The notation mess

We have the following in use for the 72-et:

] = 1/4 tone up
> = 1/6 tone up
^ = 1/12 tone up
v = 1/12 tone down
< = 1/6 tone down
[ = 1/4 tone down

We have the following in use for the 11-limit

^ = 33/32 up
> = 64/63 up
+ = 81/80 up
- = 81/80 down
< = 64/63 down
v = 33/32 down

We don't need to have two different and contradictory systems in play, surely. Can we agree to discard one or the other?

To the 11-limit system, I added the following explicit definition:

# 2187/2048 up
b 2187/2048 down

I then gave an algorithm for going from rational number notation to this notation and back. I'd like to know if anyone has any objections to the way I notated things, or if I can claim this represents what people have been doing or would like to do. Here's Genesis again, this time in a system of notation which accords to that being used for
72-et:

1 C4
81/80 C4^
33/32 C4]
21/20 D4b^<
16/15 D4b^
12/11 D4[
11/10 D4b^]
10/9 D4v
9/8 D4
8/7 D4>
7/6 E4b<
32/27 E4b
6/5 E4b^
11/9 E4b]
5/4 E4v
14/11 F4<[
9/7 E4>
21/16 F4<
4/3 F4
27/20 F4^
11/8 F4]
7/5 G4b^<
10/7 F4#v>
16/11 G4[
40/27 G4v
3/2 G4
32/21 G4>
14/9 A4b<
11/7 G4>]
8/5 A4b^
18/11 A4[
5/3 A4v
27/16 A4
12/7 A4>
7/4 B4b<
16/9 B4b
9/5 B4b^
20/11 B4v[
11/6 B4b]
15/8 B4v
40/21 B4v>
64/33 C5[
160/81 C5v

Does anyone have any comments or objections?

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> We have the following in use for the 72-et:

[snip]

> Does anyone have any comments or objections?

Whaddya say someone gets empirical about it? Maybe a couple of
people, on different coasts (hint, hint), or maybe different
countries (hint^2)?

How about a phrase or two, and write it for a body that could deal
with it right off the bat without 'instrumental surgery' - a string
quartet. Write out the stuff in varying notations and varying degress
of 'up-front' commentary. See what you get back from The Players.

Because notation is for one reason: for people to play the stuff. If
you only want to listen, do synth mock-ups, or completely electronic
pieces. But if you are talking notation, take it to the people that
will have to READ IT!!!

Everything else - *everything* - is pure speculation and whimsy. Joe
Pehrson is about the ONLY person on this/these list/s that can speak
to the recent developments in trying to put across notations of the
most recent tuning/scale/temperment developments. Or listen to Johnny
R., who has about 20+ years of working with humans who are eager to
perform this music.

Get REAL feedback from REAL performers.

Get REAL.

Me, tablature is fine, but I'm a percussionist... :)

Cheers,
Jon

--- In tuning@y..., "jonszanto" <JSZANTO@A...> wrote:

> Because notation is for one reason: for people to play the stuff.

Actually, none of the notations considered here are performance notations; they are ascii versions of what might be used in a performance and have a different purpose in mind. I think the ascii symbols of these two sets of notations may as well match, and should match if we want to avoid confusion.

> Everything else - *everything* - is pure speculation and whimsy.

I don't think what I'm talking about is whimsy. The speculation is that my mathematical formulation captures what people have been doing; it seems to me it certainly ought to.

> Get REAL feedback from REAL performers.

You might tell that to George, who is proposing a notation for use in practice; it hardly makes sense as a response to me.

> Get REAL.

No chance.

Gene,

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "jonszanto" <JSZANTO@A...> wrote:
>
> > Because notation is for one reason: for people to play the stuff.
>
> Actually, none of the notations considered here are performance
notations; they are ascii versions of what might be used in a
performance and have a different purpose in mind.

Ahhhh, I see. Somehow, mostly in peripheral reading, I had missed
that there was not one but Two areas of notation, both of which are
having trouble focusing. Sorry about the mixup, and yes, it makes
sense (to those who would want such a thing) to have an 'analytical'
notation (or whatever you would care to call it) separate from
a 'performance' notation.

> > Everything else - *everything* - is pure speculation and whimsy.
>
> I don't think what I'm talking about is whimsy.

Yes, that is now clearer. My whimsy would have only applied if you
were expecting performers to read the stuff.

> The speculation is that my mathematical formulation captures what
people have been doing; it seems to me it certainly ought to.

I'll leave that to others to comment on.

> > Get REAL.
>
> No chance.

In this instance, I hope you *don't* take my advice! On the other
hand, be sure to have a space heater up there in the ivory tower... :)

Cheers,
Jon

On Sat, 09 Feb 2002 04:30:48 -0000, SOMEONE articulated, I'd better
not say who :

>> Does anyone have any comments or objections?

Is there some source for fonts for notation (of all kinds ;)

"Pipeline in the pipeline for piping" ;)

http://www.ampcast.com/guiseppimendoza
http://www.ampfea.org/sln/browse.php?num=3&a_id=132

O!

Guiseppi Mendoza wrote:

>
>
> Is there some source for fonts for notation (of all kinds ;)
>

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

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

On Fri, 08 Feb 2002 22:00:52 -0800, SOMEONE articulated, I'd better
not say who :

>> Is there some source for fonts for notation (of all kinds ;)
>>
>-- Kraig Grady
>North American Embassy of Anaphoria island
> http://www.anaphoria.com

Yes, well, I kind of gathered that this is an open topic.
Or is it ?

I don't like the PDF file format much either, kind of like wiping your
batty with 6000gm2 paper ;)
A document management nightmare.
A waste of virtual rainforest (I could go on ;)

"Pipeline in the pipeline for piping" ;)

http://www.ampcast.com/guiseppimendoza
http://www.ampfea.org/sln/browse.php?num=3&a_id=132

--- In tuning@y..., Guiseppi Mendoza <guiseppi@m...> wrote:
> I don't like the PDF file format much either

For disseminating documents containing graphics, images, and text,
what would *you* suggest?

Cheers,
Jon

P.S. if the topic strays too much from tuning, we'll have to discuss
elsewhere...

hi Gene,

> From: genewardsmith <genewardsmith@juno.com>
> To: <tuning@yahoogroups.com>
> Sent: Friday, February 08, 2002 7:05 PM
> Subject: [tuning] The notation mess
>
>
> We have the following in use for the 72-et:
>
> ] = 1/4 tone up
> > = 1/6 tone up
> ^ = 1/12 tone up
> v = 1/12 tone down
> < = 1/6 tone down
> [ = 1/4 tone down
>
>
> We have the following in use for the 11-limit
>
> ^ = 33/32 up
> > = 64/63 up
> + = 81/80 up
> - = 81/80 down
> < = 64/63 down
> v = 33/32 down
>
> We don't need to have two different and contradictory
> systems in play, surely. Can we agree to discard one
> or the other?

basically, the two contradictory systems are the standard
72edo adopted by Joe Pehrson, Paul Erlich, Dave Keenan, and
Graham Breed (IIRC) on the one hand, and the 72edo notation
i use:

Monzo 72edo notation, tone = ratio 2^(1/6)

^ = 1/4 tone up
> = 1/6 tone up
+ = 1/12 tone up
- = 1/12 tone down
< = 1/6 tone down
v = 1/4 tone down

on the other.

my 72edo notation corresponds exactly to the 11-limit
notation which it seems you are saying is a standard,
and which of course is my 11-limit JI notation (which
is why my 72edo corresponds to it).

but the reason why these two contradictory systems
exist is because i and the few people who spoke up
who supported me (remind us or me privately who you are!)
think it sucks that ^ and v are used for 1/12-tones
instead of 1/4-tones. up and down arrows have a
fairly long history of use for 1/4-tones, and ever
since i first thought seriously about notation (which
was around 20 years ago) they always made the most
sense to me for 1/4-tones.

the two 72edo notations already agree on > and < for
the 1/6-tones, so that's no problem. and i'd be willing
(very grudgingly) to chuck the + and - in favor of
the ] and [ for the 1/12-tones.

so if me and the other 72ers who use ASCII are to meet
halfway, we'd switch the standard to ^ and v for the
1/4-tones, and use ] and [ for the 1/12-tones.
i'd agree to that. the other standard hasn't been
in use so long that it would present a big problem
to switch now, i'd think.

> To the 11-limit system, I added the following explicit definition:
>
> # 2187/2048 up
> b 2187/2048 down

a tuning newbie might wonder why you'd pick such a
large interval for such a basic notational element.

prime-factored, that's 2^-11 * 3^7, and it's the
standard Pythagorean chromatic semitone; i.e., if
the note's ratio is 3^x, for x= 1 to 7 we have

C G D A E B F# C#
0 1 2 3 4 5 6 7

this is the definition of # and b in HEWM notation, in
my version <http://www.ixpres.com/dict/hewm.htm>, in
Daniel Wolf's, and in that designed by Helmholtz and Ellis.

> I then gave an algorithm for going from rational number
> notation to this notation and back. I'd like to know if
> anyone has any objections to the way I notated things,
> or if I can claim this represents what people have been
> doing or would like to do. Here's Genesis again, this
> time in a system of notation which accords to that being
> used for 72-et:
>
> 1 C4
> 81/80 C4^
> 33/32 C4]
> 21/20 D4b^<
> 16/15 D4b^
> 12/11 D4[
> 11/10 D4b^]
> 10/9 D4v
> 9/8 D4
> 8/7 D4>
> 7/6 E4b<
> 32/27 E4b
> 6/5 E4b^
> 11/9 E4b]
> 5/4 E4v
> 14/11 F4<[
> 9/7 E4>
> 21/16 F4<
> 4/3 F4
> 27/20 F4^
> 11/8 F4]
> 7/5 G4b^<
> 10/7 F4#v>
> 16/11 G4[
> 40/27 G4v
> 3/2 G4
> 32/21 G4>
> 14/9 A4b<
> 11/7 G4>]
> 8/5 A4b^
> 18/11 A4[
> 5/3 A4v
> 27/16 A4
> 12/7 A4>
> 7/4 B4b<
> 16/9 B4b
> 9/5 B4b^
> 20/11 B4v[
> 11/6 B4b]
> 15/8 B4v
> 40/21 B4v>
> 64/33 C5[
> 160/81 C5v
>
> Does anyone have any comments or objections?
>

my primary objection is the compounding of new symbols.
72edo is such a good temperament on so many levels that
i feel that the correspondence between the rational basis
of HEWM notation and the inflections of 72edo suffice to
represent nearly anything thru the 11-limit, with compounding
only happening in conjunction with b and #.

in addition to the objections that some of us have voiced
over Ben Johnston's notation (mainly that it has a
2-dimensional rather than 1-dimensional basis), this
is another. his notation requires similar compounding
of symbols, which always keeps the ratios clear, but
is hard to read.

my personal feeling is that the 11-limit error of 72edo
is small enough for most cases, and when it isn't, i
use Dan Stearns's simple addition to it, which is to
use the tilde ~ to indicate that the intonational
inflection of the symbol with which it is compounded
is to be lessened by 1/24-tone (= one degree of 144edo).
Thus,

^ = 1/4 tone up
~^ = 5/24 tone up
> = 1/6 tone up
~> = 1/8 tone up
+ = 1/12 tone up
~+ = 1/24 tone up
~- = 1/24 tone down
- = 1/12 tone down
~< = 1/8 tone down
< = 1/6 tone down
~v = 5/24 tone down
v = 1/4 tone down

i used this in my score to _A Noiseless Patient Spider_
http://www.ixpres.com/interval/monzo/spider/spider.htm

and Dan has some example score pages in this notation too.

-monz

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

--- In tuning@y..., "monz" <joemonz@y...> wrote:

> my primary objection is the compounding of new symbols.
> 72edo is such a good temperament on so many levels that
> i feel that the correspondence between the rational basis
> of HEWM notation and the inflections of 72edo suffice to
> represent nearly anything thru the 11-limit, with compounding
> only happening in conjunction with b and #.

The only way to get a universal 11-limit notation applicable to any temperament, and not just 72, is to notate JI. One can, however, simplify things in the presence of a comma in systematic ways; however it won't work to assume that 72et is a good notation for anything you may want to notate.

> my personal feeling is that the 11-limit error of 72edo
> is small enough for most cases, and when it isn't, i
> use Dan Stearns's simple addition to it, which is to
> use the tilde ~ to indicate that the intonational
> inflection of the symbol with which it is compounded
> is to be lessened by 1/24-tone (= one degree of 144edo).

Again, this is specialized; it won't work as a general system.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:

/tuning/topicId_33858.html#33863

>
> Actually, none of the notations considered here are performance
notations; they are ascii versions of what might be used in a
performance and have a different purpose in mind. I think the ascii
symbols of these two sets of notations may as well match, and should
match if we want to avoid confusion.
>

****Hello Gene!

Well you asked for commentary about the two notations so here is mine:

The "11-limit" ascii is what Joe Monzo uses for 72-tET. Personally,
I prefer the other notation because it mirrors the Ezra Sims written
notation which, I'm sure you know, is a real *performance* notation.

So it seems sensible to keep a close correspondence between the
*real* performance notation and the *unreal* theoretical ascii
notation and that's how that notation was developed on this list.

And the reason for this?: the point is that many times the *unreal*
BECOMES the *real.* That's optimal, even if it makes a
Frankenstein... :)

JP

--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_33858.html#33881

>
> basically, the two contradictory systems are the standard
> 72edo adopted by Joe Pehrson, Paul Erlich, Dave Keenan, and
> Graham Breed (IIRC) on the one hand, and the 72edo notation
> i use:
>
>
> Monzo 72edo notation, tone = ratio 2^(1/6)
>
> ^ = 1/4 tone up
> > = 1/6 tone up
> + = 1/12 tone up
> - = 1/12 tone down
> < = 1/6 tone down
> v = 1/4 tone down
>

*****The problem is, Monz, the debates about *notation* could go on
and on forever.

Personally, I believe it's time to accept the *consensus* that was
developed on this list regarding notation.

I, *personally* have changed some of my *own* preferences to side
with the group effort.

I believe you "spoke up" when this was all happening, but people
decided they would rather use ascii symbols that conform to the Ezra
Sims/Joe Maneri notation that is already practiced.

Even though I didn't *want* to, I changed ALL my charts, graphs,
lattices, information, etc., etc., etc. to the new Blackjack key of G.

I really didn't want to do that, but went along with the consensus of
the group.

I don't know about anybody else, but, personally I don't have time to
go over and over the same things over and over again.

If something is decided by concensus, then it should *stay* that way
and be *used* either for composing or theorizing.

Otherwise, it's just a big waste of time. I don't have much time to
waste, I don't know about anybody else...

Joe

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:

/tuning/topicId_33858.html#33905

Having slept on my comments to Monz last night... well I actually
slept on a pillow and did *not* eat the newspaper as Bob Valentine
attests, I thought perhaps I was being a bit unfair.

I would write this in a personal note, or on *metatuning* where such
dramas usually unfold, but I still believe this discussion is
pertinent to this group so I'll keep it here.

Adopting the wise Margo Schulter mode of "accepting diversity" I
would have to say that most probably Joe Monzo's and, probably,
George Secor's objectives with notation are significantly different
than my own.

There have been movements in contemporary music, mostly during the
50's and 60's where the *NOTATION* is, essentially the piece, the
more "creative" the better. Each piece has a different notation as
part of this "expressivity."

