Sagittal info spreadsheet now available

http://dkeenan.com/sagittal/Sagittal2_character_map.xls

Sorry for the duplication, but in many ways this spreadsheet is more significant than the new Sagittal-2 font, although you will need to install the font to see the correct symbols in the spreadsheet.
http://dkeenan.com/sagittal/Sagittal2.0d6.ttf

This information has not been available before in a form that could be machine read and manipulated. Some of it has not been available at all.

Any help in translating it into other formats (e.g. Mac, OpenOffice) would be gratefully received.

What it contains
----------------

For all unaccented sagittal symbols it gives character codes and long and short ASCII equivalents. It gives the names of the symbols as commas, as tone fractions and as EDO degrees for 36 common EDOs up to 96. It gives the primary comma definitions in both numerator/denominator form and as prime exponent vectors. It also gives the most common meanings of the left and right accents, although the full details of accented Sagittals have not been finalised.

-- Dave Keenan

Dave Keenan wrote:

> Any help in translating it into other formats (e.g. Mac, OpenOffice) would be gratefully received.

It mostly seems to work in OpenOffice, except for the green rows, which don't use the Sagittal font for some reason. Additionally, most of the characters from 128 (boathookandarcdown) to 159 (leftarcup) don't show up properly, even in the white rows. I figured out a way around it, but it will require manually inserting all the Sagittal characters....

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
>
> Dave Keenan wrote:
>
> > Any help in translating it into other formats (e.g. Mac,
OpenOffice) would be gratefully received.
>
> It mostly seems to work in OpenOffice, except for the green rows,
which
> don't use the Sagittal font for some reason.

My main problem is that it isn't clear what the symbols are symbols
for; I guess an ascii table explaining what all the names mean is a
good idea in addition.

Dave Keenan wrote:
> http://dkeenan.com/sagittal/Sagittal2_character_map.xls
> > Sorry for the duplication, but in many ways this spreadsheet is more significant than the new Sagittal-2 font, although you will need to install the font to see the correct symbols in the spreadsheet.
> http://dkeenan.com/sagittal/Sagittal2.0d6.ttf > > This information has not been available before in a form that could be machine read and manipulated. Some of it has not been available at all.
> > Any help in translating it into other formats (e.g. Mac, OpenOffice) would be gratefully received.

Well, I couldn't figure out how to get the green background to work without changing the font on the Sagittal symbols, so I disabled the conditional style on the first column. And I manually inserted the Sagittal characters that weren't showing up properly. Unfortunately I don't have Excel so I can't compare the two. But at least the data should be useful even if the formatting doesn't match exactly.

http://www.io.com/~hmiller/music/Sagittal2_character_map.ods

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
> It mostly seems to work in OpenOffice, except for the green rows, which
> don't use the Sagittal font for some reason. Additionally, most of the
> characters from 128 (boathookandarcdown) to 159 (leftarcup) don't show
> up properly, even in the white rows. I figured out a way around it, but
> it will require manually inserting all the Sagittal characters....
>

Thanks Herman. It would be great if you can get it all fixed up and
email it to me so I can put it up on the website for others.

-- Dave Keenan

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
> My main problem is that it isn't clear what the symbols are symbols
> for; I guess an ascii table explaining what all the names mean is a
> good idea in addition.

Which names are you referring to? Do you mean the comma names in
relation to notating JI? Yes. The reader needs to know that if you
want to know how to notate some ratio, you remove any factors of 2 or
3 from it and go looking for the 2,3-reduced ratio in the name of the
comma. Alternatively, you go looking for the exponents you want for
the primes above 3 in the appropriate columns to the right.

You supply the necessary 3's by choosing the right Pythagorean nominal
and sharps or flats to go with it. And of course the 2's relate to the
octave.

Is that the sort of thing you're referring to?

Of course you may not find what you want because this spreadsheet only
gives the ratios for the unaccented symbols. We'll need a whole
'nother spreadsheet for the accented ones. Although we haven't
finalised them all yet, I suppose we could at least get the left
accented (5-schisma altered) ones and some of the right accented ones
up soon. Is anyone particularly hanging out for those?

-- Dave Keenan

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

> Is that the sort of thing you're referring to?

No, I just wanted numerator/denominator somewhere.

Hi Dave,

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

> Version 2 of the Sagittal font, with the complete symbol set,
> is now available in both TrueType and Postscript Type 1
> formats at http://dkeenan.com/sagittal/

It's great to see you back in action on the tuning list again!
And to hear about the release of Sagittal v.2.

Are you aware that we (Tonalsoft) have released Tonescape
as a free demo? If not, and if you are running a Windows XP
machine, i encourage you to try it out ... you can find the
link on our homepage.

Tonescape already has a number of different notations
available, but the only ones which relate to standard
music notation are the ones based on meantone. We would
love to include Sagittal, and i hope we can soon.

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

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@> wrote:
>
> > Is that the sort of thing you're referring to?
>
> No, I just wanted numerator/denominator somewhere.
>

Oh dear! In the Excel spreadsheet, and in Herman's OpenOffice
conversion (thanks Herman), numerator and denominator are in columns O
and P and the prime exponent vector is in columns S thru AA.

Can you see them?

-- Dave Keenan

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

> Oh dear! In the Excel spreadsheet, and in Herman's OpenOffice
> conversion (thanks Herman), numerator and denominator are in columns O
> and P and the prime exponent vector is in columns S thru AA.
>
> Can you see them?

I see them; I needed to move the slider. It would be easier to read if
reduced to one column and written as 25/24 or whatever, though I
realize people have a strange aversion to standard notation in these
parts; it also would make more sense to have it immediately by the
symbol, so you know what the heck the symbol is *for*.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@> wrote:
>
> > Oh dear! In the Excel spreadsheet, and in Herman's OpenOffice
> > conversion (thanks Herman), numerator and denominator are in columns O
> > and P and the prime exponent vector is in columns S thru AA.
> >
> > Can you see them?
>
> I see them; I needed to move the slider. It would be easier to read if
> reduced to one column and written as 25/24 or whatever, though I
> realize people have a strange aversion to standard notation in these
> parts;

Gidday Gene,

Because it's a spreadsheet it's easy for you to make it however you
want. You can insert columns and copy and paste columns to put things
where you would like them. To give you numerator/denominator in one
column right beside the symbols you could insert a new column B and
type the following formula into cell B7.
=O7&"/"&P7
Then copy and paste it down the rest of column B.

The thing is, the formulas to separate them, had they been given in
that format to start with, are a lot more complicated.

Alternatively you could insert a new column P, paste it full of
slashes "/", make it thin, and make the old column P (now Q) left
justified. Then because of the way the window is split you can bring
any column you like over next to the symbols by horizontal scrolling.

> it also would make more sense to have it immediately by the
> symbol, so you know what the heck the symbol is *for*.

I assumed that for most folks, the symbol was not *for* the numerator
and denominator of the comma (which can be dauntingly huge in some
cases), but it is for notating ratios (or their approximation) having
a certain combination of primes above 3. This is given by the first
part of the name in column G. For others is for notating a certain
tone fraction relative to 12-equal (column H) and for others a certain
number of degrees of a certain ET (column I).

Regards,
-- Dave Keenan

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
> Hi Dave,
...
> It's great to see you back in action on the tuning list again!
> And to hear about the release of Sagittal v.2.

Thanks Monz,

It's good to hear from you too. I was recently visited by Robin Perry
and in the middle of a great discussion where we were visualising a 3D
7-limit lattice wrapping around due to temperament, I remarked what a
joy it was to talk face to face with someone who spoke the same
language. I had never done that before. Robin replied that he had had
that joy with only one other person. You. :-)

> Are you aware that we (Tonalsoft) have released Tonescape
> as a free demo? If not, and if you are running a Windows XP
> machine, i encourage you to try it out ... you can find the
> link on our homepage.

That's great news, but I'm very busy. Let me know when it has Sagittal
in it. Then I'll be sure to try it. :-)

We've been plugging it on the Sagittal website as "soon to have
sagittal support" for a long time now.

> Tonescape already has a number of different notations
> available, but the only ones which relate to standard
> music notation are the ones based on meantone. We would
> love to include Sagittal, and i hope we can soon.

Great! There's never been a better time.

-- Dave Keenan

Woops!

After inserting a new column B that formula would have to be

=P7&"/"&Q7

Regards,
-- Dave Keenan

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

> Because it's a spreadsheet it's easy for you to make it however you
> want.

You mean it would be easy if you knew anything about Excel.

> I assumed that for most folks, the symbol was not *for* the numerator
> and denominator of the comma (which can be dauntingly huge in some
> cases), but it is for notating ratios (or their approximation) having
> a certain combination of primes above 3.

Speaking of dauntingly huge complexities, how well do you think you
could get a notation to work if you confined yourself, beyond the 3-
limit, only to superparticular ratios?

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
> You mean it would be easy if you knew anything about Excel.

Yes. Sorry.

Is there some file format I could put it into so you can get at it
with your favourite array-processing tools? Maybe just tab-delimited
text? Of course you won't see the actual sagittal font in that, but
you'd still have the ASCII representations.

> Speaking of dauntingly huge complexities, how well do you think you
> could get a notation to work if you confined yourself, beyond the 3-
> limit, only to superparticular ratios?

You would have noticed how many of the most popular sagittals do
represent superparticular commas. I think you could go a long way with
it, but I suspect it would eventually become inconvenient. The first
non-superparticular symbol I'd want is //| for the 25-S-diesis or
double 5-comma. Then I'd probably want some for notating 7/5 and 11/7.
Being forced to use commas as large as 14:15 and 21:22 for these could
be annoying.

-- Dave K

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

> Is there some file format I could put it into so you can get at it
> with your favourite array-processing tools?

Ascii is good. I have something called QUICK REFERENCE TO SAGITTAL
SYMBOLS SIMULATED BY ASCII CHARACTERS, but I wouldn't want to use the
symbols because they are not one character per symbol. I also have
this file, but I it isn't Sagittal-approved:

#, b 36/35
), ( 50/49-49/48
^, v 126/125
>, < 225/224
}, { 32805/32768

If you wanted to use enneadecal to notate the 7-limit, you could
start from Cb-E# (that centers on D) and then have a 225/224 symbol, a
126/125 symbol which is two 225/224's, and an 81/80 symbol which is
three 225/224's. There can be reasons for doing enneadecal in 152,
494 or even 665, but if we stick to 171 we also have the landscape
comma, and then four 225/224's give a 64/63. So you've got 171 nicely
covered with Cb-E#, plus four symbol pairs. Now, how would this best
work in Sagittal? Using ">" for 225/224 and "/" for 81/80, the C
otonal tetrad would be C-E>-G>-A#/.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
> Ascii is good.

Since there are many possible ASCII formats and you are able to open
it in OpenOffice, you can just choose "Save As ..." from the File menu
and then choose "Text CSV" as the file type and then you get to choose
whether it should be tab or comma delimited or just padded out to
fixed width columns with spaces.

> If you wanted to use enneadecal

I had to look that up. 1/19-oct period and 7.3 cent generator.

