Yahoo Tuning Groups Ultimate Backup tuning question on equal temperaments

I've been working on a new piece for viola and electronics using the
"combined hexanies" scale that Paul Erlich helped lattice a while
back...

Hexanys 1 3 5 7 9
0: 1/1 0.000 unison, perfect prime
1: 35/32 155.140 septimal neutral second
2: 9/8 203.910 major whole tone
3: 5/4 386.314 major third
4: 21/16 470.781 narrow fourth
5: 45/32 590.224 tritone
6: 3/2 701.955 perfect fifth
7: 105/64 857.095 septimal neutral sixth
8: 27/16 905.865 Pythagorean major sixth
9: 7/4 968.826 harmonic seventh
10: 15/8 1088.269 classic major seventh
11: 63/32 1172.736 octave - septimal comma
12: 2/1 1200.000 octave

My experience, so far, has been to "revel" in the idiosyncracies of
this tuning. I love, for example the interval between the 11th and
12th degrees which is, after all, only 28 cents! I've found
surprising, although it probably shouldn't be... that I "miss" having
some smaller intervals between, let's say, degree 6 and 7... it's
obviously a step and a half at 156 cents... I'm sometimes looking for
the "semitone" inbetween. But, then, I'm able to "just get over it,"
by incorporating some other figuration or melodic line that just
works as well with a different construct.

I guess my question is VERY general, but I was interested in peoples'
reactions concerning equal temperament. If the UNEQUAL temperaments
are so interesting in their idiosyncracies, why is it so imperative
to even WANT to use equal temperaments??

I understand the history of transposition, modulation and so forth...
but are people really going to want to "modulate" in traditional (or
even untraditional!) ways in non 12-tET systems? If so... who on
this list has had experience with non-12-tempered ET's within the
realm of transposition and modulation??

I understand that whatever characteristic is present in one "key" of
such an equal system is just as "good" or "bad" as in another "key."
Whoopie. However, one would NEVER find the purity of certain
intervals that could be present at certain points, which would be
discovered by a composer-- by the way -- in a just system (??)

Have alternate equal temperaments been successful for you?? and are
they WORTH the evening out of all the intervals and their special
characteristics in order to achieve it??

Any commentary or suggestions would be greatly appreciated.

Thanks!

_________ ______ ___ __ __ __
Joseph Pehrson

🔗Jacky Ligon <jacky_ekstasis@yahoo.com>

--- In tuning@egroups.com, "Joseph Pehrson" <pehrson@p...> wrote:
>
> My experience, so far, has been to "revel" in the idiosyncrasies of
> this tuning. I love, for example the interval between the 11th and
> 12th degrees which is, after all, only 28 cents! I've found
> surprising, although it probably shouldn't be... that I "miss"
having
> some smaller intervals between, let's say, degree 6 and 7... it's
> obviously a step and a half at 156 cents... I'm sometimes looking
for
> the "semitone" in-between. But, then, I'm able to "just get over
it,"
> by incorporating some other figuration or melodic line that just
> works as well with a different construct.

Joseph,

Hi!

With this post you are speaking the language I love the most. This is
the reason that I love the Just tunings so much! You may remember an
earlier post from me in which I was saying how I observed other
musician's approach to Just tunings for the first time. This is
exactly what they were doing and what I love to do all the time
is "revel in the idiosyncrasies" of the Just Scales. There is
something so beautiful about the varying size scale steps. The fact
that this is predominantly found in the tuning systems of so
called "Ethnic Musics" of the World, where the ear dictates what
sounds right, must lend some validation to the use of the Just Ratios
(or scales of unequal step sizes).

>
> I guess my question is VERY general, but I was interested in
peoples'
> reactions concerning equal temperament. If the UNEQUAL
temperaments
> are so interesting in their idiosyncrasies, why is it so imperative
> to even WANT to use equal temperaments??

This is the kind of question that I asked myself in the late 80s,
when I turned (permanently) to Just Intonation as my personal
preference. Equal Temperament practice seems to be predominantly
concerned with approximating the Just Intervals, but providing stable
equal intervals for modulation. I have always preferred a "take what
nature gives" approach. My whole approach to tuning comes from this.

>
> I understand the history of transposition, modulation and so
forth...
> but are people really going to want to "modulate" in traditional
(or
> even untraditional!) ways in non 12-tET systems? If so... who on
> this list has had experience with non-12-tempered ET's within the
> realm of transposition and modulation??

Many times in my Just Intonation compositions, I'm not really
concerned with modulation - at least in the Equal Temperament sense,
and I find it works out Just fine for me to modulate within the scale
structure that I'm using at the moment - and as you would imagine,
there are always the subjectively best modulations in a given JI
system. If I remember correctly, Harry Partch also found that it
worked well for him too. Hey - if harmonic entropy shows us that the
ear makes certain allowances in perception of intervals, then there
is a veritable infinity of resources in the modulations of JI.

>
> I understand that whatever characteristic is present in one "key"
of
> such an equal system is just as "good" or "bad" as in
another "key."
> Whoopie. However, one would NEVER find the purity of certain
> intervals that could be present at certain points, which would be
> discovered by a composer-- by the way -- in a just system (??)

IMO there is rarely a better substitute than using the Just
Intervals - except for (but not that its' necessarily better), as we
all know, when you go to higher and higher prime divisions of the
octave (53 tET and such), and then you must deal with unwieldy
keyboard mappings, or choosing some subset of a large nTET - so for
me - the best and most beautiful solution is to use the very thing
that Equal Temperaments are trying to be - JUST. An observation I
have long noticed with the Just method, is that the 1/1 tonal key
center seems always implied in a Just system, even when you are using
chords/melodies not containing the "root" (this must have something
to do with Mr. Erlich's harmonic entropy - or just plain old tonal
gravity, but I'm at this point unqualified to show the mathematical
proof). Undoubtedly though, there is something very beautiful about
tuning up your instruments, and exploring the modulatory
possibilities of a closed set of pitches.

>
> Have alternate equal temperaments been successful for you?? and are
> they WORTH the evening out of all the intervals and their special
> characteristics in order to achieve it??

As stated above, I experimented with many different TETs in the first
couple of years of my microtonal tuning experience, to find that I
love and prefer the just logic. Sometimes I feel that this does not
resonate with all here (note that not one person commented on my post
about my 13 Tone Just Intonation system), but here I must agree with
Dan Stearns - there is no reason to narrow the field of choices that
are available to us all that have chosen to be on the vanguard of
microtonal tuning in the 21st Century.

