Tartini Plus

For +8 you are referring to the double-sharp labeled "new2" (the "2"
indicating that it appears in Tartini-plus set #2), right? If so, I
will then incorporate that into Tartini-plus set #1. (I expect that
Dave will also be putting it in the Sagittal font.)

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

I would indeed like `new2` double sharp to appear in Tartini-Plus One.

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

> For number seven, you may like to consider an asterisk.

We spent a lot of time on this one trying to make it look more like
an "X" (double-sharp) with a backslash (5-comma-down) through it
rather than an asterisk, so I would ask you to reconsider this.

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

Ah, I see what you mean. The N kind of double sharp in Tartini Plus Two looks nice. But it could be a lot better like % (reversed-dots squared and filled). Also the size of `new2 double shaprs` could be reduced by a notch.

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

As long as we're talking about the double-sharp, did you notice the
difference between the double-flat (-8) in symbol sets #1 and #2?

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

Now I did. I personally prefer Tartini Plus One -8 double flat.It's much more nourishing to the eye.

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

But you are saying that somehow the "b" is not distinct enough and
that the slash should be moved slightly upward. This would make the
amount of white space intermediate between the -2 semiflat and -4
flat. I have added this as -3b at the lower right part of the
updated figure:

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

No no no, what I meant was to move the slash upward as in -3, only a little more slanted. The same goes for -7. But the way I see it, what you came up with is better than before... only if the slash weren't so thick!

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

To the immediate left of this I have placed -3a (copy of new1) and -4
(flat) and also, to the immediate right, -2 (semiflat), for an easy
(side-by-side) comparison. At the extreme right is -7b, formed by
combining -3b and -4. Do these meet with your approval?

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

I think the round of the -2 flat for Tartini Plus One should be fatter, as fat as the -3 mentioned above.Same goes for -6.

I see that I have issues with Tartini Plus One -5, +3 and +5. Here is what I suggest:

Degree +5 should be as slanted and thick as +4. The same goes for +6.
+3 would look best if mirrored and made as thick as +4.
-5 should have another flat component just as its counterpart sharp has three pikes.

Cordially,
Ozan

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
>
> > For number seven, you may like to consider an asterisk.
>
> We spent a lot of time on this one trying to make it look more like
> an "X" (double-sharp) with a backslash (5-comma-down) through it
> rather than an asterisk, so I would ask you to reconsider this.
>
> Ah, I see what you mean. The N kind of double sharp in Tartini Plus
Two looks nice.

I guess that one needs an explanation. It was intended to be more
like .\' -- the two lines are supposed to suggest the downward half-
arrow \| of the -1 symbol, something like a "V", just as occurs in
+1, +3, and +5 of Tartini-plus #2. But there is a slightly different
logic behind the up-symbols that proceeds from the employment of the
half-arrow symbol for both +1 and -1.

> But it could be a lot better like % (reversed-dots squared and
filled).

See the updated figure:
/tuning-math/files/secor/notation/
filename Symset41.gif

In the middle of the bottom staff are 7a, which I think is too much
alike in size to 8-new2 (which now appears in both sets, #1 and #2),
and also 7b and 7c, which are smaller. I still prefer 7-new1 to all
of these, for two reasons:

1) 7a thru 7c are all bolder in appearance than 8-new2, suggesting
that they should symbolize a larger alteration. (I also happen to
prefer 8-new1 over 8-new2 because of its "bolder" look.)

2) I believe that the essential appearance of the double-sharp is
associated more with its X-shape than with the exaggerated serifs of
the modern symbol, so I would rather use a type of "X" in conjunction
with the backslash than the serifs.

> Also the size of `new2 double shaprs` could be reduced by a notch.

With the resolution of 8 pixels between staff lines that I'm using,
it's not possible to have anything intermediate in size between "8
modern" and "8-new2" that can be centered on a given staff position.
As it is, +8 is still smaller in appearance than +6, and I think
nobody will have any trouble figuring out what it means.

> As long as we're talking about the double-sharp, did you notice the
> difference between the double-flat (-8) in symbol sets #1 and #2?
>
> Now I did. I personally prefer Tartini Plus One -8 double flat.It's
much more nourishing to the eye.

I have seen a piece of printed music without any space separating the
two halves of the double-flat symbol, but it seems to be the
exception. Anyway, it makes the double-flat look more like *one*
symbol.