> to notate the 7-limit, you could
> start from Cb-E# (that centers on D) and then have a 225/224 symbol, a
> 126/125 symbol which is two 225/224's, and an 81/80 symbol which is
> three 225/224's. There can be reasons for doing enneadecal in 152,
> 494 or even 665, but if we stick to 171 we also have the landscape
> comma, and then four 225/224's give a 64/63. So you've got 171 nicely
> covered with Cb-E#, plus four symbol pairs. Now, how would this best
> work in Sagittal? Using ">" for 225/224 and "/" for 81/80, the C
> otonal tetrad would be C-E>-G>-A#/.

Yes. It's valid as a sort of Miller notation where the Cb to E# are
considered compound nominals. But I'm sorry Gene, I just can't get
excited about these notations where there is a near just fifth but it
isn't spelled C-G, and the near just ninth isn't C-D. I think George
is sorry he proposed one. :-)

-- Dave K

> If you wanted to use enneadecal to notate the 7-limit, you
> could start from Cb-E# (that centers on D)

I'd use A through S, in 5ths order (B is a 5th above A).
The 19-tone scale would be written with consecutive blobs
on the lines and spaces of a 9-line chromatic staff.

> and then have a 225/224 symbol,

d and +

> a 126/125 symbol which is two 225/224's,

b and #

> and an 81/80 symbol which is three 225/224's

db and #+

> if we stick to 171 we also have the landscape
> comma, and then four 225/224's give a 64/63.

bb and x

These are my ASCI versions of the usual Tartini/Couper
symbols.

Spelling the 4:5:6:7 chord on C,

this way...C..Nd.D..Abb
12-equal...C..E..G..Bb

As long as note names are always capitalized, there
shouldn't be confusion with the flats (just as "Bb"
doesn't cause confusion today).

Looks like the apotome is 16 of these 225/224 things.
Therefore a desire to spell things diatonically would
warrant a new symbol pair for the apotome.

Comments?

-Carl

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

> Yes. It's valid as a sort of Miller notation where the Cb to E# are
> considered compound nominals. But I'm sorry Gene, I just can't get
> excited about these notations where there is a near just fifth but it
> isn't spelled C-G, and the near just ninth isn't C-D. I think George
> is sorry he proposed one. :-)

Why not? It's closer to traditional usage than choosing always the best
fifth, after all. And it has the virtue of simplicity, which it seems
to me is a considerable virtue when notating things.

It seems to me the biggest weakness of the Sagittal project so far is
the absolute insistence on the best available fifth as a notational
generator, to the exclusion of other fifths or other intervals such as
thirds. It's Procrustean in basic concept, and one of the reasons I
dropped out of the Sagittal project is that it seemed to have you two
held in an iron grip. It makes a lot of sense to do it that way when
you are notating JI, but not nearly as much sense for all temperaments,
whatever their nature and properties.

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:

> Looks like the apotome is 16 of these 225/224 things.
> Therefore a desire to spell things diatonically would
> warrant a new symbol pair for the apotome.
>
> Comments?

This is an entirely different approach--not a gentle nudge away from
standard notation, but a radical departure.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@> wrote:
>
> > Yes. It's valid as a sort of Miller notation where the Cb to E# are
> > considered compound nominals. But I'm sorry Gene, I just can't get
> > excited about these notations where there is a near just fifth but it
> > isn't spelled C-G, and the near just ninth isn't C-D. I think George
> > is sorry he proposed one. :-)
>
> Why not? It's closer to traditional usage than choosing always the
> best fifth, after all.

How do you figure that? Traditional usage has always been to notate
the chain of best fifths as ...FbCbGbDbAbEbFCGDAEBF#C#G#D#A#E#B#... In
the Pythagorean era they were Pythagorean fifths, in the meantone era
they were meantone fifths and the 12-equal era 12-equal fifths.

George and I have proposed as standard, notations whose fifths vary
from 5-edo to 7-edo. We only suggest that you make it clear to your
reader what size your notational fifth is.

> And it has the virtue of simplicity, which it seems
> to me is a considerable virtue when notating things.

Sure. As a notation for enneadecal per se, it is fine. But I thought
this was following on from Aaron's question and looking at nano and
microtemperaments as a means to a simpler 7-limit JI notation for
extensive modulation, (presumably by 3's 5's and 7's).

> It seems to me the biggest weakness of the Sagittal project so far
> is the absolute insistence on the best available fifth as a notational
> generator, to the exclusion of other fifths or other intervals such as
> thirds. It's Procrustean in basic concept, and one of the reasons I
> dropped out of the Sagittal project is that it seemed to have you two
> held in an iron grip.

There is no such absolute insistence. What is possible with Sagital
and what George or I prefer are two different things (sometimes 3 :-).
All I said was that I can't get excited about such notations. That was
a personal observation.

As I said, there are no Sagittal police. It's out there. We have
absolutely no control over how it is used, except by explaining our
conceptions of it.

It gives a consistent and aesthetic way of symbolising many many
commas, tempered or otherwise. Feel free to use them however you like,
or not at all.

People seem to love setting up straw men, calling them sagittal and
knocking them down. :-) Ah well, I guess it's only human. I'd probably
do the same if I was on the other side of it.

Then again, we probably haven't done such a great job of explaining
it. I'd love for a professional educator or writer to volunteer to
write about sagittal, particularly for non-math types.

There is also the fact that history is littered with radical new music
notations. It seems it is only those that provide for gradual
evolution that have any chance of survival. And so gradual evolution
has certainly been my bias in proposing standard "off-the-shelf"
notations for things.

You have the math totally under control, so you don't need
off-the-shelf notations. And Sagittal can be used for radical
notations too.

> It makes a lot of sense to do it that way when
> you are notating JI, but not nearly as much sense for all temperaments,
> whatever their nature and properties.

Aha! We're in total agreement. I just thought we were looking for JI
notations (via nanotemperaments).

I thought your Garibaldi suggestion was a fine one. What's the next
more complex more accurate 7 limit linear temperament that has a
single generator approximating 3?

-- Dave K

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
> How do you figure that? Traditional usage has always been to notate
> the chain of best fifths as ...FbCbGbDbAbEbFCGDAEBF#C#G#D#A#E#B#...
In
> the Pythagorean era they were Pythagorean fifths, in the meantone
era
> they were meantone fifths and the 12-equal era 12-equal fifths.

The only traditional usages are Pythagorean and meantone, and in the
meantone era they were not necessarily the best fifths at all--tney
were deliberately flat, and in theory (as in 1/4-comma meantone)
there might be a better one. In 1/4-comma meantone, we have pure
major thirds, and so the semithirds fifth, which is sharp of a pure
fifth by half of the semithirds comma and so about 2/3 of a cent
sharp is available. You don't get much more traditional in meantone
than 1/4-comma, and I think C-Bbbbbb is arguably a fifth in the
system, and clearly a better one.

The only tradition I see here is what you and George are concocting
right now, and I think it would be wise to step back and ask yourself
why you are so fixed on the point. Where's the payoff?

> George and I have proposed as standard, notations whose fifths vary
> from 5-edo to 7-edo. We only suggest that you make it clear to your
> reader what size your notational fifth is.

Really? Are you saying you sometimes use something other than the
best fifth--and if so, in what cases?

> > And it has the virtue of simplicity, which it seems
> > to me is a considerable virtue when notating things.
>
> Sure. As a notation for enneadecal per se, it is fine. But I thought
> this was following on from Aaron's question and looking at nano and
> microtemperaments as a means to a simpler 7-limit JI notation for
> extensive modulation, (presumably by 3's 5's and 7's).

The point of it is, if you can notate 171-et, you can notate the 7-
limit, and enneadecal seems like a good choice as the way to notate
171-et. 171 is the smallest equal temperament which gives effective 7-
limit JI, and this seems like the simplest solution to the question
of how to notate the 7-limit effectively just.

> Then again, we probably haven't done such a great job of explaining
> it. I'd love for a professional educator or writer to volunteer to
> write about sagittal, particularly for non-math types.

If the symbols are proposed for flexible usage then I'm sorry, you've
done a rotten job explaining it. Why not just start out by giving a
list of symbols with a primary interpretation, along with things you
think would be reasonable as a secondary interpretation? Then you
could say you envision the primary use of such a set as being a way
to extend standard staff notation, in which case something which
plays the role of a generator fifth is presumed to be available? If
that isn't made clear, it's then not that clear you are even allowed
to notate Palestrina using Sagittal, because of the non-optimality of
the 1/4 comma fifth in extended meantone. You could then go on to say
other staff arragements and other generators can be adapted to the
scheme also, and try to do with a smile on your face instead of
acting like the Sagittal Police, which is how you've been coming
across.

> There is also the fact that history is littered with radical new
music
> notations. It seems it is only those that provide for gradual
> evolution that have any chance of survival. And so gradual evolution
> has certainly been my bias in proposing standard "off-the-shelf"
> notations for things.

Yet your immediate reaction to my enneadecal proposal, which is
exactly that, was extremely negative. The same goes for the 441
proposal using the meantone rather than the best fifth, which is
arguably *more* standard.

> You have the math totally under control, so you don't need
> off-the-shelf notations. And Sagittal can be used for radical
> notations too.

I've proposed radical notations, but the above are not radical. They
are way, *way* less radical in fact than the weirdness pure Sagittal
in high-limit JI involves.

> I thought your Garibaldi suggestion was a fine one. What's the next
> more complex more accurate 7 limit linear temperament that has a
> single generator approximating 3?

Pontiac, but I seem to recall you don't like pontiac. However, it is
a strong nanotemperament, is compatible with 171, and is basically
what you would be doing if you took your system of using the best
fifth and applied it to 171. In which case, you've probably done it
already.

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> looking at nano and
> microtemperaments as a means to a simpler 7-limit JI notation for
> extensive modulation, (presumably by 3's 5's and 7's).
>

I'm afraid I haven't been following this thread, but wouldn't my
absurdly simple proposal of notating the number of 1/3-comma ~=
225/224 steps away from a Pythagorean sequence fit that bill? Then any
notes whose numbers differ by 1 or 4 or 7 (etc.) stand in a septimal
relation, to good accuracy, for example thinking of 171-et as
schismatic temperament rather than meantone.

My brain still sees Pythagorean as the most obvious way to construct
the default chain of fifths. Perhaps that is what people have been
thinking of in any case.

If you don't wanna use numbers then ... well almost anything will do.

> > have a 225/224 symbol,
>
> d and +

- anything vaguely sensible, that is. I'd like it if the symbols for
raising and lowering seemed to be opposites of one another!

> > a 126/125 symbol which is two 225/224's,
>
> b and #

why not just put two 225/224 symbols next to each other?

> > and an 81/80 symbol which is three 225/224's
>
> db and #+

But I would use a separate symbol for 81/80, since it would make
recognizing 5- vs. 7-limit easier. I would not go for a notation in
which a 5-limit comma looks *more* complicated than a 7-limit one.

Similarly (concerning Gene's proposal) I would not go for a notation
where a pure fifth looks like a third-comma-meantone fifth plus a
septimal comma...

