Yahoo Tuning Groups Ultimate Backup tuning 99-et in Sagittal

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> What's the word on this? THe Xenharmonikon article doesn't mention
it.

It's not mentioned because Dave & I haven't yet agreed on the best
way to notate it.

Since 99-ET is essentially 7-limit, I would prefer to use 7-limit
symbols, but that poses a few problems. Here's a go at it:

I'll start with the easy positions:

99: ? /| ~|) //| ? )||( ~~|| ||\ ? /||\

/| is 80:81 (5C)
~|) is 48:49 (49S)
//| is 6400:6561 (25S)

Now for the harder ones. For 1deg99, this is my recommendation:

|~ as 243:245 (245C)

|~ is also valid as 729:736 (23C) for 1deg99, which is the primary
definition for the symbol.

For 5deg99 I found these:

'(/| as 392:405 (5:49M)
.(|\ as 27:28 (7L)

'(/| happens to be (IMO) the most obvious symbol to notate a hemi-
fifth, but .(|\ (27:28) is a more popular ratio. The trouble with
these is that they're both accented symbols, and Dave has indicated
(on several occasions) that he doesn't want to use any accented
symbols to notate divisions lower than about 300. If no reasonable
alternative can be found, then I can't see any way to avoid this.
I've been willing to allow it as long as there are not two symbols in
the same set differing only by an accent mark, which would *not
require* the player to *read* the accents.

We would welcome any comments or suggestions you may have.

> Would it be possible to get Sibelius to do it?

You would need the full version of the Sagittal font, which contains
all of the above symbols (available by special request).

--George

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

🔗Hudson Lacerda <hfmlacerda@yahoo.com.br>

Gene Ward Smith escreveu:
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@...> wrote:
> > >>You would need the full version of the Sagittal font, which contains >>all of the above symbols (available by special request).
> > > Has anyone given thought to abc or lilypond support? I think working
> with a markup language would be a lot easier for people like me.
> Hudson Lacerda seems to have done something with microabc, but so far
> I can't seem to get examples.

The glyphs I created you can see in the attachments (if this list allows them). Did you have problems to get them? The are also available online, see the links at the end of this message (they are the same I posted to MMM list). I can add others, if I get samples as images (e.g. png).

If someone convert a Sagittal font set into a PostScript font, it could be used by abcm2ps (really, by ghostscript); the final file format for publishing should be PDF, embedding the font.

BTW, is there any free (as in freedom) version of Sagittal font? If so, I could try converting it to a PostScript font, or, perhaps, even into a set of PostScript operators so that abcm2ps could include them directly in the output PS files. With the PS glyphs, setting the correspondence operator/accidental is trivial. It is unlikely I would do this work on a non-free font.

Regards,
Hudson Lacerda

== abcm2ps ==
sources: <http://moinejf.free.fr>
binaries: <http://abcplus.sf.net#abcm2ps>
See ``sample4.abc'' inside abcm2ps package for the built-in quartertone
accidentals.

== PostScript code for Sagittal 72-ET ==
``microtonal.fmt'' inside:
<http://geocities.yahoo.com.br/hfmlacerda/abc/fmt.zip>
See also the sample files ``microtonalexemplo.abc'' and
``microtonalexemplo.ps''.

== microabc ==
My program to cook the microtonal cakes:
<http://geocities.yahoo.com.br/hfmlacerda/abc/microabc.zip>
Inside the folder ``examples'' you will find... some examples.

== An online example (note guitar accids. vs. clarinet accidentals): ==
<http://geocities.yahoo.com.br/hfmlacerda/abc/24et.pdf>

== A manual to use PostScript with abcm2ps ==
This is in portuguese, but there are several samples of PS code with the
corresponding results:
<http://geocities.yahoo.com.br/hfmlacerda/abc/decomanual.zip>

All the stuff above is released under GNU-GPL.

--
'-------------------------------------------------------------------.
Hudson Lacerda <http://geocities.yahoo.com.br/hfmlacerda/>
*Nï¿½o deixe seu voto sumir! http://www.votoseguro.org/
*Apï¿½ie o Manifesto: http://www.votoseguro.com/alertaprofessores/

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[ Attachment content not displayed ]

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

🔗Hudson Lacerda <hfmlacerda@yahoo.com.br>

Gene Ward Smith escreveu:
> --- In tuning@yahoogroups.com, Hudson Lacerda <hfmlacerda@...> wrote:
> > >>The glyphs I created you can see in the attachments (if this list
> > allows > >>them). > > > I'm not especially interested in them at this point. I need to see the
> ascii abc file for a microtonal piece in something such as 72-et.

I have no such a piece, just because microtonalism was not feasible to me (except for some very few 24-ET pieces) until now. I am writting microabc exactly do make that feasible. I didn't compose any piece so far for example.

But, If you send me a excerpt of a piece (in a human readable format, not a seq file), I may want transcribe it in abc as proof-of-concept.

Hudson

== THE WAR IN IRAQ COSTS ==
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_______________________________________________________
Yahoo! Acesso Grï¿½tis - Internet rï¿½pida e grï¿½tis. Instale o discador agora!
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🔗Dave Keenan <d.keenan@bigpond.net.au>

--- In tuning@yahoogroups.com, Hudson Lacerda <hfmlacerda@...> wrote:
> If someone convert a Sagittal font set into a PostScript font, it
could
> be used by abcm2ps (really, by ghostscript); the final file format
for
> publishing should be PDF, embedding the font.