> But you are saying that somehow the "b" is not distinct enough and
> that the slash should be moved slightly upward. This would make
the
> amount of white space intermediate between the -2 semiflat and -4
> flat. I have added this as -3b at the lower right part of the
> updated figure:
>
> No no no, what I meant was to move the slash upward as in -3, only
a little more slanted. The same goes for -7. But the way I see it,
what you came up with is better than before... only if the slash
weren't so thick!

I'm sorry, but I still don't know what you meant by "as in -3". I
intended the thickness of the slashes in all of the odd-numbered
symbols to be as uniform as possible, so that it could be easily
recognized as a common element of these symbols. Now I'm puzzled
that you think the slash in -3 is too thick but that the one in +3
(below) is not thick enough.

> To the immediate left of this I have placed -3a (copy of new1) and -
4
> (flat) and also, to the immediate right, -2 (semiflat), for an easy
> (side-by-side) comparison. At the extreme right is -7b, formed by
> combining -3b and -4. Do these meet with your approval?
>
> I think the round of the -2 flat for Tartini Plus One should be
fatter, as fat as the -3 mentioned above.Same goes for -6.

It was Dave Keenan's recommendation that we make the backwards flat
*significantly* smaller that the flat so as to alleviate the problem
of lateral confusability between these two symbols, and I am in
agreement with his solution, for which he did not judge half of the
present difference in width to be significant enough. (I also think
that Dave should respond to this.)

> I see that I have issues with Tartini Plus One -5, +3 and +5. Here
is what I suggest:
>
> Degree +5 should be as slanted and thick as +4.

For what reason? The +5 symbol looks as if it's intermediate in size
between +4 and +6, and the steeper slope of the slashes in the odd-
numbered symbols gives them an appearance that sets them apart from
the even-numbered ones and makes them easier to distinguish when read
rapidly. Another purpose of the steeper slope is to make the
direction of the slope more obvious; otherwise the meaning that / is
up and \ is down would be obscured, because they would look too much
alike.

> The same goes for +6.
> +3 would look best if mirrored and made as thick as +4.

Do you mean that the slash of +3 should go upward, like this / ?
We're trying to notate a sharp *decreased* by a 5-comma, hence a
*downward* slash \ . But if you're trying to make the symbols more
uniform in appearance, then I would suggest considering the #2 set,
beginning with the +3 and +5 symbols, and comparing them with their
mixed-Sagittal counterparts (directly below) to follow the underlying
logic.

> -5 should have another flat component just as its counterpart sharp
has three pikes.

There *is* another flat component: -5 is simply -1 and -4 with the
stems merged, just as -6 is a merger of -2 and -4. In the Tartini-
Couper symbols stems are not added to the down-symbols in the same
fashion as they are added to the up-symbols; otherwise, the -4 (flat)
symbol would have to have 2 stems to match the +4 (sharp) symbol,
the -6 symbol would have to have 3 stems, and the double-flat would
end up with 4 stems. With the even-numbered symbols we think that
it's okay to tinker with the dimensions a little bit, but not with
the essential features.

Best regards,

--George

George, I have written by hand the symbols which appeal to me the most in the attached JPG file.

All in all my preference is a mix of these sharps:

Tartini1) +1+2 (the prior as bold and slanted as the latter)
Tartini2) +3 +4
Tartini1) +5 +6 (the prior as bold and slanted as the latter)
New double sharp (7a)
Double sharp (modern+8)

And these flats:

Tartini1) -1 -2 (the latter equally mirrored)
Maqam -3
Tartini1) -4 -5 -6 (the latter equally mirrored)
Maqam+Flat -7
Tartini1) Double flat

This way, the set seems both aesthetically and mathematically ordered and in conformity to a great extent with maqam music practice hereabouts.

Cordially,
Ozan

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> George, I have written by hand the symbols which appeal to me the
most in the attached JPG file.

Ozan, I've copied your file, 41-tone.jpg, here so that others can
also refer to it:

/tuning/files/secor/notation/

> All in all my preference is a mix of these sharps:
>
> Tartini1) +1+2 (the prior as bold and slanted as the latter)
> Tartini2) +3 +4
> Tartini1) +5 +6 (the prior as bold and slanted as the latter)
> New double sharp (7a)
> Double sharp (modern+8)

Part of the reason for my delay in replying is that there are several
things about these symbols that took me by surprise, and I didn't
know quite what to say about them.

