Re: [tuning] will it fly?? [72/144-tET]

Joseph Pehrson wrote,

> 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??

Probably, with the requisite dedication.

> Would they want to?

No. Probably not.

> I think they would even have problems with 72...

The thing to try and bear in mind here Joe is that there already is a
preexisting 72 "school"; in other words, proof and testimony of its
doability already exists... it's airborne! The 144-tET modification on
the other hand was simply an attempt on my part to globally up the
ante (so to speak) of 72's already doable approximation of the pitch
continuum with a minimum of additional notational complexity. My
reasoning was that those who could already tackle the 72-tET notation
could then approach the modified glyphs much as most performers tend
to approach the various varieties of quartertone notations: as a note
approximately halfway between one familiar note and another... 144-tET
precisely rendered definitely wasn't the point.

As Joe Monzo pointed out, some (notably Paul Erlich) would see this as
a bad idea in the sense that it (depending on how it's used) could
easily sabotage 72-tET's impressive consistency. And as a brief note
on this -- in case your puzzling over the significance of that -- I
would say that consistency can be seen as both the measure of how far
and how well a given ET goes towards representing only the best
approximations of relative consonant intervals. So when one says that
a given equal temperament is consistent through a given odd-limit,
72-tET is consistent through the 17 odd-limit and 144-tET is
consistent through the 11 odd-limit, it means that every interval or
intervallic rotation of that odd-limit will always be represented by
its best rounded [(LOG(N)-LOG(D))*(T/LOG(2))] representations were "N"
and "D" are the numerator and the denominator of the relevant
consonant intervals, and "T" is the temperament. So using 72 and
144-tET as examples, 72 is consistent through the 17 odd-limit,
meaning that all occurrences of the 1:3:5:7:9:11:13:15:17 -- and this
is easily seen when one rotates the identity, or given odd-limit:

1/1 17/16 9/8 5/4 11/8 3/2 13/8 7/4 15/8
1/1 18/17 20/17 22/17 24/17 26/17 28/17 30/17 32/17
1/1 10/9 11/9 4/3 13/9 14/9 5/3 16/9 17/9
1/1 11/10 6/5 13/10 7/5 3/2 8/5 17/10 9/5
1/1 12/11 13/11 14/11 15/11 16/11 17/11 18/11 20/11
1/1 13/12 7/6 5/4 4/3 17/12 3/2 5/3 11/6
1/1 14/13 15/13 16/13 17/13 18/13 20/13 22/13 24/13
1/1 15/14 8/7 17/14 9/7 10/7 11/7 12/7 13/7
1/1 16/15 17/15 6/5 4/3 22/15 8/5 26/15 28/15

will always be represented by their best [(LOG(N)-LOG(D))*(T/LOG(2))]
representations were T=72. Now 144-tET is consistent through the 11
odd-limit, so while 144-tET's 13/8, 15/8, and 17/8
(LOG(N)-LOG(D))*(t/LOG(2)) approximations are all better, or rather
nearer in cents, than those of 72-tET, using these "better"
approximations would conversely lead to other multiple, or
*inconsistent* representations of relevant consonances -- hence the
term inconsistency (I would imagine). A simple example of all this in
action would be the major seventh chord in 72-tET and 144-tET were you
are considering the 8:15 to be a consonance, i.e., a best rounded
[(LOG(N)-LOG(D))*(T/LOG(2))] representation:

23----65 46---131
/ \.' / / \.' /
/.' \ / /.' \ /
0----42 0----84

Note the multiple 2:3s in the 144-tET example? The 85/144ths of an
octave ~2:3 between the 4:5 and the 8:15 is the inconsistency.
Hopefully this at least gives you some idea of the potential
situations that can arise; or perhaps you already knew! For a variety
of reasons I don't place nearly the importance on this here that Paul
does, though I can see why others would, and it can't hurt to at least
be cognizant of it and its potential compositional (or especially JI
arrangement) ramifications.

> 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.

Well I would still have to think that most any microtonal notation
,save maybe quartertones (maybe), still falls most soundly into the
laps of "specialized" performers (OK, specialized performers and rash
adventures...).

rash adventurers unite,

Dan

--- In tuning@egroups.com, "D.Stearns" <STEARNS@C...> wrote:

http://www.egroups.com/message/tuning/12234

>
> The thing to try and bear in mind here Joe is that there already is
a preexisting 72 "school"; in other words, proof and testimony of its
> doability already exists... it's airborne!

Well, I have heard some of this. I have heard Ezra Sim's music.
However, I am not a fan.... His music to me has an "academic" sound
that would sound pretty much the same REGARDLESS of the tuning he was
using... My personal impressions, of course...