A (re)'discovery' of mine recently was that 63/50 is a
nearly-equal-tempered third (turns out to be because of the landscape
comma). In my numerical 1/3-comma notation that would go

F Ab^3 F#_4 A_1

commentary: 6/5 times 7/4 times 3/5 'equals' (via tempering out the
'tertiadec') 81/64 reduced by 1/3 comma; which is 1/3 schisma away
from an ET third.

~~~T~~~

> > > have a 225/224 symbol,
> >
> > d and +
>
> - anything vaguely sensible, that is. I'd like it if the symbols for
> raising and lowering seemed to be opposites of one another!

That's a half-flat (backwards flat) and a half-sharp
(sharp sign with only one vertical -- it should have
two horizontals but + is the closest thing in asci).

> > > a 126/125 symbol which is two 225/224's,
> >
> > b and #
>
> why not just put two 225/224 symbols next to each other?
>
> > > and an 81/80 symbol which is three 225/224's
> >
> > db and #+
>
> But I would use a separate symbol for 81/80, since it would make
> recognizing 5- vs. 7-limit easier. I would not go for a notation in
> which a 5-limit comma looks *more* complicated than a 7-limit one.

Again, these are asci version of Tartini/Couper symbols.
The db is a single symbol, as is the #+ (sharp sign with
three verticals).

> In my numerical 1/3-comma notation that would go
>
> F Ab^3 F#_4 A_1

What chord is this supposed to be?

-Carl

> these are asci version of Tartini/Couper symbols.
> The db is a single symbol, as is the #+ (sharp sign with
> three verticals).
>

Oh, OK. I wasn't following that. Scrub previous critique...
now of course 126/125 looks like a normal flat or sharp. Only works
with Carl's altered nominals.

> > In my numerical 1/3-comma notation that would go
> >
> > F Ab^3 F#_4 A_1
>
> What chord is this supposed to be?
>
> -Carl
>

Not a chord (although could be taken as such - 100:120:105:126 horrid
eh?) but a demonstration of notation.

Without numbers, I'd keep the usual sagittal syntonic comma, plus
something else septimal-looking for each little step.

~~~T~~~

> > > In my numerical 1/3-comma notation that would go
> > >
> > > F Ab^3 F#_4 A_1
> >
> > What chord is this supposed to be?
>
> Not a chord (although could be taken as such - 100:120:105:126
> horrid eh?) but a demonstration of notation.

What pitches are they supposed to be? Usually if one
wants to demonstrate a notation one would choose to notate
something familiar.

-Carl

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:

> My brain still sees Pythagorean as the most obvious way to construct
> the default chain of fifths. Perhaps that is what people have been
> thinking of in any case.

That's the question. Should the fifth be the fifthjh of 19-et, which
leads to a simpler notation scheme, or should it be the best fifth of
171, which is schismatic? Either will work.

> > > a 126/125 symbol which is two 225/224's,
> >
> > b and #
>
> why not just put two 225/224 symbols next to each other?

Because one symbol is more elegant. Anyway, Dave and George seem to
not approve of doubling symbols, and since they have a ton of
symbols, why worry about it?

> Similarly (concerning Gene's proposal) I would not go for a notation
> where a pure fifth looks like a third-comma-meantone fifth plus a
> septimal comma...

Dave Keenan doesn't like it either. But is simpler and more elegant,
since it chops 171 into 19 segments, and each segment uses the 1-2-3-4
scheme in a compeltely regular manner.

> A (re)'discovery' of mine recently was that 63/50 is a
> nearly-equal-tempered third (turns out to be because of the
landscape
> comma).

For those wondering what that is, (63/50)^3/2 = 250047/250000, which
is only a third of a cent in size. Another fun factiod is that
(63/50)/(27/25)^3 = 4375/4374. Put it together and it spells
ennealimmal.

In my numerical 1/3-comma notation that would go
>
> F Ab^3 F#_4 A_1
>
> commentary: 6/5 times 7/4 times 3/5 'equals' (via tempering out the
> 'tertiadec') 81/64 reduced by 1/3 comma; which is 1/3 schisma away
> from an ET third.

Yike! In pontiac/schismatic, that's E\, that is, E flat by a 225/224
symbol. In the 1/3 comma meantone/19-et system, it's E sharp by a
comma.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:

> That's the question. Should the fifth be the fifthjh of 19-et, which
> leads to a simpler notation scheme, or should it be the best fifth of
> 171, which is schismatic? Either will work.

It should be noted that with 19 notes of Cb-E#, or 21 notes of Fb-B#,
we would need in addition six symbol pairs rather than four. We would
need a five step symbol, for 49/48 or 50/49, and a six step symbol, for
128/125.

Hi Tom,

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:

> I'm afraid I haven't been following this thread, but
> wouldn't my absurdly simple proposal of notating the number
> of 1/3-comma ~= 225/224 steps away from a Pythagorean
> sequence fit that bill? Then any notes whose numbers
> differ by 1 or 4 or 7 (etc.) stand in a septimal
> relation, to good accuracy, for example thinking of
> 171-et as schismatic temperament rather than meantone.
>
> My brain still sees Pythagorean as the most obvious way
> to construct the default chain of fifths. Perhaps that
> is what people have been thinking of in any case.

Now it's my turn to say that *i* haven't been following
*your* thread, so i really can't comment on your notation
proposal.

But i was wondering if you are familiar with my proposal
for what i dubbed "HEWM notation":

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

There are two versions: one for 11-limit JI which i think
is absurdly simple, and one based on 72-edo which is
simpler still.

When i made the proposal a few years ago, there was quite
a debate about which symbols to use for the additional
accidentals. Some folks adopted notations which work
exactly the same way as HEWM, but which align the microtonal
accidentals and commas differently, or use a few different
symbols altogether.

That said -- and my admiration for what Dave and George
have accomplished with Sagittal notwithstanding -- it
should also be noted that i am not married "till death
do us part" to *any* music notation which is stuck on
the 5-line staff. Here are two other proposals of mine:

12-edo-staff notation:
http://tonalsoft.com/enc/number/12edo-staff.aspx

Quarter-tone-staff noation:
http://tonalsoft.com/enc/q/qt-staff.aspx

I really love the quarter-tone-staff idea -- on that page
there's an example of how you can clearly notate 72-edo
with only one pair of accidentals, and most of the time
that's close enough to 11-limit JI to satisfy me.

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

Hi Tom,

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@> wrote:
> >
> > looking at nano and
> > microtemperaments as a means to a simpler 7-limit JI notation for
> > extensive modulation, (presumably by 3's 5's and 7's).
> >
>
> I'm afraid I haven't been following this thread, but wouldn't my
> absurdly simple proposal of notating the number of 1/3-comma ~=
> 225/224 steps away from a Pythagorean sequence fit that bill?

Absolutely.

> Then any
> notes whose numbers differ by 1 or 4 or 7 (etc.) stand in a septimal
> relation, to good accuracy, for example thinking of 171-et as
> schismatic temperament rather than meantone.

Right.

> My brain still sees Pythagorean as the most obvious way to construct
> the default chain of fifths. Perhaps that is what people have been
> thinking of in any case.

It's certainly what I prefer.

If I understand correctly, you are proposing to notate 7-limit JI by
basing the notation on a planar temperament with pythag fifths as one
generator and a compromise between 1/3 of a 5-comma and 1/4 of a
7-comma as the other generator. I like it.

Here's a possible derivation of a set of Sagittal accidentals for the
multiples of the 1/3-comma generator.

First we use the 5-comma and 7-comma symbols for 3 and 4 G's
[Suggest fixed-width font to view the following]

3G /| 5-comma
4G |) 7-comma

Then we include the symbols for their sum and difference

1G |( 5:7-kleisma
7G /|) 35-M-diesis

Now their doubles

6G //| 25-S-diesis
8G (/| 49-M-diesis

+-8G is enough to notate 171-EDO without needing double-sharps or
double-flats. What are we missing? 2G and 5G.

The simplest derivation of 2G is two 5-commas minus a 7-comma, 2G =
2*3G - 4G.

The exact 7:25-comma symbol is not finalised but will probably be one
of these accented symbols
|~..
'~|(..
and we can drop the accents provided the unaccented symbol is also
valid in its primary role. Only ~|( works in that regard, so we have

2G ~|( 7:25-comma (primary role is 17-comma)

The simplest derivation of 5G is two 7 commas minus a 5 comma, 5G =
2*4G - 3G.

The exact 5:49-small-diesis symbol is .~|) and dropping the accent is
also valid.

5G ~|) 5:49-small-diesis (primary role is 49-small-diesis)

Regarding 5G, you might have noticed that symbolically subtracting our
3G symbol from our 8G we have (/| - /| = (|

Now the primary role of (| is the 7:11-comma, i.e. not 7-limit, but we
could use it in this 7-limit role provided its primary role is also
valid. Unfortunately it is not. It is closer to 4 steps of 171-EDO
than 5 steps.

So summing up we have:

1G |( 5:7-kleisma
2G ~|( 7:25-comma (primary role is 17-comma)
3G /| 5-comma
4G |) 7-comma
5G ~|) 5:49-small-diesis (primary role is 49-small-diesis)
6G //| 25-S-diesis
7G /|) 35-M-diesis
8G (/| 49-M-diesis

To see the real sagittal symbols and the full ratios or prime exponent
vectors for these symbols (and the single-character ASCII form) you
can download the font and spreadsheet from
http://dkeenan.com/sagittal

-- Dave K

I'll go on record saying I like HEWM notation.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> I'll go on record saying I like HEWM notation.

I think it's pretty good too.

Everyone seems to agree on using 81/80 to get to the 5-limit and then
64/63 to get to the 7-limit, and it's these sructural features which
are really the important ones, though.

Let's look at how that can simplify: take the ratio
cents(64/63)/cents(81/80). The convergents to this are 1, 4/3, 5/4,
14/11, 19/15 ... . We start out with (64/63)/(81/80) = 5120/5103.
Hence level one, we might say, is tempering this out. Level two is
the comma (81/80)/(5120/5103)^3 = (64/63)/(5120/5103)^4 = |-34 22 -4
3>. This is tempered out by a number of equal temperaments, but most
notably 171-et. 171 also equates 225/224 with 5120/5103, which
allows us to discuss it in terms of that instead. The third level
would be to use (5120/5103)^4/(81/80) = (5120/5103)^5/(64/63) = |44 -
28 5 -4>. Again, a number of equal temperaments temper this out, but
the standout is 441-et. Hence to simplify these sorts of notational
systems in the 7-limit, fitting them to 171 or 441 seems like the way
to go. Note that in 441, 64/63 is ten steps, 81/80 is eight steps,
and the fundamental unit 5120/5103 is two steps, not one step.

For the 11-limit, we want 33/32 in the picture, and can't simply use
the convergents of a continued fraction, but we could analyze it
similarly. However, we might note to start out with that (64/63)^2/
(33/32) = 131072/130977, and tempering this out can make for a
logical simplification of the notation scheme. Both 224 and 441
extend to this; but really, simply seeing what one gets with a good
et probably now makes the most sense.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@> wrote:
> >
> > I'll go on record saying I like HEWM notation.
>
> I think it's pretty good too.

It's what I always thought Johnston notation was, until
Dave told me that it's instead based on the 5-limit diatonic
scale in JI. Yike!