1) One thing is that I didn't expect that you would be mixing symbols
from the Tartini-plus sets 1) and 2), which results in a sort of
mixed logic behind the symbols.

2) Another thing is that I didn't think about the fact that hand-
written symbols would have longer cross-strokes than the ones we are
accustomed to in printed music (and therefore also longer than those
in the symbols which Dave Keenan and I were proposing in file
Symset41.gif, which is also in the above folder). This obscures the
significance of the upward-sloping slashes in the +1 and +5 symbols,
since the cross-strokes of the +2, +4, and +6 symbols now have the
same appearance (including the same slope) as the comma-slashes.
About the only thing I could say in favor of this is that it is more
aesthetically pleasing as a unifying element.

These two things are most damaging to the +3 symbol, in which the
downward-sloping line is considerably shorted, relative to the length
of the sharp cross-stroke, so that it is now only about 1/3 the
length of the latter (whereas in our Tartini-plus #2 set it was
actually longer than the cross-stroke). Whereas we had intended that
the slash should be a prominent feature of the symbol (to indicate
the direction of the comma-alteration to the sharp), it is now so
inconspicuous that its meaning is lost.

Would you consider replacing it with the symbol from our #1 set,
preferably the older version with the longer slash labeled "3 old"
near the bottom left of the figure in Symset41.gif, in which the
downward-sloping slash is more prominent? You may object that an
opposite slope gives it a different appearance from the other
symbols, but I believe that this would be an advantage in that this
symbol would be more readily distinguished from the others, and it
would emphasize the fact that the comma is applied in a downward
(i.e., opposite) direction.

3) I was surprised by the cursive "x" you used for +8, which has a
*wavy* line that you also used in +7, where I had expected a downward-
sloping *straight* line such as I have in 7a, 7b, or 7c in the middle
of the lowest staff of my diagram, to indicate a double-sharp lowered
by a comma.

Could you replace the wavy line with a straight line in both +7 and
+8?

> And these flats:
>
> Tartini1) -1 -2 (the latter equally mirrored)
> Maqam -3
> Tartini1) -4 -5 -6 (the latter equally mirrored)
> Maqam+Flat -7
> Tartini1) Double flat

Both Dave's and my preference is for the upward-sloping slash of -3
and -7 to remain within the staff position (as in -3a or -3b of my
diagram), and also for the enclosed white space to be smaller than
that of a full flat (-4). However, we recognize that the maqam
symbol, as you have drawn it, *does* clearly indicate that it is to
be interpreted as a flat plus a comma. If you believe that this
particular symbol will be an important factor in convincing other
maqam musicians to accept the symbol set, then we must agree with
your choice.

Best,

--George

Dear George,

I see your point. But is there no way of interpreting the # sign as part of the symbols utilizing the 5-comma up slash? The apotome sharp could then be interpreted as a Classical Chromatic Semitone (70 cents) + Double Syntonic Comma (44 cents).

Also, is there some way to save Tartini-one +3 (old) sign with the slope up just in case the above clause is possible to realize? I say this because it is so awkward for me to draw a line in the direction you suggest by hand aside from the fact that a 5-comma down sign destroys the uniformity of all the sharps.

Please forgive the wavy X. That was my calligraphy which I frequently utilize for decoration or ornamentation. Do interpret it as my personal preference at this point. Of course, it should be a straight line as you suggest, to which I have no objections. But, upon closer examination, I think a simple N sign would do the trick better for a double apotome sharp.

I do believe very strongly that the maqam flat signifying the limma is a most crucial element of the set. You are not at all obliged to conform with this, but I know for one thing that maqam musicians are accustomed to reading it the way you say on sight.

Cordially,
Ozan

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> Dear George,
>
> I see your point. But is there no way of interpreting the # sign as
part of the symbols utilizing the 5-comma up slash? The apotome sharp
could then be interpreted as a Classical Chromatic Semitone (70
cents) + Double Syntonic Comma (44 cents).

That seems a rather round-about way of looking at a Pythagorean (3-
limit) interval, and anyway, I don't think that sort of thinking
would necessarily be valid for certain divisions, such as 17 (unless
you have abandoned the idea of using this for divisions other than
41).