Hi Hudson,

I laid out the Sagittal font using "Font Creator" from High-Logic.
I'm afraid I know very little about the internals of font files or
different formats. It is TrueType at
http://dkeenan.com/sagittal
I can tell you that there is no hinting (more's the pity for small
point sizes when shown on screen).

> BTW, is there any free (as in freedom) version of Sagittal font?

Can you explain what this means? We intend it to be completely free.
You can do what you like with it, we only ask that you acknowledge
the source (the above URL) and authors (George Secor and Dave
Keenan) in any derivative work.

I'd be happy to help you in any way we can, to convert it to other
useful forms. We would be happy to put them on the Sagittal website
and acknowledge your contribution there.

Thanks.
-- Dave Keenan

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

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@...> wrote:
> Since 99-ET is essentially 7-limit, I would prefer to use 7-limit
> symbols, but that poses a few problems. Here's a go at it:
>
> I'll start with the easy positions:
>
> 99: ? /| ~|) //| ? )||( ~~|| ||\ ? /||\
>
> /| is 80:81 (5C)
> ~|) is 48:49 (49S)
> //| is 6400:6561 (25S)

No arguments there.

> Now for the harder ones. For 1deg99, this is my recommendation:
>
> |~ as 243:245 (245C)
>
> |~ is also valid as 729:736 (23C) for 1deg99, which is the primary
> definition for the symbol.

Weeeell, I prefer

~| as 1024:1029 (343k)

also valid in primary role 2176:2187 (17k)

I prefer ~| for 1deg99 because
(a) it's in the subset of more commonly used symbols we
call "Athenian", and
(b) the left boathook (wavy flag) is also in the ~|) symbol for
3deg99 and so we minimise the number of different flags, and
(c) once it is realised that in this tuning the 5-comma /| is also
the 7-comma |) (but the symbol for the lower prime takes precedence)
then one can see 1 + 2 = 3 in ~| + /| = ~|)

> For 5deg99 I found these:
>
> '(/| as 392:405 (5:49M)
> .(|\ as 27:28 (7L)
>
> '(/| happens to be (IMO) the most obvious symbol to notate a hemi-
> fifth, but .(|\ (27:28) is a more popular ratio. The trouble with
> these is that they're both accented symbols, and Dave has
indicated
> (on several occasions) that he doesn't want to use any accented
> symbols to notate divisions lower than about 300.

I still feel that way. Because what happens when you have only one
accented symbol? The accent gets dropped. And you're left with an
invalid symbol.

> If no reasonable
> alternative can be found, then I can't see any way to avoid this.
> I've been willing to allow it as long as there are not two symbols
in
> the same set differing only by an accent mark, which would *not
> require* the player to *read* the accents.

Although 99-ET isn't 11-limit consistent, I think the boy who told
the Emperor he had no clothes would tell us to use the arrow /|\ and
be done with it.

What's needed is a semisharp symbol and /|\ has been a semisharp
symbol for a lot longer than it has been an 11-diesis symbol, and of
course both predate sagittal.

We can just weasel on the 11 limit interpretation because it's at
least valid for notating a 6:11 even though not an 8:11 or a 9:11.

-- Dave Keenan

🔗Carl Lumma <clumma@yahoo.com>

🔗Hudson Lacerda <hfmlacerda@yahoo.com.br>

Dave Keenan escreveu:
[...]
> Hi Hudson,

Hi Dave.

> > I laid out the Sagittal font using "Font Creator" from High-Logic. > I'm afraid I know very little about the internals of font files or > different formats.

I know nearly nothing about font creation (I have a copy of ``fontforge'', but without the needed know-how, it is not very useful).

Beside, I know just a bit about sagittal notation. I've read some online articles, and I like to browse Scala notation window, but I have no "formal" knowledge on that notation.

> It is TrueType at
> http://dkeenan.com/sagittal

I have already a version of SagittalSAT.ttf which I donlwoad in 2005-05-02. What font would you suggest?

> I can tell you that there is no hinting (more's the pity for small > point sizes when shown on screen).

I think this is not a problem when using it in PostScript. (I did convert it to .pfa so that I can analyse it later and try embed in the output of abcm2ps; .ttf is not useful to me).

BTW, it is possible (although not optimal) to use .ttf fonts with abcm2ps. Guido Gonzato's ``ABC Plus'' manual tells how to do it:
<http://abcplus.sourceforge.net/#ABCGuide>

> > >>BTW, is there any free (as in freedom) version of Sagittal font? > > > Can you explain what this means? We intend it to be completely free. > You can do what you like with it, we only ask that you acknowledge > the source (the above URL) and authors (George Secor and Dave > Keenan) in any derivative work.

There is no such a statement in a visible place. I didn't do any conversion to .pba before exactly because I thought I had not any authorization for that. However, hacking the file just now I found this strings:

<<<<
Typeface ï¿½ Dave Keenan & George Secor. 2003. All Rights Reserved. http://dkeenan.com/sagittal/RegularSagittal:1.091.09 August 3, 2004Sagittal is a system of accidentals for microtonal music Free for non-commercial use
>>>>

For "free" I mean DFSG compilant <http://www.debian.org/social_contract>.
There is one conflictant condition: "non-comercial" use. I release microabc and other stuff of mine under GNU-GPL <http://www.gnu.org/copyleft/gpl.html>, which allows comercial use beside redistributions and modifications.
Therefore, I cannot distribute my converted version of a Sagittal font (or any derivative work) along the GPL stuff without an explicit consent of the authors of the font. People interested on it should to download the font from your site (and maybe do the conversion by themselves). This is not a big problem, of course, but I would prefer to dedicate to 100% free works.