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> I'll go on record saying I like HEWM notation.
>
> -Carl
>

It was certainly a big influence on Sagittal. Its semantics is (are?)
identical, as far as it goes. Maybe 80% of what gets done with
Sagittal could also be done with HEWM. We include the Wilson + and -
symbols in the Sagittal font for those who prefer them for notating
the 5-comma. And of course the up and down arrows /|\ \!/ have the
same meaning in both. If you can accept the rounded half-arrowheads
instead of straight for the 7-comma symbols then mixed Sagittal-Wilson
is just an extension of HEWM.

-- Dave K

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > > > In my numerical 1/3-comma notation that would go
> > > >
> > > > F Ab^3 F#_4 A_1
> > >
> > > What chord is this supposed to be?
> >
> > Not a chord (although could be taken as such - 100:120:105:126
> > horrid eh?) but a demonstration of notation.
>
> What pitches are they supposed to be? Usually if one
> wants to demonstrate a notation one would choose to notate
> something familiar.
>
> -Carl

The whole message from which Carl has quoted a now-incomprehensible
excerpt explained things perfectly clearly. How many times do I have
to type things for the benefit of 'busy' people who don't bother to read?

Those numbers you see up there DO TELL YOU the pitches.

The intervals in question are 6/5, 7/4, 3/5, superposed, making up
63/50 in total.

Take it or leave it, I'm not gonna type any more.
~~~T~~~

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@> wrote:
> >
> > I'll go on record saying I like HEWM notation.
>
> I think it's pretty good too.
>
> Everyone seems to agree on using 81/80 to get to the 5-limit and then
> 64/63 to get to the 7-limit, and it's these sructural features which
> are really the important ones, though.

But I don't agree. At least for my purposes, I would prefer 225/224 as
the gateway to 7-limit, under the proviso that it is acceptable to
equate three of them with 81/80 and four of them with 64/63.

It seems to me more natural & easy to notate large commas as the sums
of small ones, rather than small commas as the differences of large ones.

~~~T~~~

> > I'll go on record saying I like HEWM notation.
> >
> > -Carl
>
> It was certainly a big influence on Sagittal. Its semantics is (are?)
> identical, as far as it goes. Maybe 80% of what gets done with
> Sagittal could also be done with HEWM. We include the Wilson + and -
> symbols in the Sagittal font for those who prefer them for notating
> the 5-comma. And of course the up and down arrows /|\ \!/ have the
> same meaning in both. If you can accept the rounded half-arrowheads
> instead of straight for the 7-comma symbols then mixed Sagittal-
> Wilson is just an extension of HEWM.

I actually don't like the HEWM accidentals monz presents,
or Wilson's +/-. I would use Tartini/Couper or Sagittals
instead. What are the Sagittals for those commas (can you
take a screenshot or something)?

I like it mainly in the context of diatonic music in JI.

-Carl

> The whole message from which Carl has quoted a now-incomprehensible
> excerpt explained things perfectly clearly. How many times do I have
> to type things for the benefit of 'busy' people who don't bother to
> read?

I'm glad you have such a high opinion of the lucidity of your
writing. It wasn't clear to *me*. The the heck is "^3" doing
in your notation. It wasn't explained in your message, was it?

-Carl

> But I don't agree. At least for my purposes, I would prefer
> 225/224 as the gateway to 7-limit, under the proviso that it
> is acceptable to equate three of them with 81/80 and four of
> them with 64/63.
>
> It seems to me more natural & easy to notate large commas as
> the sums of small ones, rather than small commas as the
> differences of large ones.

I can agree with this statement. But 225/224 has a more
complex pythagorean interface than 64/63. And I suppose
I would have to use both before agreeing that one were
better.

-Carl

Hi Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@> wrote:
> >
> > I'll go on record saying I like HEWM notation.
>
> I think it's pretty good too.
>
> Everyone seems to agree on using 81/80 to get to the
> 5-limit and then 64/63 to get to the 7-limit, and it's
> these structural features which are really the important
> ones, though.

I really appreciate the mathematical analysis which
followed (and which i snipped here). Just thought that
i should point out that the main point of debate with
HEWM were the actual symbols used for the accidentals.

I extrapolated the idea for HEWM from a knowledge of
Ben Johnston's notation, which really dissatisfied me.
To me it made a lot more sense to base the nominals on
a 3-limit system and indicate every successive prime-factor
in the same way that Johnston did for 7 and above.

Johnston used the plus and minus signs to indicate
inflections by a syntonic-comma, but what never made
sense to me was the way he based his nominals on the
5-limit diatonic scale, thus combining 3 and 5 into
the basic scale and IMO making things much more
complicated than they need to be.

So the plus and minus signs for 5 in HEWM come from
Johnston. For prime-factors 7 and 11, i was guided
primarily by a desire to be able to neatly communicate
this notation via email.

So because the less-than symbol somewhat resembles a 7,
i decided to use that and its opposite greater-than
symbol for the 3==7 xenharmonic-bridge, which i guess
you call the 7-comma -- at any rate it's the 64/63.

And because Johnston used up and down arrows to
indicate the 11 inflection, and because i had seen
them used rather frequently for quarter-tone music,
which does a good job of representing prime-factor 11,
i chose them for the 3==11 xenharmonic-bridge, 33/32.

I'm pretty sure that you and Carl already knew this
story, but there are some folks who've joined this list
over the last few years who may not have heard it before.
I hope no-one minds my retelling.

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

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

> I extrapolated the idea for HEWM from a knowledge of
> Ben Johnston's notation, which really dissatisfied me.
> To me it made a lot more sense to base the nominals on
> a 3-limit system and indicate every successive prime-factor
> in the same way that Johnston did for 7 and above.

I had wanted to add something about the name:

After i had designed HEWM on my own, i found out that
Helmholtz, Ellis, and Daniel Wolf had proposed notations
before me which followed the same structural principles:
Helmholtz and Ellis for the 5-limit, and Wolf extending
the concept up to the 23-limit.

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

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:

> But I don't agree. At least for my purposes, I would prefer 225/224 as
> the gateway to 7-limit, under the proviso that it is acceptable to
> equate three of them with 81/80 and four of them with 64/63.
>
> It seems to me more natural & easy to notate large commas as the sums
> of small ones, rather than small commas as the differences of large
ones.

This means you've adopted a nanotempering approach to the 7-limit,
whereas the other proposals want to do the just 7-limit and leave room
for other temperaments.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@>
> wrote:
>
> > That's the question. Should the fifth be the fifthjh of 19-et,
which
> > leads to a simpler notation scheme, or should it be the best
fifth of
> > 171, which is schismatic? Either will work.

Hi, Gene! I've been off-list all weekend and have returned to
discover that this has become quite a lively discussion.

First off, let me apologize for a couple of things:

1) Inadequate documentation -- There have been so many issues to
resolve lately (and very limited time to do so) that Dave & I have
not been able to give that much priority.

2) Short-sightedness -- When Dave & I first started collaborating on
Sagittal, we expected that we would be finishing up within 6 months,
or a year at most. We've just begun our 6th year and are still in
the thick of it. There doesn't seem to be any end to new and/or
unexpected issues coming up to challenge our way of thinking, so
we've constantly had to expand our horizons to keep up with new
developments taking off in different directions.

A couple of days away from the discussion have given me a little time
to reflect on what you've been saying, and I now have a better
perspective.

Our initial approach to Sagittal was to devise a way to notate
microtonal pitches & intervals for a broad range of tunings using a
single superset of accidentals. We expected that each tuning would
need to be notated in *only one way*. When the issue of additional
ways of notating tunings (via non-standard nominals and staff
configurations) came up, we then expected that the Sagittal
accidentals could be used with those, and that approach does in fact
seem to work quite well in the particular instances I've looked at.
Certainly, it makes it much less difficult for one to cope with new
staff configurations if one is already familiar with the accidentals.

Taking the nominals in a chain of 5ths *other than the best 5ths*
will then be treated not as an aberration, but simply as a case of
non-standard nominals (except that they're "non-standard" only with
respect to usual Sagittal practice), to which the accidentals may be
applied in the same manner as with any other non-standard
configuration.

The proper agenda, then, is not to debate whether the notation of 171
is better served by a chain of best 5ths or meantone 5ths, but rather
to leave that choice up to the user and, whatever the case, to
specify the set of accidentals most appropriate to that tuning.

> It should be noted that with 19 notes of Cb-E#, or 21 notes of Fb-
B#,
> we would need in addition six symbol pairs rather than four. We
would
> need a five step symbol, for 49/48 or 50/49, and a six step symbol,
for
> 128/125.

Okay, how about these (shorthand characters shown in cols. 2 & 3)?

gen. down up long comma
--- ---- -- ---- -----
1G c r |( 224:225 (primary role 5103:5120)
2G a g ~|( 126:125 (primary role 4096:4131)
3G \ / /| 80:81
4G t f |) 63:64
5G h p ~|) 48:49
6G _ = //| 6400:6561
7G u n /|) 35:36
8G & % )/|\ 392:405 (my suggestion)
or ¿ ç (/| 3969:4096 (Dave's suggestion)
9G w m (|\ 8192:8505

(If table doesn't display properly, go to top right corner of message
& click on "Show Message Option" and "Use Fixed Width Font".)

This is almost exactly what Dave has here:
/tuning/topicId_70117.html#70212
except that I've specified a different ratio for 2G (Dave has
409600:413343; both are valid), and I have a different symbol for 8G
(which doesn't require an extended ASCII character pair, as does
Dave's suggestion; both are valid).

If you happen to have flexible-pitch instruments in 19-ET, these
accidentals will tell you how much to bend the pitches to get 171-ET
and 7-limit JI.

--George

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:

> I can agree with this statement. But 225/224 has a more
> complex pythagorean interface than 64/63. And I suppose
> I would have to use both before agreeing that one were
> better.

I'm not sure what a Pythagoean interface is, but I suspect with 81/80
in the picture, 5120/5103 is small comma with more or less the same
one as 64/63, right?

Anyway, possible bridge commas someone might want to use include
36/35, 64/63, 126/125, 225/224, 5120/5103, 65625/65536, and
4375/4374. The last certainly has small size working for it. If we
decide that 4375/4374 is to be equated to the landscape comma and
that five of them equal a schisma, a number of simplifications come
into play. We have that two of the basic unit gives 2401/2400, three
420175/419904, four 703125/702464, five a schisma, and six
65625/65536. The temperament in question, the 171&3125 temperament,
is one I've not listed because of its high complexity, but since I am
now discussing it in terms of notation, I've dubbed it "ragimetric"
and listed it. Since my list is logflat badness ordered, it now shows
up second after ennealimmal. Since 4375/4374 is one step of 3125-et,
we can extend the system painlessly as 3125-et, whereupon 225/224 is
20 ragismas, and so forth. I don't know if the world is clamoring for
ultra-nano 7-limit notation beyond the scope even of 441 or 612, but
if it is, 3125 might do it.