> Also, is there some way to save Tartini-one +3 (old) sign with the
slope up just in case the above clause is possible to realize? I say
this because it is so awkward for me to draw a line in the direction
you suggest by hand aside from the fact that a 5-comma down sign
destroys the uniformity of all the sharps.

Well, it seems that slope in the up-symbols no longer has any meaning
anyway, so you might as well go ahead and do that (making the slope
very gentle, as it already is in the Tartini fractional sharps), Or
else you could just keep what you already have in 41-tone.jpg, since
that looks practically the same (and perhaps someone might see a half-
arrow \| in there.

Better yet, why not eliminate the lower part of the left vertical
line, then lower the entire symbol so the cross-bar is centered on
the intended staff position, and then extend the remaining vertical
lines slightly, which allows the half-arrow-down to be more
prominent. I've added this as "3a" on the bottom staff (5th symbol
from the left) in my file Symset41.gif located here:

/tuning-math/files/secor/notation/

The downward slash isn't centered on the staff position, but at this
point I'm so desparate to want to salvage whatever meaning I can.

> Please forgive the wavy X. That was my calligraphy which I
frequently utilize for decoration or ornamentation. Do interpret it
as my personal preference at this point. Of course, it should be a
straight line as you suggest, to which I have no objections. But,
upon closer examination, I think a simple N sign would do the trick
better for a double apotome sharp.

> Oops. that should have been the double apotome sharp minus the
syntonic comma for the N sign.

Yes, I guess that would be okay.

> I do believe very strongly that the maqam flat signifying the limma
is a most crucial element of the set. You are not at all obliged to
conform with this, but I know for one thing that maqam musicians are
accustomed to reading it the way you say on sight.

Yes, whatever you think is necessary. While Dave & I have
contributed our suggestions (using ideas that, for the most part, are
not originally ours), you understand the Maqam world far better than
we do, and it is therefore appropriate that you make the final
decisions. (This is already so different from what Dave and I had
hoped for that I don't know whether we'll be using this for
anything.) Our chief concern is that musicians who would need to be
familiar with both Tartini-plus and Sagittal would not become
confused by conflicts between the two, and I believe that we have
accomplished that goal.

Best,

--George

George,

That seems a rather round-about way of looking at a Pythagorean (3-
limit) interval, and anyway, I don't think that sort of thinking
would necessarily be valid for certain divisions, such as 17 (unless
you have abandoned the idea of using this for divisions other than
41).

I have not abondoned the general usage of the apotome sharp for 7 fifths up down 4 octaves. It just occured to me that if the 5-comma up slash will have any significance, then it must also stand valid within the sharp symbol. Could we then re-interpret two slashes one on top of the other as a tridecimal diesis (40:39)? That would amount to the apotome when coupled with double strokes which would, in its plain form, signify the Keenan boundary for the small-semitone (69-78 cents).

Well, it seems that slope in the up-symbols no longer has any meaning
anyway, so you might as well go ahead and do that (making the slope
very gentle, as it already is in the Tartini fractional sharps), Or
else you could just keep what you already have in 41-tone.jpg, since
that looks practically the same (and perhaps someone might see a half-
arrow \| in there.

I like the one I already use, because it also resembles the Persian sharp as well as the apotome sharp. Nevertheless I still which to conserve the unity of the sharps as we did with the flats. The logic can be established in some way, can it not?

Better yet, why not eliminate the lower part of the left vertical
line, then lower the entire symbol so the cross-bar is centered on
the intended staff position, and then extend the remaining vertical
lines slightly, which allows the half-arrow-down to be more
prominent. I've added this as "3a" on the bottom staff (5th symbol
from the left) in my file Symset41.gif located here:

/tuning-math/files/secor/notation/

The downward slash isn't centered on the staff position, but at this
point I'm so desparate to want to salvage whatever meaning I can.

> Please forgive the wavy X. That was my calligraphy which I
frequently utilize for decoration or ornamentation. Do interpret it
as my personal preference at this point. Of course, it should be a
straight line as you suggest, to which I have no objections. But,
upon closer examination, I think a simple N sign would do the trick
better for a double apotome sharp.

> Oops. that should have been the double apotome sharp minus the
syntonic comma for the N sign.

Yes, I guess that would be okay.

> I do believe very strongly that the maqam flat signifying the limma
is a most crucial element of the set. You are not at all obliged to
conform with this, but I know for one thing that maqam musicians are
accustomed to reading it the way you say on sight.