> a given equal temperament is consistent through a given odd-limit,
> 72-tET is consistent through the 17 odd-limit and 144-tET is
> consistent through the 11 odd-limit, it means that every interval or
> intervallic rotation of that odd-limit will always be represented by
> its best rounded [(LOG(N)-LOG(D))*(T/LOG(2))] representations were
"N" and "D" are the numerator and the denominator of the relevant
> consonant intervals, and "T" is the temperament. So using 72 and
> 144-tET as examples, 72 is consistent through the 17 odd-limit,
> meaning that all occurrences of the 1:3:5:7:9:11:13:15:17

So basically, if I am understanding your correctly, doubling the
number of pitches of 72-tET to 144 actually DECREASES the limit
consistency of the scale, from the 17th limit to the 11th!

This would certainly not advocate for the usage of it as an
"improvement" in my view...

>
> > 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.
>
> Well I would still have to think that most any microtonal notation
> ,save maybe quartertones (maybe), still falls most soundly into the
> laps of "specialized" performers (OK, specialized performers and
rash adventures...).

Actually, I disagree with you on this point. I am beginning to feel
that instrumentalists, with a little instruction, will be able to
work with the idea that there are 100 cents per semitone, and will be
able to use this, in conjunction with the idea of quartertones. I
don't know how many instrumentalists you are working with lately... I
work with them all the time... but my recent experience is that
EVERYBODY can play quartertones now...They don't even ask about it!

It is only a "small step" LITERALLY, from there to an understanding
of 100 cents per semitone. I came to the realization that this was
possible during a recent Earle Brown concert, where New York
performers were asked to do some "elaborations" on the harmonic
series...

HOWEVER, I DO believe that we MUST retain the current staff and use
the quarter-tone and cents notation if there is any hope AT ALL!

Frankly, the idea of incorporation of cents notation in conjunction
with quarter-tone notation is not AT ALL my own idea, but is
advocated by Johnny Reinhard, who we all know has had more experience
with live performers than about ANYBODY!!!

Everybody can start throwing mud pies at me now... but I am here for
a serious purpose... not to do theorizing, but to create new music
that can be widely performed and which can help, hopefully, alter our
present "landscape."

If I find out that performers cannot do quarter tone PLUS cents
notation on a regular staff, then I am going to take my blanket and
leave the room... retreating permanently to 24-tET.

I am hoping that is not going to happen...

______________ ____ ___ __ _
Joseph Pehrson

--- In tuning@egroups.com, "Joseph Pehrson" <josephpehrson@c...>
wrote:
> --- In tuning@egroups.com, "D.Stearns" <STEARNS@C...> wrote:
>
> http://www.egroups.com/message/tuning/12234
>
> >
> > The thing to try and bear in mind here Joe is that there already
is
> a preexisting 72 "school"; in other words, proof and testimony of
its
> > doability already exists... it's airborne!
>
> Well, I have heard some of this. I have heard Ezra Sim's music.
> However, I am not a fan.... His music to me has an "academic" sound
> that would sound pretty much the same REGARDLESS of the tuning he
was
> using... My personal impressions, of course...

There is much more 72-tone music going on in Boston than just Ezra
Sims. Joe Maneri has a 72-tone ear-training class at New England
Conservatory. The language is quite negotiable if learned
systematically (for which purpose the already familiar 12-tET subset
is indispensible -- you just need to learn a few smaller divisions)
and it is spreading.
>
> So basically, if I am understanding your correctly, doubling the
> number of pitches of 72-tET to 144 actually DECREASES the limit
> consistency of the scale, from the 17th limit to the 11th!
>
> This would certainly not advocate for the usage of it as an
> "improvement" in my view...
>
Agreed.
>
> If I find out that performers cannot do quarter tone PLUS cents
> notation on a regular staff, then I am going to take my blanket and
> leave the room... retreating permanently to 24-tET.
>
Well then by the same argument as above, you might as well retreat
all
the way back to 12-tET, since 12-tET is consistent through the 9-
limit, while 24-tET is only consistent through the 5-limit . . .

Obviously that would be kind of pedantic, but 24-tET is not my
favorite tuning system . . .

Hey Joe (Pehrson),

Thanks to you and Dan Stearns for the compliments on my piece.

I wanted to make it clear that probably the main reason I feel
that the 144-tET notation worked well for me in _Spider_, is
the same reason 72-tET works well for Ezra Sims: we conceive
of our music in JI and use the *transparency* of the ET notation
to *approximate* the ratios.

While I haven't tried it, I do believe _Spider_ could be performed
well by live musicians because they'd be using their *ears* to tune
to the JI pitches, using the 144-tET notation as a 'rough guide'
to get within the general frequency area. This is not unlike
using cents-values to indicate JI pitches, but the cents-values
are more accurate.