>
> Any commentary or suggestions would be greatly appreciated.

How about this: I really dig your music!
>

Yours Truly,

Jacky Ligon

🔗Joseph Pehrson <pehrson@pubmedia.com>

🔗Monz <MONZ@JUNO.COM>

> [Joseph Pehrson]
> http://www.egroups.com/message/tuning/12059
>
> ... If the UNEQUAL temperaments are so interesting in their
> idiosyncracies, why is it so imperative to even WANT to use
> equal temperaments??
>
> ... Have alternate equal temperaments been successful for you??
> and are they WORTH the evening out of all the intervals and their
> special characteristics in order to achieve it??

Hi Joe. I don't really have answers to your questions, just
a couple of comments from my own experience.

One of the main reasons I got so interested in just-intonation
is the variability of interval-size you get in a closed system
of pitches, where often a variety of specific ratios would all
fall collectively under one intervallic _gestalt_.

I find it attractive that, say, an important motive can appear
in one part of a piece with a 'pure major 3rd' of 5/4 in it,
and at another place where the same motive occurs you can
use a 'neutral 3rd' 11/9 for variation, and so on.

From time to time, I retune one of my old 12-tET pieces into JI,
and while most of the retuning follows the dictum of the closest
'traditional' 5- or 7-limit harmonies, I never fail to exploit
some of the 'weirder' intervals, on purpose. Look around on my
'Worklist' webpage for examples.

I can also agree with much of what Jacky Ligon said in his
response to you:
http://www.egroups.com/message/tuning/12064

but my exposure to many thought-provoking ideas here on this
List (primarily stemming from Paul Erlich's unbelievably consistent
logic) has forced me to reconsider many ideas about temperament.
(I have a '24-eq tune' on my site too, if you'd like to hear
something I've done with strict quartertones - some people here
really liked this little piece, Carl Lumma in particular.)

So in addition to my general preference for JI, and for
temperaments that approximate it, I'd have to say that I find
ETs musically useful too.

An equal-temerament has its own characteristic overall 'mood'
that becomes apparent while playing around with its various
pitches. This too can be musically useful. As you note, ETs
are far different from well-temperaments, meantones, and other
uneven temperaments in this respect.

> [Dan Stearns]
> http://www.egroups.com/message/tuning/12060
>
> I personally tend to use a lot of equal tunings simply for the
> beauty and musical usefulness (as I see it) inherent in them,
> and a lot of these are by no means even best seen as
> "temperaments"; i.e., 11, 13, 20, (etc.). I think this is an
> important distinction that you might not be taking into
> consideration. I also occasionally use some unusual equal
> temperaments in the usual sense; i.e., to achieve a greater
> degree of a certain desirable JI paradigm while at the same time
> tempering out another not so desirable condition of that JI
> paradigm (see the recent 5L4s, 9-tone posts)..
>

In fact, around the end of last year (you may have missed this),
we on this list came up with a broad classification of tunings:
http://www.egroups.com/message/tuning/7343

Unfortunately, I myself have contributed to confusion by ignoring
the advice I gave myself here:

http://www.egroups.com/message/tuning/7346

and indiscreetly mixing the use of 12-EDO and 12-tET on my website.
One of these days I'll have to clean all this up.

Carl Lumma suggested an alternative system:

http://www.egroups.com/message/tuning/7372

Look around in the archives all around these messages; there
were quite a few interesting comments about this subject.

I highly recommend getting acquainted with the work of Ivor Darreg,
Easley Blackwood, Dan Stearns, and Brian McLaren for a glimpse into
this 'ET universe'. All four of them have CDs and tapes of their
music, and much written material as well (McLaren and especially
Darreg have been particularly prolific as writers; alas, the past
tense is necessary when speaking of Darreg as he passed away a
few years ago).

While Blackwood's approach seems to me to be primarily founded
on the approximations various ETs have to various just intervals,
Darreg's approach was based more on exploring particular ET 'moods'
without so much reference to their JI implications (altho he
did talk about that too). McLaren and Stearns are pretty much
coming from this angle too.

As far as I know, Darreg was the first music-theorist to really
discuss the idea of individual 'moods' for various ETs, outside
of older research that more closely followed Blackwood's type
of approach.

I know Blackwood's _The Structure of Recognizable Diatonic Tunings_
is out-of-print, but you'll have no problem finding it at a
library (or used book store?) in New York. I'm not sure about
the status of the CD/tape of his landmark _Microtonal Etudes_
- others on the List can probably help you; I found a copy of
the CD at a library in Philadelphia.

Darreg's CD _Detwelvulate_ is available. I think Frog Peak has
it, and we have a few copies here at Sonic Arts.

You can write to McLaren; any interest you show in microtonal
music will prompt him to send you generous packages of his own CDs
and articles. (He's also very dedicated to spreading info about,
and music by, Darreg.)

Dan Stearns is on this List and has mp3s on the Tuning Punks site;
he's very open to extensive theorizing about his work, both
privately and on-List. (In fact, Dan, it would be nice to have
your theoretical writings collected somewhere, either in print or
on a website. It would certainly help me to follow your complex
thoughts better.)

Another thing Dan Stearns, Ezra Sims, and myself all find very
useful about ETs is their notational transparency. We all agree
(and so does Paul Erlich) that 72-tET is exrememly good for
representing a very broad set of JI tunings. Sims uses 72-tET
to represent a very complex 37-limit JI, while Erlich's analysis
of its 'consistency' gives him a more conservative view (IIRC,
72-tET 'works' up to the 11-limit; correct me if I'm wrong, Paul).

Stearns has invented a very simple modification of 72-tET notation
into 144-tET, which I also found extremely useful. Stearns
likes it for its ability to 'accurately' represent many different
smaller ETs which are all being used simultaneously, and I like
because of its good approximations of very complex JI systems.
Erlich doesn't like it because it offers added notational
complexity but no improvement in consistency over 72-tET. See:

http://www.egroups.com/message/tuning/2362
http://www.egroups.com/message/tuning/2365
http://www.egroups.com/message/tuning/2437
http://www.egroups.com/message/tuning/2471
http://www.egroups.com/message/tuning/2514

and follow the further links in these threads, for more comments.

(when you see a post by 'Brett Barbaro', that was Paul Erlich
using his roomate's computer.)

If you need more info about consistency, see my Dictionary entry

http://www.ixpres.com/interval/dict/consiste.htm

and follow the links to papers by Erlich and Ozzard-Low.

The big point I tried to make in those posts was that what
is important in a tuning may not necessarily be important
in a notation, and vice-versa.

