Yahoo Tuning Groups Ultimate Backup tuning HEWM notation out in front again

They're rounding the corner and what do we see, right up in front,
it's Monzo HEWM notation!!

So, I think the "problem" is solved by placing the plusses and
minuses for the twelfth tones in *front* of the notes, rather on top,
where they will interfere with brass articulations...

And I *have* plusses and minuses in Sibelius, so that will work OK.

The other notations are already part of the Sims font, although I may
use the Sagittal font for quartertone arrows, since they're larger.

So I may not need a font made for HEWM at all. I've "cobbled" it
together from what I have.

The response from Julia Werntz on 72-tET was illuminating. She
doesn't like the Sims symbols either, although admittedly, several
composers and performers are using it.

Sorry for all the "waffling"... (I'm not delighted with it
either... :) but if I can make a *practical* implementation of HEWM,
which seems to be happening, I will use this notation.

Sagittal will have to come up with something quite remarkable to
supersede the value of HEWM for 72-tET.

I think I very well may use HEWM in my next Blackjack piece...

Joseph Pehrson

🔗monz <monz@attglobal.net>

hi Joe,

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

> They're rounding the corner and what do we see, right up
> in front, it's Monzo HEWM notation!!

i'm a bit of a gambler! ... why didn't you *tell* me there
was a race on?!!!! i'd be winning right now! ;-)
(and i could have used the money ...)

> So, I think the "problem" is solved by placing the plusses
> and minuses for the twelfth tones in *front* of the notes,
> rather on top, where they will interfere with brass
> articulations...

yes, Joe, *OF COURSE* the plusses and minuses go *before*
the notes! isn't that the where sharps and flats go?
why would i want the other symbols to go anywhere else?

right in the second sentence on the HEWM webpage, i wrote:

>> "My version of the notational system uses prime-factors
>> and their exponents as accidentals placed before the
>> note-heads, along with the following accidental symbols,
>> whose intonational inflections are given in the table:
>> <etc.>

two examples of the prime-factors-and-exponent accidentals,
in conjunction with 12edo note-representations (i.e., without
the HEWM accidentals), appear in scores on these webpages:

http://sonic-arts.org/monzo/partch/intruder/intruder.htm

http://sonic-arts.org/monzo/rjohnson/drunken.htm

> And I *have* plusses and minuses in Sibelius, so that will
> work OK.

see? i suggested to you years ago a notation that you can
already use with your own software!

> The other notations are already part of the Sims font,
> although I may use the Sagittal font for quartertone arrows,
> since they're larger.
>
> So I may not need a font made for HEWM at all. I've "cobbled"
> it together from what I have.

good. did you ask me for this before? ... if so, i missed it.
and anyway, sorry, but i'm way too busy incorporating HEWM
into my own software to deal with that now.

> The response from Julia Werntz on 72-tET was illuminating.
> She doesn't like the Sims symbols either, although admittedly,
> several composers and performers are using it.

well ... i think (IRCC) i suggested HEWM to Sims awhile back
and he understandably balked at the idea ... altho i might
be totally wrong, and perhaps i never even suggested it to him.

but in any case, i'm willing to try pitching it to both he
and Maneri and see what happens. my feeling (just a hunch,
since i've never corresponded with him) that Maneri would
be open-minded enough to give it a shot.

> Sorry for all the "waffling"... (I'm not delighted with it
> either... :) but if I can make a *practical* implementation
> of HEWM, which seems to be happening, I will use this notation.
>
> Sagittal will have to come up with something quite remarkable
> to supersede the value of HEWM for 72-tET.

well, even tho i invented this particular version of HEWM
(of course building on Helmholtz, Ellis, and Daniel Wolf,
as indicated by the name), and have been *very* happy with
it so far, i'm personally rooting for sagittal to solve the
need for a really comprehensive system which works for
many different tunings simultaneously.

but i'm glad that you finally found HEWM useful. i saw the
value in it right away, and used it for the first page of
my score of _A Noiseless Patient Spider_, only switching to
144edo-HEWM for the rest of the piece because i needed finer
pitch discrimination than 72edo ... but i still used the HEWM
principle.

http://sonic-arts.org/monzo/spider/spider.htm

and the invention of HEWM caused me to rethink my own notational
ideas. those two links i gave near the top are 2 old versions of
my prime-factor notation, which use 12edo as the notational basis.
72edo-HEWM is far preferable, and is what i expect to use for
all of my future work ... unless sagittal turns out to be
clearly superior.

i'd like it very much if Sims and/or (especially) Maneri and
the other Bostonians would adopt 72edo-HEWM for their work.

but the big sales pitch i want to undertake is to try to get
all those JI composers who have decided to adopt Johnston
notation to switch to JI-HEWM. the pythagorean basis of
HEWM makes it *far* preferable to the 5-limit basis of
Johnston notation.

Dr. Wolf agrees with me strongly on this, and even gave a
good explanation of it: decoding Johnston notation requires
an immediate 2-step process whereby one first refers to the
5-limit JI diatonic scale which is the basis of the notation,
then determines what relationship the given ratio has to that
reference scale. if there are any accidentals besides +/-,
representing prime-factors higher than 5, then further
relationships must be determined for those too.

that latter procedure is also a part of HEWM, but at least
the initial determination is only a 1-step process, because
the plain letter-names and #/b are based on a simple
1-dimensional pythagorean chain. figuring out what the HEWM
+/- represents is also very simple, because +/- works the
same way (for 5) as all the other accidentals based on
higher primes.

> I think I very well may use HEWM in my next Blackjack piece...

i'm glad to hear that, Joe!!!

thanks. it means more to me that you adopted this after such
strong initial resistance, than it would have if you had
simply accepted the suggestion more readily.

-monz

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

/tuning/topicId_47880.html#47899

> hi Joe,
>
>
>
> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
>
> > They're rounding the corner and what do we see, right up
> > in front, it's Monzo HEWM notation!!
>
>
> i'm a bit of a gambler! ... why didn't you *tell* me there
> was a race on?!!!! i'd be winning right now! ;-)
> (and i could have used the money ...)
>

***Well, Monz, the "race" is essentially finding something before I
begin my next Blackjack piece! I can't wait around for the next
millennium for the reincarnation of Sagittal....