Yes, whatever you think is necessary. While Dave & I have
contributed our suggestions (using ideas that, for the most part, are
not originally ours), you understand the Maqam world far better than
we do, and it is therefore appropriate that you make the final
decisions. (This is already so different from what Dave and I had
hoped for that I don't know whether we'll be using this for
anything.) Our chief concern is that musicians who would need to be
familiar with both Tartini-plus and Sagittal would not become
confused by conflicts between the two, and I believe that we have
accomplished that goal.

Best,

--George

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George,

That seems a rather round-about way of looking at a Pythagorean (3-
limit) interval, and anyway, I don't think that sort of thinking
would necessarily be valid for certain divisions, such as 17 (unless
you have abandoned the idea of using this for divisions other than
41).

I have not abondoned the general usage of the apotome sharp for 7 fifths up down 4 octaves. It just occured to me that if the 5-comma up slash will have any significance, then it must also stand valid within the sharp symbol. Could we then re-interpret two slashes one on top of the other as a tridecimal diesis (40:39)? That would amount to the apotome when coupled with double strokes which would, in its plain form, signify the Keenan boundary for the small-semitone (69-78 cents).

Well, it seems that slope in the up-symbols no longer has any meaning
anyway, so you might as well go ahead and do that (making the slope
very gentle, as it already is in the Tartini fractional sharps), Or
else you could just keep what you already have in 41-tone.jpg, since
that looks practically the same (and perhaps someone might see a half-
arrow \| in there.

I like the one I already use, because it also resembles the Persian sharp as well as the apotome sharp. It will be sufficient to convince maqam musicians to abondon the evil practice of using the apotome sharp symbol as the limma sharp. This was, as you may not know, suggested by Arel and Ezgi decades ago and has remained ever since. Everyone today thinks that the sharp symbol equals 4 commas! That is only allowable in certain conditions such as enharmonic re-spelling, right?

Nevertheless I still which to conserve the unity of the sharps as we did with the flats. The logic can be established in some way, can it not?

Better yet, why not eliminate the lower part of the left vertical
line, then lower the entire symbol so the cross-bar is centered on
the intended staff position, and then extend the remaining vertical
lines slightly, which allows the half-arrow-down to be more
prominent. I've added this as "3a" on the bottom staff (5th symbol
from the left) in my file Symset41.gif located here:

/tuning-math/files/secor/notation/

The downward slash isn't centered on the staff position, but at this
point I'm so desparate to want to salvage whatever meaning I can.

Ouch. I didn't like it at all I'm afraid. That is even more difficult to draw by hand. I'll stick with my preference if you agree.

Yes, whatever you think is necessary. While Dave & I have
contributed our suggestions (using ideas that, for the most part, are
not originally ours), you understand the Maqam world far better than
we do, and it is therefore appropriate that you make the final
decisions. (This is already so different from what Dave and I had
hoped for that I don't know whether we'll be using this for
anything.) Our chief concern is that musicians who would need to be
familiar with both Tartini-plus and Sagittal would not become
confused by conflicts between the two, and I believe that we have
accomplished that goal.

Best,

--George

George, I dare not make final decisions on a matter that I still have little understanding for. It is only in these recent months that I began to grasp the utility of commas and how they are used in temperament. I only can make comments on the visual appeal and integrity of the accidentals you assorted with inspiration. The functionality and theory behind them or the variants thereof are beyond me. Nevertheless, I wish you persist in considering this another Universal Notation Project to which I will be more than happy to assist in whatever way I can.

Cordially,
Ozan

Sorry about the first reply bearing this topic. I sent it without completing my words. Please disregard it.

Ozan Yarman

Ozan,

I'm sorry this reply has again taken so long. I've been tinkering
with the symbols and didn't want to answer until I was satisfied with
what I had.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> George,
>
> That seems a rather round-about way of looking at a Pythagorean
(3-
> limit) interval, and anyway, I don't think that sort of thinking
> would necessarily be valid for certain divisions, such as 17
(unless
> you have abandoned the idea of using this for divisions other
than
> 41).
>
> I have not abondoned the general usage of the apotome sharp for 7
fifths up down 4 octaves. It just occured to me that if the 5-comma
up slash will have any significance, then it must also stand valid
within the sharp symbol.