Good intonationally-sensitive musicians can learn how to adjust
their intonation closer to, or further away from, what's
written in the score, depending on the particular requirement.
This doesn't always apply to a tuning _per se_.

In your response to Dan
http://www.egroups.com/message/tuning/12065

you elaborate on different viewpoints concerning limitations
placed on art. I think Partch said it best:

> [Harry Partch, _Genesis of a Music_, 2nd ed., p 125]
>
> To chain oneself, as a creator - to impose limitations within
> which to work - is a legitimate exercise of personal freedom;
> to be forced to endure such limitations because of a conspiracy
> of factors quite beyond the ordinary creator's control is a
> musical horse of another color.

-monz
http://www.ixpres.com/interval/monzo/homepage.html

🔗Joseph Pehrson <pehrson@pubmedia.com>

--- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:

http://www.egroups.com/message/tuning/12067

"Tuning Joe1" wrote a lot in this post in response to my questions,
as I might expect... and I really appreciate it!!!

>
> An equal-temerament has its own characteristic overall 'mood'
> that becomes apparent while playing around with its various
> pitches. This too can be musically useful. As you note, ETs
> are far different from well-temperaments, meantones, and other
> uneven temperaments in this respect.
>
OK... I'll think about this and experiment some more...

>
> Carl Lumma suggested an alternative system:
>
> http://www.egroups.com/message/tuning/7372
>
> Look around in the archives all around these messages; there
> were quite a few interesting comments about this subject.
>

Yes, I remember this now. Of course, the term "UDO" could be quite
useful...

>
> I highly recommend getting acquainted with the work of Ivor Darreg,
> Easley Blackwood, Dan Stearns, and Brian McLaren for a glimpse into
> this 'ET universe'. All four of them have CDs and tapes of their
> music, and much written material as well (McLaren and especially
> Darreg have been particularly prolific as writers; alas, the past
> tense is necessary when speaking of Darreg as he passed away a
> few years ago).
>

Will do.

>
> I know Blackwood's _The Structure of Recognizable Diatonic Tunings_
> is out-of-print, but you'll have no problem finding it at a
> library (or used book store?) in New York.

It is in the New York Public Library, but I haven't found a way to
copy it yet.

>
> Another thing Dan Stearns, Ezra Sims, and myself all find very
> useful about ETs is their notational transparency. We all agree
> (and so does Paul Erlich) that 72-tET is exrememly good for
> representing a very broad set of JI tunings. Sims uses 72-tET
> to represent a very complex 37-limit JI, while Erlich's analysis
> of its 'consistency' gives him a more conservative view (IIRC,
> 72-tET 'works' up to the 11-limit; correct me if I'm wrong, Paul).
>

Something I, ahem, hadn't even thought about...

>
> In your response to Dan
> http://www.egroups.com/message/tuning/12065
>
> you elaborate on different viewpoints concerning limitations
> placed on art. I think Partch said it best:
>
> > [Harry Partch, _Genesis of a Music_, 2nd ed., p 125]
> >

This quote says it all. I forgot about it.

Thanks so much, Monz for the detailed commentary!!!!!!!

_________ _____ __ __ _
Joseph Pehrson

🔗D.Stearns <STEARNS@CAPECOD.NET>

Jacky Ligon wrote,

> There is something so beautiful about the varying size scale steps.

I certainly agree! Though it might also be instructive to remember
something along the lines of no less a JI advocate than W. A.
Mathieu's "Trojan horse of equal temperament" here:

"Play an equal-tempered chromatic scale again, up and down several
octaves in one hand, not too fast, and let your ear savor its
regularity, its newfangled, manufactured, precisely measured
_sameness_. Don't be bored, be fascinated, mesmerized. This
sensibility opens the door for the more complex symmetrical forces
hidden inside the Trojan horse of equal temperament."

> The fact that this is predominantly found in the tuning systems of
so called "Ethnic Musics" of the World, where the ear dictates what
sounds right, must lend some validation to the use of the Just Ratios
(or scales of unequal step sizes).

Those two can certainly be quite different things though; just ratios
and unequal step sizes.

> I have always preferred a "take what nature gives" approach. My
whole approach to tuning comes from this.

Though I may not always agree with the rhetoric, I'll always defend
the choices of even the staunchest of JI advocates, or ET opponents
(where it's hard to imagine anyone outdoing Partch's example for
perspicacity and derision -- wit and spit that is!). Because after
all, these are their choices to make, and certainly it's sometimes
very hard to argue with the strength of aural causality (or a
teleological persuasion) when it comes to JI... but I can think of
many instances where the subtle or gross distinctions between tuning
and music makes the whole argument or discussion a lot more complex.
One of my favorite analogies would have music as "engineering" and
tuning as "nature," say the early inventors who were trying to emulate
nature in an attempt to master flight; emulating nature -- i.e.,
birds -- just wasn't the best model/mindset for the particular job at
hand! "If you want to make something that flies, flapping your wings
is not the way to do it. You bolt a 400-horsepower engine to a barn
door, that's how you fly. You can look at birds forever and never
discover this secret."

Well the same goes for music in some instances. Where for one, you
could see something like tempering (say meantone for instance) as a
really profound solution to a particular musical problem. In this
sense, seeing this as a "compromise" is more of a particular viewpoint
than any sort of fundamental opus contra naturam.

For me, Carl Seashore really hit the proverbial 'distinction nail' on
the head when he wrote that our profoundest appreciation's of nature
and art are detachments from the physically exact, and that they
constitute a synthesis through the medium of normal illusions... that
when in comes to musical art, in a certain important sense, all is
illusion:

"Without the blessing of normal illusions, musical art would be
hopelessly stunted"... "If there where a one-to-one relationship
between the physical sound and the mental experience or response which
it illicits, our problem would be simplified. However, these
relationships scarcely if ever exist."

> so for me - the best and most beautiful solution is to use the very
thing that Equal Temperaments are trying to be - JUST.

I sure can't argue with the first point! But I just don't think that
the second one is true... true enough, you certainly can argue a ratio
to fraction of the octave interpretation for any equal division,
perhaps even a logical tempering scheme, but there's more than a
little something to Ivor Darreg's personality (or "mood") argument --
especially when it comes to the lower numbered, or even like families,
of equal divisions.

Alternate tunings? Fertile fields in all directions if you ask me!

Dan

🔗Jacky Ligon <jacky_ekstasis@yahoo.com>

--- In tuning@egroups.com, "D.Stearns" <STEARNS@C...> wrote:
>
> Alternate tunings? Fertile fields in all directions if you ask me!