There are several books out on the market outlining all these
contemporary notations. In fact, I lent one to somebody not long
ago, I can't now even remember it's name, and never got it back...
And, I believe Gardner Read's book falls in that category, a book I
wanted to purchase, but also rather "speculative" and well over $40
in hardcover, as I recall... :)

The point is, I don't really want to dump on the "notation
individualists." Discussions about notation, and different attempts
are of value *in themselves.* (German: "das ding en sich" or some
such?? :))

I know, furthermore, that Monz, having invested *much* time and
effort in all his theories, is not about to change his system, even
if the *entire world* used a different one... Right, Monz? And,
additionally, Monz *likes* to march to a "different drummer," yes,
Monz? (Who's drumming, Harry Partch?? :) )

So, in the Margo Schulter tradition, let us "celebrate the diversity"
of approaches on such matters.

HOWEVER, and this is why I left my former exasperated message on this
server rather than deleting it, I believe the ASCII notation that we
developed on this list was intended for COMMUNICATION and to
facilitate not only the communication of Blackjack but *all* the 72-
tET pieces that are written in the Sims/Maneri *written score*
notation.

For that reason, I believe our "consensus" was important and we
should stick with it for communications on this list.

Otherwise, why did we spend all those hours trying to "hash out"
(well, *I* was just drinking something...) a particular notation that
we could all use in common??

J. Pehrson

> From: jpehrson2 <jpehrson@rcn.com>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, February 10, 2002 6:13 AM
> Subject: [tuning] Notation individualists
>
>
> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> /tuning/topicId_33858.html#33905
>
> Having slept on my comments to Monz last night... well I actually
> slept on a pillow and did *not* eat the newspaper as Bob Valentine
> attests, I thought perhaps I was being a bit unfair.
>
> I would write this in a personal note, or on *metatuning* where such
> dramas usually unfold, but I still believe this discussion is
> pertinent to this group so I'll keep it here.
>
> Adopting the wise Margo Schulter mode of "accepting diversity" I
> would have to say that most probably Joe Monzo's and, probably,
> George Secor's objectives with notation are significantly different
> than my own.

thanks, Joe, i appreciate your taking that perspective.

i dunno ... i think of our squabblings over 72edo notation
kind of like fighting over which font to use for your text.
i mean, the basics of the notation are the same, it's only
the symbols over which we have differences of opinion.

i'm sorry if i'm being a pain about sticking to my version
of 72edo notation. but as you should be able to ascertain
from my HEWM definition, i've been using these symbols for
11-limit JI for a while, and only over the last couple of
years realized how easily and how well they translate to
72edo.

i suppose you're right about us having different objectives.
my primary goal in notation is to acheive logical and historical
clarity and elegance. your primary goal is to get performances.
my notation has to serve well for both scores and analysis,
yours is only really necessary for the scores.

(yes, i know, the 72edo notation you use will also be used
by Paul, Dave, Graham, et al., on the tuning list for analysis,
but i'm talking about *your* objective.)

> I know, furthermore, that Monz, having invested *much* time and
> effort in all his theories, is not about to change his system, even
> if the *entire world* used a different one... Right, Monz? And,
> additionally, Monz *likes* to march to a "different drummer," yes,
> Monz?

i think you could say that. :)

i suppose that even in a cyber-community where i've found
lots of others who share my intense interests, i'm the kind
of person who still prefers to retain a strong sense of
individuality and uniqueness.

> (Who's drumming, Harry Partch?? :) )

umm ... more like Bill Bruford.

(refer to Yes, _Close to the Edge_, or any of Bruford's
solo albums).

-monz

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_33858.html#33933

> i dunno ... i think of our squabblings over 72edo notation
> kind of like fighting over which font to use for your text.
> i mean, the basics of the notation are the same, it's only
> the symbols over which we have differences of opinion.

*****That's pretty funny, Monz!

Ariel! Times Roman! Ariel! Times Roman! Ariel!

>
> i'm sorry if i'm being a pain about sticking to my version
> of 72edo notation. but as you should be able to ascertain
> from my HEWM definition, i've been using these symbols for
> 11-limit JI for a while, and only over the last couple of
> years realized how easily and how well they translate to
> 72edo.
>

****Ummm. OK. Now for the big "true confession." Quite frankly,
Monz, I like *yours* better! :)

Seriously. I like the quarter-tones as arrows, and I like the very
smallest, syntonic comma division as *plusses and minuses!*

The big problem comes in the translation from the Sims/Maneri
*written* notation, and the fact that I would like to *maintain* that
notation in *my* pieces since it is already established and
performers like Ted Mook, cello and Chris Washburn, trombone already
*read* it!

It's been going on for, apparently 20 or so years at New England
Conservatory, so there *are* people around who use it and refer to it.

So, naturally, if we are going to discuss these pieces in ASCII it
only makes sense to try to develop something that translates easily
from the written notation in our discussion.

***Probably the wisest solution that somebody came up with some time
ago, is just to make sure we have some kind of "legend" if there is
any confusion as to the system we are using.

Once that's clear, it probably won't be hard for people to shift back
and forth.

JP

> From: jpehrson2 <jpehrson@rcn.com>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, February 10, 2002 11:19 AM
> Subject: [tuning] Re: Notation individualists
>
>
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> /tuning/topicId_33858.html#33933
>
> > i dunno ... i think of our squabblings over 72edo notation
> > kind of like fighting over which font to use for your text.
> > i mean, the basics of the notation are the same, it's only
> > the symbols over which we have differences of opinion.
>
>
> *****That's pretty funny, Monz!
>
> Ariel! Times Roman! Ariel! Times Roman! Ariel!

i'm glad you found humor in it, but seriously, i really think
that it's as minor as this.

>
>
> >
> > i'm sorry if i'm being a pain about sticking to my version
> > of 72edo notation. but as you should be able to ascertain
> > from my HEWM definition, i've been using these symbols for
> > 11-limit JI for a while, and only over the last couple of
> > years realized how easily and how well they translate to
> > 72edo.
> >
>
> ****Ummm. OK. Now for the big "true confession." Quite frankly,
> Monz, I like *yours* better! :)
<
> Seriously. I like the quarter-tones as arrows, and I like the very
> smallest, syntonic comma division as *plusses and minuses!*

ah, well ... that's good to know! maybe i knew it all along,
and that's why i've been arguing with you so much to get you
to change back! :)

> The big problem comes in the translation from the Sims/Maneri
> *written* notation, and the fact that I would like to *maintain* that
> notation in *my* pieces since it is already established and
> performers like Ted Mook, cello and Chris Washburn, trombone already
> *read* it!
>
> It's been going on for, apparently 20 or so years at New England
> Conservatory, so there *are* people around who use it and refer to it.
>
> So, naturally, if we are going to discuss these pieces in ASCII it
> only makes sense to try to develop something that translates easily
> from the written notation in our discussion.

right, Joe, as we both seem to have agreed, our objectives are a
bit different. i'm not at all concerned with getting the NEC-trained
players to perform my stuff, and you are.

i suppose maybe the reason i've been trying so hard to dissuade
y o u personally from accepting the Sims/Maneri convention
is because it seems to me that you're more likely to get
performances from Johnny's (and other New York-based) ensembles
than from the Sims/Maneri Bosten-based crowd, and they'd be
able to handle my notational conventions without a hitch
-- as long as you include cents deviation from 12edo above
the notes! ;-)

seriously, i saw last year's notation debate as an opportunity
to establish a new (IMO much better) 72edo standard in opposition
to the Sims/Maneri one, with the hope that eventually, the
people already using Sims/Maneri would also agree that this
one was better, and then t h e y would be the ones who switch.
if that were to have been the case, you'd already be ahead of
the game by using my standard.

(ok ... so maybe i had too much egomania for breakfast today ...)

> ***Probably the wisest solution that somebody came up with some time
> ago, is just to make sure we have some kind of "legend" if there is
> any confusion as to the system we are using.

providing a legend is the most important thing.

in fact, one of the big frustrations i have in reading
the tuning-math archives is that tables are often presented
with no legend explaining what the different rows and
columns mean. these are often print-outs of programs
lists subscribers have written, but without a legend,
none of it means anything.

i always try hard to provide a legend, and often like
to use "redundant coding", showing pitches simultaneously
as prime-factor exponents, ratios, and cents. musical
notation is simply yet another way to notate this stuff.

> Once that's clear, it probably won't be hard for people to shift back
> and forth.

yep, i think you're right about that. as musicians become
more and more familiar with playing in 72edo, the notation
that's used won't matter as much. look at all the different
ways we have of writing down music that has a 12edo basis.

-monz

_________________________________________________________
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--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:

> HOWEVER, and this is why I left my former exasperated message on this
> server rather than deleting it, I believe the ASCII notation that we
> developed on this list was intended for COMMUNICATION and to
> facilitate not only the communication of Blackjack but *all* the 72-
> tET pieces that are written in the Sims/Maneri *written score*
> notation.

I wasn't talking about notations for 72-et, but for more general notations. It seems to me 72-et should conform to those, either by
using the Sims notation for the 11-limit and extending it if need be, or by changing the 72-et to conform to any standard (if such really exists) for general notation. Joe and Manuel are using one system, and you and others another, and this is confusing and unnecessary. Since they are so similar, it hardly makes sense to adopt a "let's do both" approach, which *would* make sense with George's notation.

--- In tuning@y..., "monz" <joemonz@y...> wrote:

> seriously, i saw last year's notation debate as an opportunity
> to establish a new (IMO much better) 72edo standard in opposition
> to the Sims/Maneri one, with the hope that eventually, the
> people already using Sims/Maneri would also agree that this
> one was better, and then t h e y would be the ones who switch.
> if that were to have been the case, you'd already be ahead of
> the game by using my standard.

Why is it much better? It seems to me that they are both more or less the same, which is my objection--they are *so* similar it is a ready source of confusion. George's arrows don't have that problem; his arrows are not intended as an ascii system, but as something to notate a score.

--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_33858.html#33936

> right, Joe, as we both seem to have agreed, our objectives are a
> bit different. i'm not at all concerned with getting the NEC-
trained players to perform my stuff, and you are.
>
> i suppose maybe the reason i've been trying so hard to dissuade
> y o u personally from accepting the Sims/Maneri convention
> is because it seems to me that you're more likely to get
> performances from Johnny's (and other New York-based) ensembles
> than from the Sims/Maneri Bosten-based crowd, and they'd be
> able to handle my notational conventions without a hitch
> -- as long as you include cents deviation from 12edo above
> the notes! ;-)
>
> seriously, i saw last year's notation debate as an opportunity
> to establish a new (IMO much better) 72edo standard in opposition
> to the Sims/Maneri one, with the hope that eventually, the
> people already using Sims/Maneri would also agree that this
> one was better, and then t h e y would be the ones who switch.
> if that were to have been the case, you'd already be ahead of
> the game by using my standard.

****Hi Joe...

Well, the thing is these players are not just in Boston anymore.
They're here in *New York* and other places as well. Ted Mook has
been here in New York for years, and so for Chris Washburne. So
there are *many* performers who use and are *used* to the Sims/Maneri
system.

Another thing, Monz, your system really doesn't work all that well in
*performance.* The Sims/Maneri symbols for the small 12th of a whole
tone as *arrows* are easier to read than little plusses and minuses.
And the symbols get *larger* as we get toward the big "brackets" of
the square root and "inverted" square root sign. A player can
quickly judge which of the three "inflections" pertain by just
looking at the *size* of the symbol.

For me, personally, therefore, I have decided to stick with the
Sims/Maneri symbols for my written scores.

For this reason, the ASCII version of the notation that most closely
corresponds with this 72-tET *written* notation that I am using works
best for me.

I think the Sims/Maneri is more pervasive and has been better
established than you think it is. Maybe somebody can prove this
incorrect, but, in the meantime, I would rather err on the "safe"
side and provide a notation that people either have experienced, or
will in the future...

However, for *other* types of analysis, outside of 72-tET, it really
doesn't matter what is used, as long as there is a legend so it's
clear...

Joe

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:

/tuning/topicId_33858.html#33938

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> > HOWEVER, and this is why I left my former exasperated message on
this
> > server rather than deleting it, I believe the ASCII notation that
we
> > developed on this list was intended for COMMUNICATION and to
> > facilitate not only the communication of Blackjack but *all* the
72-
> > tET pieces that are written in the Sims/Maneri *written score*
> > notation.
>
> I wasn't talking about notations for 72-et, but for more general
notations. It seems to me 72-et should conform to those, either by
> using the Sims notation for the 11-limit and extending it if need
be,

****Sure, Gene, that makes sense, but that's where the disagreement
lies. Since I prefer my *written* scores in the "established" (until
proven that it really isn't so established... but I doubt it after 20
years of teaching!) Sims/Maneri notation, I would prefer the ASCII
that corresponds to it.

And others, like Joe Monzo and, apparently, Manuel, would like the
*other* system.

So it seems like there is rather an "impass" as far a unaninimity of
opinion is concerned...

JP

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:

/tuning/topicId_33858.html#33941

> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > seriously, i saw last year's notation debate as an opportunity
> > to establish a new (IMO much better) 72edo standard in opposition
> > to the Sims/Maneri one, with the hope that eventually, the
> > people already using Sims/Maneri would also agree that this
> > one was better, and then t h e y would be the ones who switch.
> > if that were to have been the case, you'd already be ahead of
> > the game by using my standard.
>
> Why is it much better? It seems to me that they are both more or
less the same, which is my objection--they are *so* similar it is a
ready source of confusion. George's arrows don't have that problem;
his arrows are not intended as an ascii system, but as something to
notate a score.

***It's true, they really *are* similar and the problem is that after
20 years of training musicians in NEC and elsewhere, there is a core
group of 72-tET performers already "out there" who know the
Sims/Maneri.

As I mentioned, I know at least *two* of them in New York, and
everybody saw Ted Mook's recent post about his conversion of Partch's
music into the Sims system, so *he* is certainly intent on using it.

Before I would want to change to a different system, I would have to
have *concrete* evidence that there is really *no* 72-tET school out
there, in Boston and, now, elsewhere.

So, far, I remain unconvinced... These players seem to be around...

JP

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> I wasn't talking about notations for 72-et, but for more general
notations. It seems to me 72-et should conform to those, either by
> using the Sims notation for the 11-limit and extending it if need
be,

I think this is a good plan.

> or by changing the 72-et to conform to any standard (if such
> really exists) for general notation.

I don't believe any such standard exists. It seems we all agree on the
approach of using accidentals to represent certain commas whether
notating 11-limit JI or ETs. We even agree on which commas to use. We
are only arguing over the choice of symbols (both real ones for rapid
reading under poor conditions in scores, and their ASCII substitutes
for email etc.).

> Joe and Manuel are using one
system, and you and others another, and this is confusing and
unnecessary. Since they are so similar, it hardly makes sense to adopt
a "let's do both" approach, which *would* make sense with George's
notation.

Monz and Manuel are not using the same symbols. Here are Manuel's
11-limit ASCII symbols. As Gene pointed out, the diesis symbols are
not strictly needed, so I've omitted them

^ 33/32
7 septimal comma sharp, 64/63
/ comma sharp, 81/80
\ comma flat, 80/81
L septimal comma flat, 63/64
v 32/33

The "7" and "L" are closer to the real Sims accidentals for
sixth-tones and are not left-right confusable, but ">" and "<" are
probably better ASCII substitutes as the "7" may be confused with an
octave number.

By the way Gene, I think the octave number should come _after_ all the
accidentals. And it would be more correct to notate Partch's scales
with the 1/1 as "G". Otherwise your notation looks fine to me.

