HEWM, relationship to standard western staff notation

Tuning list,

I am looking for information on HEWM notation beyond what I have been
able to locate on the web. On:

http://www.tonalsoft.com/enc/h/hewm.aspx

it seems to give the vector notation for each note name, and then
accidentals up to and including 11-limit just symbols (I'm not
considering the tempered version). This all seems simple enough, but I
have several questions:

1. Does a list exist up to a much higher limit for this notation
(preferably up to 61 limit, but I'll take what I can get). Similarly,
if an algorithm is used to generate any next symbol (like arrow, plus,
or otherwise) and the vector in the series, that would also be
sufficient.

2. Does a peer reviewed, academic, journal have a list such as that,
on the above web page, published for any limit at all (up to 11 or
higher)? I know journal papers such as this exist for the Ben Johnston
notation, but haven't been able to find equivalent info for HEWM from
an academic, peer reviewed, source. Any hints, if such a paper exists?

3. For the 11 limit accidental in HEWM, are the ^ and v symbols
supposed to indicate up and down arrows in an actual music score(I
assume)?

Thanks in advance,

Andreas

Hi Andreas,

--- In tuning@yahoogroups.com, "Andreas Stefik" <stefika@...> wrote:
>
> Tuning list,
>
> I am looking for information on HEWM notation beyond what
> I have been able to locate on the web.

I doubt if you'll find anything else yet.
Aside from the historical background that i give
on my webpage, i was pretty much the inventor of HEWM.

... So at least i should be able to answer your questions.
:)

Let's see ...

> On:
>
> http://www.tonalsoft.com/enc/h/hewm.aspx
>
> it seems to give the vector notation for each note name,
> and then accidentals up to and including 11-limit just
> symbols (I'm not considering the tempered version). This
> all seems simple enough, but I have several questions:
>
> 1. Does a list exist up to a much higher limit for this
> notation (preferably up to 61 limit, but I'll take what
> I can get).

No. I created HEWM specifically to notate 11-limit JI.

My webpage used to have a graphic showing Daniel Wolf's
proposal for accidentals up to the 23-limit, and i've
just hunted that graphic down (thanks to the Wayback
Machine at http://web.archive.org/) and added it back
into my webpage. However, please read what follows below
it, since Dr. Wolf has emphasized that he still supports
the principles embodied in his version of the HEWM notation,
but that he no longer supports all of the symbols exactly
as he proposed them at that time.

The only unequivocal recommendation i can give for a
better accurate notation for JI higher than 11-limit HEWM
(or 23-limit HEWM if you accept Dr. Wolf's symbols)
is Sagittal. See the Sagittal website:

http://dkeenan.com/sagittal/

... in particular, the Xenharmonikon article describing
it in detail:

http://dkeenan.com/sagittal/Sagittal.pdf

> Similarly, if an algorithm is used to generate
> any next symbol (like arrow, plus, or otherwise) and the
> vector in the series, that would also be sufficient.

The was no real algorithm involved in HEWM.
My choice of symbols was dictated by:

3-limit: # and b from standard musical usage;

5-limit: + and - because they seemed to me to be
best suited to the smallest amount of pitch inflection
and also because 5-limit intervals are in some sense
more "basic" and so i wanted the least intrusive symbols
for them;

7-limit: > and < because they somewhat resemble the
7 and inverted-7 used by Ben Johnston, and also because
to me the mathematical ideas of "greater than" and
"less than" seem to indicate something larger than
"plus" and "minus";

11-limit: ^ and v because they somewhat resemble the
up and down arrows that have been used by several
quartertone composers to represent the quartertone
pitches, and also because they seem to me to be a
rotation of the 7-limit symbols and by pointing up
and down seem to indicate a still larger pitch inflection.

Again, i will refer you to Sagittal, for an example of
a microtonal notation which *does* follow an algorithm.
All the little hooks and barbs which make up the Sagittal
arrows have specific pitch meanings, and their combinations
follow rules according to the mathematics of the tunings.

Note that i highly recommend Sagittal, but that i still
strongly support HEWM for 11-limit JI and even moreso
in the tempered version for 72-edo, and with one additional
symbol (suggested by Dan Stearns) for 144-edo; for this
latter see:

http://tonalsoft.com/enc/number/144edo.aspx

One of the main reasons i like HEWM is its ease of use
in ASCII email communication (like this post).

> 2. Does a peer reviewed, academic, journal have a list
> such as that, on the above web page, published for any
> limit at all (up to 11 or higher)? I know journal papers
> such as this exist for the Ben Johnston notation, but
> haven't been able to find equivalent info for HEWM from
> an academic, peer reviewed, source. Any hints, if such
> a paper exists?

None that i know of. Johnston had a long career as a
university professor, and his notation has had a strong
influence on a lot of JI composers and theorists.
All i have to promote my ideas is my website and these
Yahoo groups, which both do the job to some extent, but
it's not the kind of daily contact that a teacher has
with his students for four years.

> 3. For the 11 limit accidental in HEWM, are the ^ and v
> symbols supposed to indicate up and down arrows in an
> actual music score(I assume)?

Yes. I didn't actually say that above, but in my own
scores i tend to add the stem to the arrow-head to make
real arrows.

You can see examples of my own usage of 72-edo and
144-edo HEWM in my handwritten sketch to my piece
_A Noiseless Patient Spider_:

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

-monz
http://tonalsoft.com
Tonescape microtonal music software

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Hi Andreas,

You're welcome.

One thing i should have mentioned in my response to you
but didn't, is that the 72-edo HEWM idea was not original:
it is essentially the same as that used by the "Boston
Microtonal School", as outlined in articles by Ezra Sims
and in Joe Maneri's ear-training book. However, i never
liked Sims's choice of symbols, instead preferring the
ones i chose because of the reasons i stated in my response
to you.

As i said, my version of HEWM was designed originally
for JI, and it was just fortuitous that it happened to
work so well with 72-edo as well. The tilde (~) extension
to 144-edo made it all the better for me.

There has been criticism of my use of 144-edo, because as
a tuning it really doesn't represent JI ratios very well.
But as i've always countered in the past, this usage is
for notational purposes only. It is not meant to suggest
the use of 144-edo as a tuning, but is only as a convenient
notational approximation for whatever actual tuning is used.

I find it very interesting, for example, that 144-edo
gives not only an exact notation for 12-edo, but also
a pretty good approximate notation for 11-edo and 13-edo.

-monz
http://tonalsoft.com
Tonescape microtonal music software

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