Dan,

Hello!

I completely agree! I truly believe that all of the possibilities
represent valid areas of exploration. I was trying to hammer out my
reply during a 1/2 hour lunch break - so my eloquence may have
slipped a bit. Did I fail to say "IMO" and "for me"? I would humbly
like to state that I'm a perpetual student of tuning theory and
practice, and anything I say today may be shaken by the next thing I
learn - which may in turn guide me into new areas of microtonal bliss
(please note that I constantly try out different tunings and never
seem to settle for just one thing only - even though it is somewhat
appealing to me to work with a system long enough to really
internalize it's strengths and weaknesses). I came to this list on
the recommendation of Joe Monzo - and honestly - with great humility
and a spirit of wanting to learn from all of the other points of view
that are represented here. In this spirit of humility, I am
absolutely unable to have anything even remotely resembling a dogma
about tuning, as it would be in direct conflict with my attitude of
wanting to absorb as much as humanly possible from all of those much
wiser than myself. My only regret is that I didn't come here to learn
from all of you friends 3 years ago when I was able to scrape up
enough money to get my first computer and private internet access. I
can't begin to explain in mere words how it has - in just a brief
time - enhanced my music making. I look so much forward to the
stimulating exchange of ideas that I've found here everyday. Coffee
is first in the morning though - then my digest!

When I speak of "taking what nature gives", I do mean the nature of
the simple integer ratios (as well as the fact that they are found in
the verticality of the harmonic series), through which we seem to
always compare our ntETs with. It has for the longest time made sense
for my own practices to use the ratios rather than the approximations
offered in equal temperaments, but I have also experienced the great
beauty found in making music with a number of ntets. And if I, in my
own way understand a bit of what Ivor means when he referred
to "moods"; it must be the ineffable emotional quality of any tuning
that makes it a unique sound unto itself - something we experience
like the sun rising or the force of gravity - but can only discuss in
the abstractions of mathematics or the symbols of language. This has
so many rich and infinite possibilities for making beautiful music -
and I would never advocate any frozen way of doing things. Hey - this
is what we are trying to break away from anyway - right?

Respectfully,

Jacky Ligon

🔗Monz <MONZ@JUNO.COM>

> [Dan Stearns]
> http://www.egroups.com/message/tuning/12073
>
> ... I can think of many instances where the subtle or gross
> distinctions between tuning and music makes the whole argument
> or discussion a lot more complex. One of my favorite analogies
> would have music as "engineering" and tuning as "nature," say
> the early inventors who were trying to emulate nature in an
> attempt to master flight; emulating nature -- i.e., birds --
> just wasn't the best model/mindset for the particular job at
> hand! "If you want to make something that flies, flapping your
> wings is not the way to do it. You bolt a 400-horsepower engine
> to a barn door, that's how you fly. You can look at birds
> forever and never discover this secret."

Hi Dan,

I can appreciate the points you made before, after, and within
this quote, and totally agree with your conclusion ('fertile
fields in all directions'). My only contention is with your
little analogy here...

That 'bolt a 400-horsepower engine to a barn door, that's
how you fly' bit bothers me a bit, because since a very young
age the Wright Brothers have been heroes to me, and while I
understand the point this author (who is it ?) is making,
that quote denigrates the Wrights's achievement a great deal.

I think a consideration of this point is entirely _a propos_
here, because their method was not unlike Partch's, of all
people!

The Wright Brothers didn't simply 'bolt a 400-horsepower engine
to a barn door'! They conducted *years* of careful empirical
research into the behavior of different airfoil shapes in
wind-tunnels, building all of their contraptions themselves
as they went along.

There was already a considerable body of theory regarding the
possibility of flight by the time the Wrights came along, and
many of their predecessors paid *dearly* - with their lives!
- for the mistakes of blindly following those theories.

So the Wrights had ample reason not to trust any of that
theory, and ultimately their clear reasoning and (even more
importantly) painstaking work and observation ultimately
paid off.

I would say that there's a very clear parallel there with
the work to which Partch devoted his life.

-monz
http://www.ixpres.com/interval/monzo/homepage.html

🔗Paul Erlich <PERLICH@ACADIAN-ASSET.COM>

--- In tuning@egroups.com, "Joseph Pehrson" <
pehrson@p...> wrote:
> I understand the history of transposition, modulation and so
forth...
> but are people really going to want to "modulate" in traditional
(or
> even untraditional!) ways in non 12-tET systems?

You better believe it!

If so... who on
> this list has had experience with non-12-tempered ET's within the
> realm of transposition and modulation??

Me, for one. Notice the table of decatonic key
signatures at the end of my paper. Notice the
modulation in TIBIA. Etc.

Blackwood was very interested in the novel
modulational
possibilities of alternate ETs. Listen to his music
and read his PNM articles.

>
> I understand that whatever characteristic is present in one "key"
of
> such an equal system is just as "good" or "bad" as in another
"key."
> Whoopie. However, one would NEVER find the purity of certain
> intervals that could be present at certain points, which would be
> discovered by a composer-- by the way -- in a just system (??)

First of all, what do you mean "discovered by a
composer"? Secondly, JI runs into comma
difficulties even playing in one "key" -- whether it's
a traditional diatonic key (we've gone over this
before) or something more specifically
xenharmonic such as my decatonic keys.
>
> Have alternate equal temperaments been successful for you??

You bet!

>and are
> they WORTH the evening out of all the intervals and their special
> characteristics in order to achieve it??

Well, you can always start with an ET and "uneven
out" the intervals, as in a well-temperament or the
decatonic/Indian 22-tone scale in my paper. There
are also a whole bunch of options _between_ ET
and JI -- for any periodicity block, tempering out
all the commas leads to an ET or well-
temperament; tempering none of the commas leads
to JI; and tempering only _some_ of the commas
leads to these intermediate possibilities (such as
meantone and some of the tunings Dave Keenan
posted a while back).

But to me, the transposability and uniformity of
ETs are a very valuable feature, valuable enough
to have led to the adoption of two of them by
Western civilization and Thai civilization,
respectively.

🔗Paul Erlich <PERLICH@ACADIAN-ASSET.COM>

--- In tuning@egroups.com, " Monz" <
MONZ@J...> wrote:

> While Blackwood's approach seems to me to be primarily founded
> on the approximations various ETs have to various just intervals,

Blackwood puts more important on the diatonic
logic of common practice harmony and finds strict
JI unworkable for that purpose. Hence his interest
in 19-tET. In 15-tET, he finds ways of connecting
traditional-sounding triads using symmetrical 6-
and 10-tone pitch sets. In 18-tET, he adopts a
language based on that of composers who used
whole-tone scales extensively. In 23-tET, he uses
the two profoundly non-JI scales of Indonesia. . . .