I agree with Rappoport that "+", "-" are a very poor choice for actual
scores due to possible merging with staff lines and confusion with
ledger lines.

If I had a dollar for every time I've _written_ the wrong one of "/"
and "\", let alone _read_ them wrong ... and I'm not even trying to
sight-read them on scores.

It's those damn up and down arrows that are causing all the problems.
They are by far the most obvious accidentals available in ASCII which
are not left-right confusable, which is probably one reason why
different people have used them for just about everything. The fact
that people _have_ used them for just about everything means we can
pretty much ignore any particular claims regarding their historical
usage.

George Secor, do the semantics of these 11-limit systems agree with
yours, as far as they go? Is there any chance that you could rework
your set of symbols so that it becomes an extension of the Sims/Maneri
notation and doesn't contain any pairs of symbols which are left-right
confusable, or n_n+1 confusable for n>=2?

Notice how few such pairs of symbols there are in any real alphabet or
set of numerals. In ours: Left-right: bd pq. Note that slanting these
helps to remove the left-right-confusability. FE and nm would be 2-3
confusable if one of their strokes was not made different from the
others. SZ JL 3E 5Z would be LR-confusable if one of each pair was not
angular while the other was curved.

I don't think that context is anywhere near as good a disambiguator in
the score for a piece of music in an unusual tuning, as it is for
sentences in a natural language.

Also consider why folks found it
necessary to invent a new symbol x for double-sharp, instead of just
using ##, when this looks like only a 1-2 confusability.

We can worry about the ASCII versions later, but you could give them
_some_ thought as you go. It's out of the question to use more than
two ASCII symbols to represent one accidental, and far preferable to
use a single ASCII symbol.

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

> By the way Gene, I think the octave number should come _after_ all the
> accidentals. And it would be more correct to notate Partch's scales
> with the 1/1 as "G". Otherwise your notation looks fine to me.

Thanks for the input. The choice of order was based on the sequence of primes--the symbols for 2,3,5,7 and 11 appear in that order. Another choice would be according to the size of interval the symbol represents. What is your reason for wanting the octave number (notating 2) to appear last?

> George Secor, do the semantics of these 11-limit systems agree with
> yours, as far as they go?

Good question! I've been wrong twice now about what semantics George has in mind, and it would be nice to pin it down. My approach is to create an explicit mapping "fractions" <--> "symbols", and it seems this works to give the desired result, so I'd like to pin *that* part down at least.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
>
> > By the way Gene, I think the octave number should come _after_ all
the
> > accidentals. And it would be more correct to notate Partch's
scales
> > with the 1/1 as "G". Otherwise your notation looks fine to me.
>
> Thanks for the input. The choice of order was based on the sequence
of primes--the symbols for 2,3,5,7 and 11 appear in that order.
Another choice would be according to the size of interval the symbol
represents. What is your reason for wanting the octave number
(notating 2) to appear last?
>

Because that's the established order, at least with A-G,#,b. Look at
the user guide for any MIDI device. You could consider it as being in
order of decreasing importance. The human perception of
octave-equivalence makes the octave number the least important.

You don't really have it in 2,3,5,7,11 order, do you? Because both the
letters and the #s and bs are about 3s.

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

> You don't really have it in 2,3,5,7,11 order, do you? Because both the
> letters and the #s and bs are about 3s.

When I started out, I analyzed it as the 3-limit (2&3 both, therefore)
expressed in terms of 9/8 and 2187/2048, and then that slightly transformed. However, after the transformation we are left with seven letters, a number representing numbers of octaves (which could be replaced by so many octave symbols if you had a consistency fetish) and a symbol pair representing 2187/2048. The seven letters now become seven notes of a Pythagorean scale deep in bass country, and everything else multipliers by 2, 2187/2048, 81/80, 64/63, and 33/32.
The 2 seems to me to be about 2, though the Pythagorean scale is clearly a 2&3 scale. 2187/2048 is 2&3, and the rest are 2&3&p for some additional prime p, so it certainly looks like a 2,3,5,7,11 order. As for 2 being the least important to notate, I refer you to the recent discussion of octave equivalence and messed-up melodies. 2 is both the biggest multiplier and the smallest prime, and looks like the winner to me.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
>
> > You don't really have it in 2,3,5,7,11 order, do you? Because both
the
> > letters and the #s and bs are about 3s.
>
> When I started out, I analyzed it as the 3-limit (2&3 both,
therefore)
> expressed in terms of 9/8 and 2187/2048, and then that slightly
transformed. However, after the transformation we are left with seven
letters, a number representing numbers of octaves (which could be
replaced by so many octave symbols if you had a consistency fetish)
and a symbol pair representing 2187/2048. The seven letters now become
seven notes of a Pythagorean scale deep in bass country, and
everything else multipliers by 2, 2187/2048, 81/80, 64/63, and 33/32.
> The 2 seems to me to be about 2, though the Pythagorean scale is
clearly a 2&3 scale. 2187/2048 is 2&3, and the rest are 2&3&p for some
additional prime p, so it certainly looks like a 2,3,5,7,11 order. As
for 2 being the least important to notate, I refer you to the recent
discussion of octave equivalence and messed-up melodies. 2 is both the
biggest multiplier and the smallest prime, and looks like the winner
to me.
>

You lost me with your 2's and 3's. The fact that octave numbers come
last doesn't stand or fall with my feeble attempt at a justification
for it. It's an established standard which I see no reason to change.
With the other modifiers, I think it best to put them in order of
decreasing size in cents (This is in text. On scores the order is
reversed). That's what a musician will be thinking about when playing
it, not which prime it relates to.

I agree with Gene that using the 11-limit JI symbols is
a good way to notate 72-tET, and I would have no
problem accepting Wolf's accidentals as shown on Joe's
HEWM-page for 72-tET. We could even go to 13-limit and
take the symbol for 27/26 to represent 4 steps.

To see these in Scala, go to Help->Legend: Accidentals->Just
By the way, if someone doesn't like them for some reason,
they can be easily changed. The files *.xpm which contain
the symbols are simple text files, and can be edited by
hand, so the graphic appearance is customisable. As I am
using these in more places now, it might be worth the trouble.
On the other hand, on the Windows platform they still look
a bit crappy due to some weird bug that's not mine.
It appears to be worse on Windows 98/ME than on NT/2000.
With the X-Window System on Linux they look as they should,
however the Linux version is slightly behind.

Manuel

> From: dkeenanuqnetau <d.keenan@uq.net.au>
> To: <tuning@yahoogroups.com>
> Sent: Monday, February 11, 2002 3:03 AM
> Subject: [tuning] Re: Notation individualists
>
>
> --- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> > . . . As for 2 being the least important to notate, I refer
> > you to the recent discussion of octave equivalence and
> > messed-up melodies. 2 is both the biggest multiplier and
> > the smallest prime, and looks like the winner to me.
> >
>
> You lost me with your 2's and 3's. The fact that octave
> numbers come last doesn't stand or fall with my feeble attempt
> at a justification for it. It's an established standard which
> I see no reason to change.

Gene, your points about 2 are well taken, but Dave's right --
the "octave" has a l w a y s come last when it appears
in a notation.

and for practical purposes (i.e., musicians reading parts in
rehearsal or performance), it hardly ever even appears; it's
generally only used in theoretical writings or, as Dave noted,
in dealing with MIDI.

> With the other modifiers, I think it best to put them in
> order of decreasing size in cents (This is in text. On
> scores the order is reversed). That's what a musician will
> be thinking about when playing it, not which prime it relates
> to.

oddly enough, Dave's exactly right about this too.
even tho my theory and notation is all based on
prime-factorization, looking back on my scores and
theoretical writings now i can see that i've always
done it the way he says too: by decreasing size in cents
(text) and increasing size (score).

i wonder why we like the positions reversed like that?
it would be interesting to investigate that.

-monz

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

/tuning/topicId_33858.html#33951

> --- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> > I wasn't talking about notations for 72-et, but for more general
> notations. It seems to me 72-et should conform to those, either by
> > using the Sims notation for the 11-limit and extending it if need
> be,
>
> I think this is a good plan.
>
> > or by changing the 72-et to conform to any standard (if such
> > really exists) for general notation.
>
> I don't believe any such standard exists. It seems we all agree on
the
> approach of using accidentals to represent certain commas whether
> notating 11-limit JI or ETs. We even agree on which commas to use.
We
> are only arguing over the choice of symbols (both real ones for
rapid
> reading under poor conditions in scores, and their ASCII
substitutes
> for email etc.).
>
> > Joe and Manuel are using one
> system, and you and others another, and this is confusing and
> unnecessary. Since they are so similar, it hardly makes sense to
adopt
> a "let's do both" approach, which *would* make sense with George's
> notation.
>
> Monz and Manuel are not using the same symbols. Here are Manuel's
> 11-limit ASCII symbols. As Gene pointed out, the diesis symbols are
> not strictly needed, so I've omitted them
>
> ^ 33/32
> 7 septimal comma sharp, 64/63
> / comma sharp, 81/80
> \ comma flat, 80/81
> L septimal comma flat, 63/64
> v 32/33
>
> The "7" and "L" are closer to the real Sims accidentals for
> sixth-tones and are not left-right confusable, but ">" and "<" are
> probably better ASCII substitutes as the "7" may be confused with
an
> octave number.
>
> By the way Gene, I think the octave number should come _after_ all
the
> accidentals. And it would be more correct to notate Partch's scales
> with the 1/1 as "G". Otherwise your notation looks fine to me.
>
> I agree with Rappoport that "+", "-" are a very poor choice for
actual
> scores due to possible merging with staff lines and confusion with
> ledger lines.
>
> If I had a dollar for every time I've _written_ the wrong one
of "/"
> and "\", let alone _read_ them wrong ... and I'm not even trying to
> sight-read them on scores.
>
> It's those damn up and down arrows that are causing all the
problems.
> They are by far the most obvious accidentals available in ASCII
which
> are not left-right confusable, which is probably one reason why
> different people have used them for just about everything. The fact
> that people _have_ used them for just about everything means we can
> pretty much ignore any particular claims regarding their historical
> usage.
>
> George Secor, do the semantics of these 11-limit systems agree with
> yours, as far as they go? Is there any chance that you could rework
> your set of symbols so that it becomes an extension of the
Sims/Maneri
> notation and doesn't contain any pairs of symbols which are left-
right
> confusable, or n_n+1 confusable for n>=2?
>
> Notice how few such pairs of symbols there are in any real alphabet
or
> set of numerals. In ours: Left-right: bd pq. Note that slanting
these
> helps to remove the left-right-confusability. FE and nm would be 2-
3
> confusable if one of their strokes was not made different from the
> others. SZ JL 3E 5Z would be LR-confusable if one of each pair was
not
> angular while the other was curved.
>
> I don't think that context is anywhere near as good a disambiguator
in
> the score for a piece of music in an unusual tuning, as it is for
> sentences in a natural language.
>
> Also consider why folks found it
> necessary to invent a new symbol x for double-sharp, instead of
just
> using ##, when this looks like only a 1-2 confusability.
>
> We can worry about the ASCII versions later, but you could give
them
> _some_ thought as you go. It's out of the question to use more than
> two ASCII symbols to represent one accidental, and far preferable
to
> use a single ASCII symbol.

****I really love this post of Dave Keenan's!

It looks like a motion to *retain* the accepted Sims/Maneri notation
and simply elaborate upon it. The Sim/Maneri is *legible* and is
already in practice so I say, "Bravo!"

JP

--- In tuning@y..., manuel.op.de.coul@e... wrote:

/tuning/topicId_33858.html#33967

> I agree with Gene that using the 11-limit JI symbols is
> a good way to notate 72-tET, and I would have no
> problem accepting Wolf's accidentals as shown on Joe's
> HEWM-page for 72-tET. We could even go to 13-limit and
> take the symbol for 27/26 to represent 4 steps.
>

****In most things I would humbly defer to Manuel, the Scala-master!
However, frankly, I think the Wolf symbols are unreadable and
the "craziest" things I have ever seen! :)

JP

--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_33858.html#33973

>
> oddly enough, Dave's exactly right about this too.
> even tho my theory and notation is all based on
> prime-factorization, looking back on my scores and
> theoretical writings now i can see that i've always
> done it the way he says too: by decreasing size in cents
> (text) and increasing size (score).
>
> i wonder why we like the positions reversed like that?
> it would be interesting to investigate that.
>
>

***Monz, this is interesting, but I want to know a little bit more
about it. You're saying modifiers of a note start with the largest
cent value modifiers and then put the smaller ones next, yes?

But, what's the bit about the *size* again? I'd like to follow this.

Thanks!

Joe

Joseph wrote:

>****In most things I would humbly defer to Manuel, the Scala-master!
>However, frankly, I think the Wolf symbols are unreadable and
>the "craziest" things I have ever seen! :)

Thanks for the opinion. I've never had to sight-read them but
I see that some differ only by a tiny stroke.
However I don't mind "crazyness" if it helps to distinguish.

Manuel

--- In tuning@y..., manuel.op.de.coul@e... wrote:

/tuning/topicId_33858.html#34090

> Joseph wrote:
>
> >****In most things I would humbly defer to Manuel, the Scala-
master!
> >However, frankly, I think the Wolf symbols are unreadable and
> >the "craziest" things I have ever seen! :)
>
> Thanks for the opinion. I've never had to sight-read them but
> I see that some differ only by a tiny stroke.
> However I don't mind "crazyness" if it helps to distinguish.
>
> Manuel

****Thanks, Manuel, for your input. Sure, I'm mostly just concerned
with *legibility* and, frankly, I would prefer that the "craziness"
be in the *music!* and not the *notation!*

Joseph

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> --- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> > I wasn't talking about notations for 72-et, but for more general
> notations. It seems to me 72-et should conform to those, either by
> > using the Sims notation for the 11-limit and extending it if need
> be,
>
> I think this is a good plan.
>
> > or by changing the 72-et to conform to any standard (if such
> > really exists) for general notation.
>
> I don't believe any such standard exists. It seems we all agree on
the
> approach of using accidentals to represent certain commas whether
> notating 11-limit JI or ETs. We even agree on which commas to use.
We
> are only arguing over the choice of symbols (both real ones for
rapid
> reading under poor conditions in scores, and their ASCII
substitutes
> for email etc.).
>
> > Joe and Manuel are using one
> system, and you and others another, and this is confusing and
> unnecessary. Since they are so similar, it hardly makes sense to
adopt
> a "let's do both" approach, which *would* make sense with George's
> notation.
>
> Monz and Manuel are not using the same symbols. Here are Manuel's
> 11-limit ASCII symbols. As Gene pointed out, the diesis symbols are
> not strictly needed, so I've omitted them
>
> ^ 33/32
> 7 septimal comma sharp, 64/63
> / comma sharp, 81/80
> \ comma flat, 80/81
> L septimal comma flat, 63/64
> v 32/33
>
> The "7" and "L" are closer to the real Sims accidentals for
> sixth-tones and are not left-right confusable, but ">" and "<" are
> probably better ASCII substitutes as the "7" may be confused with
an
> octave number.
>
> By the way Gene, I think the octave number should come _after_ all
the
> accidentals. And it would be more correct to notate Partch's scales
> with the 1/1 as "G". Otherwise your notation looks fine to me.
>
> I agree with Rappoport that "+", "-" are a very poor choice for
actual
> scores due to possible merging with staff lines and confusion with
> ledger lines.
>
> If I had a dollar for every time I've _written_ the wrong one
of "/"
> and "\", let alone _read_ them wrong ... and I'm not even trying to
> sight-read them on scores.
>
> It's those damn up and down arrows that are causing all the
problems.
> They are by far the most obvious accidentals available in ASCII
which
> are not left-right confusable, which is probably one reason why
> different people have used them for just about everything. The fact
> that people _have_ used them for just about everything means we can
> pretty much ignore any particular claims regarding their historical
> usage.
>
> George Secor, do the semantics of these 11-limit systems agree with
> yours, as far as they go?