>
>
> > So, I think the "problem" is solved by placing the plusses
> > and minuses for the twelfth tones in *front* of the notes,
> > rather on top, where they will interfere with brass
> > articulations...
>
>
> yes, Joe, *OF COURSE* the plusses and minuses go *before*
> the notes! isn't that the where sharps and flats go?
> why would i want the other symbols to go anywhere else?
>

***Got it. Glad that's cleared up...

>
> > The other notations are already part of the Sims font,
> > although I may use the Sagittal font for quartertone arrows,
> > since they're larger.
> >
> > So I may not need a font made for HEWM at all. I've "cobbled"
> > it together from what I have.
>
>
> good. did you ask me for this before? ... if so, i missed it.
> and anyway, sorry, but i'm way too busy incorporating HEWM
> into my own software to deal with that now.
>

***Well, Monz, in any case, it's unnecessary, since I'm able to use
HEWM in Sibelius "as is..." I've even made a "library" (Sibelius-
talk for saveable environments) to use with it.

>
>
> > The response from Julia Werntz on 72-tET was illuminating.
> > She doesn't like the Sims symbols either, although admittedly,
> > several composers and performers are using it.
>
>
> well ... i think (IRCC) i suggested HEWM to Sims awhile back
> and he understandably balked at the idea ... altho i might
> be totally wrong, and perhaps i never even suggested it to him.
>
> but in any case, i'm willing to try pitching it to both he
> and Maneri and see what happens. my feeling (just a hunch,
> since i've never corresponded with him) that Maneri would
> be open-minded enough to give it a shot.
>

***That could be, since Maneri was using a more *practical* set of
symbols before he met Sims, according to Julia Werntz...

>
> i'd like it very much if Sims and/or (especially) Maneri and
> the other Bostonians would adopt 72edo-HEWM for their work.
>
> but the big sales pitch i want to undertake is to try to get
> all those JI composers who have decided to adopt Johnston
> notation to switch to JI-HEWM. the pythagorean basis of
> HEWM makes it *far* preferable to the 5-limit basis of
> Johnston notation.
>
> Dr. Wolf agrees with me strongly on this, and even gave a
> good explanation of it: decoding Johnston notation requires
> an immediate 2-step process whereby one first refers to the
> 5-limit JI diatonic scale which is the basis of the notation,
> then determines what relationship the given ratio has to that
> reference scale. if there are any accidentals besides +/-,
> representing prime-factors higher than 5, then further
> relationships must be determined for those too.
>
> that latter procedure is also a part of HEWM, but at least
> the initial determination is only a 1-step process, because
> the plain letter-names and #/b are based on a simple
> 1-dimensional pythagorean chain. figuring out what the HEWM
> +/- represents is also very simple, because +/- works the
> same way (for 5) as all the other accidentals based on
> higher primes.
>

***Why sure, we've been over this before on the list. I find the
Johnston notation *extremely* confusing. I believe the *assumption*
that the unaltered pitches are the *JUST* 5-limit ones, is way off-
base considering the original nature of the notation and the staff
(Pythagorean-based...)

>
>
> > I think I very well may use HEWM in my next Blackjack piece...
>
>
> i'm glad to hear that, Joe!!!
>
> thanks. it means more to me that you adopted this after such
> strong initial resistance, than it would have if you had
> simply accepted the suggestion more readily.
>

***Well, "stuff happened" in the interim, like, basically, I *used*
the Sims more :) I had interaction with performers who couldn't
remember what the *quartertones* signified... I can't blame them,
because *I* couldn't figure it out quickly either! :)

Added to this is the comment, echoed by Julia Werntz, that the idea
of having the *full arrow* a *smaller* alteration than the *half
arrow* is just illogical...

I'm all in favor of the development of a *generalized* notation, and
applaud the attempts at Sagittal, but perhaps one notation does not
serve all purposes.

For 72-tET it is obvious that HEWM has been very carefully thought
out...

Thanks!

Joe P.

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> They're rounding the corner and what do we see, right up in front,
> it's Monzo HEWM notation!!

Joseph, I thought I would be content just to read the postings for a
while as I worked on other things, but you're making this sound like
a horse race, and I'd hate to have the sagittal horse get eliminated
by taking "time out" for a few weeks.

> So, I think the "problem" is solved by placing the plusses and
> minuses for the twelfth tones in *front* of the notes, rather on
top,
> where they will interfere with brass articulations...
>
> And I *have* plusses and minuses in Sibelius, so that will work OK.
>
> The other notations are already part of the Sims font, although I
may
> use the Sagittal font for quartertone arrows, since they're larger.
>
> So I may not need a font made for HEWM at all. I've "cobbled" it
> together from what I have.
>
> The response from Julia Werntz on 72-tET was illuminating. She
> doesn't like the Sims symbols either, although admittedly, several
> composers and performers are using it.
>
> Sorry for all the "waffling"... (I'm not delighted with it
> either... :) but if I can make a *practical* implementation of
HEWM,
> which seems to be happening, I will use this notation.

And you make it sound as if the race is all but over (unless you're
just testing this out, in which case, by all means go for it! -- but
then I would ask that you allow the horses to run on a level playing
field and also test out the improvements to the sagittal symbols that
Dave and I are making).

> Sagittal will have to come up with something quite remarkable to
> supersede the value of HEWM for 72-tET.
>
> I think I very well may use HEWM in my next Blackjack piece...
>
> Joseph Pehrson

I'm a little puzzled by your recent liking of HEWM notation, so I'm
asking you to clarify something.

As it presently stands, HEWM and sagittal have the same notational
semantics as applied to 72-ET (or to state it in plain English, there
are three pairs of symbols in each notation that *stand for* exactly
the same things in both JI and 72-ET). This is no accident -- in
designing sagittal Dave and I drew upon a number of very good ideas
that have already been used by others, and Monz has also put some
very good things into HEWM.