> > I'd be happy to help you in any way we can, to convert it to other > useful forms. We would be happy to put them on the Sagittal website > and acknowledge your contribution there.
> > Thanks.
> -- Dave Keenan

I will try with .pba and figure a way to use it along abcm2ps. It seems easy to do, let's to check. If a have success, I will send you the .pba font so that people can donwload it. (You could try to do that conversion too, here I got warnings from fontforge.)

Cheers,
Hudson

== THE WAR IN IRAQ COSTS ==
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_______________________________________________________ Yahoo! doce lar. Faï¿½a do Yahoo! sua homepage. http://br.yahoo.com/homepageset.html

🔗Hudson Lacerda <hfmlacerda@yahoo.com.br>

Dave Keenan escreveu:
[...]
> I'd be happy to help you in any way we can, to convert it to other > useful forms. We would be happy to put them on the Sagittal website > and acknowledge your contribution there.
[...]

Dave, I found that the format I need is ``PostScript Type 3.0'', but I got many errors because the glyph names are invalid (the same problem exists for .pfa format).

Here is the error message from fontforge when just viewing the info for the glyph \Y/ :

<<<<
Bad Name

A glyph name must be ASCII, without spaces and may not contain the characters "([{<>}])", and should contain only alphanumerics, periods and underscores.
>>>>

The problem exists for many glyphs, because you've named almost all them using the invalid chars.

It seems that fontforge doesn't allow those chars because such problems on certain output font formats.

== THE WAR IN IRAQ COSTS ==
http://nationalpriorities.org/index.php?option=com_wrapper&Itemid=182
.-------------------------------------------------------------------'
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_______________________________________________________
Yahoo! Acesso Grï¿½tis - Internet rï¿½pida e grï¿½tis. Instale o discador agora!
http://br.acesso.yahoo.com

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, Hudson Lacerda <hfmlacerda@...> wrote:
>
> Gene Ward Smith escreveu:
> > --- In tuning@yahoogroups.com, Hudson Lacerda <hfmlacerda@> wrote:
> >
> >
> >>The glyphs I created you can see in the attachments (if this list
> >
> > allows
> >
> >>them).
> >
> >
> > I'm not especially interested in them at this point. I need to
see the
> > ascii abc file for a microtonal piece in something such as 72-et.
>
> I have no such a piece, just because microtonalism was not feasible
to
> me (except for some very few 24-ET pieces) until now. I am writting
> microabc exactly do make that feasible. I didn't compose any piece
so
> far for example.
>
> But, If you send me a excerpt of a piece (in a human readable
format,
> not a seq file), I may want transcribe it in abc as proof-of-
concept.
>
> Hudson

If you need something short and simple to transcribe, then you might
want to consider the musical example in our Sagittal notation paper
(from Xenharmonikon 18, due out any day now).

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

Figure 6 on page 11 is 7 measures long. It's in just intonation, the
ratios are given below the notated example, and the accidental
symbols are all explained in the accompanying text. If you need a
reference pitch, I suggest C=264 Hz.

--George Secor

🔗Hudson Lacerda <hfmlacerda@yahoo.com.br>

Hi Dave,

I missed the chars / and % from the fontforge error message. Here is the revised message (when viewing the info for \Y/ ):

<<<<
Bad Name

A glyph name must be ASCII, without spaces and may not contain the
characters "([{<>}])/%", and should contain only alphanumerics, periods
and underscores
>>>>

There were also these problems (refered to the current versions of the fonts I just downloaded):

localhost Sagittal $ fontforge Sagittal72.ttf
Copyright (c) 2000-2004 by George Williams.
Executable based on sources from 14:09 18-Dec-2004.
FontForge used to be named PfaEdit.
Warning: Glyph 100 is named ~/)3 which should mean it is mapped to
Unicode U+0000, but Glyph 63 already has that encoding.
Glyph 2 is called ".notdef", a singularly inept choice of name (only glyph 0
may be called .notdef)
FontForge will rename it.

localhost Sagittal $ fontforge SagittalSAT.ttf
Copyright (c) 2000-2004 by George Williams.
Executable based on sources from 14:09 18-Dec-2004.
FontForge used to be named PfaEdit.
Warning: Glyph 196 is named ~/)3 which should mean it is mapped to
Unicode U+0000, but Glyph 159 already has that encoding.
Glyph 2 is called ".notdef", a singularly inept choice of name (only glyph 0
may be called .notdef)
FontForge will rename it.

Could you export the fonts as PostScript Type 3 (.pt3)? If the software you use allows those PS-invalid glyph names, then it should be able to convert the names to export .pt3 files.

Regards,
Hudson

== THE WAR IN IRAQ COSTS ==
http://nationalpriorities.org/index.php?option=com_wrapper&Itemid=182
.-------------------------------------------------------------------'
--

_______________________________________________________
Yahoo! Acesso Grï¿½tis - Internet rï¿½pida e grï¿½tis. Instale o discador agora!
http://br.acesso.yahoo.com

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

I am honored that you mentioned my name dear George and Dave, despite the
fact that I couldn't contribute much to Sagittal Notation. I applaud your
success.