Along these lines, I might mention that temperaments where 2401/2400
is a single step include 1578 and 1848, both strong 11-limit systems
also, so 1578&1848 might be something to think about. They both have
the property that landscape is tempered out and 2401/2400 equates to
4375/4374. Other ragisma-unit systems are 3125&3395 and 3125&3566,
but I don't see a reason to go there at the moment.

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

> So because the less-than symbol somewhat resembles a 7,
> i decided to use that and its opposite greater-than
> symbol for the 3==7 xenharmonic-bridge, which i guess
> you call the 7-comma -- at any rate it's the 64/63.

7-comma is the Sagittal name; I call it a septimal comma.

> I'm pretty sure that you and Carl already knew this
> story, but there are some folks who've joined this list
> over the last few years who may not have heard it before.
> I hope no-one minds my retelling.

Yes, basically there was a proposal to extend the idea to higher prime
limits and at the same time use George's new arrow notation, but it
grew beyond that and after a while only Dave and George knew what the
conversation was even about.

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

> Our initial approach to Sagittal was to devise a way to notate
> microtonal pitches & intervals for a broad range of tunings using a
> single superset of accidentals.

The very first idea was to notate higher limit JI, and to have an eye
on the simplifications introduced by 72-et, IIRC.

> We expected that each tuning would
> need to be notated in *only one way*.

Which was frustrating to me, becasuse I was thinking of such issues
as how to notate a piece in ennealimmal, etc. These days I am often
using an et in more than one way, which means that a fixed notation
for the et, of almost any kind, makes more sense.

> Taking the nominals in a chain of 5ths *other than the best 5ths*
> will then be treated not as an aberration, but simply as a case of
> non-standard nominals (except that they're "non-standard" only with
> respect to usual Sagittal practice), to which the accidentals may
be
> applied in the same manner as with any other non-standard
> configuration.

I like that point of view, obviously.

> > It should be noted that with 19 notes of Cb-E#, or 21 notes of Fb-
> B#,
> > we would need in addition six symbol pairs rather than four. We
> would
> > need a five step symbol, for 49/48 or 50/49, and a six step
symbol,
> for
> > 128/125.
>
> Okay, how about these (shorthand characters shown in cols. 2 & 3)?
>
> gen. down up long comma
> --- ---- -- ---- -----
> 1G c r |( 224:225 (primary role 5103:5120)
> 2G a g ~|( 126:125 (primary role 4096:4131)
> 3G \ / /| 80:81
> 4G t f |) 63:64
> 5G h p ~|) 48:49
> 6G _ = //| 6400:6561
> 7G u n /|) 35:36
> 8G & % )/|\ 392:405 (my suggestion)
> or ¿ ç (/| 3969:4096 (Dave's suggestion)
> 9G w m (|\ 8192:8505

This looks good. It should be noted that only the first four symbols,
together with 19 compound nominals from Cb to E#, are needed for the
enneadecal notation system.

> If you happen to have flexible-pitch instruments in 19-ET, these
> accidentals will tell you how much to bend the pitches to get 171-
ET
> and 7-limit JI.

That's certainly a thought. Put those 19-et clarinets to work!

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
> I would use Tartini/Couper or Sagittals
> instead. What are the Sagittals for those commas (can you
> take a screenshot or something)?

Hi Carl,

Please see the bottom row of symbols in figure 2 on page 4 of the
Xenharmonikon 18 article at
http://dkeenan.com/sagittal.pdf
where they have been since you kindly converted an earlier version of
this document to pdf many years ago. :-)

-- Dave

> > I would use Tartini/Couper or Sagittals
> > instead. What are the Sagittals for those commas (can you
> > take a screenshot or something)?
>
> Hi Carl,
>
> Please see the bottom row of symbols in figure 2 on page 4 of the
> Xenharmonikon 18 article at
> http://dkeenan.com/sagittal.pdf
> where they have been since you kindly converted an earlier version of
> this document to pdf many years ago. :-)
>
> -- Dave

I get a 'not found' on that. -Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
> I get a 'not found' on that. -Carl

Sorry Carl. That should have been
http://dkeenan.com/sagittal/sagittal.pdf

And see their definitions in Table 1 on page 8.

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> (can you take a screenshot or something)?

Try

http://dkeenan.com/sagittal/Sagittal2_Character_Map.pdf

So now you can look at it without having to install the free Sagittal
font or download the free OpenOffice software.

-- Dave Keenan

I note that because of the great width of the original spreadsheet, it
appears in the PDF as two vertical strips, one after the other. The
symbol and its character code appear with both.

The numerator, denominator and prime exponent vector appear in the
second strip, so just keep scrolling down 'til you see them.

-- Dave Keenan

> Try
> users.bigpond.net.au/d.keenan/sagittal/Sagittal2_Character_Map.pdf
>
> So now you can look at it without having to install the free Sagittal
> font or download the free OpenOffice software.
>
> -- Dave Keenan

There's an idea - embed the font in a PDF.

But this is a huge amount of info to wade through, and the
up/down of accidental pairs (if S. has up/down pairs) aren't
hown together, and ... it would take me 15 minutes of study
to locate the HEWM accidentals on here.

-Carl

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
>
> > So because the less-than symbol somewhat resembles a 7,

Oops, my bad ... i meant this the other way around:
the greater-than symbol resembles a 7.

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

> > I get a 'not found' on that. -Carl
>
> Sorry Carl. That should have been
> http://dkeenan.com/sagittal/sagittal.pdf
>
> And see their definitions in Table 1 on page 8.

That's more like what I'm looking for! Do I assume the
down versions are derived by flipping the up ones?

-Carl

> > I can agree with this statement. But 225/224 has a more
> > complex pythagorean interface than 64/63. And I suppose
> > I would have to use both before agreeing that one were
> > better.
>
> I'm not sure what a Pythagoean interface is, but I suspect with
> 81/80 in the picture, 5120/5103 is small comma with more or
> less the same one as 64/63, right?

Uh. I just meant the map for 7/4 is +2 4ths with 64/63,
and something worse with 225/224.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > > I get a 'not found' on that. -Carl
> >
> > Sorry Carl. That should have been
> > http://dkeenan.com/sagittal/sagittal.pdf
> >
> > And see their definitions in Table 1 on page 8.
>
> That's more like what I'm looking for! Do I assume the
> down versions are derived by flipping the up ones?

Absolutely.

Reflected, not rotated.

Sort of sounds like "shaken, not stirred".

The name is Bosanquet, James Bosanquet.

Well actually it's Robert Holford Macdowall Bosanquet, but you can
call me James for short.

http://en.wikipedia.org/wiki/Robert_Holford_Macdowall_Bosanquet

-- Dave K

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
> There's an idea - embed the font in a PDF.
>
> But this is a huge amount of info to wade through, and the
> up/down of accidental pairs (if S. has up/down pairs) aren't
> hown together, and ... it would take me 15 minutes of study
> to locate the HEWM accidentals on here.

Yes. You're quite right. This is the character map for the font so it
is laid out in the same order as the font. It's purpose is more for
calculation, such a Herman was doing with it. I misunderstood what you
were after. The PDF of the XH18 article is what you want.

-- Dave K

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > > I can agree with this statement. But 225/224 has a more
> > > complex pythagorean interface than 64/63. And I suppose
> > > I would have to use both before agreeing that one were
> > > better.
> >
> > I'm not sure what a Pythagorean interface is, but I suspect with
> > 81/80 in the picture, 5120/5103 is small comma with more or
> > less the same one as 64/63, right?
>
> Uh. I just meant the map for 7/4 is +2 4ths with 64/63,
> and something worse with 225/224.
>
> -Carl

'Something worse' is +10 5ths lowered by two 81/80's and a 225/224.
Since I think of 7/4 as an aug6 and the 5-limit 'just' aug6 is
225/128, this doesn't give me a problem.

It depends how you see the 7-limit being applied musically. And I
don't see any reason to try and standardise notation between two or
more quite different musical approaches.

If you think of 7/4 as functionally a seventh you aren't going to like
my notational approach and you'd be perfectly justified in asking for
64/63 to get priority. Then your notation would look different from
mine ... which I don't see as a big drawback because the resulting
music would sound quite different too.