The sharp cross-strokes weren't intended to be 5-comma slashes. In
Tartini-plus symbol set #1 the 5-comma slashes were intentionally
made longer and with a much steeper slope than the sharp cross-
strokes in order to make the distinction obvious. The sharp cross-
strokes have a very gentle slope and barely extend beyond the
vertical strokes, which is how they appear in printed music.

Unfortunately, when they are hand-written, the cross-strokes tend to
be longer, but a distinction could still be made by minimizing the
slope in the even-numbered up-symbols. I was disappointed to see
that you did not want to maintain this distinction, seeking instead a
more uniform appearance. If you think that's necessary, then I would
not recommend giving any of the slashes in the up-symbols much slope
(except for +7, which you wanted to resemble "N"), in which case the
meaning of the +1 symbol would be indicated by its resemblance to a
plus "+" sign. I've put these into a diagram here:
/tuning-math/files/secor/notation/
in file Tplus41.gif, in the 2nd staff (labeled "Maqam version").

> Could we then re-interpret two slashes one on top of the other as a
tridecimal diesis (40:39)? That would amount to the apotome when
coupled with double strokes which would, in its plain form, signify
the Keenan boundary for the small-semitone (69-78 cents).

The ratio you are proposing for a double-stroke is beyond the 11
limit, which is okay for 41. However, most of the other important
octave divisions (notably 24, 31 and 72) are more properly treated as
11-limit tunings (at most), and so it would be much more meaningful
to keep the semisharp symbol defined as 32:33.

An alternative is to interpret the two strokes as two 5-commas, which
would amount to ~43.0 cents, which is very close to 39:40 (~43.8c).
But following this logic, you would also need to interpret the two
slashes in the +2 (semisharp) symbol as two 5-commas, which would
make it unusable as the +1 symbol in 31-ET, since the 5-comma
vanishes in 31. There would also be problems justifying the meaning
of the semisharp symbol in 17-ET and 24-EDO.

So your suggestion is not very good for the symantics to be
meaningful for very many octave divisions.

> Well, it seems that slope in the up-symbols no longer has any
meaning
> anyway, so you might as well go ahead and do that (making the
slope
> very gentle, as it already is in the Tartini fractional sharps),
Or
> else you could just keep what you already have in 41-tone.jpg,
since
> that looks practically the same (and perhaps someone might see a
half-
> arrow \| in there.
>
> I like the one I already use, because it also resembles the Persian
sharp as well as the apotome sharp. It will be sufficient to convince
maqam musicians to abondon the evil practice of using the apotome
sharp symbol as the limma sharp. This was, as you may not know,
suggested by Arel and Ezgi decades ago and has remained ever since.
Everyone today thinks that the sharp symbol equals 4 commas! That is
only allowable in certain conditions such as enharmonic re-spelling,
right?

That's strictly true only in a few divisions (27, 34, 41), and it has
nothing to do with enharmonic respelling. Anyway, that could be a
powerful argument to use in persuading other maqam theorists to adopt
a 41-tone frame of reference. (The 34 division is much less
desirable, because it's inconsistent at the 7 limit.) But they would
need to recognize that the "limma sharp" is equivalent to 3 commas in
41.

> Nevertheless I still which to conserve the unity of the sharps as
we did with the flats. The logic can be established in some way, can
it not?

The logic that we have maintained, at least until your latest
proposal, is that the slant of a single stroke should indicate the
direction of comma alteration from tones in a Pythagorean sequence.
I would like to see that continued by reinstating the distinction of
slope (/ vs. \, and a steeper slope for the single strokes). It
would also help to reinstate the longer slash-length in the single-
strokes, but that's not as critical.

In the case of your +3 symbol, this would, at the very least, involve
changing the direction of the slope of the slash to \. Is this too
much to ask?

> Better yet, why not eliminate the lower part of the left vertical
> line, then lower the entire symbol so the cross-bar is centered on
> the intended staff position, and then extend the remaining vertical
> lines slightly, which allows the half-arrow-down to be more
> prominent. I've added this as "3a" on the bottom staff (5th symbol
> from the left) in my file Symset41.gif located here:
>
> /tuning-math/files/secor/notation/
>
> The downward slash isn't centered on the staff position, but at
this
> point I'm so desparate to want to salvage whatever meaning I can.
>
> Ouch. I didn't like it at all I'm afraid. That is even more
difficult to draw by hand. I'll stick with my preference if you agree.