So whatever you may favor in one notation over the other is purely a
matter of the appearance of the symbols themselves.

The problem that you are having with sagittal is in the symbols for 2
degrees, but I find it very surprising that you haven't had anything
negative to say about the HEWM symbols for 2deg. After all of the
things you've said so far about symbol confusability, I thought that
you would surely realize that < and > are just sitting there waiting
to be confused with one another, in two ways:

1) The symbols themselves are laterally confusable, i.e., they are
*exact* lateral mirror images of one another, which makes it
difficult to tell them apart, and

2) Even if you can get past reason 1, it's also easy to get confused
about their meanings in that it's not easy to remember which one is
*up* and which is *down* (since, as others have previously noted,
they seem to point left and right, not up and down). This is
precisely the problem you found with the Sims symbols for 3 degrees
(for which reason 1 does not apply).

I don't understand how you can judge < and > as not confusable, while
judging /| and |), which are *not* lateral mirror images of each
other, to be laterally confusable (or is this something that you have
overlooked).

Your response will help Dave and me in writing the reply that we will
eventually be posting (because there are many more things yet to
say). Thank you.

--George

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:

/tuning/topicId_47880.html#47925

> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:

> > They're rounding the corner and what do we see, right up in
front, it's Monzo HEWM notation!!
>

> Joseph, I thought I would be content just to read the postings for
a while as I worked on other things, but you're making this sound
like a horse race, and I'd hate to have the sagittal horse get
eliminated by taking "time out" for a few weeks.
>

:) :)

***Hi George!

No, of course, we wouldn't want *this* to happen! Of course, take
your time and make something good. As I mentioned in my last post,
I'm still amenable to change. However, the demand is *right now*
regarding my *own* music, since I'm sick of the Sims notation.
People can't differentiate the quartertones easily, and that's a
serious problem. The HEWM makes a *lot* of sense, conversely...

> And you make it sound as if the race is all but over (unless you're
> just testing this out, in which case, by all means go for it! --
but then I would ask that you allow the horses to run on a level
playing field and also test out the improvements to the sagittal
symbols that Dave and I are making).
>

***Well, yes, I'm *testing* out the HEWM notation. Sure, I'll "test"
the Sagittal as well, if it truly seems like something worth
testing... Let me explain that this is *totally* independent of the
theoretical significance of the overall notation. I'm obviously only
looking for something that I can use for *composition* with 72-
tET... Therefore, I'm willing to accept an *inferior* theoretical
product if I must... Of course, if I can have *both* worlds...

> I'm a little puzzled by your recent liking of HEWM notation, so I'm
> asking you to clarify something.
>

> As it presently stands, HEWM and sagittal have the same notational
> semantics as applied to 72-ET (or to state it in plain English,
there are three pairs of symbols in each notation that *stand for*
exactly the same things in both JI and 72-ET). This is no accident --
in designing sagittal Dave and I drew upon a number of very good
ideas that have already been used by others, and Monz has also put
some very good things into HEWM.
>

***Yes, definitely so... ( and much better than Johnson JI notation,
I might add...)

> So whatever you may favor in one notation over the other is purely
a matter of the appearance of the symbols themselves.
>

***That is correct.

> The problem that you are having with sagittal is in the symbols for
2 degrees, but I find it very surprising that you haven't had
anything negative to say about the HEWM symbols for 2deg. After all
of the things you've said so far about symbol confusability, I
thought that you would surely realize that < and > are just sitting
there waiting to be confused with one another, in two ways:
>
> 1) The symbols themselves are laterally confusable, i.e., they are
> *exact* lateral mirror images of one another, which makes it
> difficult to tell them apart, and
>
> 2) Even if you can get past reason 1, it's also easy to get
confused about their meanings in that it's not easy to remember which
one is *up* and which is *down* (since, as others have previously
noted, they seem to point left and right, not up and down). This is
> precisely the problem you found with the Sims symbols for 3 degrees
> (for which reason 1 does not apply).
>
> I don't understand how you can judge < and > as not confusable,
while judging /| and |), which are *not* lateral mirror images of
each other, to be laterally confusable (or is this something that you
have overlooked).
>
> Your response will help Dave and me in writing the reply that we
will eventually be posting (because there are many more things yet to
> say). Thank you.
>

***Well, the answer to this question, George, is that I'm *not* using
the ascii equivalents < and > in my notation for sixth tones. Not in
the written score.

These symbols are simply the ascii *shorthand* for the notation.

The actual symbols I use for the sixthtones are *half arrows*. One
points upward and the other points downward.

I *only* use half arrows that have flags *pointing to the left.* I
don't use anything pointing to the right at all. So there is no
lateral confusability in this...

Regardless, I wouldn't get "bent out of shape" over this... I already
switched from Sims to HEWM after kicking and screaming that I never
would before (as Monz will attest), so there's no determining that I
won't switch again as need be in the future...

I think the crucial thing to all this is that one has a *CLEAR
LEGEND* in the score so that the poor performer can readily figure
out what all us wackos are really doing...

I'm only sorry that I'm not finding time to continue reading Tuning
Math... there's been quite a bit over there lately that I can
understand and which is of interest to me. But, I have to do some
*fundraising* for our composers' group, so I doubt I'll find time to
catch up with the 2000 remaining messages... :)

Please continue on in peace! No rush!

best,

Joseph

🔗monz <monz@attglobal.net>

hi George,

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:

> [to Joseph Pehrson]
>
> I'm a little puzzled by your recent liking of HEWM notation,
> so I'm asking you to clarify something.
>
> As it presently stands, HEWM and sagittal have the same
> notational semantics as applied to 72-ET (or to state it
> in plain English, there are three pairs of symbols in each
> notation that *stand for* exactly the same things in both
> JI and 72-ET). This is no accident -- in designing sagittal
> Dave and I drew upon a number of very good ideas that have
> already been used by others, and Monz has also put some
> very good things into HEWM.

thanks for the acknowledgement.