> Darreg's approach was based more on exploring particular ET 'moods'
> without so much reference to their JI implications (altho he
> did talk about that too). McLaren and Stearns are pretty much
> coming from this angle too.

Don't forget Warren Burt!

> I know Blackwood's _The Structure of Recognizable Diatonic Tunings_
> is out-of-print, but you'll have no problem finding it at a
> library (or used book store?) in New York.

Also read his articles in Perspectives of New
Music.

I'm not sure about
> the status of the CD/tape of his landmark _Microtonal Etudes_
> - others on the List can probably help you; I found a copy of
> the CD at a library in Philadelphia.

If you live in NYC, you should find it within the
first few big stores you try. The CD is actually
calles _Microtonal_, and includes the contents of
his LP, plus 15-tET guitarcuts and a bonus 19-tET
Fanfare.
>
> Another thing Dan Stearns, Ezra Sims, and myself all find very
> useful about ETs is their notational transparency. We all agree
> (and so does Paul Erlich) that 72-tET is exrememly good for
> representing a very broad set of JI tunings. Sims uses 72-tET
> to represent a very complex 37-limit JI, while Erlich's analysis
> of its 'consistency' gives him a more conservative view (IIRC,
> 72-tET 'works' up to the 11-limit; correct me if I'm wrong, Paul).

It's 17-limit; that is, 72-tET is consistent through
the 17-odd limit. Within the 11-odd-limit (aka the
ratios in Partch's diamond), 72-tET is remarkable
accurate, committing no errors larger than 4 cents.

🔗Joseph Pehrson <josephpehrson@compuserve.com>

🔗Herman Miller <hmiller@IO.COM>

🔗Monz <MONZ@JUNO.COM>

> [Paul Erlich]
> http://www.egroups.com/message/tuning/12092
>
> --- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:
>
> > While Blackwood's approach seems to me to be primarily founded
> > on the approximations various ETs have to various just intervals,
>
> Blackwood puts more important on the diatonic
> logic of common practice harmony and finds strict
> JI unworkable for that purpose. Hence his interest
> in 19-tET. In 15-tET, he finds ways of connecting
> traditional-sounding triads using symmetrical 6-
> and 10-tone pitch sets. In 18-tET, he adopts a
> language based on that of composers who used
> whole-tone scales extensively. In 23-tET, he uses
> the two profoundly non-JI scales of Indonesia. . . .

I humbly bow to your expertise here. While I own a copy of
Blackwood's book, I haven't yet read it, so I'm only familiar
with his music, and I haven't really studied *that* in too
much depth.

(I started making my own version of his _Microtonal Etudes_
a few years back, but when I played the beginning of '16-ET'
for Carl Lumma, he trashed it, so I guess I lost interest...
I liked my version better than Blackwood's, but that particular
one is one of Carl's favorites, and he said Blackwood's original
had a 'swing' that I didn't capture... oh well... another
masterpiece aborted...)

Thanks for the clarification. I would definitely agree with your
first sentence, given the title of his book...

> Don't forget Warren Burt!

Yep, sorry I left him out. Even tho Warren has contacted us at
Sonic Arts (he's an old friend of Jonathan's), I don't really
know him or his work.

-monz
http://www.ixpres.com/interval/monzo/homepage.html

🔗Mats �ljare <oljare@hotmail.com>

>I guess my question is VERY general, but I was interested in peoples'
>reactions concerning equal temperament. If the UNEQUAL temperaments
>are so interesting in their idiosyncracies, why is it so imperative
>to even WANT to use equal temperaments??
>
>I understand the history of transposition, modulation and so forth...
>but are people really going to want to "modulate" in traditional (or
>even untraditional!) ways in non 12-tET systems? If so... who on
>this list has had experience with non-12-tempered ET's within the
>realm of transposition and modulation??

Setting aside all matters of instrument construction,since i am currently only using MIDI for anything else than 12tet,to me using equal temperaments is a matter of compositional convenience.

When i have written or tried to write music in unequal scales it has always suffered from that certain notes i want to use simply"ain�t there".This is always the case no matter how much i extend the JI or ET subset tunings.The only way to avoid this is to go equal.

Once i got the"feel"for what intervals are available(and not available)in 17,19,22tet or whatever,then that�s all there is to know.Using an unequal tuning(i�ve recently started dabbling in unequal/JI 12-tone sets more,for the added benefits of being able to improvise on the MIDI keyboard),each root has it�s own quirks and anomalies,which might be extremely effective if used right,but most of these effects can also be achieved in equal temperaments.

��
Mats �ljare
Eskilstuna,Sweden
http://www.angelfire.com/mo/oljare
_________________________________________________________________________
Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com.

Share information about yourself, create your own public profile at http://profiles.msn.com.

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

🔗Joseph Pehrson <pehrson@pubmedia.com>

--- In tuning@egroups.com, "Paul Erlich" <PERLICH@A...> wrote:

http://www.egroups.com/message/tuning/12089

> >
> > I understand that whatever characteristic is present in one "key"
> of
> > such an equal system is just as "good" or "bad" as in another
> "key."
> > Whoopie. However, one would NEVER find the purity of certain
> > intervals that could be present at certain points, which would be
> > discovered by a composer-- by the way -- in a just system (??)
>
> First of all, what do you mean "discovered by a
> composer"? Secondly, JI runs into comma
> difficulties even playing in one "key" -- whether it's
> a traditional diatonic key (we've gone over this
> before) or something more specifically
> xenharmonic such as my decatonic keys.
> >

This is funny. You know, the fact that Paul really didn't know what
I meant by this reinforces my view that Paul approaches music from a
"precompositional" standpoint, not an "experiencial" standpoint which
is more common for practiced composers.

I wouldn't want to hurt Paul's feelings about this :) :) :), but when
I'm talking (corresponding) to Kraig Grady or Jacky Ligon, both of
whose musics I admire, incidentally, I have the feeling that they are
basing their posts on experiences they have actually had listening to
and writing music.

With Paul, it is the opposite. I have the feeling he constructs
intellectual systems, and that's the most important part for him. It
is only later that some of these become "auditory."

There is nothing new about this. There have been legions of
theorists in the music schools who have had similar approaches...
most of them concerned with the realm of 12-tone theory. Some of
them thought they were composers... but almost all really were not.