Dave & Gene,

Over the weekend I finally settled on how I would notate 46 and 53-
EDO with the sagittal symbols, which was a challenge, since they
divide the sharp and flat alterations into five parts. For these
(and for 96) I decided to employ symbols that I was previously using
in the 41-EDO native notation, but with a slightly different meaning,
which I will specify below. (And I also removed those extra symbols
from the 41-EDO native notation, for which I now prefer to use only a
subset of the 72-EDO symbols.)

Rather than go into a lot of explanation about this, why don't I just
direct you to:

/tuning/files/secor/notation/EDOvsJI.doc

from which you can print out full-octave diagrams of 72, 41, 31, 22,
46, and 96 for study.

Having finally decided on all of this, I can now commit to the
semantics of the sagittal notation. So we don't have any
misunderstandings, I will start from the very beginning.

There are 7 nominals in a Pythagorean series of fifths from F to B.
A sagittal sharp /||\ or flat \||/ alters by a Pythagorean chromatic
semitone (2187:2048) and the double sharp/flat by twice that.

A left (Didymus) flag symbol /| (up) or \| (down) alters by 81:80.
A right (Archytus) flag symbol |\ (up) or |/ (down) alters by 64:63.
An up /|\ or down \|/ arrow (combination of the two flags) alters by
a unidecimal diesis (33:32), which conflates 385:384.

If the notation is used for a system in which a fifth is an even
number of degrees (e.g., 17, 31, 41, or 72-EDO), then the number of
system degrees that a sharp or flat alters is also even (being equal
to 7f-4n, where f is the number of degrees in the fifth and n is the
number of degrees in the octave). In this case, a sagittal sharp or
flat will be twice the alteration of the unidecimal diesis, which
conflates 243:242.

In systems having a decent representation of 11:9, but having a fifth
with an odd number of degrees (e.g., 46 or 53-EDO), I have employed
some of the extra symbols (discarded from my tentative 41-EDO native
notation) to indicate what amounts to a sharp less a unidecimal
diesis (or flat plus a unidecimal diesis); this can be observed in
the 46-tone full-octave diagram (don't strain your eyes on the
screen; print it out!): Pythagorean E-flat is 11 degrees above C, and
11/9 (33:32 up) is 13 degrees; the latter uses a two-stroke symbol
with a reverse-facing arrow, indicating a decreased alteration in
comparison to the sagittal flat.

I am going to have to define this amount of reverse alteration as two
Didymus commas rather than a unidecimal diesis. This permits
consistent employment of all of the extra symbols to notate 96-EDO
(Didymus comma = 1 degree, Archytas = 3 degrees, unidecimal diesis =
4 degrees) and 48-EDO (as a subset of 96). Both of these are
inconsistent at the 7 limit, but the symbols do a very nice job with
them, which brings us very close to saying that the sagittal notation
can "do it all." (Also see the complete octave diagram for 96-EDO.)

> Is there any chance that you could rework
> your set of symbols so that it becomes an extension of the
Sims/Maneri
> notation and doesn't contain any pairs of symbols which are left-
right
> confusable, or n_n+1 confusable for n>=2?
>
> Notice how few such pairs of symbols there are in any real alphabet
or
> set of numerals. In ours: Left-right: bd pq. Note that slanting
these
> helps to remove the left-right-confusability. FE and nm would be 2-
3
> confusable if one of their strokes was not made different from the
> others. SZ JL 3E 5Z would be LR-confusable if one of each pair was
not
> angular while the other was curved.

I said that if anyone came up with any recommendations as to how the
sagittal notation could be improved, I would be happy to consider
them. That time has come.

For reasons that I have already covered, I do not consider
compatibility with the Sims/Maneri symbols an improvement; whereas
those symbols are almost completely arbitrary, there is not a single
line in any of the sagittal symbols that is arbitrary or capricious --
everything has a meaning that allows the notation to be applied
consistently and intuitively to a diversity of EDO's.

As long as you're using 12-EDO instruments with extended techniques
to get microtones (just as our predecessors made do with valveless
brass instruments in centuries past to get the "missing" tones
however they could), then Sims/Maneri will do. But once the
microtonal breakthrough comes (and if you don't ever expect it to
come, then you might as well log off and find something else to give
you your jollies), and once we realize that there might be easier and
better ways to achieve it, then we are going to want some real
microtonal instruments (multi-system, if you please), and we are
going to want a notation that is going to serve them well. The new
notation can then be learned as a part of the process of learning the
new instruments. (Or, for those so inclined to get a head start, it
can be learned now, so that there will already be a group of people
familiar with it when the time comes.) I would like to see that
there is a comprehensive plan ready to be implemented when this
happens, which is why I've been pursuing this approach.

Re left-right-confusability: Last night I tried a couple of ways to
distinguish the laterally mirrored pairs of symbols. One was to give
half of them an "ugly makeover" by making the diagonal lines much,
much thicker; it looked -- well, ugly! The other was to give the
diagonal lines a curve, but is it enough? I'll let you judge. If
you look at

/tuning/files/secor/notation/Figures.bmp

you will now see Figure 4a, which is a revision of Figure 4, which I
left there so you can see what was there before. The modified
symbols are in the 72-tone line. I selected the ones that I modified
on the basis of what least occurs in the native notations, so the
only place that these modified symbols are used in native notations
is for 36, 72, and 96-EDO.

The net effect of this is that, in the (72-EDO) transcendental
notation, the modified symbols will identify tones that differ from
the Pythagorean series (extended ratios of 3) by an Archytas comma
(64:63), or that differ from ratios of 11 by a Didymus comma. So
those curved lines do provide a useful function in addition to
distinguishing left from right.

So, that was a pretty good suggestion you made, Dave!

--George

--- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:

> Rather than go into a lot of explanation about this, why don't I
just
> direct you to:
>
>
/tuning/files/secor/notation/EDOvsJI.doc
>
> from which you can print out full-octave diagrams of 72, 41, 31,
22,
> 46, and 96 for study.

these are really nice (96 seems like an odd choice, though, compared
with say 94 or 99) . . . but including the extended ratios doesn't
seem like a good idea. for example, 81:80 is represented by 1 degree
in 22, yet the diagram shows it closer to 0 degrees. seems confusing
and misleading.

> But once the
> microtonal breakthrough comes (and if you don't ever expect it to
> come, then you might as well log off and find something else to
give
> you your jollies), and once we realize that there might be easier
and
> better ways to achieve it, then we are going to want some real
> microtonal instruments (multi-system, if you please), and we are
> going to want a notation that is going to serve them well.

that's awfully dismissive of the dissenting opinions that have been
expressed, who see the future in electronic means, or cents, etc.
well, playing devil's advocate to your suggestion that i might as
well log off and find something else to give me my jollies, i'm not
convinced that having all these *equal-tempered* systems (and there
would have to be an arbitrary pitch standard for all of them, like a-
440) would be very representative of what all microtonal composers
will want, and what is likely to be realized. how would you notate a
shift from one system to another if the common tone were not a-440 or
whatever you're using as your standard? considerations like these led
me to propose 76-equal and 152-equal as the best *closed* tuning
systems which will allow me to use a large number of the
melodic/harmonic systems i'm interested in (both in strict and in
adaptive forms) and allow me to connect them via any pitch. can your
notation deal with these well?

> I would like to see that
> there is a comprehensive plan ready to be implemented when this
> happens, which is why I've been pursuing this approach.

i wish you the best of luck, and will support you in any way i can,
but i think what's more likely to happen is that electronic music,
which is already quite microtonal, will advance far more rapidly than
acoustic music, both in its ability to convey human expression and in
the kind of pitch and post-pitch (meaning the huge unexploited gray
area between pitch and timbre) techniques it will employ. though we
seem to share somewhat similar theoretical desires, the fact is that
musical culture as a whole may not share them, and certainly won't be
terribly interested in your particular scheme of multi-system
instruments until there is some highly significant music pushing in
that direction. is there?

what i've suggested in the past is that pushing for a single and
inclusive-of-present-practice new microtonal system, namely 72-equal,
may be a more realistic and sellable goal for the present generation
of acoustic instrumentalists. the music of partch, wychnegradsky,
xenakis and others can serve as an adequate demonstration of the type
of effects and emotions achievable in 72-equal, while an entire
lifetime of musical training in 12-equal continues to be applicable.
meanwhile, i'll happily continue making my own music on my own
instruments in 22- and 31-equal, and others will do similar things,
no doubt. the revolution you're looking for, if it occurs, will have
to be rooted in musical practice, or the edge of practice, that is of
concern to musicians. a complex system of several large interlocking
equal temperaments will need a particularly convincing body of music
close to the hearts of many performers to 'sell' them on it. but of
course the music is difficult to produce *before* the instruments
have even been implemented. so it seems like a rather insurmountable
hurdle.

the electronic path seems the natural one to go down to jump hurdles
like these. you can invent a whole new musical culture within your
computer. and once the music is there, it's there, it doesn't need to
be sight-read, instruments don't need to be invented and
learned . . . the composer will be freed from all
the 'intermediaries' in the way of translating a musical idea to
aural reality. this is the future that we seem to be on the brink of.

anyway, just some rambling devil's advocate thoughts for you . . .

--- In tuning@y..., "paulerlich" <paul@s...> wrote:

/tuning/topicId_33858.html#34124

>
>
> i wish you the best of luck, and will support you in any way i can,
> but i think what's more likely to happen is that electronic music,
> which is already quite microtonal, will advance far more rapidly
than acoustic music, both in its ability to convey human expression
and in the kind of pitch and post-pitch (meaning the huge unexploited
gray area between pitch and timbre) techniques it will employ. though
we seem to share somewhat similar theoretical desires, the fact is
that musical culture as a whole may not share them, and certainly
won't be terribly interested in your particular scheme of multi-
system instruments until there is some highly significant music
pushing in that direction. is there?
>
> what i've suggested in the past is that pushing for a single and
> inclusive-of-present-practice new microtonal system, namely 72-
equal, may be a more realistic and sellable goal for the present
generation of acoustic instrumentalists. the music of partch,
wychnegradsky, xenakis and others can serve as an adequate
demonstration of the type of effects and emotions achievable in 72-
equal, while an entire lifetime of musical training in 12-equal
continues to be applicable.

****Well, Paul, your certainly "singing my tunes" here!

Although, come to think of it, I learned some of this stuff from
*you*... :)

JP

--- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
> There are 7 nominals in a Pythagorean series of fifths from F to B.
> A sagittal sharp /||\ or flat \||/ alters by a Pythagorean chromatic
> semitone (2187:2048) and the double sharp/flat by twice that.
>
> A left (Didymus) flag symbol /| (up) or \| (down) alters by 81:80.
> A right (Archytus) flag symbol |\ (up) or |/ (down) alters by 64:63.
> An up /|\ or down \|/ arrow (combination of the two flags) alters by
> a unidecimal diesis (33:32),

So farthe semantics agrees.

> which conflates 385:384.

So what happens in an ET where none of the 3 commas vanish and neither
does 384:385? Say 29 or 58-tET?

> In systems having a decent representation of 11:9, but having a
fifth
> with an odd number of degrees (e.g., 46 or 53-EDO), I have employed
> some of the extra symbols (discarded from my tentative 41-EDO native
> notation) to indicate what amounts to a sharp less a unidecimal
> diesis (or flat plus a unidecimal diesis); this can be observed in
> the 46-tone full-octave diagram (don't strain your eyes on the
> screen; print it out!): Pythagorean E-flat is 11 degrees above C,
and
> 11/9 (33:32 up) is 13 degrees; the latter uses a two-stroke symbol
> with a reverse-facing arrow, indicating a decreased alteration in
> comparison to the sagittal flat.
>
> I am going to have to define this amount of reverse alteration as
two
> Didymus commas rather than a unidecimal diesis.

Ok. So this is a little messy, but hey you can't have everything.

> For reasons that I have already covered, I do not consider
> compatibility with the Sims/Maneri symbols an improvement; whereas
> those symbols are almost completely arbitrary, there is not a single
> line in any of the sagittal symbols that is arbitrary or capricious

No. But sometimes there are just too many lines in them.

> everything has a meaning that allows the notation to be applied
> consistently and intuitively to a diversity of EDO's.

I might be inclined to argue about that "intuitively".

> But once the
> microtonal breakthrough comes (and if you don't ever expect it to
> come, then you might as well log off and find something else to give
> you your jollies),

I disagree entirely. It could remain a niche forever and I'd have
just as much fun.

> I would like to see that
> there is a comprehensive plan ready to be implemented when this
> happens, which is why I've been pursuing this approach.

But you are willing to be 100% incompatible with what already exists.
You go as far as to replace the sharp and flat symbols and to rename
the commas. It doesn't bode well.

> Re left-right-confusability: Last night I tried a couple of ways to
> distinguish the laterally mirrored pairs of symbols. One was to
give
> half of them an "ugly makeover" by making the diagonal lines much,
> much thicker; it looked -- well, ugly! The other was to give the
> diagonal lines a curve, but is it enough?

It's a good idea, but I don't think it's enough. There are just too
many symbols that look too much alike.

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
>
> > Rather than go into a lot of explanation about this, why don't I
> just
> > direct you to:
> >
> >
>
/tuning/files/secor/notation/EDOvsJI.doc
> >
> > from which you can print out full-octave diagrams of 72, 41, 31,
> 22,
> > 46, and 96 for study.
>
> these are really nice (96 seems like an odd choice, though,
compared
> with say 94 or 99) . . . but including the extended ratios doesn't
> seem like a good idea. for example, 81:80 is represented by 1
degree
> in 22, yet the diagram shows it closer to 0 degrees. seems
confusing
> and misleading.

In going for 96 I had the music of Julian Carillo in mind, should we
wish to quote an example using the sagittal notation. But then you
give a couple of very odd choices (76 & 152) below.

> > But once the
> > microtonal breakthrough comes (and if you don't ever expect it to
> > come, then you might as well log off and find something else to
> give
> > you your jollies), and once we realize that there might be easier
> and
> > better ways to achieve it, then we are going to want some real
> > microtonal instruments (multi-system, if you please), and we are
> > going to want a notation that is going to serve them well.
>
> that's awfully dismissive of the dissenting opinions that have been
> expressed, who see the future in electronic means, or cents, etc.
> well, playing devil's advocate to your suggestion that i might as
> well log off and find something else to give me my jollies,

Okay, you're right; I got a little carried away there. (Come on
back, everybody! We can still get along and have fun even if the
rest of the world ignores us or thinks we're a bit strange. Isn't
that what *xenharmonics* is about, anyway?)

> i'm not
> convinced that having all these *equal-tempered* systems (and there
> would have to be an arbitrary pitch standard for all of them, like
a-
> 440) would be very representative of what all microtonal composers
> will want, and what is likely to be realized. how would you notate
a
> shift from one system to another if the common tone were not a-440
or
> whatever you're using as your standard? considerations like these
led
> me to propose 76-equal and 152-equal as the best *closed* tuning
> systems which will allow me to use a large number of the
> melodic/harmonic systems i'm interested in (both in strict and in
> adaptive forms) and allow me to connect them via any pitch. can
your
> notation deal with these well?