Cordially,
Ozan

----- Original Message -----
From: "George D. Secor" <gdsecor@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 08 ï¿½ubat 2006 ï¿½arï¿½amba 20:19
Subject: [tuning] Re: 99-et in Sagittal

> --- In tuning@yahoogroups.com, Hudson Lacerda <hfmlacerda@...> wrote:
> >
> > Gene Ward Smith escreveu:
> > > --- In tuning@yahoogroups.com, Hudson Lacerda <hfmlacerda@> wrote:
> > >
> > >
> > >>The glyphs I created you can see in the attachments (if this list
> > >
> > > allows
> > >
> > >>them).
> > >
> > >
> > > I'm not especially interested in them at this point. I need to
> see the
> > > ascii abc file for a microtonal piece in something such as 72-et.
> >
> > I have no such a piece, just because microtonalism was not feasible
> to
> > me (except for some very few 24-ET pieces) until now. I am writting
> > microabc exactly do make that feasible. I didn't compose any piece
> so
> > far for example.
> >
> > But, If you send me a excerpt of a piece (in a human readable
> format,
> > not a seq file), I may want transcribe it in abc as proof-of-
> concept.
> >
> > Hudson
>
> If you need something short and simple to transcribe, then you might
> want to consider the musical example in our Sagittal notation paper
> (from Xenharmonikon 18, due out any day now).
>
> http://dkeenan.com/sagittal/Sagittal.pdf
>
> Figure 6 on page 11 is 7 measures long. It's in just intonation, the
> ratios are given below the notated example, and the accidental
> symbols are all explained in the accompanying text. If you need a
> reference pitch, I suggest C=264 Hz.
>
> --George Secor
>
>
>

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@> wrote:
> > Since 99-ET is essentially 7-limit, I would prefer to use 7-limit
> > symbols, but that poses a few problems. Here's a go at it:
> >
> > I'll start with the easy positions:
> >
> > 99: ? /| ~|) //| ? )||( ~~|| ||\ ? /||\
> >
> > /| is 80:81 (5C)
> > ~|) is 48:49 (49S)
> > //| is 6400:6561 (25S)
>
> No arguments there.
>
> > Now for the harder ones. For 1deg99, this is my recommendation:
> >
> > |~ as 243:245 (245C)
> >
> > |~ is also valid as 729:736 (23C) for 1deg99, which is the
primary
> > definition for the symbol.
>
> Weeeell, I prefer
>
> ~| as 1024:1029 (343k)
>
> also valid in primary role 2176:2187 (17k)
>
> I prefer ~| for 1deg99 because
> (a) it's in the subset of more commonly used symbols we
> call "Athenian", and

Sorry -- it used to be, but not any more. Anyway, |~ is in the
trojan set.

> (b) the left boathook (wavy flag) is also in the ~|) symbol for
> 3deg99 and so we minimise the number of different flags, and

True.

> (c) once it is realised that in this tuning the 5-comma /| is also
> the 7-comma |) (but the symbol for the lower prime takes
precedence)
> then one can see 1 + 2 = 3 in ~| + /| = ~|)

Good observation. Okay, I'll consider this.

> > For 5deg99 I found these:
> >
> > '(/| as 392:405 (5:49M)
> > .(|\ as 27:28 (7L)
> >
> > '(/| happens to be (IMO) the most obvious symbol to notate a hemi-
> > fifth, but .(|\ (27:28) is a more popular ratio. The trouble
with
> > these is that they're both accented symbols, and Dave has
indicated
> > (on several occasions) that he doesn't want to use any accented
> > symbols to notate divisions lower than about 300.
>
> I still feel that way. Because what happens when you have only one
> accented symbol? The accent gets dropped.

What do you mean by this? Is this some sort of rule you came up
with? Or do you mean that it would often be overlooked by a sloppy
or inattentive (i.e., typical) user?

> And you're left with an
> invalid symbol.

True. But let's look at the alternative:

> > If no reasonable
> > alternative can be found, then I can't see any way to avoid
this.
> > I've been willing to allow it as long as there are not two
symbols in
> > the same set differing only by an accent mark, which would *not
> > require* the player to *read* the accents.
>
> Although 99-ET isn't 11-limit consistent, I think the boy who told
> the Emperor he had no clothes would tell us to use the arrow /|\
and
> be done with it.
>
> What's needed is a semisharp symbol and /|\ has been a semisharp
> symbol for a lot longer than it has been an 11-diesis symbol, and
of
> course both predate sagittal.
>
> We can just weasel on the 11 limit interpretation because it's at
> least valid for notating a 6:11 even though not an 8:11 or a 9:11.

In other words, it's okay to use a symbol that's valid 1/3 of the
time, but not one that's completely invalid? This is a joke, yes?
(no? ;-)

Considering that that one of the most basic tenets of Sagittal is
that the symbols have *harmonic* meaning, I have great difficulty
using an 11 symbol for a division in which the 11th harmonic is >48%
error (in terms of a single degree).

I have an idea how we can resolve our difference of opinion -- and I
think it would be best if we were to continue this discussion off-
list.

--George

🔗George D. Secor <gdsecor@yahoo.com>

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

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

> Considering that that one of the most basic tenets of Sagittal is
> that the symbols have *harmonic* meaning, I have great difficulty
> using an 11 symbol for a division in which the 11th harmonic is >48%
> error (in terms of a single degree).