> So whatever you may favor in one notation over the other
> is purely a matter of the appearance of the symbols themselves.

George, i had already established this with Joe two years ago.

HEWM, Sims, and Herf 72edo notations all work the same way.
the only difference between them is choice of symbols.

> The problem that you are having with sagittal is in the
> symbols for 2 degrees, but I find it very surprising that
> you haven't had anything negative to say about the HEWM
> symbols for 2deg. After all of the things you've said so
> far about symbol confusability, I thought that you would
> surely realize that < and > are just sitting there waiting
> to be confused with one another, in two ways:
>
> 1) The symbols themselves are laterally confusable, i.e.,
> they are *exact* lateral mirror images of one another,
> which makes it difficult to tell them apart, and
>
> 2) Even if you can get past reason 1, it's also easy to
> get confused about their meanings in that it's not easy
> to remember which one is *up* and which is *down* (since,
> as others have previously noted, they seem to point
> left and right, not up and down). This is precisely the
> problem you found with the Sims symbols for 3 degrees
> (for which reason 1 does not apply).
>
> I don't understand how you can judge < and > as not confusable,
> while judging /| and |), which are *not* lateral mirror images
> of each other, to be laterally confusable (or is this
> something that you have overlooked).

i'm not Joe Pehrson, but hopefully you'll find my 2 cents useful.

i can understand why you might see < and > as confusable.
but i personally never have any problem with them.

when i see, for example, A< and A> , i think of them in
my mind as "A-less" and "A-greater", and that eliminates
confusion between the two. i remember something i learned
in grade school: that < looks like a crooked "L" for "less than".

to complete the description of the note-names:

A^ and Av are "A-up" and "A-down".

and A+ and A- are, obviously, "A-plus" and "A-minus".

-monz

🔗alternativetuning <alternativetuning@yahoo.com>

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hi George,
>
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
>
> > [to Joseph Pehrson]
> >
> > I'm a little puzzled by your recent liking of HEWM notation,
> > so I'm asking you to clarify something.
> > ...
> > The problem that you are having with sagittal is in the
> > symbols for 2 degrees, but I find it very surprising that
> > you haven't had anything negative to say about the HEWM
> > symbols for 2deg. After all of the things you've said so
> > far about symbol confusability, I thought that you would
> > surely realize that < and > are just sitting there waiting
> > to be confused with one another, in two ways:
> >
> > 1) The symbols themselves are laterally confusable, i.e.,
> > they are *exact* lateral mirror images of one another,
> > which makes it difficult to tell them apart, and
> >
> > 2) Even if you can get past reason 1, it's also easy to
> > get confused about their meanings in that it's not easy
> > to remember which one is *up* and which is *down* (since,
> > as others have previously noted, they seem to point
> > left and right, not up and down). This is precisely the
> > problem you found with the Sims symbols for 3 degrees
> > (for which reason 1 does not apply).
> >
> > I don't understand how you can judge < and > as not confusable,
> > while judging /| and |), which are *not* lateral mirror images
> > of each other, to be laterally confusable (or is this
> > something that you have overlooked).
>
> i'm not Joe Pehrson, but hopefully you'll find my 2 cents useful.
>
> i can understand why you might see < and > as confusable.
> but i personally never have any problem with them.
>
> when i see, for example, A< and A> , i think of them in
> my mind as "A-less" and "A-greater", and that eliminates
> confusion between the two. i remember something i learned
> in grade school: that < looks like a crooked "L" for "less than".

When I originally introduced sagittal here on the tuning list back in
January 2001 I didn't think that this would be a problem either, but
others (notably Dave Keenan) disagreed with me concerning this very
application -- using /| and |\ as the symbols for 1deg and 2deg72.
Once Dave and I began working together on improvements to the
notation, we found that by having |) as a new symbol for the 7-comma
(one which is not an exact lateral mirroring of the 5-comma symbol),
we could then use |\ for another interval -- the 55 comma (54:55, the
difference between the 11-diesis and the 5-comma), a symbol that
would not occur in the most commonly used tunings. We therefore made
it a point to minimize lateral confusability in the simplest
applications.

Unfortunately, even though /| and |) are not exact mirror images of
one another, Joseph still does not think that they are sufficiently
different in appearance from one another to eliminate confusion.
That being the case, I could not see how he could possibly accept
having < and > in the same symbol set, so I asked for clarification.
In his reply:
/tuning/topicId_47880.html#47927
he said:

> These symbols are simply the ascii *shorthand* for the notation.
>
> The actual symbols I use for the sixthtones are *half arrows*. One
> points upward and the other points downward.
>
> I *only* use half arrows that have flags *pointing to the left.* I
> don't use anything pointing to the right at all. So there is no
> lateral confusability in this...

From this I assume that he is using the half arrow symbols that he
already has in the Sims-Mook 72-ET font (right Joseph?).

Monz, are these these the actual symbols that you intended to
represent with the < and > ascii characters, or has Joseph cobbled
together his own version of HEWM notation?

> to complete the description of the note-names:
>
> A^ and Av are "A-up" and "A-down".
>
> and A+ and A- are, obviously, "A-plus" and "A-minus".

Yes, I have no problem with these. The only reason why Dave and I
didn't use graphic versions of + and - is that we wanted all of the
new symbols to have as their equal-but-opposite counterparts symbols
that are vertically mirrored.

--George

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "alternativetuning"
<alternativetuning@y...> wrote:
> George wrote
>
> >
> > I don't understand how you can judge < and > as not confusable,
while
> > judging /| and |), which are *not* lateral mirror images of each
> > other, to be laterally confusable (or is this something that you
have
> > overlooked).
>
> /| and |) are hard to read because they are not single characters
and

Those are only ascii representations of symbols, and what we were
discussing was reading the actual *symbols* that these represent.
BTW, we *do* have a single-character ascii shorthand for the most
commonly used sagittal symbols. For the 72-ET set these are:

degs of 72-ET: -3 -2 -1 +1 +2 +3
ascii long: \!/ !) \! /| |) /|\
ascii short: v t \ / f ^

> because they are not mirrors, its harder to think of them as a pair.