Okay, then, forget about that one!

> Yes, whatever you think is necessary. While Dave & I have
> contributed our suggestions (using ideas that, for the most part,
are
> not originally ours), you understand the Maqam world far better
than
> we do, and it is therefore appropriate that you make the final
> decisions. (This is already so different from what Dave and I had
> hoped for that I don't know whether we'll be using this for
> anything.) Our chief concern is that musicians who would need to
be
> familiar with both Tartini-plus and Sagittal would not become
> confused by conflicts between the two, and I believe that we have
> accomplished that goal.
>
> George, I dare not make final decisions on a matter that I still
have little understanding for. It is only in these recent months that
I began to grasp the utility of commas and how they are used in
temperament. I only can make comments on the visual appeal and
integrity of the accidentals you assorted with inspiration. The
functionality and theory behind them or the variants thereof are
beyond me. Nevertheless, I wish you persist in considering this
another Universal Notation Project to which I will be more than happy
to assist in whatever way I can.

I could conceive of this as a multi-cultural sort of notation, in
which variations (or dialects) in some of the symbols might occur
according to the needs or preferences of localized cultures. In the
file Tplus41.gif, which I mentioned above, I have shown on the first
two staves variations of these. For example, the -3 symbol in #2 is
as you have drawn it (Maqam version), while in #1 the slash has been
lowered to the position of the notehead (a "Western" version). For
+2, +4, and +6 the symbols in #1 are as they would appear in a font,
whereas in #2 the cross-members are longer, as they would be when
hand-written. (And, as I indicated above, I am hoping to persuade
you to have the +1, +3, and +5 symbols in #2 match those in #1.)

BTW, did you notice that I made the curved part of the maqam -3
symbol slightly narrower than in the -4 (flat) symbol? It would
probably not be written that way by hand, but in a font the slight
difference in size might help to emphasize that the -3 symbol has a
smaller alteration (and perhaps make it more acceptable to the
western world).

Best regards,

--George

Ah, there you are George... let us continue improving our Tartini symbols, shall we?

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

> I have not abondoned the general usage of the apotome sharp for 7
fifths up down 4 octaves. It just occured to me that if the 5-comma
up slash will have any significance, then it must also stand valid
within the sharp symbol.

The sharp cross-strokes weren't intended to be 5-comma slashes. In
Tartini-plus symbol set #1 the 5-comma slashes were intentionally
made longer and with a much steeper slope than the sharp cross-
strokes in order to make the distinction obvious. The sharp cross-
strokes have a very gentle slope and barely extend beyond the
vertical strokes, which is how they appear in printed music.

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

I realize that very well. But I still aim to relate the slopes // with two commas, so that the symbol set will be complete in meaning.

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

Unfortunately, when they are hand-written, the cross-strokes tend to
be longer, but a distinction could still be made by minimizing the
slope in the even-numbered up-symbols. I was disappointed to see
that you did not want to maintain this distinction, seeking instead a
more uniform appearance.

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

Likewise, I'm dissapointed that you do not wish to consider some way of integrating all the cross-strokes uniformly.

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

If you think that's necessary, then I would
not recommend giving any of the slashes in the up-symbols much slope
(except for +7, which you wanted to resemble "N"),

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

N looks perfect with the Tartini-Plus Maqam version. Can you change +8 here with the +8 of the mixed sagittal on the same page?

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

in which case the
meaning of the +1 symbol would be indicated by its resemblance to a
plus "+" sign.

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

That one is splendid. I like +1 Maqam version a lot.

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

I've put these into a diagram here:
/tuning-math/files/secor/notation/
in file Tplus41.gif, in the 2nd staff (labeled "Maqam version").

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

It looks swell, but the logic should be as impeccable as with the Western version if we can achieve that.

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

> Could we then re-interpret two slashes one on top of the other as a
tridecimal diesis (40:39)? That would amount to the apotome when
coupled with double strokes which would, in its plain form, signify
the Keenan boundary for the small-semitone (69-78 cents).

The ratio you are proposing for a double-stroke is beyond the 11
limit, which is okay for 41. However, most of the other important
octave divisions (notably 24, 31 and 72) are more properly treated as
11-limit tunings (at most), and so it would be much more meaningful
to keep the semisharp symbol defined as 32:33.