Before you run off to email, I'd like to comment.

When notating 99-edo in 11-limit terms, you can consider that you are
notating an et val, not just an edo. That is, 99 has two reasonable
11-limit vals. One is the rounded val: round99 = <99 157 230 278 342|.
This has commas {121/120, 176/175, 1375/1372, 2200/2187}. Taking the
first three of these commas gives the 68&99, the 11-limit extension of
hemiwuerschmidt in which the octave-equivalent part of the wedgie is
<<16 2 5 9 ...||. The second val is <99 157 230 278 343|. This one has
commas {243/242, 441/440, 896/891, 3136/3125}. Taking the first three
commas here gives 41&58, the 11-limit extension of hemififths which
has an oe part to the wedgie of <<2 25 13 5 ...||. It would make sense
to notate these differently. Both linear temperaments, of course, have
a relatively low complexity and high error for 11, which someone might
want and which certainly could be used.

🔗Hudson Lacerda <hfmlacerda@yahoo.com.br>

George D. Secor escreveu:
[...]
> If you need something short and simple to transcribe, then you might > want to consider the musical example in our Sagittal notation paper > (from Xenharmonikon 18, due out any day now).
> > http://dkeenan.com/sagittal/Sagittal.pdf
> reference pitch, I suggest C=264 Hz.
[...]

Hi George,

Thanks for the suggestion.

I have no a complete set of Sagittal accidentals. So far, I wrote only the 24 glyphs used for SA72, as one can see from the posted links.

If Dave or someone else have success in converting the Sagittal .ttf fonts into .pt3, the things would be easier, no mention the higher quality of the glyphs (I am not very able to draw PS graphics).

Now, concerning to abcm2ps, here is a microtonal introduction and reflexion on possibilities:

In ABC, one have:
= for natural
^ for sharp
_ for flat
^^ for double sharp
__ for double flat.
Example: =C ^F ^^D _A __B

Microtonal accidentals have a ratio (intended to be read as related to 12ET semitone, but this doesn't matter for a printable score):

^/C or ^1/2C is C quartertone sharp.

abcm2ps supports ratio components (numerator and denominator) from 1 to 256. Therefore, one can define up to 65536 accidentals _only for sharp_ (^). Taking in account ^ and _ (__, ^^ and = are also valid, though), we have: 2 * 65536 = _131072_ accidentals.

However, even if one can actually *define* such a huge number of different accidentals, currently abcm2ps allows to *use* up to _32_ microtonal accidentals in a single piece of music (common accidendals ^ ^^ = _ __ are not taken in account).

(One can have several pieces in a single ABC file, and it is possible to redefine the accidentals inside a piece.)

Therefore, having available 32 accidentals, one can divide a whole tone in _32_ parts *without* use enharmonic notes (the common ^ ^^ = _ __ are still available, then the total can be actually 37 parts).

But lets suppose one wants to use 16 sharp accidentals plus 16 flat accidentals:

=C ^1/C ^2/C ^3/C ^4/C ... ^15/C ^16/C =D
=C _16/D _15/D _14/D _13/D ... _2/D _1/D =D

One can notate this way, for instance, an ET with 17 degrees for a whole tone, plus, to say, 11 degrees for a semitone:

2*11 + 5*17 = 22 + 85 = 107 ET

The maximum number of divisions depends upon the use of commons accidentals ^, ^^, _ and __ (providing 4 more divisions a of a whole tone) and the number of steps defined for a semitone.

The difficult part, then, doesn't lie in abcm2ps microtone limitations (it is free software, one can just increase the value for the MAXMICRO in `abcparse.c' and make a few more needed adjusts), but in the music to be notated instead. For instance, clusters like

[=C^/C^C_/D=D^D]

will be a pain in the neck to adjust graphically, independently of the used music notation program, even to notate by hand in a paper.

If someone have an algorithm to optimize the relative positions of the noteheads (and accidentals) for such complex clusters and chords, let me know, or send it directly to Jean-Franï¿½ois Moine (abcm2ps' maintainer). Then, soon or later, abcm2ps will can handle automatically such problems, avoiding the difficult manual adjustments.

Regards,
Hudson

== THE WAR IN IRAQ COSTS ==
http://nationalpriorities.org/index.php?option=com_wrapper&Itemid=182
.-------------------------------------------------------------------'
--

_______________________________________________________
Yahoo! Acesso Grï¿½tis - Internet rï¿½pida e grï¿½tis. Instale o discador agora!
http://br.acesso.yahoo.com

🔗Hudson Lacerda <hfmlacerda@yahoo.com.br>

George D. Secor escreveu:
> Figure 6 on page 11 is 7 measures long. It's in just intonation, the > ratios are given below the notated example, and the accidental > symbols are all explained in the accompanying text. If you need a > reference pitch, I suggest C=264 Hz.

I did a PostScript sample (see attachments), still missing a couple of glyphs (marked with a red `?').

Here is the ABC code (convert it to PostScript with abcm2ps):

------------------------------------------------------------------------

%%format microtonal

%%scale .9
%%continueall 1
%%maxshrink .999
%%measurenb 1
%%measurefont * 10
%%stretchlast

%%postscript /nt0{gsave 1 0 0 setrgbcolor
%%postscript 4.5 sub M/Helvetica 12 selectfont(?)showc grestore}!