I'm glad you think so, because they *aren't* supposed to be a pair.
The pairs of sagittal symbols are *vertically* mirrored pairs (see
the above table).

> < and > are single characters, we all know them from maths, and the
> mirroring is analogue to their values.

Yes, that's a good way to remember them. However, the point that is
often raised about these is that laterally mirrored pairs of
characters are apt to be misread as the other character of the pair,
a problem distinct from (and in addition to) that of remembering
which character symbolizes which direction (up or down).

--George

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>

> From this I assume that he is using the half arrow symbols that he
> already has in the Sims-Mook 72-ET font (right Joseph?).
>

***hello George! This is absolutely correct.

> Monz, are these these the actual symbols that you intended to
> represent with the < and > ascii characters, or has Joseph cobbled
> together his own version of HEWM notation?
>

***My understanding is that Monz' ascii symbols are just convenient
representations of the *true* symbols which are from the Sims font.
If not, we have a problem here, since I'm using the Sims symbols for
sixth tones... :)

> > to complete the description of the note-names:
> >
> > A^ and Av are "A-up" and "A-down".
> >
> > and A+ and A- are, obviously, "A-plus" and "A-minus".
>
> Yes, I have no problem with these. The only reason why Dave and I
> didn't use graphic versions of + and - is that we wanted all of
the
> new symbols to have as their equal-but-opposite counterparts
symbols
> that are vertically mirrored.
>

***Yes, Julia Werntz also mentions this as a limitation of HEWM.
It's the only set of symbols that are different from the other two
sets... However, Daniel Wolf makes a good case on the HEWM site
that + and - are well regarded for very small alterations: hence
the syntonic comma...

Joseph

🔗Dave Keenan <d.keenan@bigpond.net.au>

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> ***Well, the answer to this question, George, is that I'm *not* using
> the ascii equivalents < and > in my notation for sixth tones. Not in
> the written score.
>
> These symbols are simply the ascii *shorthand* for the notation.
>
> The actual symbols I use for the sixthtones are *half arrows*. One
> points upward and the other points downward.

I think this is a good move, and while Monz doesn't see the need, at
least I see no reason why he should object.

I hope you are also slanting and broadening the horizontal strokes on
the + and - signs for the twelfthtones, as Daniel Wolf and others do.

See the graphic about halfway thru Monz's
http://sonic-arts.org/dict/hewm.htm
under the heading "Daniel Wolf's version of HEWM".

Below that Dr Wolf explains why:
"For shifts of 81/80 and 80/81, the syntonic comma, I use plus and
minus signs respectively. This follows Erv Wilson, from whom I have
also taken the practice of slanting significantly broadened horizontal
strokes to ca. 45 degrees for increased readability and distinction
from the staff lines. The horizontal stroke on the plus sign slants
upward, that on the minus sign downward, the direction of the slant
intended to increase the sense of direction conveyed by the interval.
(I find that building a bit of redundancy into a notation is not a
significant violation of my need for elegance in a notation)."

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
>
> > From this I assume that he is using the half arrow symbols that
he
> > already has in the Sims-Mook 72-ET font (right Joseph?).
>
> ***hello George! This is absolutely correct.
>
> > Monz, are these these the actual symbols that you intended to
> > represent with the < and > ascii characters, or has Joseph
cobbled
> > together his own version of HEWM notation?
>
> ***My understanding is that Monz' ascii symbols are just convenient
> representations of the *true* symbols which are from the Sims
font.
> If not, we have a problem here, since I'm using the Sims symbols
for
> sixth tones... :)

In other words, the < and > in ascii represent *Sims* symbols (unlike
the other two pairs, -+ and v^, which don't). So there's no reason
why you really need to use this *particular pair* for 2deg72, other
than that it happens to suit your purposes and is already
conveniently available to you in a font.

Dave thought that this "is a good move", but I disagree. Should you
ultimately decide to use HEWM for 72-ET, I think that it would more
helpful to players who are called upon to read notations for other
tunings if you were to make a complete break with the Sims notation
and use a different pair of symbols for 2deg.

> > > to complete the description of the note-names:
> > >
> > > A^ and Av are "A-up" and "A-down".
> > >
> > > and A+ and A- are, obviously, "A-plus" and "A-minus".
> >
> > Yes, I have no problem with these. The only reason why Dave and
I
> > didn't use graphic versions of + and - is that we wanted all of
the
> > new symbols to have as their equal-but-opposite counterparts
symbols
> > that are vertically mirrored.
>
> ***Yes, Julia Werntz also mentions this as a limitation of HEWM.
> It's the only set of symbols that are different from the other two
> sets...

I wouldn't call a difference in appearance a limitation of HEWM, but
rather an advantage.

> However, Daniel Wolf makes a good case on the HEWM site
> that + and - are well regarded for very small alterations: hence
> the syntonic comma...

You just reminded me of a second reason why Dave and I didn't use +
and - for the 5-comma. Aan interval over 21 cents is really not very
small at all -- Dave and I ultimately had to come up with symbols for
10 rational intervals smaller than that, and we wanted to have the
physical size of the symbols correlated to the size of the intervals
they are representing. This is virtually impossible to accomplish if
the 5-comma symbols are physically so small to begin with.

--George

🔗monz <monz@attglobal.net>

hi Joseph and George,

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>

> > The only reason why Dave and I didn't use graphic versions
> > of + and - is that we wanted all of the new symbols to have
> > as their equal-but-opposite counterparts symbols
> > that are vertically mirrored.
> >
>
> ***Yes, Julia Werntz also mentions this as a limitation of
> HEWM. It's the only set of symbols that are different from
> the other two sets... However, Daniel Wolf makes a good
> case on the HEWM site that + and - are well regarded for
> very small alterations: hence the syntonic comma...

with my great preference for logic, i can appreciate this
criticism.

however, # and b look *nothing* like each other, and musicians
have had no problem learning to accept them as indicating
opposite-but-equal pitch inflections.

i personally have absolutely no problem with + and - , ever.
i find that they work very well to indicate the smallest
adjustment that's usually necessary in my music.