I can concede that in some ways using cents-values makes more
sense ;-) Here's the argument:

In the Stearns 144-tET notation, there are 9 different symbols:

4 pairs (which form the 72-tET basis):

# and b for 1/2-tones = 100 cents
^ and v for 1/4-tones = 50 cents
> and < for 1/6-tones = 33.1/3 cents
+ and - for 1/12-tones = 16.2/3 cents

and the ~ to mitigate the action of any of the above by 50%,
indicating any of the 1/24-tone (8.1/3-cent) inflections that
fall between any of the above. The ~ only appears accompanying
one of the 8 pairs of symbols above, and incorporates the
directional logic of the symbol with which it is used; the ~
is a 'mitigator' of the action indicated by the 'main' symbol.

For example, if C is our reference tone of 0 cents, E~v indicates
a pitch 1/24-tone above the 1/4-tone below E, or 358.1/3 cents.

In the simplest version of the cents system, there are 10 different
symbols: the digits 0 to 9. In combination with the 12 pitches
of the 12-tET chromatic scale, this would suffice to indicate any
pitch to within 1 cent. You'd need only one, not both, of either
# or b, to indicate the 12 different pitches. Similarly, the cents
would indicate an adjustment in either the sharp or flat direction,
but not both. So altogether there are 11 different symbols.
If you use *both* # and b with the cents system, that's 12 symbols.

But this is not the most common way the cents system is used.
Most often, I've seen + or - cents applied to the chromatic
pitches. So now we're up to 13 different symbols, and we're
incorporating the kind of directional logic that the 144-tET
system uses with less symbols. See where I'm going with this?

Admittedly, it's something like comparing apples and oranges,
because the cents system takes advantage of our ability to
use the decimal place-holder system of calculation to make
the 10 digital symbols represent 100 discrete measurements,
whereas each of the symbols in 144-tET has one specific meaning
(imagine writing cents-values in Roman numerals!). So the ratio
of accuracy to symbol-complexity is much higher in the cents
system.

Anyway, that's some more to think about regarding 144-tET.
I find it a useful guide or approximation to JI.

And Dan Stearns likes 144-tET notation because he finds it
a useful systematic approximation to the *simulatenous* use of
many different smaller ETs, which is often how Johnny uses
the cents system.

Also, I wanted to chime in that I think 24-tET notation is
a wonderful notation for breaking the bonds of 12-tET and
approximating a whole new universe of microtonal pitches.
I know Paul Erlich strongly disagrees, because 12-tET scores
much higher marks in the consistency game, but still, in its
use as a *notational approximation*, I find it useful.

And Joe, if you insist that staff-notation must be retatained,
what do you think about prime-factor notation? Developing this
was my first important contribution to tuning theory, back
around 1992 - not that I invented it, but I'd never really
seen it used *as* a form of staff-notation. IMO, it's the
simplest accurate JI music-notation.

But for performance possibility, I'd still recommend 72- or
(if you're willing to take the plunge) 144-tET notation.

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

> [me, monz]
> http://www.egroups.com/message/tuning/12254
>
> And Joe, if you insist that staff-notation must be retatained,
> what do you think about prime-factor notation?

Sorry about the typo: 'retatained' should obviously be 'retained'.

Also, I had this interesting observation:

There are regional geographical 'schools' of microtonal
music-notation developing today: the 72-tET-ers around Maneri
and Sims in Boston, the 'cents-ers' around Reinhard in New York,
the 31-tET-ers around the Stichting (sp?) Huygens-Fokker in
Amsterdam.

This is not unlike the way various different 'schools' of
regional neumatic notation developed in medieval Europe.
(Care to comment, Margo?)

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

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

http://www.egroups.com/message/tuning/12254

> But this is not the most common way the cents system is used.
> Most often, I've seen + or - cents applied to the chromatic
> pitches. So now we're up to 13 different symbols, and we're
> incorporating the kind of directional logic that the 144-tET
> system uses with less symbols. See where I'm going with this?
>

As I mentioned to Paul... this logic is irrefutable.

> Admittedly, it's something like comparing apples and oranges,
> because the cents system takes advantage of our ability to
> use the decimal place-holder system of calculation to make
> the 10 digital symbols represent 100 discrete measurements,
> whereas each of the symbols in 144-tET has one specific meaning
> (imagine writing cents-values in Roman numerals!). So the ratio
> of accuracy to symbol-complexity is much higher in the cents
> system.
>

However, there is also the factor of the familiarity with the decimal
system rather than learning a new notation... which, I believe it
will seem like, more or less, to working musicians encountering this
for the first time. This will be a factor.