X:6
T: Figure 6
T: A Musical Example in Sagittal Notation
C:Example taken from
C:http://dkeenan.com/sagittal/Sagittal.pdf
K:none
L:1/2
M:none
K:C
%
% 1
%
"(pure)"\
[C_1/12EG] [CF_1/12A] |
%
% 2
%
[C_1/12EG_8/12B] [C_5/12EG_5/12B] |
%
% 3
%
_6/12B/ _5/12A/ [C_1/12EG] &\
[CF] x |
%
% 4
%
[D-^3/12F-_8/12B_1/12B-]/ [DF=AB]/ [C_1/12EGc]/ [C_8/12EG=B]/ |
%
% 5
%
=B/ A/ [G,_2/12FG_1/12B] &\
[D^5/12F] x |
%
% 6
%
_2/12F _1/12E/ D/ &\
[C-G-'c-']2 |
%
% 7
%
_1/12E2 &\
[CGc]2 |]

------------------------------------------------------------------------

== THE WAR IN IRAQ COSTS ==
http://nationalpriorities.org/index.php?option=com_wrapper&Itemid=182
.-------------------------------------------------------------------'
--

[ Attachment content not displayed ]

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

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@> wrote:
>
> > Considering that that one of the most basic tenets of Sagittal is
> > that the symbols have *harmonic* meaning, I have great difficulty
> > using an 11 symbol for a division in which the 11th harmonic is
>48%
> > error (in terms of a single degree).
>
> Before you run off to email, I'd like to comment.

On second thought, perhaps it's better to continue the discussion
here.

> When notating 99-edo in 11-limit terms, you can consider that you
are
> notating an et val, not just an edo. That is, 99 has two reasonable
> 11-limit vals. One is the rounded val: round99 = <99 157 230 278
342|.
> This has commas {121/120, 176/175, 1375/1372, 2200/2187}. Taking the
> first three of these commas gives the 68&99, the 11-limit extension
of
> hemiwuerschmidt in which the octave-equivalent part of the wedgie is
> <<16 2 5 9 ...||. The second val is <99 157 230 278 343|. This one
has
> commas {243/242, 441/440, 896/891, 3136/3125}. Taking the first
three
> commas here gives 41&58, the 11-limit extension of hemififths which
> has an oe part to the wedgie of <<2 25 13 5 ...||. It would make
sense
> to notate these differently. Both linear temperaments, of course,
have
> a relatively low complexity and high error for 11, which someone
might
> want and which certainly could be used.

It's the duality or ambiguity of 11 in 99-ET that persuades me to
avoid symbols involving 11.

I wrote:

> I have an idea how we can resolve our difference of opinion ...

What I have in mind is first to determine a symbol sequence for 198-
ET (which is 15-limit consistent) in such a way that the even-
numbered symbols in the sequence would be valid for 99-ET. Here's
the 11-limit set I came up with:

198: )|( |~ ~~| /| |\ ~|) (|( //| /|\ '(/| (|)

)|( is 891:896 (7:11k)
|~ is 243:245 (245C), also valid as 729:736 (23C)
~~| is 98:99 (11:49C), also valid as 99:100 (11:25C)
/| is 80:81 (5C)
|\ is 54:55 (55C)
~|) is 48:49 (49S)
(|( is 44:45 (5:11S), also valid as 1664:1701 (7:13S)
//| is 6400:6561 (25S)
/|\ is 32:33 (11M)
'(/| is 392:405 (5:49M)
(|) is 704:729 (11L)

Since /|\ is the obvious choice for 9deg198, it should be eliminated
from the 99-ET set. ~| is eliminated as 1deg99, since it would be
3deg198.

In the above list there are a pair of alternatives:

Instead of '(/|: '(|\ as 27:28 (7L)
Instead of ~~|: ~|( as 4096:4131 (17C)

Both of the alternatives have the advantage of substituting athenian-
level symbol cores for non-athenian ones. Each also has the
disadvantage of being the wrong size relative to an adjacent symbol.
Another reason unfavorable to 17C is that 198 is not consistent at
the 17 limit (relative to 9, 13, and 15). Anyway, I'm open to
considering either of them.

Dave, I still need to give a better reply to your point that:

> ... what happens when you have only one
> accented symbol? The accent gets dropped. And you're left with an
> invalid symbol.

I have to assume that you're referring to a user who fails to
appreciate the significance of that tiny accent mark, and I would
hope that anyone sophisticated enough to be using a division as
complicated as 99 could be persuaded to be more careful in this
regard. Since we have provided *exact* symbols for ratios as popular
as 7L and 5:49M, which will be very useful for notating some of these
temperament families that Gene has been advocating, I don't think we
should disqualify them from notating ET's in those families because
someone might get sloppy-droppy with the accents.

On another note, I saw that 198 is not 1,5,25-consistent, but I don't
think that's a sufficient reason not to use //| for 8deg, as long as
it works for 99-ET. Alternatives (valid in both 99 and 198) are:

~|\ as 16384:16767 (23S)
'|~) as 112:115 (7:115M)

Either one would raise the notational prime-limit to 23, and I don't
think there is good justification for that.

--George

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

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@...> wrote:
> > > Considering that that one of the most basic tenets of Sagittal
is
> > > that the symbols have *harmonic* meaning, I have great
difficulty
> > > using an 11 symbol for a division in which the 11th harmonic
is
> >48%
> > > error (in terms of a single degree).