... and for those cases where i do need to indicate smaller
adjustments (as in _A Noiseless Patient Spider_), i simply
follow Dan Stearns's suggestion of adding one symbol,
the tilde ~ , to indicate that the adjustment by one of
the 6 regular 72edo symbols is halved. see:

http://sonic-arts.org/dict/144edo.htm

i've gotten quite comfortable with that system.

-monz

🔗alternativetuning <alternativetuning@yahoo.com>

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

/tuning/topicId_47880.html#47947

> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
> > ***Well, the answer to this question, George, is that I'm *not*
using
> > the ascii equivalents < and > in my notation for sixth tones.
Not in
> > the written score.
> >
> > These symbols are simply the ascii *shorthand* for the notation.
> >
> > The actual symbols I use for the sixthtones are *half arrows*.
One
> > points upward and the other points downward.
>
> I think this is a good move, and while Monz doesn't see the need, at
> least I see no reason why he should object.
>
> I hope you are also slanting and broadening the horizontal strokes
on
> the + and - signs for the twelfthtones, as Daniel Wolf and others
do.
>

***Hi Dave,

I wish I could, but I don't have a font for that (hint, hint, hint :)

I'm just using the endemic plusses and minuses in Sibelius which,
admittedly, isn't as good, since it gets messed up with the ledger
lines...

best,

Joseph

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:

/tuning/topicId_47880.html#47948

> In other words, the < and > in ascii represent *Sims* symbols
(unlike
> the other two pairs, -+ and v^, which don't).

***But, George, the other ascii symbols represent other symbols,
too. The v^ are big arrows like you have in Sagittal and the - and +
would represent, ideally, the Wolf symbols (but they don't, since I
don't yet have a font for that...)

So there's no reason
> why you really need to use this *particular pair* for 2deg72, other
> than that it happens to suit your purposes and is already
> conveniently available to you in a font.
>

***True...

> Dave thought that this "is a good move", but I disagree. Should
you
> ultimately decide to use HEWM for 72-ET, I think that it would more
> helpful to players who are called upon to read notations for other
> tunings if you were to make a complete break with the Sims notation
> and use a different pair of symbols for 2deg.
>

***Well, lay it on me bro... (just joking...)

Seriously, I await further developments. My mind is entirely open...
in fact, as some have noticed, a bit *too* open...

best,

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

/tuning/topicId_47880.html#47949

> hi George,
>
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
>
> > [regarding Joseph Pehrson]
> >
> > From this I assume that he is using the half arrow symbols
> > that he already has in the Sims-Mook 72-ET font (right Joseph?).
> >
> > Monz, are these these the actual symbols that you intended to
> > represent with the < and > ascii characters, or has Joseph
> > cobbled together his own version of HEWM notation?
>
>
> in my scores, i have used both the actual < and > symbols,
> and also the half-arrows pointing down and up respectively.
>
> i've generally preferred the half-arrows for actual score
> notation, but from constant use of < and > in emails it's
> become easier for me to use them in scores as well.
>
> another advantage they have is that they're more clearly
> differentiated from the regular arrows which go with the
> quarter-tone, but even here, i've occassionally begun
> using the v and ^ symbols (i.e., the arrow-tops) in scores,
> without the arrow-stems.
>

***Hi Monz,

Well, here we part company. I don't find the ascii HEWM with the
invertible symbols any better than the current only *SLIGHTLY*
differentiated symbols of HEWM....

It's exactly the same problem of lateral ambiguity, as George Secor
has carefully pointed out...

It makes a *big* difference to use those or the Sims half-arrows in
*my* book...

🔗monz <monz@attglobal.net>

hi Joe (should i refer to you as "Joseph", like everyone else?),

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
>
> /tuning/topicId_47880.html#47947
>
> I'm just using the endemic plusses and minuses in Sibelius
> which, admittedly, isn't as good, since it gets messed up
> with the ledger lines...

*aha*! *here's* the big difference why you and i
don't and do (respectively) like the plusses and minuses.

along with the HEWM accidentals, i also prefer
*alternative staff notations* such as

http://sonic-arts.org/dict/12edo-staff.htm

http://sonic-arts.org/dict/qt-staff.htm

where you're content (for practical reasons -- i understand)
to stick with the regular diatonic 5-line staff.

so you have to be concerned with ledger-lines, but
with my alternative staff notations, i don't. on all
of them the idea is to have one ledger-line lying between
stacked staves, with each staff representing one 8ve of pitch.

plusses and minuses are not so confusing on a notation
like that.

Joe/Joseph, direct me to a score of yours that you'd
like to see in my own notations, and i'll try to set aside
time to make the translations.

-monz

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
>
> > I'm just using the endemic plusses and minuses in Sibelius
> > which, admittedly, isn't as good, since it gets messed up
> > with the ledger lines...
>
> *aha*! *here's* the big difference why you and i
> don't and do (respectively) like the plusses and minuses.

Using conventional plus and minus characters on a musical staff isn't
very good, chiefly because the horizontal strokes tend to get lost
when they coincide with *staff* lines.

It would be good to observe that the + and - symbols have their
origin in the slash marks that Bosanquet used to notate the 5-comma
(and multiples thereof), or more specifically, degrees of 53-ET. I
happen to have a photocopy (which Erv Wilson sent me years ago) of
Bosanquet's 1875 treatise on temperament and the generalised
keyboard, which contains examples of his comma notation (which I
believe also appears in Helmholtz's book). The symbols already have
the characteristics that Dave Keenan is recommending. The quasi-
horizontal strokes have a slope (according to the direction of pitch
alteration), and they are thick enough so that staff lines do not
interfere with reading them. Adding the vertical stroke to the comma-
up symbol was a modification that Erv Wilson recommended in order to
distinguish it more readily from the comma-down symbol, with the
resulting resemblance of the two symbols to plus and minus signs
making the direction of alteration immediately obvious.