The problem is/was that these people could rotate hexachords up the
wazoo, but they really were not hearing anything... nor was their
music informed by perceptional/auditory experiences.

So, what I am saying, is there is a certain AUDITORY logic that is
DIFFERENT from mathematical/conceptual/theoretical logic, and it
would lead people to different conclusions.

I believe it lead Harry Partch to a just system, and this is also why
I am saying that if one were to have a way of making music where ANY
system is possible... and we are actually NOW, with synthesizers,
Scala, and so forth, in this position, certain RESONANCES, as Jacky
Ligon expresses, will DICTATE THE NATURE of the tuning system.

So, if you are believing my argument, one would "gravitate" toward
just intervals, REGARDLESS of the particular constructs one set up...
whether you began with equal temperament, meantone... with SOME
commas taken care of, or just, which has the commas.

Furthermore, I really don't believe, particularly in an "advanced"
21st century music, using the full range of possibilities, that the
commas really mean anything.

Sure, if you want to play "Mary Had a Little Lamb" and transpose
through all keys in 12 or 19 or whatever, commas could be a problem,
if you want to return to the same place.

But who really wants to do that??

Anybody want to back me up?? It's fun to take on Paul... or do I
just hear "chickens..." braach, braach, braach, braach...
_____________ ____ ___ ___ _
Joseph Pehrson

🔗Joseph Pehrson <pehrson@pubmedia.com>

🔗Jacky Ligon <jacky_ekstasis@yahoo.com>

Joseph,

Hi!

First off, I must preface this reply, with that you just have such a
delightful sense of humor!!! I think I must have drawn some attention
to myself here at my office because I was laughing so hard at you
post!

> --- In tuning@egroups.com, "Paul Erlich" <PERLICH@A...> wrote:
> >
> > First of all, what do you mean "discovered by a
> > composer"? Secondly, JI runs into comma
> > difficulties even playing in one "key" -- whether it's
> > a traditional diatonic key (we've gone over this
> > before) or something more specifically
> > xenharmonic such as my decatonic keys.
> > >

This is really fascinating, and I am aware of this too. But the thing
that's always interested me about this can be summed up best by the
following question: Why does it sound so beautiful? I think part of
the answer may be found in some of the same phenomenon observed
through the lense of Harmonic Entropy - that the human hearing and
perceptual mechanisms stubbornly defy our greatest attempts to find
universality in tuning. I want to mention that I read something in a
book about Acoustics a few years ago, that the subtle and not so
subtle physical differences in the inner ears of human beings causes
a great range of different kinds of perceptions of music - I will try
to track down this information tonight. So it could be that many of
us are hearing different things and appreciate (and have affinities
for) so many myriad of various tuning systems, because of these very
physical differences. You know, this is so analogous to Sub-Atomic
Physics too - because of the different ways that you can "look" at
sub-atomic matter actually effect what you see. In other words, what
is perceived is only as good as the mechanism of perception, and or
the way of perceiving and analyzing the results of the data
perceived.

--- In tuning@egroups.com, "Joseph Pehrson" <pehrson@p...> wrote:
>
> This is funny. You know, the fact that Paul really didn't know what
> I meant by this reinforces my view that Paul approaches music from
a
> "precompositional" standpoint, not an "experiential" standpoint
which
> is more common for practiced composers.

Won't touch that one with a ten foot pole! Isn't Paul a guitarist and
keyboardist too?

>
> I wouldn't want to hurt Paul's feelings about this :) :) :), but
when
> I'm talking (corresponding) to Kraig Grady or Jacky Ligon, both of
> whose musics I admire, incidentally, I have the feeling that they
are
> basing their posts on experiences they have actually had listening
to
> and writing music.

Yes, but I sometimes wish I could better supplement it all with the
deeper understanding that comes from the mathematical analysis of
Paul's world - I am in humble awe of it all. I'm honored that you
would say this though - and it is true that much of anything that I
would have to contribute would be based on musical practice.

>
> With Paul, it is the opposite. I have the feeling he constructs
> intellectual systems, and that's the most important part for him.
It
> is only later that some of these become "auditory."

I would really love to hear some more mp3s! It does help to be able
to hear real musical examples of concepts - it's the ultimate way to
back it up. I have a friend that visited me from the Atlanta area a
while back, and I was showing him my JI spreadsheets. His comment was
so interesting that I would like to reveal it here: "Yeah, it's very
interesting to fetish over these charts, but I can't hear it". I
guess one could construe this as naive, but there is a grain of
profound truth to this too. I think it's one thing to chart, lattice,
listen to isolated chord examples and theorize - but yet another to
make the concepts into living breathing music that evolves over time.
The fundamental pitch relationships are only a facet of total music
*in my humblest opinion*.

>
> There is nothing new about this. There have been legions of
> theorists in the music schools who have had similar approaches...
> most of them concerned with the realm of 12-tone theory. Some of
> them thought they were composers... but almost all really were not.

And then you got wondrous beings like Oliver Messian that notated the
birds - I'll always adore him for his fusion of
nature/engineering/music.

>
> The problem is/was that these people could rotate hexachords up the
> wazoo, but they really were not hearing anything... nor was their
> music informed by perceptional/auditory experiences.

See above.

>
> So, what I am saying, is there is a certain AUDITORY logic that is
> DIFFERENT from mathematical/conceptual/theoretical logic, and it
> would lead people to different conclusions.

It is always noteworthy to me that many of us will use the simple
integer ratios as our guideposts. I like to build my house from them!!

>
> I believe it lead Harry Partch to a just system, and this is also
why
> I am saying that if one were to have a way of making music where
ANY
> system is possible... and we are actually NOW, with synthesizers,
> Scala, and so forth, in this position, certain RESONANCES, as Jacky
> Ligon expresses, will DICTATE THE NATURE of the tuning system.

Yes, the ear, time and timbre rules. I am never able to separate the
results of the three.

>
> So, if you are believing my argument, one would "gravitate" toward
> just intervals, REGARDLESS of the particular constructs one set
up...
> whether you began with equal temperament, meantone... with SOME
> commas taken care of, or just, which has the commas.

Isn't this partially what the findings of Harmonic Entropy have
revealed to us?

>
> Furthermore, I really don't believe, particularly in an "advanced"
> 21st century music, using the full range of possibilities, that the
> commas really mean anything.

Forgive me all for agreeing with Joseph on this, as I will "revel in
these idiosyncrasies" as soon as I can get back to my studio.