Are you suggesting a *transfer* (that's the term Ivor Darreg
proposed) in mid-composition from one tuning system to another? If
so, all you have to do is indicate that with a special direction on
the manuscript in the appropriate places and switch to the notation
that applies (once you figure out how to change the instruments from
one system to another on the fly, or is this all electronic?).
Besides, you're raising issues here (such as pitch standards) that
are completely independent of the problem of accommodating systems A,
B, and C with a single notation.

> > I would like to see that
> > there is a comprehensive plan ready to be implemented when this
> > happens, which is why I've been pursuing this approach.
>
> i wish you the best of luck, and will support you in any way i can,
> but i think what's more likely to happen is that electronic music,
> which is already quite microtonal, will advance far more rapidly
than
> acoustic music, both in its ability to convey human expression and
in
> the kind of pitch and post-pitch (meaning the huge unexploited gray
> area between pitch and timbre) techniques it will employ. though we
> seem to share somewhat similar theoretical desires, the fact is
that
> musical culture as a whole may not share them, and certainly won't
be
> terribly interested in your particular scheme of multi-system
> instruments until there is some highly significant music pushing in
> that direction. is there?

I agree that the electronic medium is the most practical avenue for
microtonality at present, and this is the approach that I will be
taking for the time being. However, what I will be writing will not
be impractical for or unperformable on new acoustic instruments, and
a major objective that I have in mind is to write music that people
will *want* to hear on acoustic instruments, thus creating a demand
for them (on the assumption that "real" instruments will be preferred
to an electronic "imitation"). (You also mentioned something similar
to this below, but stopped short of my objective.)

> what i've suggested in the past is that pushing for a single and
> inclusive-of-present-practice new microtonal system, namely 72-
equal,
> may be a more realistic and sellable goal for the present
generation
> of acoustic instrumentalists. the music of partch, wychnegradsky,
> xenakis and others can serve as an adequate demonstration of the
type
> of effects and emotions achievable in 72-equal, while an entire
> lifetime of musical training in 12-equal continues to be
applicable.

In my first several years of microtonal experimentation, I felt that
common sense dictated that 22 was the upper limit of what I would
consider a reasonable number of tones per octave, and as the years
passed I raised this to 31 and finally 41. This was on the basis of:
1) what can we be expected to hear? and 2) what can we be expected to
handle? I strongly believe in 72 as a basis for notation, but using
this as a standard system for microtonal performance is another
matter. Can we expect a significant number of composers and
musicians to buy the idea that 72-EDO is practical outside of the
electronic medium?

> meanwhile, i'll happily continue making my own music on my own
> instruments in 22- and 31-equal, and others will do similar things,
> no doubt. the revolution you're looking for, if it occurs, will
have
> to be rooted in musical practice, or the edge of practice, that is
of
> concern to musicians. a complex system of several large
interlocking
> equal temperaments will need a particularly convincing body of
music
> close to the hearts of many performers to 'sell' them on it. but of
> course the music is difficult to produce *before* the instruments
> have even been implemented. so it seems like a rather
insurmountable
> hurdle.

The classic chicken-egg problem.

> the electronic path seems the natural one to go down to jump
hurdles
> like these. you can invent a whole new musical culture within your
> computer. and once the music is there, it's there, it doesn't need
to
> be sight-read, instruments don't need to be invented and
> learned . . . the composer will be freed from all
> the 'intermediaries' in the way of translating a musical idea to
> aural reality. this is the future that we seem to be on the brink
of.

Yet I am hoping that if the music produced by electronic means is
good enough, there will be a demand for acoustic instruments that are
capable of producing it.

> anyway, just some rambling devil's advocate thoughts for you . . .

In many ways we are not very far apart from each other in what we
would like to achieve, so ramble on!

--George

--- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:

> > i'm not
> > convinced that having all these *equal-tempered* systems (and
there
> > would have to be an arbitrary pitch standard for all of them,
like
> a-
> > 440) would be very representative of what all microtonal
composers
> > will want, and what is likely to be realized. how would you
notate
> a
> > shift from one system to another if the common tone were not a-
440
> or
> > whatever you're using as your standard? considerations like these
> led
> > me to propose 76-equal and 152-equal as the best *closed* tuning
> > systems which will allow me to use a large number of the
> > melodic/harmonic systems i'm interested in (both in strict and in
> > adaptive forms) and allow me to connect them via any pitch. can
> your
> > notation deal with these well?
>
> Are you suggesting a *transfer* (that's the term Ivor Darreg
> proposed) in mid-composition from one tuning system to another? If
> so, all you have to do is indicate that with a special direction on
> the manuscript in the appropriate places and switch to the notation
> that applies (once you figure out how to change the instruments
from
> one system to another on the fly, or is this all electronic?).
> Besides, you're raising issues here (such as pitch standards) that
> are completely independent of the problem of accommodating systems
A,
> B, and C with a single notation.

no they're not completely independent! if you want to transfer with a
common tone on, say, 'c', while the tuning systems are connected by a
common 'a', you're in quite a pinch, aren't you?

> In my first several years of microtonal experimentation, I felt
that
> common sense dictated that 22 was the upper limit of what I would
> consider a reasonable number of tones per octave,

note that the blackjack scale only has 21 notes per octave.

> Can we expect a significant number of composers and
> musicians to buy the idea that 72-EDO is practical outside of the
> electronic medium?

it's already happening -- at new england conservatory, at the richter-
herf institute, among byzantine choral directors such as g. bilalis,
etc. etc. perhaps you'd like to contact julie werntz again (you
contacted her already, didn't you) and ask her this question.

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
> > There are 7 nominals in a Pythagorean series of fifths from F to
B.
> > A sagittal sharp /||\ or flat \||/ alters by a Pythagorean
chromatic
> > semitone (2187:2048) and the double sharp/flat by twice that.
> >
> > A left (Didymus) flag symbol /| (up) or \| (down) alters by 81:80.
> > A right (Archytus) flag symbol |\ (up) or |/ (down) alters by
64:63.
> > An up /|\ or down \|/ arrow (combination of the two flags) alters
by
> > a unidecimal diesis (33:32),
>
> So farthe semantics agrees.
>
> > which conflates 385:384.
>
> So what happens in an ET where none of the 3 commas vanish and
neither
> does 384:385? Say 29 or 58-tET?

Like 22-EDO, 29 divides the sharp and flat alteration into 3 parts,
and the same sequence of symbols is used for the two systems. This
does not involve the semisharp and semiflat (single full arrow)
symbols; thus there is not a problem with this.

When it comes to mapping just or near-just tones onto 29, I found
that the 72-EDO transcendental notation worked extremely well for
what I tried, and I believe that the transcendental notation would be
preferable to using the 29-EDO native notation for a situation such
as this (even though the two correlated well).

Are you serious about 58-EDO, or are you just trying to find
something to shoot me down? Yes, I'll have problems coming up with a
native notation for this EDO, but considering that the deviation of
half of the odd harmonic numbers within the limit of consistency (17)
is over 30 percent of a system degree, I don't think that there is
going to be much demand for this one.

I tried to come up with a notation that would accommodate most of the
best divisions within what I considered to be a reasonable limit of
practicality (41-EDO), plus a few more (46, 48, 53, 72, and 96-EDO).
If this can't do it all, at least I would like it to do just about
all that most anyone in the "practical" arena would care to do.

> > In systems having a decent representation of 11:9, but having a
> fifth
> > with an odd number of degrees (e.g., 46 or 53-EDO), I have
employed
> > some of the extra symbols (discarded from my tentative 41-EDO
native
> > notation) to indicate what amounts to a sharp less a unidecimal
> > diesis (or flat plus a unidecimal diesis); this can be observed
in
> > the 46-tone full-octave diagram (don't strain your eyes on the
> > screen; print it out!): Pythagorean E-flat is 11 degrees above C,
> and
> > 11/9 (33:32 up) is 13 degrees; the latter uses a two-stroke
symbol
> > with a reverse-facing arrow, indicating a decreased alteration in
> > comparison to the sagittal flat.
> >
> > I am going to have to define this amount of reverse alteration as
> two
> > Didymus commas rather than a unidecimal diesis.
>
> Ok. So this is a little messy, but hey you can't have everything.

Thanks for giving me some slack on that one.

> > For reasons that I have already covered, I do not consider
> > compatibility with the Sims/Maneri symbols an improvement;
whereas
> > those symbols are almost completely arbitrary, there is not a
single
> > line in any of the sagittal symbols that is arbitrary or
capricious
>
> No. But sometimes there are just too many lines in them.

But fewer lines than you would have in any combination of symbols
that might replace them.

> > everything has a meaning that allows the notation to be applied
> > consistently and intuitively to a diversity of EDO's.
>
> I might be inclined to argue about that "intuitively".
>
> > But once the
> > microtonal breakthrough comes (and if you don't ever expect it to
> > come, then you might as well log off and find something else to
give
> > you your jollies),
>
> I disagree entirely. It could remain a niche forever and I'd have
> just as much fun.

Right! (I already ate those words in another posting.)

> > I would like to see that
> > there is a comprehensive plan ready to be implemented when this
> > happens, which is why I've been pursuing this approach.
>
> But you are willing to be 100% incompatible with what already
exists.
> You go as far as to replace the sharp and flat symbols and to
rename
> the commas. It doesn't bode well.

I renamed one comma after Archytas in exact analogy to the one
already named after Didymus, and Margo Schulter already seconded the
motion. All in favor? ... All opposed? ...

Replacing a pair of symbols with a couple of others (while retaining
their names and meanings) isn't incompatibility, unless you're saying
that musicians are incompatible with any sort of change in music (in
which case there is no hope left for microtonality, and we might as
well get our jollies ... Oops! I didn't mean to say that! Please
don't anybody log off on account of this.).

> > Re left-right-confusability: Last night I tried a couple of ways
to
> > distinguish the laterally mirrored pairs of symbols. One was to
> give
> > half of them an "ugly makeover" by making the diagonal lines
much,
> > much thicker; it looked -- well, ugly! The other was to give the
> > diagonal lines a curve, but is it enough?
>
> It's a good idea, but I don't think it's enough. There are just too
> many symbols that look too much alike.

The same could be said for Chinese or Japanese, which characters are
far more numerous and far more detailed, yet they can be read quickly
with a reasonable amount of practice (as my daughter, who has been
studying these on her own, will attest). And once you learn the
sagittal symbols, you can do a lot more with them than with the
Sims/Maneri notation.

Anyway, for the left-right-confusability issue I still have another
idea to try, and we'll see if that looks any better.

Stay tuned!

--George

--- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:

> Are you serious about 58-EDO, or are you just trying to find
> something to shoot me down?

58 is a fine et, and in fact the first that can represent all the notes of Partch's Genesis scale. For that matter, 152 is a reasonable sstem, and not strange at all.

Here are some consistent, logarithmically flat badness scores comparing 41, 58, 72 and 152 in various odd limits. The "logarithmicall flat" business means that smaller ets are priviledged over larger ones even more than relative intonation measures such as consistency do, but even so, 58 holds its own in the
higher limits. Among these four, it scores best in the 13 and 15 limits, and second best in 3 and 17. It comes in third for 7,9, and 11, but these are all good 11-limit systems.

------41-------------58-------------72-----------152

3 .67803586 4.18614652 8.4456072 13.0263696
5 1.380445520 2.499272068 1.517361774 1.056578095
7 .7433989824 1.270307523 .7439328269 1.505255510
9 .8004237371 1.270307523 .9759757458 1.505255510
11 .9169187332 .9740696116 .6833785091 .9903527838
13 1.010934526 .8435935409 1.015331601 2.045437290
15 1.010934526 .9018214272 1.015331601 2.045437290
17 1.138442704 .9309801788 .8804340296 1.730047589
19 1.042105199 1.393450457 1.070085977 1.602574348

I wouldn't dismiss 58!

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
>
> > > i'm not
> > > convinced that having all these *equal-tempered* systems (and
> there
> > > would have to be an arbitrary pitch standard for all of them,
> like
> > a-
> > > 440) would be very representative of what all microtonal
> composers
> > > will want, and what is likely to be realized. how would you
> notate
> > a
> > > shift from one system to another if the common tone were not a-
> 440
> > or
> > > whatever you're using as your standard? considerations like
these
> > led
> > > me to propose 76-equal and 152-equal as the best *closed*
tuning
> > > systems which will allow me to use a large number of the
> > > melodic/harmonic systems i'm interested in (both in strict and
in
> > > adaptive forms) and allow me to connect them via any pitch. can
> > your
> > > notation deal with these well?
> >
> > Are you suggesting a *transfer* (that's the term Ivor Darreg
> > proposed) in mid-composition from one tuning system to another?
If
> > so, all you have to do is indicate that with a special direction
on
> > the manuscript in the appropriate places and switch to the
notation
> > that applies (once you figure out how to change the instruments
> from
> > one system to another on the fly, or is this all electronic?).
> > Besides, you're raising issues here (such as pitch standards)
that
> > are completely independent of the problem of accommodating
systems
> A,
> > B, and C with a single notation.
>
> no they're not completely independent! if you want to transfer with
a
> common tone on, say, 'c', while the tuning systems are connected by
a
> common 'a', you're in quite a pinch, aren't you?

I can't believe that we're talking about something as bizarre as
this. No, I never expected that anyone would really want to do
anything like that, and if this is something that you really want to
do, then I think you're the one who is in a pinch: Where are the
instruments on which you propose to do this, and how do you expect
this to be done? And if it's all electronic, then I guess you *can*
do anything you want, but you're going to need a special notation to
keep track of it. Nobody could expect a generalized notation to do
something as esoteric as that without getting extremely complicated.
>
> > In my first several years of microtonal experimentation, I felt
> that
> > common sense dictated that 22 was the upper limit of what I would
> > consider a reasonable number of tones per octave,
>
> note that the blackjack scale only has 21 notes per octave.

And Canasta 31. And StudLoco 41. These are all within the realm of
practicality, as far as I'm concerned.

> > Can we expect a significant number of composers and
> > musicians to buy the idea that 72-EDO is practical outside of the
> > electronic medium?
>
> it's already happening -- at new england conservatory, at the
richter-
> herf institute, among byzantine choral directors such as g.
bilalis,
> etc. etc. perhaps you'd like to contact julie werntz again (you
> contacted her already, didn't you) and ask her this question.

No, I didn't contact her already. I'm just echoing the conventional
wisdom that I believe persuades most of the rest of academia that it
isn't practical, just as I'm getting the argument around here that
replacing sharps and flats with new symbols isn't practical. If you
were to ask me 25 years ago which of these two things would be more
practical, what answer would you have expected me (or anyone else) to
give?

I'm sorry if I seem to be getting a little irritated lately, but I'm
beginning to feel like I'm in front of a firing squad.

I guess I need to concentrate a bit more on:

Love / joy / peace / patience / kindness ...

--George

George,

I'm kind of a peripheral correspondent on the notation matters: while
I perform music (classical for the main) all the time, it is all in
the realm of 12tet, and while I have performed a lot of 'microtonal'
music, 99% of it was in the Harry Partch Ensemble, which used Harry's
notational schemes based (for the most part) on representational or
tablature type notation.

But I'm interested to see how things develop in a time of 'newness'
and the notation discussions have been interesting. With all that as
a prelude, I note in your last post:

--- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
> I'm sorry if I seem to be getting a little irritated lately, but
> I'm beginning to feel like I'm in front of a firing squad.

