Yahoo Tuning Groups Ultimate Backup tuning HEWM and 96-EDO , and a problem with 144-EDO

Hi monzo

as you have used HEWM for 31 and 41-EDO in http://www.tonalsoft.com/enc/c/canasta.aspx
i think it is also useful for 96-EDO because function of 12.5 is like 16.6666 to produce major third of near 5/4 and so:
b # semitone 100

v ^ 1/4-tone 50

< > 3/16-tone 37.5 (4.16666 greater than one degree of 72-EDO)

?????? 1/8-tone 25

- + 1/16-tone 12.5 (4.16666 less than one degree of 72-EDO)

but may be ++ and --(or=) are useful for 25 cent so for 0 to 100cent we can have:

100 C#,Db

87.5 C#-,Db-

75 C#--(or C#=),C<+,Db--(orDb=),Db<+

62.5 C#<,Db<

50 C^,C#v,Dbv

37.5 C>

25 C++,C>-

12.5 C+

0 C

what is your idea about 96 and HEWM?

and also a problem about 144-EDO sign of ~:

for some degrees like 1 , it shows a reduction of 8&1/3 cent from degree of 2 ,but for 11th degree it shows an increase of 8&1/3 cent from 10th degree?

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

Shaahin Mohajeri

Tombak Player & Researcher , Microtonal Composer

My web site?? ???? ????? ?????? <http://240edo.googlepages.com/>

My farsi page in Harmonytalk ???? ??????? ?? ??????? ??? <http://www.harmonytalk.com/mohajeri>

Shaahin Mohajeri in Wikipedia ????? ?????? ??????? ??????? ???? ???? <http://en.wikipedia.org/wiki/Shaahin_mohajeri>

________________________________

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of monz
Sent: Thursday, May 31, 2007 8:33 AM
To: tuning@yahoogroups.com
Subject: [tuning] Re: HEWM, relationship to standard western staff notation

Hi Andreas,

--- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.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 <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/ <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/ <http://dkeenan.com/sagittal/>

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

http://dkeenan.com/sagittal/Sagittal.pdf <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 <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 <http://sonic-arts.org/monzo/spider/spider.htm>

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

🔗monz <monz@tonalsoft.com>

Hi Mohajeri,

--- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@...> wrote:
>
> Hi monzo
>
> as you have used HEWM for 31 and 41-EDO in
http://www.tonalsoft.com/enc/c/canasta.aspx
> i think it is also useful for 96-EDO because function
> of 12.5 is like 16.6666 to produce major third of near
> 5/4 and so:
> b # semitone 100
>
> v ^ 1/4-tone 50
>
> < > 3/16-tone 37.5 (4.16666 greater than
> one degree of 72-EDO)

You mean two degrees of 72-edo.

>
> ?????? 1/8-tone 25
>
> - + 1/16-tone 12.5 (4.16666 less than
> one degree of 72-EDO)
>
> but may be ++ and --(or=) are useful for 25 cent so
> for 0 to 100cent we can have:
>
> 100 C#,Db
>
> 87.5 C#-,Db-
>
> 75 C#--(or C#=),C<+,Db--(orDb=),Db<+
>
> 62.5 C#<,Db<
>
> 50 C^,C#v,Dbv
>
> 37.5 C>
>
> 25 C++,C>-
>
> 12.5 C+
>
> 0 C
>
> what is your idea about 96 and HEWM?

It seems to me like trying to make a square peg
fit into a round hole. 72-edo and 96-edo only
have the quarter-tones and semitones in common,
all the other degrees don't match.

Since i designed HEWM for JI, the + and - signs
are meant to represent the syntonic-comma pitch
inflection, ~21.5 cents. The 25-cent interval of
96-edo is fairly close to that, and so it should
have the symbols which represent the syntonic-comma.
Then you need something else for the 12.5-cent inflection.

Additionally, i don't like the double ++ and --
because i think they look too much like the single
symbols. My recommendation for adapting HEWM to
96-edo is to use + and - for 25-cent and to find
another pair for 12.5-cent, perhaps the / and \
which others like a lot.

> and also a problem about 144-EDO sign of ~:
>
> for some degrees like 1 , it shows a reduction
> of 8&1/3 cent from degree of 2, but for 11th degree
> it shows an increase of 8&1/3 cent from 10th degree?
>
> http://www.tonalsoft.com/enc/number/144edo.aspx

Yes, when Dan Stearns first presented the idea to me
i found that confusing too. But after using it for
awhile, it makes sense and you get used to it.

The tilde ~ represents a 1/2 reduction of whatever
other accidental it accompanies. Therefore, for degree 1
it appears with the plus sign ~+ and means an increase
of 1/2 of the plus sign, and for degree 11 it appears
with the minus sign and means a decrease of 1/2 of
the minus sign.

The six pairs of regular accidentals appear in pairs
which increase or decrease the pitch, so the tilde symbol
has the same action but only half as much.

I like it because with the addition of only one more
symbol it increases the notation resolution from 72-edo
all the way to 144-edo.

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

🔗Gene Ward Smith <genewardsmith@sbcglobal.net>

🔗Mohajeri Shahin <shahinm@kayson-ir.com>

hi monz

As you have used E-,E and E+ for 383.3333 , 400 and 416.6666 in http://www.tonalsoft.com/enc/number/72edo.aspx ( what i see is - is used for -16.6666 from 400 cent and + for 16.6666 from 400 cent , + and - are using for 1/12 tone changes although you have mentioned about JI basis of HEWM in http://www.tonalsoft.com/enc/h/hewm.aspx),but i think it is also possible considering + and - for 1/16 tone to get 387.5 , 400 and 412.5.
and about 25 cent, if considering 400-25=375 , then what about my major third of 387.5 cent in 96-EDO?May be you considered 412.5-25=387.5?

Shaahin Mohajeri

Tombak Player & Researcher , Microtonal Composer

My web site?? ???? ????? ?????? <http://240edo.googlepages.com/>

My farsi page in Harmonytalk ???? ??????? ?? ??????? ??? <http://www.harmonytalk.com/mohajeri>

Shaahin Mohajeri in Wikipedia ????? ?????? ??????? ??????? ???? ???? <http://en.wikipedia.org/wiki/Shaahin_mohajeri>

________________________________

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of monz
Sent: Thursday, May 31, 2007 8:35 PM
To: tuning@yahoogroups.com
Subject: [tuning] Re: HEWM and 96-EDO , and a problem with 144-EDO

Hi Mohajeri,

--- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com> , "Mohajeri Shahin" <shahinm@...> wrote:
>
> Hi monzo
>
> as you have used HEWM for 31 and 41-EDO in
http://www.tonalsoft.com/enc/c/canasta.aspx <http://www.tonalsoft.com/enc/c/canasta.aspx>
> i think it is also useful for 96-EDO because function
> of 12.5 is like 16.6666 to produce major third of near
> 5/4 and so:
> b # semitone 100
>
> v ^ 1/4-tone 50
>
> < > 3/16-tone 37.5 (4.16666 greater than
> one degree of 72-EDO)

You mean two degrees of 72-edo.

It seems to me like trying to make a square peg
fit into a round hole. 72-edo and 96-edo only
have the quarter-tones and semitones in common,
all the other degrees don't match.

Yes, when Dan Stearns first presented the idea to me
i found that confusing too. But after using it for
awhile, it makes sense and you get used to it.

The six pairs of regular accidentals appear in pairs
which increase or decrease the pitch, so the tilde symbol
has the same action but only half as much.

I like it because with the addition of only one more
symbol it increases the notation resolution from 72-edo
all the way to 144-edo.

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