Dave's recommendations are therefore not modifications at all, but
essential characteristics of the original Bosanquet/Wilson symbols.

--George

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>

/tuning/topicId_47880.html#47970

wrote:
> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> > --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
> wrote:
> >
> > > I'm just using the endemic plusses and minuses in Sibelius
> > > which, admittedly, isn't as good, since it gets messed up
> > > with the ledger lines...
> >
> > *aha*! *here's* the big difference why you and i
> > don't and do (respectively) like the plusses and minuses.
>
> Using conventional plus and minus characters on a musical staff
isn't
> very good, chiefly because the horizontal strokes tend to get lost
> when they coincide with *staff* lines.
>
> It would be good to observe that the + and - symbols have their
> origin in the slash marks that Bosanquet used to notate the 5-
comma
> (and multiples thereof), or more specifically, degrees of 53-ET.
I
> happen to have a photocopy (which Erv Wilson sent me years ago) of
> Bosanquet's 1875 treatise on temperament and the generalised
> keyboard, which contains examples of his comma notation (which I
> believe also appears in Helmholtz's book). The symbols already
have
> the characteristics that Dave Keenan is recommending. The quasi-
> horizontal strokes have a slope (according to the direction of
pitch
> alteration), and they are thick enough so that staff lines do not
> interfere with reading them. Adding the vertical stroke to the
comma-
> up symbol was a modification that Erv Wilson recommended in order
to
> distinguish it more readily from the comma-down symbol, with the
> resulting resemblance of the two symbols to plus and minus signs
> making the direction of alteration immediately obvious.
>
> Dave's recommendations are therefore not modifications at all, but
> essential characteristics of the original Bosanquet/Wilson symbols.
>
> --George

***I sure wish I had a *font* for these. Maybe Dave Keenan can
create them with the font program he has been using for Sagittal. I
don't have a font making program at present...

best,

Joseph

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
>
> /tuning/topicId_47880.html#47948
>
> > In other words, the < and > in ascii represent *Sims* symbols
(unlike
> > the other two pairs, -+ and v^, which don't).
>
> ***But, George, the other ascii symbols represent other symbols,
> too. The v^ are big arrows like you have in Sagittal and the - and
+
> would represent, ideally, the Wolf symbols (but they don't, since I
> don't yet have a font for that...)
>
> > So there's no reason
> > why you really need to use this *particular pair* for 2deg72,
other
> > than that it happens to suit your purposes and is already
> > conveniently available to you in a font.
>
> ***True...
>
> > Dave thought that this "is a good move", but I disagree. Should
you
> > ultimately decide to use HEWM for 72-ET, I think that it would
more
> > helpful to players who are called upon to read notations for
other
> > tunings if you were to make a complete break with the Sims
notation
> > and use a different pair of symbols for 2deg.
>
> ***Well, lay it on me bro... (just joking...)
>
> Seriously, I await further developments. My mind is entirely
open...
> in fact, as some have noticed, a bit *too* open...

Okay, here it is in a nutshell. Dave and I have agreed on a
modification for the 7-comma sagittal symbol pair, the one used for
2deg72, in order to differentiate it more from the 5-comma symbol
pair (for 1deg72) in appearance. We believe that we've succeeded in
our efforts (and have also gathered some evidence to support that),
but (because of certain things you have said) we have reason to
believe that there may still not be enough of a difference to satisfy
you.

Anyway, we're setting that question aside for now. The outcome will
have no effect on the notation of a lot of ETs, since there are many
that can be notated without using both pairs of symbols, and we
expect that others will want to use sagittal notation for that
purpose (or that there might be others that may happen to disagree
with you and will want to use sagittal for applications that do use
*both* pairs of symbols).

Keeping these possibilities in mind, Dave agrees with me (yes, we've
discussed this off-list since yesterday's postings) that it's helpful
for everyone involved if we can avoid having symbols in your HEWM
implementation and in sagittal that do not use the *same* symbols to
mean completely different things. The symbols for 72-ET in the two
notations already have two things in common:

1) The 1deg72 symbols clarify Bosanquet's up and down slashes, / and
\, but by different means; and
2) The 3deg72 symbol (quartertone arrow, which usage is already well
established) is the same for both.

The problem is that the Sims symbol for 2deg72 is virtually identical
to the sagittal 5-comma (or 1deg-72) symbol, so your carrying that
over into HEWM would result in all sorts of confusion for those who
wished (or were required) to read parts (on one occasion) containing
your HEWM graphics and (on another occasion) parts written in
sagittal notation. It's unfortunate that Ezra Sims chose a a half-
arrow symbol with an upward sloping line to represent (in 72) a 7-
comma-up instead of a 5-comma-up (or for that matter, a full arrow to
represent 1deg72 instead of a quartertone, in utter disregard of
established precedents), but there's nothing we (who seek to notate
multiple tunings using the best ideas) can do about that now but walk
away from it.

Inasmuch as you have already discarded the Sims 1deg and 3deg
symbols, I don't think that it would be inappropriate to make a
complete break and use something besides the Sims 2deg72 symbol for
that purpose. In fact, I notice that Monz just said that he would
prefer something having less of a resemblance to the quartertone
arrows (message #47947):

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> ...
> in my scores, i have used both the actual < and > symbols,
> and also the half-arrows pointing down and up respectively.
>
> i've generally preferred the half-arrows for actual score
> notation, but from constant use of < and > in emails it's
> become easier for me to use them in scores as well.
>
> another advantage they have is that they're more clearly
> differentiated from the regular arrows which go with the
> quarter-tone, but even here, i've occassionally begun
> using the v and ^ symbols (i.e., the arrow-tops) in scores,
> without the arrow-stems.
>
> -monz

Here's the bottom line -- what I call the 2/3 solution. Dave and I
now have a new and improved sagittal symbol pair for the 7-comma --
with *curved* flags on the *right* side (as before), for which the
down-arrow even happens to resemble Daniel Wolf's 7-comma-down symbol
(differing only in that the sagittal flag is curved). If Dave were
to provide you with a font containing:
For 1deg: new + and - symbols that fulfill the Bosanquet/Wilson
requirements,
For 2deg: the new (improved) sagittal 7-comma pair, and
For 3deg: the sagittal 11-diesis up and down arrows that you already
have,
would you be willing to give it a try?