Yeah, unfortunately that's not uncommon, especially if you don't toe
the (invisible) party line(s). Having known most of these folks for a
while, I'd hazard that the vast majority of it is simply over-active
debating glands, but a few others have eventually just thrown up
their hands and left. I hope that *you* won't, but there may come a
time when you've discussed as much as you can and decide to just get
on with matters; I know that is my experience.

It has been rewarding to see a name/voice that has come up in the
past actually make a presence, as you have. Don't let the occasional
buzzing of mosquitoes send you back inside...

Fraternally,
Jon

--- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:

> > no they're not completely independent! if you want to transfer with
> a
> > common tone on, say, 'c', while the tuning systems are connected by
> a
> > common 'a', you're in quite a pinch, aren't you?
>
> I can't believe that we're talking about something as bizarre as
> this.

bizarre is in the eye of the beholder. you treasure transpositional possibilities -- this takes that a small step further.

> No, I never expected that anyone would really want to do
> anything like that, and if this is something that you really want to
> do, then I think you're the one who is in a pinch: Where are the
> instruments on which you propose to do this, and how do you expect
> this to be done?

i've proposed 76-equal and it doubling, 152-equal, because they are capable of this for a large number of temperaments/moss/omnitetrachordal systems i'm interested in. including: the decatonic system in my paper; the 14-tone system i mention in my paper in connection with 26-equal; vicentino-like adaptive ji in 152, octatonic/diminished scales, the wonderful 'octal' system in 152, and more.

> And if it's all electronic, then I guess you *can*
> do anything you want, but you're going to need a special notation to
> keep track of it. Nobody could expect a generalized notation to do
> something as esoteric as that without getting extremely complicated.

76-equal and 152-equal are not that complicated.
>
> > > Can we expect a significant number of composers and
> > > musicians to buy the idea that 72-EDO is practical outside of the
> > > electronic medium?
> >
> > it's already happening -- at new england conservatory, at the
> richter-
> > herf institute, among byzantine choral directors such as g.
> bilalis,
> > etc. etc. perhaps you'd like to contact julie werntz again (you
> > contacted her already, didn't you) and ask her this question.
>
> No, I didn't contact her already. I'm just echoing the conventional
> wisdom that I believe persuades most of the rest of academia that it
> isn't practical, just as I'm getting the argument around here that
> replacing sharps and flats with new symbols isn't practical. If you
> were to ask me 25 years ago which of these two things would be more
> practical, what answer would you have expected me (or anyone else) to
> give?
>
> I'm sorry if I seem to be getting a little irritated lately, but I'm
> beginning to feel like I'm in front of a firing squad.

sorry -- this should just be a healthy clash of ideas. i feel i've made a friend in you already and certainly don't want to hurt that friendship in any way. here, let me buy you a virtual beer :)

--- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
> I'm sorry if I seem to be getting a little irritated lately, but I'm
> beginning to feel like I'm in front of a firing squad.
>
> I guess I need to concentrate a bit more on:
>
> Love / joy / peace / patience / kindness ...

Hi George,

Please don't be upset that we aren't buying the whole package. I for
one am very grateful for your core idea, which is to base the notation
of ETs on Pythagorean plus the commas 80:81, 63:64, 32:33.

This is sort of a combination of Manuel Op de Coul's idea (or was it
someone else's originally?) to notate 11-limit JI using Pythagorean
plus accidentals to represent these 3 commas up and down (and a
redundant pair for 125:128 for convenience), with Paul Rapoport's idea
that ETs should be notated based on commas. He chose all 5-limit
commas: 80:81, 125:128, 2025:2048, 32768:32805, all of which vanish in
12-tET.

This is all the more impressive since you didn't know about either of
these at the time.

You will see that Gene and I have taken this idea and are running with
it. The part we don't buy is that combinations of these commas and
sharps and flats should always be notated as a single symbol, even
though you have reduced the number of combinations by assuming certain
even smaller commas always vanish, such as 384:385.

We figure that limiting ourselves to at most two accidentals against
any note (and one of those usually # or b) is quite enough and has a
solid track record.

I feel that by trying to pack too much information into a single
symbol you are losing readability and throwing away established
symbols to no great gain.

I suspect that as you try to consistently notate more and more of the
ETs below 41, you will find you need more and more symbols. By keeping
the comma symbols separate we have all possible pairs
already available.

It's interesting to consider whether native readers of Chinese or
Japanese would be more at home with your single-symbol system rather
than the max-two-symbol system Gene and I are working on. But I
suspect westerners will prefer the latter.

On 2/13/02 1:54 PM, "tuning@yahoogroups.com" <tuning@yahoogroups.com> wrote:

> Message: 20
> Date: Wed, 13 Feb 2002 20:53:13 -0000
> From: "paulerlich" <paul@stretch-music.com>
> Subject: Re: Notation individualists
>
>
> it's already happening -- at new england conservatory, at the richter-
> herf institute, among byzantine choral directors such as g. bilalis,
> etc. etc. perhaps you'd like to contact julie werntz again (you
> contacted her already, didn't you) and ask her this question.

A byzantine choral director? What's that???? Have I missed a time warp
opportunity? Damn!

Gerald Eskelin

--- In tuning@y..., Gerald Eskelin <stg3music@e...> wrote:
> On 2/13/02 1:54 PM, "tuning@y..." <tuning@y...> wrote:
> > it's already happening -- at new england conservatory, at the
> > richter-herf institute
>
> A byzantine choral director? What's that???? Have I missed a time
> warp opportunity? Damn!

Not only that, but this is the first time in my life I've heard of
the Richter-Herf Institute (I'm sure they would appreciate the caps).
I'm off to do a Google search, but I'll be damned if it doesn't sound
like another niche situation. Time will tell...

Besides, it's a youth movement: I believe Paul meant a "bitchin' teen
choral director"!

Cheers,
Jon

--- In tuning@y..., Gerald Eskelin <stg3music@e...> wrote:
> On 2/13/02 1:54 PM, "tuning@y..." <tuning@y...> wrote:
>
> > Message: 20
> > Date: Wed, 13 Feb 2002 20:53:13 -0000
> > From: "paulerlich" <paul@s...>
> > Subject: Re: Notation individualists
> >
> >
> > it's already happening -- at new england conservatory, at the
richter-
> > herf institute, among byzantine choral directors such as g.
bilalis,
> > etc. etc. perhaps you'd like to contact julie werntz again (you
> > contacted her already, didn't you) and ask her this question.
>
> A byzantine choral director? What's that???? Have I missed a time
warp
> opportunity? Damn!

/tuning/topicId_27604.html#27604

> From: jonszanto <JSZANTO@ADNC.COM>
> To: <tuning@yahoogroups.com>
> Sent: Wednesday, February 13, 2002 8:27 PM
> Subject: [tuning] Re: Notation individualists
>
>
> --- In tuning@y..., Gerald Eskelin <stg3music@e...> wrote:
> > On 2/13/02 1:54 PM, "tuning@y..." <tuning@y...> wrote:
> > > it's already happening -- at new england conservatory, at the
> > > richter-herf institute
> >
> > A byzantine choral director? What's that???? Have I missed a time
> > warp opportunity? Damn!
>
> Not only that, but this is the first time in my life I've heard of
> the Richter-Herf Institute (I'm sure they would appreciate the caps).
> I'm off to do a Google search, but I'll be damned if it doesn't sound
> like another niche situation. Time will tell...

i'm surprised to read this, Jon. i just recently mentioned
an old post i sent about Herf:
/tuning/topicId_32971.html#33141

> I posted something here last Spring about the process by
> which Sims derived his tuning :
>
> /tuning/topicId_22968.html#23086?expand=1
> > 23086 From: monz <joemonz@y...>
> > Date: Fri May 18, 2001 2:33am
> > Subject: Re: Miracle/Canasta 72-tet
>
> There's info there about Franz Richter Herf's theories too.
> His name has also come up recently in connection with 72-EDO.

-monz

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

--- In tuning@y..., "monz" <joemonz@y...> wrote:
> i'm surprised to read this, Jon. i just recently mentioned
> an old post i sent about Herf:

Monz, you gotta realize that one, one-line mention of Herf buried in
a posting on Sims notation is quite easy to escape my attention. I
have, however, gone to the Institute's home page and taken a look at
what they are involved with. I certainly wish them well, and will be
curious to see what kind of impact on the world at large their work
will have...

Cheers,
Jon

hi Jon,

> From: jonszanto <JSZANTO@ADNC.COM>
> To: <tuning@yahoogroups.com>
> Sent: Wednesday, February 13, 2002 11:34 PM
> Subject: [tuning] Re: Notation individualists
>
>
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
> > i'm surprised to read this, Jon. i just recently mentioned
> > an old post i sent about Herf:
>
> Monz, you gotta realize that one, one-line mention of Herf buried in
> a posting on Sims notation is quite easy to escape my attention. I
> have, however, gone to the Institute's home page and taken a look at
> what they are involved with. I certainly wish them well, and will be
> curious to see what kind of impact on the world at large their work
> will have...

you're right, that was a pretty small bit on Herf.

there's a _Perspectives of New Music_ article on Herf by
Horst-Peter Hesse, which is how i first found out about
Herf. i could probably dig that out and give you a copy.

apparently a lot of people on the list are surprised at
the sort-of long history of 72edo enthusiasm. when you
realize how good it is at approximating 11-limit JI, it
makes sense.

-monz

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

--- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> hi Jon,
>
>
> > From: jonszanto <JSZANTO@A...>
> > To: <tuning@y...>
> > Sent: Wednesday, February 13, 2002 11:34 PM
> > Subject: [tuning] Re: Notation individualists
> >
> >
> > --- In tuning@y..., "monz" <joemonz@y...> wrote:
> > > i'm surprised to read this, Jon. i just recently mentioned
> > > an old post i sent about Herf:
> >
> > Monz, you gotta realize that one, one-line mention of Herf buried
in
> > a posting on Sims notation is quite easy to escape my attention.
I
> > have, however, gone to the Institute's home page and taken a look
at
> > what they are involved with. I certainly wish them well, and will
be
> > curious to see what kind of impact on the world at large their
work
> > will have...
>
>
> you're right, that was a pretty small bit on Herf.
>
> there's a _Perspectives of New Music_ article on Herf by
> Horst-Peter Hesse, which is how i first found out about
> Herf. i could probably dig that out and give you a copy.

what we really need is an english translation of these -- i've seen
these in the library and it looks (from the diagrams, i can't read
german) like a variety of amazing minds contributed to these symposia:

Richter Herf, Franz (Hg.): Mikrotöne I.
Bericht über das Internationale Symposion Mikrotonforschung, Musik
mit Mikrotönen, Ekmelische Musik, Salzburg, 10. - 12. Mai 1985.
Innsbruck: Edition Helbling, 1986.

Richter Herf, Franz (Hg.): Mikrotöne II.
Bericht über das 2. Internationale Symposion Mikrotonforschung, Musik
mit Mikrotönen, Ekmelische Musik, Salzburg, 22. - 24. Mai 1987.
Innsbruck: Edition Helbling, 1988.

Hesse, Horst-Peter: Grundlagen der Harmonik in mikrotonaler Musik.
Innsbruck: Edition Helbling, 1989.

Hesse, Horst-Peter (Hg.): Mikrotöne III.
Bericht über das 3. Internationale Symposion Mikrotonforschung, Musik
mit Mikrotönen, Ekmelische Musik, Salzburg, 28. - 30. April 1989.
Innsbruck: Edition Helbling, 1990.

Hesse, Horst-Peter (Hg.): Mikrotöne IV.
Bericht über das 4. Internationale Symposion Mikrotonforschung, Musik
mit Mikrotönen, Ekmelische Musik, Salzburg, 2. - 5. Mai 1991.
München: Musikedition Nymphenburg 2001, 1993.

Dave wrote:

> This is sort of a combination of Manuel Op de Coul's idea
> (or was it someone else's originally?)

It's rather obvious and Rasch, Rapoport, Wolf, etc. all had this same
idea.

A limit of no more than two accidentals is a good basic assumption but
I would be careful to turn it into a dogma. It's probably hard to maintain

if you want a consistent meaning of the symbols across all ETs, and not
get
too many different symbols. In any case the principle of consistent
meaning
precedes for me. I've been improving some notations in Scala by reducing
the length of combinations, but haven't succeeded everywhere yet to make
them no longer than two.
I managed to do it for 152-tET:
Legend, from small to large:
> fraction of syntonic comma, in this case 1/3
^ diaschisma
/ syntonic comma
) diesis
# apotome

C C> C^ C/ C/> C) C)> C)^ C)/ Dbv C)) Db Db> C#v C#< C# C#> C#^ C#/ D(v
D(<
D( D\< D\ Dv D< D D> D^ D/ D/> D) D)> D)^ D)/ Ebv D)) Eb Eb> D#v D#< D#
D#>
D#^ D#/ E(v E(< E( E\< E\ Ev E< E E> E^ E/ E/> E) F( E)^ F\ Fv F< F F> F^
F/
F/> F) F)> F)^ F)/ Gbv F)) Gb Gb> F#v F#< F# F#> F#^ F#/ G(v G(< G( G\<
G\
Gv G< G G> G^ G/ G/> G) G)> G)^ G)/ Abv G)) Ab Ab> G#v G#< G# G#> G#^ G#/

A(v A(< A( A\< A\ Av A< A A> A^ A/ A/> A) A)> A)^ A)/ Bbv A)) Bb Bb> A#v
A#<
A# A#> A#^ A#/ B(v B(< B( B\< B\ Bv B< B B> B^ B/ B/> B) C( B)^ C\ Cv C<
C

Before anyone says that ) and > are difficult to distinguish, let me
remind that the graphic counterpart of > is a solid triangle.

Manuel

> From: paulerlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Thursday, February 14, 2002 12:18 AM
> Subject: [tuning] Re: Notation individualists
>
>
>
> what we really need is an english translation of these -- i've seen
> these in the library and it looks (from the diagrams, i can't read
> german) like a variety of amazing minds contributed to these symposia:
>
> Richter Herf, Franz (Hg.): Mikrot�ne I.
> Bericht �ber das Internationale Symposion Mikrotonforschung, Musik
> mit Mikrot�nen, Ekmelische Musik, Salzburg, 10. - 12. Mai 1985.
> Innsbruck: Edition Helbling, 1986.
>
> <etc.>

hmmm . . . Ezra Sims also had an article published in an
issue of Mikrot�ne, and i think it's the best one he's written
on his own work in 72edo. he sent it to me a few years ago
when we were corresponding.

Sims, Ezra.
"Harmonic Ordering in Quintet (1987).
A Use of Harmonics as Horizontal and Vertical Determinants",
Mikrot�ne III, Edition Helbling, Innsbruck, 1990, pp. 123-137.

and besides, the Quintet (1987) is a fantastic piece . . . my
favorite of all Sims's work that i've heard so far. he was
generous enough to send me a copy of the score too.

the _PNM_ article Sims wrote is listed in the Tuning and
Temperament Biblography
http://www.xs4all.nl/~huygensf/doc/bib.html#S

as being published also in Mikrot�ne:

Sims, Ezra.
"Reflections on This and That - Perhaps a Polemic",
Perspectives of New Music vol. 29 no. 1, 1992, pp. 236-257.
Mikrot�ne IV, Filmkunst-Musikverlag, M�nchen, 1993.

i don't know if that's a German translation or a reprint
of the English version.