Another factor, which Johnny Reinhard mentions, further along the
post
line #12256, is the fact that 72-tET can not accomodate AS MANY
different kinds of tuning as the cents method can.

Which tunings can it NOT do?? It obviously can't do 19 or 31 equal...
right??

The best way to find out the practicality, probably, is to try out
pieces in BOTH quarter +/- 50 or 72-tET and find out the reactions.

This is presuming, of course, that the musicians have not been
"privvy" to the specialized instruction in Boston which, admittedly,
I did not understand even penetrated the bastions of the New England
Conservatory!

> Anyway, that's some more to think about regarding 144-tET.

I'm still thinking about 72... but that's OK....

>
> Also, I wanted to chime in that I think 24-tET notation is
> a wonderful notation for breaking the bonds of 12-tET and
> approximating a whole new universe of microtonal pitches.
> I know Paul Erlich strongly disagrees, because 12-tET scores
> much higher marks in the consistency game, but still, in its
> use as a *notational approximation*, I find it useful.
>

Well, it's all over the place... so, like it or not, MOST composers
nowadays have been using it. I would wager that there are VERY FEW
living or recently deceased composers who have never written a
quarter-tone!

>
> And Joe, if you insist that staff-notation must be retatained,
> what do you think about prime-factor notation? Developing this
> was my first important contribution to tuning theory, back
> around 1992 - not that I invented it, but I'd never really
> seen it used *as* a form of staff-notation. IMO, it's the
> simplest accurate JI music-notation.
>

I have your book here in a prominant place on my bookshelf, but I am
not immediately "gleaning" what the prime-factor notation is. But,
then, I believe I have an early, unedited version of the work...

_____________ ____ ___ __
Joseph Pehrson

> [Joseph Pehrson]
> http://www.egroups.com/message/tuning/12260
>
> I have your book here in a prominant place on my bookshelf,

Thanks! My own copies are usually buried in a pile somewhere...

> but I am not immediately "gleaning" what the prime-factor
> notation is. But, then, I believe I have an early, unedited
> version of the work...

Yes, you, like everyone else who's bought or been given one,
have a sloppy, ugly, partially-edited copy. With my head twisted
in so many directions on so many different projects, finishing
my book is starting to look like a life-long occupation...
I promise, everyone who buys an 'ugly' copy will eventually
get a 'finished' one without extra charge.

Anyway, the prime-factor notation is explained early on in
my book, before I get into all the historical lattice-diagrams.

That section was the original paper I wrote, which later formed
the nucleus of my book. The paper is online at:
http://www.ixpres.com/interval/monzo/article/article.htm

Hope that helps. It's really pretty simple.

Daniel Wolf also wrote a letter appearing near the end of
a _1/1_ a couple of years ago, in which he proposed a notation
using exactly the same concepts as mine, but with various
typographic symbols representing an exponent of +1 and -1 for
the prime-factors up to the 23-limit. I believe I reference
it in my paper.

My system and Wolf's were both reactions against, and hopefully
improvements upon, the 5-limit-based JI notation of Ben Johnston.
You can find articles about that in _Perspectives of New Music_.

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

Hi Joe,

Back when you first started this discussion in the middle of
last week, I sent a post
http://www.egroups.com/message/tuning/12067

wherein I provided links to earlier discussions we had about
this from last year.

One of those old posts:

http://www.egroups.com/message/tuning/2362

is the one where I laid out the entire 144-tET '8ve'.

It seems that perhaps you missed this message from last week
# 12067); take a look - it will give you a lot more debate to
consider.

Remember that *any* notation, whether its describing music,
language, or whatever, is less precise than the actual data!
Things in the real world seem to happen in an analog fashion,
and our notations, codes, symbols, etc., can only work in
a digital format! We can only describe coded information in
discrete 'bits'.

This is a big aprt of the reason why I keep arguing that
notations and tunings are two different things, and that
musicians can learn to cope with the inevitable inadequacies
of a notational system. Look at how Partch handled it!
His notations are all tablatures which cannot be understood
without intimate knowledge of the instruments themselves.

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

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

http://www.egroups.com/message/tuning/12268

>
>
> Back when you first started this discussion in the middle of
> last week, I sent a post
> http://www.egroups.com/message/tuning/12067
>
> wherein I provided links to earlier discussions we had about
> this from last year.
>

Hi Monz...

Yes, I did study your post carefully, but the only links I didn't
really go totally through were the ones concerning notation. I was
more concerned at that moment with the difference between the just
systems and ETs, and was not thinking at that moment much about the
notational systems.

Now, however, I certainly understand the relevance of them...

I learn more and more virtually every day on this list!

Thanks, as ever, for your help!

Joe (too)
_________ ____ __ __ __ _
Joseph Pehrson