>
> Sure, if you want to play "Mary Had a Little Lamb" and transpose
> through all keys in 12 or 19 or whatever, commas could be a
problem,
> if you want to return to the same place.

Again, as I mentioned yesterday - I find that I can reliably modulate
in a closed just system, as I believe Partch very well could.

>
> But who really wants to do that??
>
> Anybody want to back me up?? It's fun to take on Paul... or do I
> just hear "chickens..." braach, braach, braach, braach...

Is there something afoul here?!! He he!

As always, a pleasure,

Jacky Ligon

🔗Monz <MONZ@JUNO.COM>

> [Joseph Pehrson]
> http://www.egroups.com/message/tuning/12108
>
> This is funny. You know, the fact that Paul really didn't
> know what I meant by this reinforces my view that Paul
> approaches music from a "precompositional" standpoint,
> not an "experiencial" standpoint which is more common
> for practiced composers.
> ...
>
> Anybody want to back me up?? It's fun to take on Paul... or do I
> just hear "chickens..." braach, braach, braach, braach...

Hi Joe.

I would say that, in common with my view of 'sonance' as
a continuum between two polar opposites - as opposed to a
view where only those opposite poles of consonance and
dissonance exist, here too we may find a continuum of
compositional approaches.

I'm quite familiar with many composers and improvisers
who are comfortable inhabiting either of the poles, but
lots of us others prefer to stay in more 'temperate' zones,
where we sometimes construct a system *before* we create
the music, and sometimes *discover* the system after the
music's been created. Our procedures go thru 'seasonal'
and 'meteorological' changes.

Many, many times, I've done a bit of constructing to get
an initial inspiration for a piece, then keep it mainly
in the background as the composition of the piece progresses
and the auditory logic takes on a life of its own.

I've used this metaphor here before, and many others have
before me (composers like Beethoven and Mahler, for instance):
composing a piece can be very much like raising a child.
These two composers both used the 'birthing' metaphor,
but (braach, braach, braach) I'm too chicken to risk
offending any feminists out there by making that claim
myself, so I'll just say 'raising'. But my point is, there's
a kind of 'nature vs. nurture' dichotomy going on here too.
Just as in the issue of raising offspring, there's lots of
room in between those two extremes, and most likely, the
best way is to be found within that area of flexibility.

(A worthwhile digression here: The issue of the importance
of flexibility in many facets of life was really brought
home to me a long time ago when I read Gregory Bateson's
_Steps to an Ecology of Mind_. This is a *fantastic* book
that I heartily recommend to anyone interested in metaphysical
stuff.)

(Another digression: One of the reasons I keep extolling the
value and beauty of the internet, is that the liberal exchange
of information seems to be the best way to foster this
attitude of encompassing flexibility. According to Bateson's
theories, flexibility is the ultimate key to survival. After
decades of wondering whether we humans would be able to ensure
our survival against the threat of our own technological
prowess - and stupidity - I think maybe the internet will be
the key to 'getting over the hump' and allowing us to move
on collectively.)

And in support of Paul, I can say two things:

1) I've jammed with him personally, and when he plays guitar,
he can rock.

2) His theories are so consistent, in my view, that they often
reveal a perfectionistic beauty that's irresistible to me.
(Probably very similar to what captivated the 12-tone serialists
a few decades ago. And I *LIKE* a lot of that music too!)

I've taken him on in debate before, and it was worthwhile.
Dialog with him on this List has profoundly changed some of
my deepest ideas about tuning, and the only other person
whose work did that before him was Partch. Pretty good
company, if you ask me.

-monz
http://www.ixpres.com/interval/monzo/homepage.html

🔗Monz <MONZ@JUNO.COM>

> [Joseph Pehrson]
> http://www.egroups.com/message/tuning/12116
>
> Thank you so much, Mats, for your commentary. Actually,
> I personally find this a more persuasive argument for equal
> temperaments than "it has a special sound of its own."
> So does everything...

Ah, but Joe... that *precisely* why Johnny (and I) disagree
with you about this on such a fundamental level.

I don't presume to speak for Johnny; I'm just relaying my
impression of his tuning philosophies. But at least in my
own case, I can assure you that no methodological procedure
with ever usurp the place of the actual sound or 'mood' of
a tuning in determining whether or not I use it. At least,
not completely and not anymore.

(This used to be the case in the dim past, when I used 12-tET
because I didn't know there was any other choice, which is
precisely why that Partch quote I just passed on here yesterday
has stuck in my mind so obstinately.)

In regard to Johnny's ideas, I'd like expound a little more.
I've covered this here before, so maybe you can get more
from the archives.

As is probably the case with most microtonalists who have already
grappled with the variety of tunings available and more-or-less
settled on a particular one, or set, I too was a bit put off by
Johnny's ideas of 'polymicrotonality' and 'all music is microtonal'.

It was listening to his piece _Raven_ that really got me to
come around to seeing his perspective. As you well know, Johnny
has great theatrical flair, and I came to realize that in his
mind each specific tuning covers a particular emotional expanse
in the overall scheme of his composition. Each one is used
to demarcate particular motives, phrases, sections, etc.

In many of his compositions, and particularly for me in _Raven_,
these microtonal mixtures provide a broad palette, a sort of
kaleidoscopic background, against which the compositional
gestures unfold, each gesture clearly delineated by its tuning.

I thought that might clarify a bit the basis of this disagreement
you mentioned yesterday. Both point of view are valid, they're
just different.

-monz
http://www.ixpres.com/interval/monzo/homepage.html

🔗Joseph Pehrson <josephpehrson@compuserve.com>

--- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:

http://www.egroups.com/message/tuning/12144

> Ah, but Joe... that *precisely* why Johnny (and I) disagree
> with you about this on such a fundamental level.
>
> I don't presume to speak for Johnny; I'm just relaying my
> impression of his tuning philosophies. But at least in my
> own case, I can assure you that no methodological procedure
> with ever usurp the place of the actual sound or 'mood' of
> a tuning in determining whether or not I use it. At least,
> not completely and not anymore.
>
> (This used to be the case in the dim past, when I used 12-tET
> because I didn't know there was any other choice, which is
> precisely why that Partch quote I just passed on here yesterday
> has stuck in my mind so obstinately.)
>
>
> In regard to Johnny's ideas, I'd like expound a little more.
> I've covered this here before, so maybe you can get more
> from the archives.
>
> As is probably the case with most microtonalists who have already
> grappled with the variety of tunings available and more-or-less
> settled on a particular one, or set, I too was a bit put off by
> Johnny's ideas of 'polymicrotonality' and 'all music is microtonal'.
>
> It was listening to his piece _Raven_ that really got me to
> come around to seeing his perspective. As you well know, Johnny
> has great theatrical flair, and I came to realize that in his
> mind each specific tuning covers a particular emotional expanse
> in the overall scheme of his composition. Each one is used
> to demarcate particular motives, phrases, sections, etc.
>
> In many of his compositions, and particularly for me in _Raven_,
> these microtonal mixtures provide a broad palette, a sort of
> kaleidoscopic background, against which the compositional
> gestures unfold, each gesture clearly delineated by its tuning.
>
> I thought that might clarify a bit the basis of this disagreement
> you mentioned yesterday. Both point of view are valid, they're
> just different.