At the moment I don't want notation to be exactly Just, just just
enough. The thinking is that, given the notation, the 'performer' may
retain some schisma-or-smaller-sized choice or uncertainty around the
Just value - which I think is realistic. If this allowance for
'schismatic slop' happens to allow for a simplification of notation
then I'm happy.

~~~T~~~

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:

> At the moment I don't want notation to be exactly Just, just just
> enough. The thinking is that, given the notation, the 'performer' may
> retain some schisma-or-smaller-sized choice or uncertainty around the
> Just value - which I think is realistic. If this allowance for
> 'schismatic slop' happens to allow for a simplification of notation
> then I'm happy.

This makes a whole lot of sense in acoustic perfomance situations. I
can see someone, however, wanting an extremely accurate
MIDI/electronic notation, too.

Cheers,
Aaron.

> The name is Bosanquet, James Bosanquet.
>
> Well actually it's Robert Holford Macdowall Bosanquet, but you can
> call me James for short.
>
> http://en.wikipedia.org/wiki/Robert_Holford_Macdowall_Bosanquet
>
> -- Dave K

Awesome! I never knew what RHM stood for before. Gotta lubbit.

-Carl

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@> wrote:
> >
> > > > I can agree with this statement. But 225/224 has a more
> > > > complex pythagorean interface than 64/63. And I suppose
> > > > I would have to use both before agreeing that one were
> > > > better.
> > >
> > > I'm not sure what a Pythagorean interface is, but I suspect with
> > > 81/80 in the picture, 5120/5103 is small comma with more or
> > > less the same one as 64/63, right?
> >
> > Uh. I just meant the map for 7/4 is +2 4ths with 64/63,
> > and something worse with 225/224.
> >
> > -Carl
>
> 'Something worse' is +10 5ths lowered by two 81/80's and a 225/224.

Thanks.

> Since I think of 7/4 as an aug6 and the 5-limit 'just' aug6 is
> 225/128, this doesn't give me a problem.
>
> It depends how you see the 7-limit being applied musically. And I
> don't see any reason to try and standardise notation between two or
> more quite different musical approaches.

Agree.

> If you think of 7/4 as functionally a seventh you aren't going
> to like my notational approach and you'd be perfectly justified
> in asking for 64/63 to get priority.

It seems to me most genres that treat it as a consonance spell
it as a 7th.

> At the moment I don't want notation to be exactly Just, just just
> enough.

I think having the different symbols might help, because it
can tell the performer which harmonic to hit. You can use
the 72-tET equivalences to be refactor accidental pileups
if you run into them, but otherwise use them sparingly.

-Carl

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

http://dkeenan.com/sagittal/Sagittal2_Character_Map.pd
f
>
> So now you can look at it without having to install the free Sagittal
> font or download the free OpenOffice software.

But you won't have a clue what the symbols are symbols for without
consulting something else.

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:

> At the moment I don't want notation to be exactly Just, just just
> enough. The thinking is that, given the notation, the 'performer' may
> retain some schisma-or-smaller-sized choice or uncertainty around the
> Just value - which I think is realistic. If this allowance for
> 'schismatic slop' happens to allow for a simplification of notation
> then I'm happy.

If you are going to allow schismatic slop, then 171 is about as complex
as you want to go, so you would seem to be on the right track with this
business. Allowing larger slop tolerances would allow for more drastic
simplifications, of course.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@> wrote:
>
> http://dkeenan.com/sagittal/Sagittal2_Character_Map.pd
> f
> >
> > So now you can look at it without having to install the free Sagittal
> > font or download the free OpenOffice software.
>
> But you won't have a clue what the symbols are symbols for without
> consulting something else.

If you mean "Where are the numerator and denominator?" again, this
time you have to scroll _down_ to see them, not sideways. The PDF
generation process insisted on slicing the spreadsheet into two
vertical strips and putting them one after the other.

But you should be happy with this, because you get to see the ratio
right next to the symbol in this second strip.

If you mean that people need more explanation of Sagittal than just
the character map, you're absolutely right. Which is why there is a
whole Sagittal website
http://dkeenan.com/sagittal/
(or just Google "sagittal notation")
containing both formal
http://dkeenan.com/sagittal/Sagittal.pdf
and informal (and hopefully humorous)
http://dkeenan.com/sagittal/gift/GiftOfTheGods.htm
introductions to Sagittal.

-- Dave K

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@...> wrote:
> This is almost exactly what Dave has here:
> /tuning/topicId_70117.html#70212
> except that I've specified a different ratio for 2G (Dave has
> 409600:413343; both are valid), and I have a different symbol for 8G
> (which doesn't require an extended ASCII character pair, as does
> Dave's suggestion; both are valid).

Hi George,

The symbol )/|\ for the 5:49-medium-diesis is not valid for 8
generators of this planar temperament. I suspect you have been misled
by its being valid for 171-EDO. The 5-schisma vanishes in 171-EDO but
not in the planar temperament being notated. For example, a schisma up
from C would be B#\ .

-- Dave K

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

> The symbol )/|\ for the 5:49-medium-diesis is not valid for 8
> generators of this planar temperament. I suspect you have been misled
> by its being valid for 171-EDO. The 5-schisma vanishes in 171-EDO but
> not in the planar temperament being notated. For example, a schisma up
> from C would be B#\ .

Except he's also indicated he wanted some schismatic slop, which
suggests to me the schisma should also be tempered out. Do that and you
are using term temperament, with generator a fifth and period 400
cents. As previously noted, that means 225/224 is equated to 5120/5103
and 3136/3125, two of them to 126/125 and 4000/3969, three to
2048/2025, 3125/3087, and 81/80, four to 64/63, five to 50/49, six to
128/125 and seven to 36/35.

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > The name is Bosanquet, James Bosanquet.
> >
> > Well actually it's Robert Holford Macdowall Bosanquet, but you can
> > call me James for short.
> >
> > http://en.wikipedia.org/wiki/Robert_Holford_Macdowall_Bosanquet
> >
> > -- Dave K
>
> Awesome! I never knew what RHM stood for before. Gotta lubbit.

Definitely an essential character for my first steampunk novel.

-Carl

> > > http://en.wikipedia.org/wiki/Robert_Holford_Macdowall_Bosanquet
> > >
> > > -- Dave K
> >
> > Awesome! I never knew what RHM stood for before. Gotta lubbit.
>
> Definitely an essential character for my first steampunk novel.
>
> -Carl

From the Wikipedia bio I found:

http://www.sibeliusmusic.com/cgi-bin/show_score.pl?scoreid=96007

This piece made me cringe for some reason, and I could barely
read the score on my display, but it seems like the composer
got Sibelius to do Bosanquet / accidentals and their tunings.
Wonder how he did that.

-Carl

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@> wrote:
>
> > The symbol )/|\ for the 5:49-medium-diesis is not valid for 8
> > generators of this planar temperament. I suspect you have been misled
> > by its being valid for 171-EDO. The 5-schisma vanishes in 171-EDO but
> > not in the planar temperament being notated. For example, a schisma up
> > from C would be B#\ .
>
> Except he's also indicated he wanted some schismatic slop, which
> suggests to me the schisma should also be tempered out. Do that and you
> are using term temperament, with generator a fifth and period 400
> cents. As previously noted, that means 225/224 is equated to 5120/5103
> and 3136/3125, two of them to 126/125 and 4000/3969, three to
> 2048/2025, 3125/3087, and 81/80, four to 64/63, five to 50/49, six to
> 128/125 and seven to 36/35.
>

'He' is me, and it should be noted that the resulting error is in most
musical cases a lot less than a schisma. (Does anyone use the interval
C-B# functionally?)

The one thing that's puzzling me is why people are talking about '2G',
'5G' etc. for cumulative deviations from the nominals. Does this stand
for anything? 'Generator'?

~~~T~~~

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:

> > >
> > > http://en.wikipedia.org/wiki/Robert_Holford_Macdowall_Bosanquet
> > >
>
> Definitely an essential character for my first steampunk novel.
>
> -Carl
>

Anachronistic calliope with Liston's shaders
http://en.wikipedia.org/wiki/Henry_Liston

Clark

You mean the mirrored flats? They are an integral part of Sibelius.

Oz.

----- Original Message -----
From: "Carl Lumma" <clumma@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 07 Mart 2007 �ar�amba 11:04
Subject: [tuning] Re: Sagittal info spreadsheet now available

> > > > http://en.wikipedia.org/wiki/Robert_Holford_Macdowall_Bosanquet
> > > >
> > > > -- Dave K
> > >
> > > Awesome! I never knew what RHM stood for before. Gotta lubbit.
> >
> > Definitely an essential character for my first steampunk novel.
> >
> > -Carl
>
> >From the Wikipedia bio I found:
>
> http://www.sibeliusmusic.com/cgi-bin/show_score.pl?scoreid=96007
>
> This piece made me cringe for some reason, and I could barely
> read the score on my display, but it seems like the composer
> got Sibelius to do Bosanquet / accidentals and their tunings.
> Wonder how he did that.
>
> -Carl
>
>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> You mean the mirrored flats? They are an integral part of Sibelius.
>
> Oz.

No, the slashes.

-Carl

> > > > http://en.wikipedia.org/wiki/Robert_Holford_Macdowall_Bosanquet
> > > >
> >
> > Definitely an essential character for my first steampunk novel.
> >
> > -Carl
> >
>
> Anachronistic calliope with Liston's shaders
> http://en.wikipedia.org/wiki/Henry_Liston
>
> Clark

Does anyone know anything more about this instrument?

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:

> http://www.sibeliusmusic.com/cgi-bin/show_score.pl?scoreid=96007
>
> This piece made me cringe for some reason, and I could barely
> read the score on my display, but it seems like the composer
> got Sibelius to do Bosanquet / accidentals and their tunings.
> Wonder how he did that.

Here's more 53-et stuff:

http://www.sibeliusmusic.com/cgi-bin/user_page.pl?url=commator

Serious looking Ukranian dude. I wonder if he knows about the tuning
list.

He must have implanted them as symbols.

----- Original Message -----
From: "Carl Lumma" <clumma@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 07 Mart 2007 �ar�amba 18:45
Subject: [tuning] Re: Sagittal info spreadsheet now available

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > You mean the mirrored flats? They are an integral part of Sibelius.
> >
> > Oz.
>
> No, the slashes.
>
> -Carl
>
>

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
> 'He' is me, and it should be noted that the resulting error is in most
> musical cases a lot less than a schisma. (Does anyone use the interval
> C-B# functionally?)
>
> The one thing that's puzzling me is why people are talking about '2G',
> '5G' etc. for cumulative deviations from the nominals. Does this stand
> for anything? 'Generator'?

Hi Tom,

Yes. In this case your 1/3-comma. Sorry I didn't make that clear. I
was considering it as one generator of a planar temperament, the other
being your Pythagorean fifth.

There was a fine point about which Sagittal symbol was best for 8 of
these. I thought it should be the symbol whose meaning is a double
septimal comma. For reasons unknown, George Secor suggested another
symbol whose meaning is a schisma larger than that. It isn't important.

-- Dave K

> > But this is a huge amount of info to wade through, and the
> > up/down of accidental pairs (if S. has up/down pairs) aren't
> > hown together, and ... it would take me 15 minutes of study
> > to locate the HEWM accidentals on here.
>
> Yes. You're quite right. This is the character map for the font
> so it is laid out in the same order as the font. It's purpose
> is more for calculation, such a Herman was doing with it. I
> misunderstood what you were after. The PDF of the XH18 article
> is what you want.

Yes, thanks (as I've already said in an off-list message), the
XH18 preprint had the goods.

I realize this may not be a fruitful time for criticism, and
I won't be getting into a detailed thread about this one way
or another, but I thought I would voice two concerns I have
about the Sagittal symbols.

1. If you told me the lot of them were as visually different
as possible (given that one also has to quickly distinguish
that they fall into two classes: up and down), I would believe
you. But it seems that when using a subset (like the HEWM
subset) we could do better. Tartini/Couper seems to be one
example.

2. Easley Blackwood put his arrows through circles, to make
it clear which line or space the accidental applied to. I
thought the result looked a bit much like a note, and was a
bit to tall on the page (yes, I suppose one could say the same
thing about traditional flats).
The Tartini/Couper symbols likewise seem to have a good
center of gravity over the height of a staff space.
But Sagittals seem top- or bottom-heavy, and if you shrink
them to the size of a staff space they might become hard
to read (or would they?).

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
> I realize this may not be a fruitful time for criticism, and
> I won't be getting into a detailed thread about this one way
> or another, but I thought I would voice two concerns I have
> about the Sagittal symbols.
>
> 1. If you told me the lot of them were as visually different
> as possible (given that one also has to quickly distinguish
> that they fall into two classes: up and down), I would believe
> you. But it seems that when using a subset (like the HEWM
> subset) we could do better. Tartini/Couper seems to be one
> example.

Hi Carl,

You're absolutely right. You can always make any given subset
internally more distinct. But the only way to have all (or even only
the most popular) subsets as internally distinct as possible is to
make them incompatible with each other or to make them less logical in
some way. In a consistent system designed to cover all tunings there
are an enormous number of tradeoffs to be considered. Everyone
naturally tends to think that their application is the most important.

One of the features of Sagittal, that makes the notation of complex
tunings more manageable, is what we call "flag arithmetic". A flag is
a half-arrowhead, of which there are 4 shapes and 2 sides on which to
put them. If you see a symbol that _looks_ like it is composed from
two other symbols then you can rest assured that it corresponds to the
sum of their pitch alterations (or very nearly so).

You may remember that the Sagittal symbols were thrashed out on this
list and the tuning-math list for over a year. Many people had input
into them. It really was the best we could collectively come up with
in a consistent system, and so I'm glad you find that believable.

However
-------

As Ralph Waldo Emerson famously said, "A foolish consistency is the
hobgoblin of little minds".

You are right that the universal logic of the system means that
simpler tunings have paid a price in symbol distinctness, and they
really shouldn't have to.