-monz

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

On 2/14/02 1:56 AM, "tuning@yahoogroups.com" <tuning@yahoogroups.com> wrote:
>>
>>> Message: 20
>>> Date: Wed, 13 Feb 2002 20:53:13 -0000
>>> From: "paulerlich" <paul@s...>
>>> Subject: Re: Notation individualists
>>>
>>>
>>> it's already happening -- at new england conservatory, at the
> richter-
>>> herf institute, among byzantine choral directors such as g.
> bilalis,
>>> etc. etc. perhaps you'd like to contact julie werntz again (you
>>> contacted her already, didn't you) and ask her this question.
>>
>> A byzantine choral director? What's that???? Have I missed a time
>> warp
>> opportunity? Damn!
>
> /tuning/topicId_27604.html#27604

Thanks, Paul. Got it. So all I have to do is go to New York in order to hear
the sounds? Good enough!

J

--- In tuning@y..., "jonszanto" <JSZANTO@A...> wrote:
> George,
>
> ... I note in your last post:
>
> --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
> > I'm sorry if I seem to be getting a little irritated lately, but
> > I'm beginning to feel like I'm in front of a firing squad.
>
> Yeah, unfortunately that's not uncommon, especially if you don't
toe
> the (invisible) party line(s). Having known most of these folks for
a
> while, I'd hazard that the vast majority of it is simply over-
active
> debating glands, but a few others have eventually just thrown up
> their hands and left. I hope that *you* won't, but there may come a
> time when you've discussed as much as you can and decide to just
get
> on with matters; I know that is my experience.
>
> It has been rewarding to see a name/voice that has come up in the
> past actually make a presence, as you have. Don't let the
occasional
> buzzing of mosquitoes send you back inside...
>
> Fraternally,
> Jon

Thanks, Jon! From now on I'll be bringing some virtual insect
repellant with me wheneven I sign on.

--George

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
>
> > > no they're not completely independent! if you want to transfer
with
> > a
> > > common tone on, say, 'c', while the tuning systems are
connected by
> > a
> > > common 'a', you're in quite a pinch, aren't you?
> >
> > I can't believe that we're talking about something as bizarre as
> > this.
>
> bizarre is in the eye of the beholder. you treasure transpositional
possibilities -- this takes that a small step further.

Hmmm, that would make a good saying: "One small step for a
microtonalist -- one giant step for microtonality," or something like
that. (Or how about, watch out for that first step -- it's a doozy!)

When I mentioned that you could put a comment on the manuscript about
transferring to another tuning, I thought that you could specify a
pitch reference at the same time, and that would take care of it as
far as the notation was concerned. The problem would reside in how
to achieve it in the performance. Now you are proposing tonal
systems that will handle it for you. I guess I need to pinch myself
to see if this is all a dream.

> > ... I'm sorry if I seem to be getting a little irritated lately,
but I'm
> > beginning to feel like I'm in front of a firing squad.
>
> sorry -- this should just be a healthy clash of ideas. i feel i've
made a friend in you already and certainly don't want to hurt that
friendship in any way. here, let me buy you a virtual beer :)

Yes, I've referred to this sort of thing as a "collision of ideas."
(: And a virtual soda will do. Thanks! :)

--George

Hello, there, George Secor and everyone, and please let me give a
different viewpoint on this thread by saying how excited and delighted
I am with the sagittal notation for 46-EDO, which also seems very
intuitively to fit my almost identical just 11:14 regular tuning and
some other temperaments in the general vicinity.

First, before getting into the 46-EDO aspects, please let me emphasize
my endorsement of the term "comma of Archytas" or "Archytan comma" --
or "Archytas' comma," if you like -- for the 63:64 (~27.26 cents).

Archytas deserves the notice: a medieval European theorist such as
Jacobus of Liege, for example, discusses the diatonic tetrachord of
Archytas at 28:27:24:21, and in another passage on 7-based ratios
demonstrates the 64:63. As someone who often leans toward a kind of JI
based on ratios of 2-3-7-9, I'm delighted to have the difference
between steps of 9:8 and 8:7 associated with a theorist famed for
favoring these steps. We speak of the comma of Didymus, and George
Secor has given credit where credit is due in naming this other
notable comma most appropriately.

When I wrote some articles a bit more than a year ago on a JI system
with two 12-note Pythagorean chains a 63:64 apart, I noted that it
made available tetrachords identical to those of Archytas -- the term
"comma of Archytas" is something that I would like to have had
available then, and now it is, thanks to your inventing it (I wonder
if there are any precedents -- in any event, it's about time).

Now for sagittal notation in 46-EDO: one of the strengths of this
system is that it's very intuitive for me as someone following a
neo-medieval kind of outlook not necessarily the conventional wisdom
in this forum or elsewhere.

First, the 5d46 modifications up or down ("five degrees of 46," with
my ASCII "d" imperfectly representing a degree symbol) are in fact
equivalent to familiar sharps and flats -- new symbol, friendly and
familiar concept.

Secondly, I find that many of my likeliest notes and intervals to use
translate very simply into the sagittal notation. Sometimes a
conventional spelling using only sharps or flats neatly solves the
problem, and sometimes a diesis modification provides a ready
alternative: but lots of points on my grid are nicely covered by one
approach or the other.

That's my opening accolade, and I look forward to your more thorough
exposition to which I may add some musical examples from my own
stylistic point of view.

Mainly, I want to say: this is a beautiful notation that meets me, as
one user, more than halfway. I look forward to sharing some musical
examples, and congratulate you upon this elegant achievement.

Most appreciatively,

Margo Schulter
mschulter@value.net

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
>
> George Secor, do the semantics of these 11-limit systems agree with
> yours, as far as they go? Is there any chance that you could rework
> your set of symbols so that it becomes an extension of the
Sims/Maneri
> notation and doesn't contain any pairs of symbols which are left-
right
> confusable, or n_n+1 confusable for n>=2?

Dave,

I have read your latest posting regarding my notation and have quite
a bit to say, but I don't have enough time available to reply right
now (although I did answer some of it in #34231).

I stayed up rather late last night reworking some of the symbols (in
a rather stylish makeover), and you can look at them in Figure 4A,
which I have updated:

/tuning/files/secor/notation/figures.bmp

See if you think this is any better.

And thank you for your comments. I think we have made a major
breakthrough in understanding where our differences lie.

--George

> CORRECTION TO FIGURES URL:
>

I'll get it right yet! (The blasted thing is case-sensitive.)

/tuning/files/secor/notation/Figures.bmp

--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_33858.html#34212

>
> you're right, that was a pretty small bit on Herf.
>
> there's a _Perspectives of New Music_ article on Herf by
> Horst-Peter Hesse, which is how i first found out about
> Herf. i could probably dig that out and give you a copy.
>
> apparently a lot of people on the list are surprised at
> the sort-of long history of 72edo enthusiasm. when you
> realize how good it is at approximating 11-limit JI, it
> makes sense.
>

***Could someone please post the Institute link? I've never "Herf"
of it...

JP

--- In tuning@y..., Gerald Eskelin <stg3music@e...> wrote:

/tuning/topicId_33858.html#34228

> >> A byzantine choral director? What's that???? Have I missed a time
> >> warp
> >> opportunity? Damn!
> >
> > /tuning/topicId_27604.html#27604
>
> Thanks, Paul. Got it. So all I have to do is go to New York in
order to hear the sounds? Good enough!
>
> J

****I believe you'd also need a "time machine," Jerry, since I
believe those were *last* year's series of AFMM concerts... :)

Joseph

--- In tuning@y..., manuel.op.de.coul@e... wrote:
> Dave wrote:
>
> > This is sort of a combination of Manuel Op de Coul's idea
> > (or was it someone else's originally?)
>
> It's rather obvious and Rasch, Rapoport, Wolf, etc. all had this
same
> idea.

Do you mean that they all proposed to notate 11-limit JI using
accidentals for only 80:81, 63:64 and 32:33? Did they all also propose
using these commas for notating ETs?

> A limit of no more than two accidentals is a good basic assumption
but
> I would be careful to turn it into a dogma. It's probably hard to
maintain
>
> if you want a consistent meaning of the symbols across all ETs, and
not
> get
> too many different symbols.

Yes. I think that when you get into the rarefied heights of ETs like
152-tET one can expect more than 2 accidentals on occasion. But one
should be careful not to give in too easily.

> In any case the principle of consistent
> meaning
> precedes for me. I've been improving some notations in Scala by
reducing
> the length of combinations, but haven't succeeded everywhere yet to
make
> them no longer than two.
> I managed to do it for 152-tET:
> Legend, from small to large:
> > fraction of syntonic comma, in this case 1/3
> ^ diaschisma
> / syntonic comma
> ) diesis
> # apotome

In 152-tET we have

1/3 syntonic comma = 1 step
diaschisma = 2 steps
syntonic comma = 3 steps
diesis = 5 steps
apotome = 15 steps
major whole tone = 26 steps

> C C> C^ C/ C/> C) C)> C)^ C)/ Dbv C)) Db Db> C#v C#< C#
> C#> C#^ C#/ D(v D(< D( D\< D\ Dv D< D ...

I understand that the program Gene and I have embarked on involves
being able to notate in such a way that the letters are monotonic with
pitch. e.g no modified D should be of lower pitch than any modified C.
This is sure a tough call with 152-tET.

Also, you are using Rappoport's 5-limit commas where we are using one
comma per prime and we don't beleive in using symbols which are
variable fractions of a comma. We can do it like this:

In 152-tET we have

jh 19-comma (512:513) = 1 step
jf 17-comma (4096:4131) = 2 steps
v^ syntonic comma = 3 steps
[] 11-diesis = 7 steps
b# apotome = 15 steps
A:B major whole tone = 26 steps

We can't use the {} 13-comma (1024:1053) = 6 steps because 152-tET is
not 3,13-consistent. So it looks like this:

D
Dh
Df
D^
D]v
D]j
D]y
D]
Ebv
Ebj
Eby
Eb
Ebh
Ebf
Eb^
Eb^h or Ebff
E[v
E[j
E[y
E[
E[h
E]f
E[^
Ev
Ej
Ey
E
...

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

> We can't use the {} 13-comma (1024:1053) = 6 steps because 152-tET is
> not 3,13-consistent. So it looks like this:

I don't see the need of making that a dogma. The 152-et is one that would be natural to notate using a lot of symbols, because it is a high-limit system. By the way, are you using "j" for different things?

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> ***Could someone please post the Institute link? I've never "Herf"
> of it...

http://www.moz.ac.at/user/herf/index_gb.html

Cheers,
Jon

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> In 152-tET we have
>
> jh 19-comma (512:513) = 1 step
> jf 17-comma (4096:4131) = 2 steps
> v^ syntonic comma = 3 steps
> [] 11-diesis = 7 steps
> b# apotome = 15 steps
> A:B major whole tone = 26 steps

That should have been:

yh 19-comma (512:513) = 1 step

Dave wrote:
>Do you mean that they all proposed to notate 11-limit JI using
>accidentals for only 80:81, 63:64 and 32:33? Did they all also propose
>using these commas for notating ETs?

Rasch proposed a set of commas, but I don't remember if he also
proposed a set of symbols for them, or if those commas were different
from Daniel Wolf's. The paper was never published.
The addition of higher limit commas would be an extension of
Rapoport's system, who left that possibility open.

>I understand that the program Gene and I have embarked on involves
>being able to notate in such a way that the letters are monotonic with
>pitch. e.g no modified D should be of lower pitch than any modified C.

I was only giving the shortest ones of the enharmonic equivalents.
In monotonic order they can be longer.

>Also, you are using Rappoport's 5-limit commas where we are using one
>comma per prime and we don't beleive in using symbols which are
>variable fractions of a comma.

Don't you think it's more artificial to look in the very high limits
trying to find some comma which will match to one step?
Isn't the division of a familiar comma into a small number of parts
a more relevant concept acoustically?

Addition of another comma for 152-tET could be an improvement.
Since the septimal comma has the same size as the syntonic, we can take
the next 11-limit one, 33/32 which is 7 steps and quite accurate.
The 13-limit 27/26 is 9 steps, but maybe we'd get too many different
symbols then. Using Dave's symbols [] we'd get, again giving the shortest
enharmonic equivalents:

C C> C^ C/ C/> C) C)> C] C]> C]^ C]/ Db C]) C#v C#< C# C#> C#^ C#/ D[ D(<
D(
D\< D\ Dv D< D D> D^ D/ D/> D) D)> D] D]> D]^ D]/ Eb D]) D#v D#< D# D#>
etc.

I don't favour abandoning lower limit comma's for these high limit
exotic ones, like 4096:4131.
For a few ETs I found that adding the septimal comma to the notation makes
an improvement, namely for 67, 88 and 98-tET.
Like Gene I don't see consistency as a necessary requirement for using
a comma. For some ETs that could mean that only the Pythagorean comma can
be used?

Manuel

--- In tuning@y..., "jonszanto" <JSZANTO@A...> wrote:

/tuning/topicId_33858.html#34267

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> > ***Could someone please post the Institute link? I've
never "Herf"
> > of it...
>
> http://www.moz.ac.at/user/herf/index_gb.html
>
> Cheers,
> Jon

Thanks, Jon!

Ich denke meine Deutsch mussen besser gegetten bald auch! Ach!

JP

Jerry, all joking aside, it is important that things that happen in New York are considered even if they are not experienced first hand (as elsewhere). In the same way that important unpublished material needs to be considered on this list, regional realities must be "heard" trees falling in the forest.

best, Johnny

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

> I understand that the program Gene and I have embarked on involves
> being able to notate in such a way that the letters are monotonic
with
> pitch. e.g no modified D should be of lower pitch than any modified
C.

really? how odd . . . wouldn't C# be higher than Db in 17-equal, for
example?

> Also, you are using Rappoport's 5-limit commas where we are using
one
> comma per prime and we don't beleive in using symbols which are
> variable fractions of a comma. We can do it like this:
>
> In 152-tET we have
>
> jh 19-comma (512:513) = 1 step
> jf 17-comma (4096:4131) = 2 steps
> v^ syntonic comma = 3 steps
> [] 11-diesis = 7 steps
> b# apotome = 15 steps
> A:B major whole tone = 26 steps

couldn't we use some 7-comma instead?

--- In tuning@y..., Afmmjr@a... wrote:
> Jerry, all joking aside, it is important that things that happen in
New York are considered even if they are not experienced first hand

Ditto for the West Coast, which is usually dissed...

Cheers,
Jon

--- In tuning@y..., manuel.op.de.coul@e... wrote:
> Don't you think it's more artificial to look in the very high limits
> trying to find some comma which will match to one step?

Not in the case high numbered ETs like 15-tET but one should certainly
exhaust all the possibilities of lower primes first.

> Isn't the division of a familiar comma into a small number of parts
> a more relevant concept acoustically?

For lower numbered ETs, yes. But what I object to is the use of the
same symbol to mean 1/2 comma in one case and 1/3 comma in another.
And if we have different symbols for each then we start to get too
many symbols.

> Addition of another comma for 152-tET could be an improvement.
> Since the septimal comma has the same size as the syntonic, we can
take
> the next 11-limit one, 33/32 which is 7 steps and quite accurate.
> The 13-limit 27/26 is 9 steps, but maybe we'd get too many different
> symbols then. Using Dave's symbols [] we'd get, again giving the
shortest
> enharmonic equivalents:
>
> C C> C^ C/ C/> C) C)> C] C]> C]^ C]/ Db C]) C#v C#< C# C#> C#^ C#/
D[ D(<
> D(
> D\< D\ Dv D< D D> D^ D/ D/> D) D)> D] D]> D]^ D]/ Eb D]) D#v D#< D#
D#>
> etc.
>
> I don't favour abandoning lower limit comma's for these high limit
> exotic ones, like 4096:4131.