Thank you, Monz, for this clarification. It helps me understand what
Johnny is trying to do. Curiously enough... I speak with him every
few days, and I've never understood this except now with your own
presentation of it! But then, Johnny frequently accuses me of "not
listening to him," and he may be correct in that regard...

Best
___________ ____ __ __ _
Joseph Pehrson

🔗Joseph Pehrson <josephpehrson@compuserve.com>

🔗Monz <MONZ@JUNO.COM>

> [Joseph Pehrson, on Dan Stearns's 144-tET notation]
> http://www.egroups.com/message/tuning/12232
>
> How is it really possible to write practical music in a 144-tET
> system?? People seem to have problems enough playing in 48!!
> Can a "average" musician negotiate this?? Would they want to?
> I think they would even have problems with 72...
>
> Maybe I'm the only person on this list concerned with this, but
> I REALLY AM interested in the response and evolution of the
> "average" concert musician in xenharmonic musics.
>
> I want PERFORMANCES!!

Joe, if you look back in the List archives regarding the posts
Dan and I made about his 144-tET notation, you'll see that a
few other people were concerned enough to argue about it (mainly
Paul Erlich).

Here's an opinion from Dan:
http://www.egroups.com/message/tuning/8503

IMO, yes, 144-tET is very useful as a sort of all-purpose
microtonal notation. I used it last year for _A Noiseless
Patient Spider_. The program notes for that piece are at:
http://www.ixpres.com/interval/monzo/spider/spider.htm

Except for the central 'meditation' section (which used a
13-tone 5-limit system) the tuning was a very complex mixture
of 12-tET and (IIRC) 13-limit JI. Dan had introduced me to
his 144-tET notation just a short time before, and I found
it very handy in navigating my way thru the composition of
the piece, which I did completely on the computer.

Altho my piece was realized electronically, and so therefore
I don't have concrete proof that 'average' musicians would
like it or be able to handle it, I could easily imagine,
with the familiarity of the Stearns 144-tET notation that
I had by the time the piece was finished, that other musicians
would handily dispose of its difficulties.

One thing I tried to emphasize in my old posts about this
notation was its easy divisability into smaller subset ETs,
including our familiar 12-tET. I think this helps a lot,
and certainly makes it easier to follow 72-tET notation,
as developed by Sims or Herf.

Stearns's amplification of this into 144-tET only involves
one new symbol which only takes one writing stroke, the tilde ~.

Dan also posted some of his handwritten scores in this notation.
I looked back in the archives to find the URLs, but didn't have
enough time to find them... look somewhere around the 2600s
(May 1999) - I think that's where they are. He used 144-tET
notation to represent the simultaneous use of 13-tET, 19-tET
and 20-tET (IIRC).

Remember, the point I'm making here is *not* that musicians
want to have an actual 144-tET *system* at their disposal,
only that they can internalize the logic of the system and
use its members as they come across them in notation, and
mold its notational idiosyncrasies to suit the actual tuning
desired by the composer.

-monz
http://www.ixpres.com/interval/monzo/homepage.html

🔗Joseph Pehrson <josephpehrson@compuserve.com>

--- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:

http://www.egroups.com/message/tuning/12240

>
> Joe, if you look back in the List archives regarding the posts
> Dan and I made about his 144-tET notation, you'll see that a
> few other people were concerned enough to argue about it (mainly
> Paul Erlich).
>
> IMO, yes, 144-tET is very useful as a sort of all-purpose
> microtonal notation. I used it last year for _A Noiseless
> Patient Spider_. The program notes for that piece are at:
> http://www.ixpres.com/interval/monzo/spider/spider.htm
>
Yes, A NOISELESS PATIENT SPIDER is a wonderful piece, and I enjoyed
it tremendously. However, the fact that it is electronic and was
performed by YOURSELF does not, in my view, advocate for the fact
that it is in a universal, performable system...

>
> Altho my piece was realized electronically, and so therefore
> I don't have concrete proof that 'average' musicians would
> like it or be able to handle it, I could easily imagine,
> with the familiarity of the Stearns 144-tET notation that
> I had by the time the piece was finished, that other musicians
> would handily dispose of its difficulties.
>

I will have to see the notation, but my "gut reaction" is that it is
"not going to fly" with the "average" performer... Most performers
look at all of this stuff as a "job," (unfortunately) to be
"dispensed with" as easily as possible. It is NOT a labor of love or
interest, as it is with people on this list and a FEW dedicated
performers. At least, that's how most New York musicians are...
(Yes, Reinhard has a FEW in his intrepid band that are exceptions...
same for Dean Drummond...)

>
> One thing I tried to emphasize in my old posts about this
> notation was its easy divisability into smaller subset ETs,
> including our familiar 12-tET. I think this helps a lot,
> and certainly makes it easier to follow 72-tET notation,
> as developed by Sims or Herf.
>

Well... of course that would advocate for it, but I would have to see
it physically before I could believe in its universal functionality.
Perhaps you should bring a sample next time you come to visit me.
(If you still want to after this post! :) :) :)

> Stearns's amplification of this into 144-tET only involves
> one new symbol which only takes one writing stroke, the tilde ~.
>
And, a reduction, if I'm understanding this, from 11 limit
consistency to 17. Wow. I'm impressed.

> Dan also posted some of his handwritten scores in this notation.

Like I say... SEEING is believing... even more, HEARING..

EVEN MORE if lots of people want to play it!!!!!!!

>
> Remember, the point I'm making here is *not* that musicians
> want to have an actual 144-tET *system* at their disposal,

danke gott!

> only that they can internalize the logic of the system and
> use its members as they come across them in notation, and
> mold its notational idiosyncrasies to suit the actual tuning
> desired by the composer.
>

UMMMMM. OMMMMM. That sounds a bit "theoretical" to me...
>

In continuing friendship (I hope)
________________ ____ ___ __ __
Joseph Pehrson