And they _don't_ have to! :)

We long ago provided the Wilson/Wolf sloping + and - symbols as
alternative symbols for the 5-comma. Joseph Pehrson uses them along
with the remaining Sagittal symbols for 72-EDO. You can see them in
the bottom row of figure 12 on page 20 of the Sagittal XH18 article.
http://dkeenan.com/sagittal/sagittal.pdf

And now, in Sagittal-2, we have provided the very symbols you mention.
The Tartini/Couper symbols. You will see them at the start and end of
the character map.
http://dkeenan.com/sagittal/Sagittal2_Character_Map.pdf
(Don't forget you can right-click to zoom).

Please feel free to substitute the Tartini-Couper symbols for the
Sagittal full arrows /|\ and \!/ or whichever Sagittal symbol
corresponds to a half-apotome in the tuning being notated. So for
example you can have a 72-EDO or HEWM-like notation that uses the
Sagittal symbols only for the 7-comma, Wilson symbols for the 5-comma
and Tartini-Couper (which Erv also used) for the 11-diesis.

I have designed the outlines of these symbol's so they are all
compatible in visual style.

> 2. Easley Blackwood put his arrows through circles, to make
> it clear which line or space the accidental applied to. I
> thought the result looked a bit much like a note, and was a
> bit to tall on the page (yes, I suppose one could say the same
> thing about traditional flats).
> The Tartini/Couper symbols likewise seem to have a good
> center of gravity over the height of a staff space.
> But Sagittals seem top- or bottom-heavy, and if you shrink
> them to the size of a staff space they might become hard
> to read (or would they?).

Carl,

Are you implying that you have never seen sagittal symbols on a staff?

Criticism of Sagittal is welcome -- how else can it be improved? But
if you're going to do so, please do us the courtesy of first reading
at least this one document from start to finish.
http://dkeenan.com/sagittal/sagittal.pdf

An enormous amount of effort has gone into making it as clear,
complete and accurate as possible, and it has been available for
nearly 3 years now.

Please see figure 6 on page 11, figure 7 on page 13 and figure 11 on
page 18. You might also see some of Margo Schulter's scores via the
Make_Micro_Music list (produced using Hudson Lacerda's MicroABC
software). You can also have Scala show you any Sagittal notation on
the staff.

You will see that Sagittals work, visually, exactly like conventional
flats. They have a bold head and a thin tail. What's more, we agree
with you that the tails of flats are too tall and so sagittals have
slightly shorter tails. Sagittal tails are the same length as those of
a conventional natural. Sagittals are designed so that you don't need
to stagger them when notating a chord containing thirds as you are
forced to do with conventionals and Tartini/Coupers.

As with the conventional flat, it is the center of gravity of the head
of a sagittal that indicates the line or space to which it applies.
George and I carefully examined all 232 symbols at very low resolution
on a staff, against both lines and spaces, to ensure that they were
not obscured and that it was clear what they applied to. Many small
adjustments were made and retested, made and retested ...

But please let us know where you think it might yet be improved.

Thank you for the opportunity to explain these things. Now I really
must get back to my microtonal instrument building project. :-)

-- Dave K

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
> As Ralph Waldo Emerson famously said, "A foolish consistency is the
> hobgoblin of little minds".

I note that Emerson never explained how to tell a foolish consistency
from a wise one.

-- Dave K

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
> You don't get much more traditional in meantone
> than 1/4-comma, and I think C-Bbbbbb is arguably a fifth in the
> system, and clearly a better one.

That's hilarious Gene. I had no idea that quadrupley diminished
sevenths were in use in the meantone era. ;-)

> Really? Are you saying you sometimes use something other than the
> best fifth--and if so, in what cases?

We sometimes suggest using _better_ fifths than those avaiable, in
notating ETs so that C:G:D would remain an approximation to 1:3:9. But
we also give native fifth notations using such bad fifths as those of
5-edo and 7-edo and their multiples

See
http://dkeenan.com/sagittal/sagittal.pdf
page 15:

"Listed in Figure 8 are the divisions that require no symbols other
than those in the spartan set. In some of these divisions the fifths
have such large errors that the divisions are not 1,3,9-consistent. In
such cases it may be preferable to notate these as subsets of larger
divisions, even though their native-fifth notations generally require
fewer symbols."

And I have used _worse_ fifths in the MOS/DE-compound-nominal
notations for rank-2 temperaments that I helped Herman Miller develop.
Often these are not using fifths at all.

Search on "compound nominal" in tuning-math.

> The point of it is, if you can notate 171-et, you can notate the 7-
> limit, and enneadecal seems like a good choice as the way to notate
> 171-et.

That's your opinion, and I understand your reasons. Please accept that
others are entitled to different opinions.

> > Then again, we probably haven't done such a great job of explaining
> > it. I'd love for a professional educator or writer to volunteer to
> > write about sagittal, particularly for non-math types.
>
> If the symbols are proposed for flexible usage then I'm sorry, you've
> done a rotten job explaining it. Why not just start out by giving a
> list of symbols with a primary interpretation, along with things you
> think would be reasonable as a secondary interpretation?

See the second paragraph on page 1.

"In the early stages of the discussion, one idea that surfaced
repeatedly was that a set of symbols indicating prime-number commatic
alterations to tones in a Pythagorean series might be used to notate
both rational intervals (e.g. just intonation) and equal divisions of
the octave. ... As a first step, Gene Ward Smith suggested that it
would be desirable that there be no more than one comma symbol per
prime number, and a selection of 19-limit commas was tentatively
identified to define the semantics of the notation."

And see table 1 on page 8.

It is a list of symbols with primary and secondary interpretations.

> Then you
> could say you envision the primary use of such a set as being a way
> to extend standard staff notation, in which case something which
> plays the role of a generator fifth is presumed to be available? If
> that isn't made clear, it's then not that clear you are even allowed
> to notate Palestrina using Sagittal, because of the non-optimality of
> the 1/4 comma fifth in extended meantone. You could then go on to say
> other staff arragements and other generators can be adapted to the
> scheme also,

See the first paragraph of page 2 (the fourth paragraph of the article):

"The Sagittal notation uses a conventional staff on which the natural
notes are in a single series of fifths, with sharps and flats (and
doubles thereof) indicating tones that are members of that same
series, regardless of the particular tonal system being notated (see
footnote 2). Therefore, if the notation is used for just intonation,
these notes will indicate a Pythagorean tuning. For an equal division
of the octave, they will indicate the tones in a series built on that
division's best approximation of a fifth."

Footnote 2 reads:

"The Sagittal accidentals may also be used in a consistent manner with
systems that do not use a conventional staff, or have more or less
than seven nominals, which may not be in a series of fifths, but that
is beyond the scope of this article."

> and try to do with a smile on your face instead of
> acting like the Sagittal Police, which is how you've been coming
> across.

You missed have the smileys. I guess you could have mistaken them for
sagittals in ASCII (sounds like sardines in aspic). :-) Look, there
goes one now. :-)

I'll try harder to do as you say. But you should know that you've been
coming across as a completely humorless narcissist ever since you've
been on the list. I try not to let it bother me. :-)

> Yet your immediate reaction to my enneadecal proposal, which is
> exactly that, was extremely negative.

I think you're projecting. :-)

> I've proposed radical notations, but the above are not radical. They
> are way, *way* less radical in fact than the weirdness pure Sagittal
> in high-limit JI involves.

Yup. I have to agree with you there. :-)

> > I thought your Garibaldi suggestion was a fine one. What's the next
> > more complex more accurate 7 limit linear temperament that has a
> > single generator approximating 3?
>
> Pontiac, but I seem to recall you don't like pontiac.

I made a joke about the name, or rather its derivation. I got over it.
:-) I've never had any problem with the temperament itself.

> However, it is
> a strong nanotemperament, is compatible with 171, and is basically
> what you would be doing if you took your system of using the best
> fifth and applied it to 171. In which case, you've probably done it
> already.

Please see figure 9 on page 16. It differs from the notations
suggested recently only because it is 11-limit.

-- Dave K

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

> > The point of it is, if you can notate 171-et, you can notate the
7-
> > limit, and enneadecal seems like a good choice as the way to
notate
> > 171-et.
>
> That's your opinion, and I understand your reasons. Please accept
that
> others are entitled to different opinions.

But do *you* realize that? And can you explain why you think it is a
bad choice?

> Footnote 2 reads:
>
> "The Sagittal accidentals may also be used in a consistent manner
with
> systems that do not use a conventional staff, or have more or less
> than seven nominals, which may not be in a series of fifths, but
that
> is beyond the scope of this article."

Then why the vapors when people actually suggest such things?

> I'll try harder to do as you say. But you should know that you've
been
> coming across as a completely humorless narcissist ever since you've
> been on the list. I try not to let it bother me. :-)

So your idea is that you can raise the tone of the conversation and
demonstrate your own sweetly gentle brand of humor by engaging in
personal attacks here? If that's a joke, it isn't a particularly
funny one. I don't think personal attacks should be engaged in on
this list, by anyone, ever. Color me humorless.

> > Pontiac, but I seem to recall you don't like pontiac.
>
> I made a joke about the name, or rather its derivation. I got over
it.
> :-) I've never had any problem with the temperament itself.

You expressed dismay over how complex it was and suggested it was
useless, if that counts.

> > 2. Easley Blackwood put his arrows through circles, to make
> > it clear which line or space the accidental applied to. I
> > thought the result looked a bit much like a note, and was a
> > bit to tall on the page (yes, I suppose one could say the same
> > thing about traditional flats).
> > The Tartini/Couper symbols likewise seem to have a good
> > center of gravity over the height of a staff space.
> > But Sagittals seem top- or bottom-heavy, and if you shrink
> > them to the size of a staff space they might become hard
> > to read (or would they?).
>
> Carl,
>
> Are you implying that you have never seen sagittal symbols on
> a staff?

It was seeing them on a staff that prompted this comment.

> An enormous amount of effort has gone into making it as clear,
> complete and accurate as possible, and it has been available for
> nearly 3 years now.
>
> Please see figure 6 on page 11, figure 7 on page 13 and figure 11 on
> page 18. You might also see some of Margo Schulter's scores via the
> Make_Micro_Music list (produced using Hudson Lacerda's MicroABC
> software). You can also have Scala show you any Sagittal notation on
> the staff.

I have two of her scores right here. They're very spacious,
as are the examples in your paper, and all the accidentals seem
enormous.

> You will see that Sagittals work, visually, exactly like
> conventional flats. They have a bold head and a thin tail.
> What's more, we agree with you that the tails of flats are
> too tall and so sagittals have slightly shorter tails.

Looking at them at first, they didn't look like tails, but
rather like part of the body of a sharp. I see now the arrow
bit is supposed to be the center of gravity.

> But please let us know where you think it might yet be improved.
>
> Thank you for the opportunity to explain these things. Now I really
> must get back to my microtonal instrument building project. :-)

I guess I'll have to think about it.

-Carl

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
> And can you explain why you think it is a
> bad choice?

Yes. For the reason Tom Dent already gave. Most folks expect their
best 1:3:9 approximations to be notated C:G:D or G:D:A etc.

I repeat: Your enneadecal notation is a fine one.

I totally encourage anyone notating 171-EDO or 7-limit JI to consider
using it.