By the way. I have a feeling that the 1,3,p-commas we choose should
all vanish in 12-tET (at least where 12-tET is 1,3,p-consistent), but
I don't know why. Thanks Dan Stearns, for reminding me that it's
really 1,3,p I meant when I was writing 3,p-consistent. And of course
we're assuming octave equivalence.

> For a few ETs I found that adding the septimal comma to the notation
makes
> an improvement, namely for 67, 88 and 98-tET.
> Like Gene I don't see consistency as a necessary requirement for
using
> a comma. For some ETs that could mean that only the Pythagorean
comma can
> be used?

Some N-ET's should only be notated as every kth step of kN-ET.

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
>
> > I understand that the program Gene and I have embarked on involves
> > being able to notate in such a way that the letters are monotonic
> with
> > pitch. e.g no modified D should be of lower pitch than any
modified
> C.
>
> really? how odd . . . wouldn't C# be higher than Db in 17-equal, for
> example?

Well of course it would, but the thing is not to be forced to use
both. Thinking of these as different notes is foreign to 12-tET
trained types. It would seem an advantage to be able limit sharps and
flats to say Eb Bb F# C# G#.

> > Also, you are using Rappoport's 5-limit commas where we are using
> one
> > comma per prime and we don't beleive in using symbols which are
> > variable fractions of a comma. We can do it like this:
> >
> > In 152-tET we have
> >
> > yh 19-comma (512:513) = 1 step
> > jf 17-comma (4096:4131) = 2 steps
> > v^ syntonic comma = 3 steps
> > [] 11-diesis = 7 steps
> > b# apotome = 15 steps
> > A:B major whole tone = 26 steps
>
> couldn't we use some 7-comma instead?

63:64 is the same size as 80:81 in this case. What 7-comma did you
have in mind?

On 2/15/02 3:54 PM, "paulerlich" <paul@stretch-music.com> wrote:

> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
>
>> I understand that the program Gene and I have embarked on involves being able
>> to notate in such a way that the letters are monotonic with pitch. e.g no
>> modified D should be of lower pitch than any modified C.
>>

It's always nice to pick a random post on the list and see evidence of ideas
I've had or am having. I tried this in 31 awhile back, mapping the major
chord convergence... If you look at the two models, one with
note/accidental/hair and the other with note/multiple-inflections, I think
somewhere in the middle is a pretty easy way to visualize the
multidimensionality of intervals, more toward the second.

Came up with a few symbols off the top of my head and once the list was done
I looked through it later, and I could see, with a little practice, yeah
that's this note plus a 25:24 minus a 128:125 or whatever. It looked a LOT
nicer visually than seeing a "B-double sharp minus four syntonic commas" and
trying to figure out how it related to the notes above or below it.

I say somewhere in the middle because trying to force the letter issue
seemed a little obsessive after awhile, and after awhile, there was a sort
of diffusion of assignment; should it be 3 of these minus 2 of those? Or 5
of these plus one of those? Etc.

> really? how odd . . . wouldn't C# be higher than Db in 17-equal, for example?

Thought I'd stick half a nostril in here.

I also did the above mapping in 41 and 53, just 3rd limit stuff. Where "*"
is whatever symbol you assign to the Pythagorean comma, it seemed like it
would just take getting used to a "C#*" being a "Db" along the same lines of
being much younger and trying to get used to seeing a C# and Db and trying
to think of them as the same piano note.

So instead of 17 being:

D Eb D# E F Gb F# G Ab G# A Bb A# B C Db C# D

It could look like this:
(again where "*" is whatever symbol you assign to the Pythagorean comma)
((...and where putting it before is flattening, after is sharpening))

D Eb Eb* E F *F# G *G# A Bb Bb* B C *C# D

Which if you run your eyes over it, feels a little more banded:

D -> Eb Eb* E -> F *F# -> G *G# -> A -> Bb Bb* B -> C *C# -> D

Instead of:

D -> Eb <- D# -> E -> F -> Gb <- F# -> G -> Ab <- G# -> A -> Bb <- A# -> B
-> C -> Db <- C# -> D,

Where literally every other note you're jerking back and forth one letter.

Marc

--- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:
Good to hear from you Marc.

> So instead of 17 being:
>
> D Eb D# E F Gb F# G Ab G# A Bb A# B C Db C# D
>
> It could look like this:
> (again where "*" is whatever symbol you assign to the Pythagorean
comma)
> ((...and where putting it before is flattening, after is
sharpening))
>
> D Eb Eb* E F *F# G *G# A Bb Bb* B C *C# D

Yes that's exactly what I've got (except you missed a coupla notes
there) only I've used a pair of symbols to represent the
undecimal-diesis (32:33) down [ and up ].

D Eb Eb] E F F#[ F# G G#[ Ab] A Bb Bb] B C C#[ C# D

It has to be the 11-comma because the 7-comma (63:64) vanishes and the
5-comma (80:81) is either 1 step or 2 steps depending if you want the
1:5 intervals to come out right or the 3:5's. i.e. 17-tET is
1,3,5-inconsistent.

Gene, avoiding using a 1,3,p-comma for notation when that comma has
two possible values in a given ET, isn't a dogma for me. It just seems
like a very good idea.

If there's one thing I must arrogantly assert without any supporting
argument, it's that there must be _no_ dogmas. ;-)

>
>
> Which if you run your eyes over it, feels a little more banded:
>
> D -> Eb Eb* E -> F *F# -> G *G# -> A -> Bb Bb* B -> C
*C# -> D
>
>
> Instead of:
>
> D -> Eb <- D# -> E -> F -> Gb <- F# -> G -> Ab <- G# -> A -> Bb <-
A# -> B
> -> C -> Db <- C# -> D,
>
> Where literally every other note you're jerking back and forth one
letter.
>
>
> Marc

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

> Gene, avoiding using a 1,3,p-comma for notation when that comma has
> two possible values in a given ET, isn't a dogma for me. It just seems
> like a very good idea.

I agree that avoiding it is good when possible, as it is also likely to avoid some confusion.

On 2/16/02 3:30 AM, "dkeenanuqnetau" <d.keenan@uq.net.au> wrote:

> --- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:
> Good to hear from you Marc.
>

Thanks. I type when I'm able. I can walk this year too.

>> D Eb Eb* E F *F# G *G# A Bb Bb* B C *C# D
>>
> Yes that's exactly what I've got (except you missed a coupla notes there) only
> I've used a pair of symbols to represent the undecimal-diesis (32:33) down [
> and up ].
>
> D Eb Eb] E F F#[ F# G G#[ Ab] A Bb Bb] B C C#[ C# D
>

OOPS. Yes miscopied, sorry. Should have been:

D Eb Eb* E F *F# F# G *G# G# A Bb Bb* B C *C# C# D

...whiiiiiiich :::looking:::

Yeah, that's what you got. The 12 row expanded with 17 inflectors. Oh
actually I like your symmetry a lot more with the "G#[ Ab]". I wonder what
I would do if I ever fully awoke.

I forgot to put in the uninflected accidentals. Like I said. Haven't typed
in awhile. Always good broadstrokes, always sloppy mechanics. I lost more
math contests in high school from miscopying plus and minus signs. It's a
wonder I even know what temperaments I use. Coffee time.

I could use a good abduction. Any parallel civilizations watching? I'm
still here yknow. And I know the consequences of so I haven't broken any
time travel confidance by revealing the aaaaaaaaa!!!*&@#$UDGs09h38NB!@#!(@*

> It has to be the 11-comma because the 7-comma (63:64) vanishes and the
> 5-comma (80:81) is either 1 step or 2 steps depending if you want the 1:5
> intervals to come out right or the 3:5's. i.e. 17-tET is 1,3,5-inconsistent.
>
> Gene, avoiding using a 1,3,p-comma for notation when that comma has two
> possible values in a given ET, isn't a dogma for me. It just seems like a very
> good idea.
>
> If there's one thing I must arrogantly assert without any supporting argument,
> it's that there must be _no_ dogmas. ;-)
>

My dogma got run ova by someone else's karma.

Orph-ON :::clap clap:::
Orph-OFF :::clap clap:::

--- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
> I stayed up rather late last night reworking some of the symbols (in
> a rather stylish makeover), and you can look at them in Figure 4A,
> which I have updated:
>
>
/tuning/files/secor/notation/Figures.bmp
>
> See if you think this is any better.

I like the one and two shaft arrows, but I think you should have kept
up the concave curve (as if the arrows are coming towards you) when
you went to the 3 and 4(X) shaft arrows, instead of switching to
concave. Also I think you need to open up more of a hole in the X with
the straight slanting head.

> And thank you for your comments. I think we have made a major
> breakthrough in understanding where our differences lie.

That's good.

--- In tuning@y..., Guiseppi Mendoza <guiseppi@m...> wrote:
> On Sat, 09 Feb 2002 04:30:48 -0000, SOMEONE articulated, I'd better
> not say who :
>
> >> Does anyone have any comments or objections?
>
> Is there some source for fonts for notation (of all kinds ;)

Try
https://www.mindeartheart.org/micro.html

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> --- In tuning@y..., Guiseppi Mendoza <guiseppi@m...> wrote:
> > On Sat, 09 Feb 2002 04:30:48 -0000, SOMEONE articulated, I'd
better
> > not say who :
> >
> > >> Does anyone have any comments or objections?
> >
> > Is there some source for fonts for notation (of all kinds ;)

Also for George Secor's benefit, I'd like to recall this excellent
post by Graham Breed in which he gives URLs for standard Unicode
character sets, with musical symbols.

/tuning/topicId_23583.html#23615

Given something George said recently, maybe the Japanese Katakana
character set would be a good place to look for symbols for new
accidentals. Its characters aren't as "busy" looking as most of
those in the full Chinese character set.

Dave wrote:
>> Isn't the division of a familiar comma into a small number of parts
>> a more relevant concept acoustically?

>For lower numbered ETs, yes. But what I object to is the use of the
>same symbol to mean 1/2 comma in one case and 1/3 comma in another.

Ach, each symbol represents a different value in cents for different
ETs anyway. I don't see why a varying size in terms of comma fraction
is a big deal.

>And if we have different symbols for each then we start to get too
>many symbols.

Yes.

>Some N-ET's should only be notated as every kth step of kN-ET.

You probably write "should" because of your consistency requirement
for the commas used, which I don't share. How would your system
take care of for instance 105-tET?

Manuel

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
> > I stayed up rather late last night reworking some of the
symbols ...
> > See if you think this is any better.
>
> I like the one and two shaft arrows, but I think you should have
kept
> up the concave curve (as if the arrows are coming towards you) when
> you went to the 3 and 4(X) shaft arrows, instead of switching to
> concave. Also I think you need to open up more of a hole in the X
with
> the straight slanting head.

Per your suggestion, I tried reworking them in two different ways in
Figures 4a and 4b:

/tuning/files/secor/notation/Figures.bmp

I previously hesitated to make them as you suggested above (see 4b)
because this makes the new symbols somewhat larger than others that
signify pitch alteration by a greater amount. I think that making
the curve in the opposite direction (as in 4a) better preserves the
size/alteration correlation. Do you agree?
>
> > And thank you for your comments. I think we have made a major
> > breakthrough in understanding where our differences lie.
>
> That's good.

Indeed! Over the weekend I figured out how to notate both 27 and 58-
EDO with the sagittal symbols, which I will address in a separate
message (which will probably require a separate figure). I decided
that, as long as these systems are important to others, it would be
worth my while to take them into account. (Taking the weekend off can
work wonders for one's attitude and ability to think clearly!)

And again, thank you!

--George

Love / joy / peace / patience / kindness / goodness ...

--- In tuning@y..., manuel.op.de.coul@e... wrote:
in /tuning/topicId_33858.html#34402

> Ach, each symbol represents a different value in cents for different
> ETs anyway. I don't see why a varying size in terms of comma
fraction
> is a big deal.
>
> >And if we have different symbols for each then we start to get too
> >many symbols.
>
> Yes.

So why not admit that what we're both really wanting is a symbol that
represents a single step of the ET? At least then you wouldn't need
symbol pairs for the variable fraction of every comma.

The way I see it, calling it a _variable_ fraction of some particular
5-limit comma (there is sometimes more than one to choose from) is no
less specious than calling it a whole comma involving some higher
prime.

> >Some N-ET's should only be notated as every kth step of kN-ET.
>
> You probably write "should" because of your consistency requirement
> for the commas used, which I don't share.

Not for that reason, although I value 1,3,9-consistency in this
regard, so that one can assume for example that C:D is a 1:9 while
both C:G and G:D are 2:3s. Sometimes enough primes are consistent but
I still wouldn't notate the ET using its own best approximation of a
2:3 because this approximation is a very poor one. This was Dan
Stearns excellent suggestion. He'd rather know that some tunings have
a super and a sub fifth, than pretend that one of them is a perfect
fifth. 47-tET is a borderline example of that. And if we notate 11-tET
according to its native "perfect fifth" (instead of that of 22-tET) we
obscure the fact that it has reasonable 1:7:9:11 chords.

> How would your system
> take care of for instance 105-tET?

Ok. So this ET is absolutely dismal on the low number consistency
front. Neither 1,3,5 nor 1,3,7 nor 1,3,9 nor 1,3,13, and the proposed
17 and 19 commas are a negative number of steps. So I'm left with only
the undecimal diesis [] at 4 steps (the proposed 23-comma is also
4-steps).

But it's perfect fifth is essentially that of 2/9-comma meantone and
many of its second-best approximations are quite acceptable. Because
its perfect fifth is good I see no reason to notate it as every 2nd
step of 210-tET or any such.

Presumably you would use the diesis (3 steps) and 1/n-diesis (in this
case 1/3-diesis = 1 step) symbols. I guess one never needs to ask
whether the diesis will be consistent since it is only a 1,5-comma not
1,3,5, (except in the unlikely event that you're worried about 1,5,25
consistency). This is a nice feature.

Oh well, I guess in this case I'll choose the values I want from some
inconsistent commas. See, I said it wasn't a dogma. :-)

The syntonic comma is 0 steps for best 1:5s and 1 step for best 3:5s.
The septimal comma is 3 steps for best 1:7s and 4 steps for best 3:7s.
I'll use the septimal comma symbols <> to mean 3 steps and the
syntonic comma symbols v^ to mean 1 step. So we have

D D^ D>v D> D] Ebv Eb Eb< Eb<^ Ebv Eb Eb^ E[v E[ E< E<^ Ev E

with the identities
>^ = ]
<v = [
#< = ]
b> = [

So we could do without the [] if we want and accept the occasional
triple accidental.

--- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
> Per your suggestion, I tried reworking them in two different ways in
> Figures 4a and 4b:
>
>
/tuning/files/secor/notation/Figures.bmp
>
> I previously hesitated to make them as you suggested above (see 4b)
> because this makes the new symbols somewhat larger than others that
> signify pitch alteration by a greater amount.

So why not use the curved strokes for the septimal comma and the
straight ones for the syntonic comma, since the septimal comma _is_
bigger and represents twice as many steps in 72-tET.

> I think that making
> the curve in the opposite direction (as in 4a) better preserves the
> size/alteration correlation. Do you agree?

Maybe so, but it has other serious problems. The concave stroke gets
pretty well lost in the \X and /X symbols. They both just looks like
X. The \| symbol with concave head looks too much like an eighth-rest
symbol for my liking.

I still like them all convex.

Shouldn't the curved strokes always be on the same side?