Right.

I guess weaseling on the fact that 6:11s work is like saying that a
stopped clock is correct twice a day.

> It's the duality or ambiguity of 11 in 99-ET that persuades me to
> avoid symbols involving 11.
>
> I wrote:
>
> > I have an idea how we can resolve our difference of opinion ...
>
> What I have in mind is first to determine a symbol sequence for
198-
> ET (which is 15-limit consistent) in such a way that the even-
> numbered symbols in the sequence would be valid for 99-ET. Here's
> the 11-limit set I came up with:

That sort of thing can sometimes be useful as a mental tie-breaker,
but it can never be proscriptive as it can never be allowed to cause
one violate the principle of keeping simple things simple. A bigger
ET can't be allowed to "reach down" and complexify a smaller one
just because it's a superset of it and has the same best fifth size.

> 198: )|( |~ ~~| /| |\ ~|) (|( //| /|\ '(/| (|)
>
> )|( is 891:896 (7:11k)
> |~ is 243:245 (245C), also valid as 729:736 (23C)
> ~~| is 98:99 (11:49C), also valid as 99:100 (11:25C)
> /| is 80:81 (5C)
> |\ is 54:55 (55C)
> ~|) is 48:49 (49S)
> (|( is 44:45 (5:11S), also valid as 1664:1701 (7:13S)
> //| is 6400:6561 (25S)
> /|\ is 32:33 (11M)
> '(/| is 392:405 (5:49M)
> (|) is 704:729 (11L)
>
> Since /|\ is the obvious choice for 9deg198, it should be
eliminated
> from the 99-ET set.

Nah. That's not a good reason to eliminate it. If it was, a
helluvalot of simple ETs would have to have more complex notations
than they have now.

The 1,3,9,11-inconsistency is however a good reason to eliminate /|\

> ~| is eliminated as 1deg99, since it would be
> 3deg198.

Again, not a valid reason to eliminate it.

> In the above list there are a pair of alternatives:
>
> Instead of '(/|: '(|\ as 27:28 (7L)

The nice thing about '(/| is that the down version .(\! looks like a
bit like a (accented) backwards flat, a well known semisharp symbol.

The nice things about '(|\ are the athenian core and the lower odd-
limit. I'll go for this one for 5deg99 and accept that we have to
use an accented symbol.

> Instead of ~~|: ~|( as 4096:4131 (17C)

I'm happy to wait until someone really needs it before we
standardise a notation for 198-ET.

> Both of the alternatives have the advantage of substituting
athenian-
> level symbol cores for non-athenian ones.

Yes.

> Each also has the
> disadvantage of being the wrong size relative to an adjacent
symbol.

Not in 99-ET. The sequence //| '(|\ )||( is in the standard
(Pythagorean) order.

> Another reason unfavorable to 17C is that 198 is not consistent at
> the 17 limit (relative to 9, 13, and 15). Anyway, I'm open to
> considering either of them.
>
> Dave, I still need to give a better reply to your point that:
>
> > ... what happens when you have only one
> > accented symbol? The accent gets dropped. And you're left with
an
> > invalid symbol.
>
> I have to assume that you're referring to a user who fails to
> appreciate the significance of that tiny accent mark,

Yes. You got it right.

> and I would
> hope that anyone sophisticated enough to be using a division as
> complicated as 99 could be persuaded to be more careful in this
> regard. Since we have provided *exact* symbols for ratios as
popular
> as 7L and 5:49M, which will be very useful for notating some of
these
> temperament families that Gene has been advocating, I don't think
we
> should disqualify them from notating ET's in those families
because
> someone might get sloppy-droppy with the accents.

OK. I'll go along with that, and favour the 7L symbol.

> On another note, I saw that 198 is not 1,5,25-consistent, but I
don't
> think that's a sufficient reason not to use //| for 8deg, as long
as
> it works for 99-ET. Alternatives (valid in both 99 and 198) are:
>
> ~|\ as 16384:16767 (23S)
> '|~) as 112:115 (7:115M)
>
> Either one would raise the notational prime-limit to 23, and I
don't
> think there is good justification for that.

I agree.

I still like ~| for 1deg99. Did you say its primary role isn't 17k
any more? How did I miss that! I think I must have misread or
misinterpreted something you wrote, or you miswrote.

I think all those reasons I gave for favouring it still stand.

-- Dave Keenan

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@> wrote:
> > > > Considering that that one of the most basic tenets of
Sagittal is
> > > > that the symbols have *harmonic* meaning, I have great
difficulty
> > > > using an 11 symbol for a division in which the 11th harmonic
is >48%
> > > > error (in terms of a single degree).
>
> Right.
>
> I guess weaseling on the fact that 6:11s work is like saying that a
> stopped clock is correct twice a day.

Yep, you got it!

> > It's the duality or ambiguity of 11 in 99-ET that persuades me to
> > avoid symbols involving 11.
> >
> > I wrote:
> >
> > > I have an idea how we can resolve our difference of opinion ...
> >
> > What I have in mind is first to determine a symbol sequence for
198-
> > ET (which is 15-limit consistent) in such a way that the even-
> > numbered symbols in the sequence would be valid for 99-ET.
Here's
> > the 11-limit set I came up with:
>
> That sort of thing can sometimes be useful as a mental tie-breaker,

Yes.