This symbol set has 2 out of 3 symbol pairs that are *strictly
correct* for both HEWM and sagittal, and confusability is minimized
both *within* HEWM and *between* HEWM and sagittal.

Comments?

--George

🔗Dave Keenan <d.keenan@bigpond.net.au>

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> ***I sure wish I had a *font* for these. Maybe Dave Keenan can
> create them with the font program he has been using for Sagittal. I
> don't have a font making program at present...

Hi Joseph,

By now you should have taken delivery of one Joseph-Pehrson-special
TrueType font containing sloping + and - signs. I hope you find them
suitable. Let me know if you want them changed in some way.

I remembered how much you dislike the little Bosanquet slashes, so I
have made the otherwise horizontal strokes on the + and - much bigger
and bolder than those, and sloped them at 45 degrees as recommended by
Daniel Wolf.

I've called the font "HEWM S" where the "S" stands for "Sagittal
compatible" and I hope you will consider also using its version of the
sixthtone half-arrows, so that although you are not using Sagittal, at
least we don't have any clashes where the same symbol means different
things in the two systems.

As George pointed out, such clashes are completely unavoidable between
Sims and HEWM (or Sims and Sagittal), and having departed from the
Sims twelfthtone and quartertone symbols there is no real reason to
hold on to its sixthtone symbols.

Placing the HEWM half arrowheads on the right makes them slightly more
distinct from the sloping lines of the + and - symbols, and curving
them (now more pronounced) makes them more distinct from the full
arrows as well as the + and - symbols.

Regards,
-- Dave Keenan
Brisbane, Australia
http://dkeenan.com/

🔗monz <monz@attglobal.net>

hi George,

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:

>
> <huge snip>
>
>
> Here's the bottom line -- what I call the 2/3 solution.
> Dave and I now have a new and improved sagittal symbol
> pair for the 7-comma -- with *curved* flags on the *right*
> side (as before), for which the down-arrow even happens
> to resemble Daniel Wolf's 7-comma-down symbol (differing
> only in that the sagittal flag is curved). If Dave were
> to provide you with a font containing: For 1deg: new + and -
> symbols that fulfill the Bosanquet/Wilson requirements,
> For 2deg: the new (improved) sagittal 7-comma pair, and
> For 3deg: the sagittal 11-diesis up and down arrows that
> you already have, would you be willing to give it a try?
>
> This symbol set has 2 out of 3 symbol pairs that are
> *strictly correct* for both HEWM and sagittal, and
> confusability is minimized both *within* HEWM and
> *between* HEWM and sagittal.
>
> Comments?

sounds terrific. can we see it?

... actually, i think it's high time i put a "sagittal"
definition into the Tuning Dictionary. can you send or
point me to graphics and explanations?

George, i really appreciate the amount of thought you're
putting into the question of microtonal notation. thanks.

-monz

🔗Dave Keenan <d.keenan@bigpond.net.au>

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> sounds terrific. can we see it?

We hope to put up a bitmap version of "HEWM-S" soon, showing the
symbols in the two possible relations to the staff lines. But it's not
ready yet.

> ... actually, i think it's high time i put a "sagittal"
> definition into the Tuning Dictionary. can you send or
> point me to graphics and explanations?

Here's a possible definition:

The word "sagittal" (pronounced "SAJ-i-tl") means "arrow-like". Think
of Sagittarius the archer.

The Sagittal notation system is a comprehensive system for notating
musical pitch in all possible scales and tunings - a universal set of
microtonal accidentals, equally suited to extended just intonation,
equal divisions of whatever, and anything in between. It is called
Sagittal because it uses various arrow-like symbols, pointing up or
down to indicate raising or lowering of pitch.

Sagittal was developed by George Secor and Dave Keenan, with a major
early contribution from Gene Ward Smith, and in cooperation with many
others on the Yahoo Groups tuning and tuning-math.

-end of definition-

As for graphics and explanations, we're still working on them and
you'll eventually be able to direct people to a sagittal website.

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hi George,
>
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
>
> >
> > <huge snip>
> >
> > Here's the bottom line -- what I call the 2/3 solution.
> > Dave and I now have a new and improved sagittal symbol
> > pair for the 7-comma -- with *curved* flags on the *right*
> > side (as before), for which the down-arrow even happens
> > to resemble Daniel Wolf's 7-comma-down symbol (differing
> > only in that the sagittal flag is curved). If Dave were
> > to provide you with a font containing: For 1deg: new + and -
> > symbols that fulfill the Bosanquet/Wilson requirements,
> > For 2deg: the new (improved) sagittal 7-comma pair, and
> > For 3deg: the sagittal 11-diesis up and down arrows that
> > you already have, would you be willing to give it a try?
> >
> > This symbol set has 2 out of 3 symbol pairs that are
> > *strictly correct* for both HEWM and sagittal, and
> > confusability is minimized both *within* HEWM and
> > *between* HEWM and sagittal.
> >
> > Comments?
>
> sounds terrific. can we see it?

Here's a bitmap version of the "2/3 solution" symbols for 72-ET:

/tuning-math/files/secor/notation/HEWM-
S.gif

The latest bitmap version of the 72-ET sagittal symbol set (with
updated 7-comma symbols) may be seen at the bottom of this figure:

/tuning-math/files/secor/kbds/KbDec72.gif

> ...
> George, i really appreciate the amount of thought you're
> putting into the question of microtonal notation. thanks.

I figure that we're all in this together, and if we don't think
everything through in the course of our efforts, then we haven't done
our very best to advance the cause of alternative tunings. If
newcomers to microtonality see a score with a notation that looks
professional in quality, then I think that they are likely to come
away with the impression that ours is a movement to be taken
seriously.

--George