An alternative is to interpret the two strokes as two 5-commas, which
would amount to ~43.0 cents, which is very close to 39:40 (~43.8c).
But following this logic, you would also need to interpret the two
slashes in the +2 (semisharp) symbol as two 5-commas, which would
make it unusable as the +1 symbol in 31-ET, since the 5-comma
vanishes in 31. There would also be problems justifying the meaning
of the semisharp symbol in 17-ET and 24-EDO.

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

In that case, the quarter-tone sharp (+2) symbol should not be used with these tunings. But do you agree with me that all the slopes should be understood as 5-commas?

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

So your suggestion is not very good for the symantics to be
meaningful for very many octave divisions.

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

Not unless you agree to an extra symbol in those cases.

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

> I like the one I already use, because it also resembles the Persian
sharp as well as the apotome sharp. It will be sufficient to convince
maqam musicians to abondon the evil practice of using the apotome
sharp symbol as the limma sharp. This was, as you may not know,
suggested by Arel and Ezgi decades ago and has remained ever since.
Everyone today thinks that the sharp symbol equals 4 commas! That is
only allowable in certain conditions such as enharmonic re-spelling,
right?

That's strictly true only in a few divisions (27, 34, 41), and it has
nothing to do with enharmonic respelling. Anyway, that could be a
powerful argument to use in persuading other maqam theorists to adopt
a 41-tone frame of reference. (The 34 division is much less
desirable, because it's inconsistent at the 7 limit.) But they would
need to recognize that the "limma sharp" is equivalent to 3 commas in
41.

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

That will most likely resolve the Turkish-Arabic conflict in regards to the expression of the sesquitone in maqams like Usshaq, Huzzam and Saba. Yes, I see now that 41 tones per octave is the least number for a perfect explanation of a complete closed cycle of maqam music perdes. The apotome and limma sharps are very well represented in 41tET, as well as quarter-tones. I will use this notation with your permission if we can make a conclusion.

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

> Nevertheless I still which to conserve the unity of the sharps as
we did with the flats. The logic can be established in some way, can
it not?

The logic that we have maintained, at least until your latest
proposal, is that the slant of a single stroke should indicate the
direction of comma alteration from tones in a Pythagorean sequence.
I would like to see that continued by reinstating the distinction of
slope (/ vs. \, and a steeper slope for the single strokes). It
would also help to reinstate the longer slash-length in the single-
strokes, but that's not as critical.

In the case of your +3 symbol, this would, at the very least, involve
changing the direction of the slope of the slash to \. Is this too
much to ask?

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

Could we instead use the persian koron here for +3 like this: ||< This would give an accurate indication as to which direction the 5-comma is to be taken. So we would have in our arsenal not only / and \ but also < and > as comma accents.

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

> George, I dare not make final decisions on a matter that I still
have little understanding for. It is only in these recent months that
I began to grasp the utility of commas and how they are used in
temperament. I only can make comments on the visual appeal and
integrity of the accidentals you assorted with inspiration. The
functionality and theory behind them or the variants thereof are
beyond me. Nevertheless, I wish you persist in considering this
another Universal Notation Project to which I will be more than happy
to assist in whatever way I can.

I could conceive of this as a multi-cultural sort of notation, in
which variations (or dialects) in some of the symbols might occur
according to the needs or preferences of localized cultures. In the
file Tplus41.gif, which I mentioned above, I have shown on the first
two staves variations of these. For example, the -3 symbol in #2 is
as you have drawn it (Maqam version), while in #1 the slash has been
lowered to the position of the notehead (a "Western" version). For
+2, +4, and +6 the symbols in #1 are as they would appear in a font,
whereas in #2 the cross-members are longer, as they would be when
hand-written. (And, as I indicated above, I am hoping to persuade
you to have the +1, +3, and +5 symbols in #2 match those in #1.)

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

And I'm hoping to persuade you to consider vice versa, conforming to my latest suggestions.

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

BTW, did you notice that I made the curved part of the maqam -3
symbol slightly narrower than in the -4 (flat) symbol? It would
probably not be written that way by hand, but in a font the slight
difference in size might help to emphasize that the -3 symbol has a
smaller alteration (and perhaps make it more acceptable to the
western world).

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

I have no objections to that. In fact, I think you did a fine job there with the cosmetic touches.

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

Best regards,

--George

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

Cordially,
Ozan