> but it can never be proscriptive as it can never be allowed to
cause
> one violate the principle of keeping simple things simple. A bigger
> ET can't be allowed to "reach down" and complexify a smaller one
> just because it's a superset of it and has the same best fifth size.

Okay. So then, ...

> > 198: )|( |~ ~~| /| |\ ~|) (|( //| /|\ '(/| (|)
> >
> > )|( is 891:896 (7:11k)
> > |~ is 243:245 (245C), also valid as 729:736 (23C)
> > ~~| is 98:99 (11:49C), also valid as 99:100 (11:25C)
> > /| is 80:81 (5C)
> > |\ is 54:55 (55C)
> > ~|) is 48:49 (49S)
> > (|( is 44:45 (5:11S), also valid as 1664:1701 (7:13S)
> > //| is 6400:6561 (25S)
> > /|\ is 32:33 (11M)
> > '(/| is 392:405 (5:49M)
> > (|) is 704:729 (11L)
> >
> > Since /|\ is the obvious choice for 9deg198, it should be
eliminated
> > from the 99-ET set.
>
> Nah. That's not a good reason to eliminate it. If it was, a
> helluvalot of simple ETs would have to have more complex notations
> than they have now.

Perhaps, but it might carry some weight if you have another reason to
go along with it, namely:

> The 1,3,9,11-inconsistency is however a good reason to eliminate /|\

> > ~| is eliminated as 1deg99, since it would be
> > 3deg198.
>
> Again, not a valid reason to eliminate it.
>
> > In the above list there are a pair of alternatives:
> >
> > Instead of '(/|: '(|\ as 27:28 (7L)
>
> The nice thing about '(/| is that the down version .(\! looks like
a
> bit like a (accented) backwards flat, a well known semisharp symbol.
>
> The nice things about '(|\ are the athenian core and the lower odd-
> limit. I'll go for this one for 5deg99 and accept that we have to
> use an accented symbol.

Okay. Hooray!

> > Instead of ~~|: ~|( as 4096:4131 (17C)
>
> I'm happy to wait until someone really needs it before we
> standardise a notation for 198-ET.

I thought that as long as we're looking at one, we might as well do
both.

> > Both of the alternatives have the advantage of substituting
athenian-
> > level symbol cores for non-athenian ones.
>
> Yes.
>
> > Each also has the
> > disadvantage of being the wrong size relative to an adjacent
symbol.
>
> Not in 99-ET. The sequence //| '(|\ )||( is in the standard
> (Pythagorean) order.

Right.

After I sent that, I then realized that |~ (taken as 243:245, 245C)
is technically smaller than ~|( (as 4096:4131, 17C), so there's
really no size discrepancy.

> > Another reason unfavorable to 17C is that 198 is not consistent
at
> > the 17 limit (relative to 9, 13, and 15). Anyway, I'm open to
> > considering either of them.

> ...
> I still like ~| for 1deg99. Did you say its primary role isn't 17k
> any more? ...

No, it's still 17k. What I said was in reply to:

[DK:]
> I prefer ~| for 1deg99 because
> (a) it's in the subset of more commonly used symbols we
> call "Athenian", and

[GS:]
Sorry -- it used to be [in the athenian set], but not any more.
Anyway, |~ is in the trojan set.

> I think all those reasons I gave for favouring it still stand.

I think that reason (a) was the most important one, but it no longer
stands.

The other two are still good:

> (b) the left boathook (wavy flag) is also in the ~|) symbol for
> 3deg99 and so we minimise the number of different flags, and
> (c) once it is realised that in this tuning the 5-comma /| is also
> the 7-comma |) (but the symbol for the lower prime takes
precedence)
> then one can see 1 + 2 = 3 in ~| + /| = ~|)

Those have to be weighed against the reasons for preferring |~ over
~|, which are:

1) Unlike ~|, |~ is in the trojan set (and used in 2 edo's below
100), so it might be considered a more common symbol, and
2) Unlike ~|, |~ can be used in both 99 and 198-ET.

--George

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

Hi Hudson,

Sorry to take so long, but you will now find new versions of the
Sagittal font at
htp://users.bigpond.net.au/d.keenan/sagittal

They now contain an explicit statement that they are free under the
GPL. And all the glyphs now have proper postscript names. Nothing
else has changed, so anyone who is sucessfully using the previous
versions does not need to update them.

Please let me know if you have any other problems converting them to
postscript. And as I mentioned before, I'd be happy to put up the
converted files (and anything else that might help people to use
them) on the Sagittal website, with acknowledgement of your
contribution.

About the two different files SagittalSAT.ttf and Sagittal72.ttf:

They both contain the font called "Sagittal" so you can only install
one of them at a time. They are both subsets of a larger set whose
details have not yet been finalised. The same glyphs have the same
character-codes or mappings in all of these files. We have files
with different subsets to make it easier for people who don't need
the less common symbols, to find the glyphs they need.

SagittalSAT.ttf is a subset containing the union of the subsets
described in our Xenharmonikon paper as Spartan, Athenian and Trojan.

Sagittal72.ttf contains only those symbols needed to notate 72-ET (a
subset of the Spartan set). These also notate many common ETs below
72, 5-odd-limit JI and harmonics to the 12th.

To notate the musical example in the paper you will need the full
Spartan set and so you will need to use the SagittalSAT.ttf file.

Regards,
-- Dave Keenan