just a thought...

_______ ____ ___ _
Joseph Pehrson

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗jpehrson@rcn.com

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:

/tuning/topicId_19988.html#20606

>
> Joseph!
> i don't think there is a leap above a forth in the whole piece
which occurs in an octave and a half range. Thirds are the most
common interval throughout.
>
> A former lister here used to refer to this being an
"inharmonic" timbre whereas on a vibraphone, it is the air column,
that we hear except at the very initial attack producing a sine.
> That some would say anything to dismiss this work was not uncommon.
>

Hi Kraig!

Actually, you're right, upon listening again. Actually this
particular work "A Farewell Ring" is quite "tonal." But then, it's
NOT using a HEXANY is it?? I thought you said it was the EIKOSANY??

In any case, it's interesting that I should think of your music as
"disjunct." Maybe I was thinking more of the "Creation of the
Worlds" but, upon listening to that again, I have to confess that
even THAT isn't particularly disjunct.

So why does it seem to me that your music sounds "abstract??" Maybe
it's the "combination tones" or such like... actually the intervals
themselves aren't so disjunt. (I should quickly add that the
adjective "abstract" is a COMPLIMENT in MY book... maybe not in
somebody else's!)

That's really interesting... since the music sounds VERY
sophisticated to me, and yet it's using some pretty simple elements...

_______ ____ ____ _
Joseph Pehrson

🔗Kraig Grady <kraiggrady@anaphoria.com>

jpehrson@rcn.com wrote:

> Hi Kraig!
>
> Actually, you're right, upon listening again. Actually this
> particular work "A Farewell Ring" is quite "tonal." But then, it's
> NOT using a HEXANY is it??

the 1-3-5-7

> I thought you said it was the EIKOSANY??
> So why does it seem to me that your music sounds "abstract??"

Yes! you must be confusing the two. The Creation of the Worlds has an abstract quality I believe
in that it has no tonal center or at least one that is continually suspended. It also lacks any
repetition of themes (in the sense of contours) although the pitch structure is awfully tight.

The structure BTW is mentioned in
http://www.anaphoria.com/cps.PDF
What I would call my only really inspired thing in Xenharmonikon

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

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

🔗Robert Walker <robert_walker@rcwalker.freeserve.co.uk>

Hi Kraig,

The three squares are really helpful for finding ones way around, thanks.

> Robert!
> Each dyad occurs twice and if you take this pair, you have what makes up a square. or the sets
> AB AC
> BD CD
>
> AB AD
> BC CD
>
> AC AD
> BC BD

I'm not sure I quite understand your notation here yet.

What are the A, B etc? Notes, diads, or triads?
I think I must be missing something...

Here is what I understand so far by the squares -
example of 1 3 5 7 hexany, which is the one I'm working
with at present:

1/1 8/7 6/5 48/35 8/5 12/7 2/1

squares are
1/1 6/5 48/35 8/7 1/1
(6/5 8/7 5/6 7/8)

48/35 12/7 2/1 8/5 48/35
(5/4 7/6 4/5 6/7)

and
8/7 12/7 6/5 8/5 8/7
(3/2 7/10 4/3 5/7)

(and then any consonant diad in the square makes consonant triads with
the two other notes of the hexany.)

>
> Hopefully Erv will let me put up some of his Hexany diagrams soon!

Look forward to seeing them.

>
> I also have gotten good things out of taking 3 dyads in a row and using these as in
> [AB AC] [AD CD] [ BD BC] the other possibility being
> [BC AB] [AC AD] [CD BD}
>

Robert

Re: Scales and lattices

🔗Robert Walker <robert_walker@rcwalker.freeserve.co.uk>

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