> So your idea is that you can raise the tone of the conversation and
> demonstrate your own sweetly gentle brand of humor by engaging in
> personal attacks here? If that's a joke, it isn't a particularly
> funny one. I don't think personal attacks should be engaged in on
> this list, by anyone, ever. Color me humorless.

I totally agree.

No. It wasn't a personal attack, just my observation of how it seems
to me. As, I assume, was your observation that I seemed to be behaving
like an unsmiling Sagittal Policeman, despite the fact that I invented
the term myself recently while telling people there are none, and that
they can do whatever they like with Sagittal. Twice. Once to Aaron
(with a smiley) and once to you (sorry I omitted the smiley the second
time).

You probably won't understand this, but it felt a bit like a personal
attack when you said we'd "done a rotten job explaining it", when you
apparently hadn't actually checked our documentation to see _how_ we'd
explained it.

That you hadn't checked, can be judged by the fact that all the things
you suggested we should have done, we actually had done. Pretty much
in the order you suggested.

> You expressed dismay over how complex [pontiac] was and suggested it
> was useless, if that counts.

I may have done. If so, you've now changed my mind. :-)

-- Dave K

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > > > > http://en.wikipedia.org/wiki/
Robert_Holford_Macdowall_Bosanquet
> > > > >
> > >
> > > Definitely an essential character for my first steampunk novel.
> > >
> > > -Carl
> > >
> >
> > Anachronistic calliope with Liston's shaders
> > http://en.wikipedia.org/wiki/Henry_Liston
> >
> > Clark
>
> Does anyone know anything more about this instrument?
>
> -Carl
>
http://www.geocities.com/threesixesinarow/1830edine.htm
http://www.geocities.com/threesixesinarow/farey.htm
(note the slashes)

The patent claims using lever operated shades at the mouths and ends
of the pipes, and a self-operated mechanical regulator for the
bellows. (I think calliopes weren't patented till after 1850 http://
en.wikipedia.org/wiki/Calliope_(music), maybe one was made like that
but I imagined something like http://prodgers13.home.comcast.net/
liner/Resolution_in_blue.htm but more earsplitting)

Clark

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@> wrote:
> >
>(C.L.)I can agree with this statement. But 225/224 has a more
> complex pythagorean interface than 64/63.
> > >
>(T.D)I'm not sure what a Pythagorean interface is, but I suspect with
> > > 81/80 in the picture, 5120/5103 is small comma with more or
> > > less the same one as 64/63, right?
> >
>(C.L)I just meant the map for 7/4 is +2 4ths with 64/63,
> > and something worse with 225/224.
> >
>(T.D)
> 'Something worse' is +10 5ths lowered by two 81/80's and a 225/224.
> Since I think of 7/4 as an aug6 and the 5-limit 'just' aug6 is
> 225/128, this doesn't give me a problem.
>
> It depends how you see the 7-limit being applied musically. And I
> don't see any reason to try and standardise notation between two or
> more quite different musical approaches.
>
> If you think of 7/4 as functionally a seventh you aren't going to
> like
> my notational approach and you'd be perfectly justified in asking
> for 64/63 to get priority.

Classically there are 3 different types commata,
classified according their 3,5,7 limits:

3-limit or di(a)tonic
http://en.wikipedia.org/wiki/Pythagorean_comma
P:= 53441:524288 = 3^12 * 2^-19

5-limit (Didimus' or Ptolemaios')
http://en.wikipedia.org/wiki/Syntonic_comma
S:= 81:80 = 5^-1 * 3^4 * 2^-4

7-limit (Archytas') 'ecmelic':= byond 5-limit
http://en.wikipedia.org/wiki/Septimal_comma
A:= 64:63 = 7^-1 * 3^-2 *2^5

The standard refinement P:S defines the common usual
5-limit syntonic
http://en.wikipedia.org/wiki/Schisma
s:= P:S = 32805:32768 = 5 * 3^8 * 2^-15 ~~1.9537...cents~~

and respectively the ratio of A:P the less familiar 'ecmelic'
7-limit "Septimal_schisma"
a:= A:P = 33554432/33480783 = 7^-1 * 3^-14 * 2^25 ~~3.80408...cents~~
corresponding to the 5-limit_schisma and 7-limit_comma procedure.

With that both types of schismata, the product a*s^2 yields for the
http://www.xs4all.nl/~huygensf/doc/intervals.html
"225/224 septimal kleisma" inherent within the 'ecmelic' 7-limit
225:224 := 7^-1 * 5^-2 * 3^2 * 2^-5 ~~7.71152...cents := a+2s~~
a decomposition into 3 the schismatically subfactors

a*s*s=225/224

Hence I do prefer the above "Septimal_schisma" instead
the Septimal_comma= 64:63 = (7:4) as 'pythagorean-interface'

7:4 = (3^14:2^23):a schismatic-bridge
the same as
7:4 = (16:9):A commatic-enharmonics

analogous to the 'pythagorean-interface' in
the corresponding syntonic 5-limit case respectively:

5:4 = (3^8:2^13)*s schismatic-bridge
the same as
5:4 = (81:64):S commatic-enharmonics

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

> No. It wasn't a personal attack, just my observation of how it seems
> to me.

http://en.wikipedia.org/wiki/Personal_attack

"It is considered a personal attack when a person starts referencing
a supposed flaw or weakness in an individual's personality, beliefs,
lifestyle, convictions or principles, and use it as a debate tactic
or as a means of avoiding discussion of the relevance or truthfulness
the person's statement."

> You probably won't understand this, but it felt a bit like a
personal
> attack when you said we'd "done a rotten job explaining it"

I apolgize if I hurt your feelings, and am sorry to have done so.
However, the phrase "personal attack" has an objective meaning, and
it is things which fall under that rubric, or insulting personal
commentary in general, which I think should be considered out of
bounds.

Do not do it here.

Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
> Do not do it here.

So it is *your* list now, to issue ultimatums to the membership? It
doesn't appear that your particular home is built of shatter-proof
glass, so you ought to be careful when (or desist entirely from)
telling people how to behave.

Asking them, or discussing it in an open manner, is another story.
However, it is one I don't think you are interested in writing.

Jon

--- In tuning@yahoogroups.com, "Jon Szanto" <jszanto@...> wrote:
>
> Gene,
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@>
> wrote:
> > Do not do it here.
>
> So it is *your* list now, to issue ultimatums to the membership?

Dave just didn't seem to be getting it. And are you saying you favor
allowing personal attacks? How far does that extend? Is anti-Semtism
also OK? What about racial slurs? We have had, please recall, problems
of that kind.

Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
> Dave just didn't seem to be getting it.

Yes, I'm sure in your eyes, it was all in Dave's court. This is the
standard modus operandi.

> And are you saying you favor allowing personal attacks?

No, and no to all the insulting insinuations that followed. It takes
good will from all parties involved to have civil discussions, and
that, my friend, includes you.

Jon

> Do not do it here.

Geez, Gene, you gettin' power-trip syndrome?

-Carl

> > Do not do it here.
>
> So it is *your* list now, to issue ultimatums to the membership?

...Jon's definitely still got his self-righteous taunts.

This is a perfect example of why your statement, Gene, is
not correct. There's no way to objectively determine if a
statement is a personal attack. Though Jon's clearly is
in my mind.

-Carl

> > And are you saying you favor allowing personal attacks?
>
> No, and no to all the insulting insinuations that followed. It takes
> good will from all parties involved to have civil discussions, and
> that, my friend, includes you.
>
> Jon

How ironic, to me Jon: I've read this entire thread, and your
posts have been the most objectionable.

-Carl

Carl,

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
> > So it is *your* list now, to issue ultimatums to the membership?

> Though Jon's clearly is [a personal attack] in my mind.

Then you tell me, dear boy: I object to Gene attempting to
unilaterally determine the behavior of people on this list, when he is
not the list owner; that being the case, how would you propose I show
my rejection of this notion, proposed by one person, without directly
confronting that person?

Never mind. I'm not really interested.

Jon

Carl,

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
> How ironic, to me Jon: I've read this entire thread, and your
> posts have been the most objectionable.

Pretty good, since I've only had one post, and it didn't seem very
different from you accusing Gene of power-tripping. You know what
though? I really don't care, as once again you and Gene have peed in
the pool. Nice time for a break from all this blather. I wish Ozan the
best in his audio/midi adventures, and hope Dave continues his work,
with George, on the Saggital project, in spite of ... everything.

Jon

--- In tuning@yahoogroups.com, "Jon Szanto" <jszanto@...> wrote:
>
> Gene,
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@>
> wrote:
> > Dave just didn't seem to be getting it.
>
> Yes, I'm sure in your eyes, it was all in Dave's court. This is the
> standard modus operandi.

No, in my eyes it was not. I was no doubt highly annoying, and Dave's
comments were fairly mild. But his was over a line I think needs to be
drawn.

Do you understand what I am saying here?

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > Do not do it here.
>
> Geez, Gene, you gettin' power-trip syndrome?

I should have said "please". But Dave was denying he made any kind of
personal attack, which was just factually wrong.

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > > Do not do it here.
> >
> > So it is *your* list now, to issue ultimatums to the membership?
>
> ...Jon's definitely still got his self-righteous taunts.
>
> This is a perfect example of why your statement, Gene, is
> not correct. There's no way to objectively determine if a
> statement is a personal attack. Though Jon's clearly is
> in my mind.

Jon did not say "You have obnoxious personal qualities X, Y and Z", so
it isn't. I don't think this is really that hard.

--- In tuning@yahoogroups.com, "Jon Szanto" <jszanto@...> wrote:

> Pretty good, since I've only had one post, and it didn't seem very
> different from you accusing Gene of power-tripping. You know what
> though? I really don't care, as once again you and Gene have peed in
> the pool.

You want to see why starting down the road of personal attacks is a bad
idea, Jon? Read what you just posted.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Jon Szanto" <jszanto@> wrote:
>
> > Pretty good, since I've only had one post, and it didn't
> > seem very different from you accusing Gene of power-tripping.
> > You know what though? I really don't care, as once again
> > you and Gene have peed in the pool.
>
> You want to see why starting down the road of personal attacks
> is a bad idea, Jon? Read what you just posted.

Guys, i know it's important to air grievances about behavior
and to discuss group etiquette here when it seems to have
been breached. But after a certain point, this kind of stuff
should be migrated to private email correspondence. Let's
try to keep posts here more on-topic.

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

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

> Guys, i know it's important to air grievances about behavior
> and to discuss group etiquette here when it seems to have
> been breached. But after a certain point, this kind of stuff
> should be migrated to private email correspondence. Let's
> try to keep posts here more on-topic.

We have reached no consensus on what group etiquette is or ought to be,
and that is the most important thing which could come out of this.

How about simply: "Post unto others as you would have them reply."

________________________________

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf
Of Gene Ward Smith
Sent: Friday, March 09, 2007 11:42 AM
To: tuning@yahoogroups.com
Subject: [tuning] Re: Sagittal info spreadsheet now available

--- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com> , "monz"
<monz@...> wrote:

> Guys, i know it's important to air grievances about behavior
> and to discuss group etiquette here when it seems to have
> been breached. But after a certain point, this kind of stuff
> should be migrated to private email correspondence. Let's
> try to keep posts here more on-topic.

We have reached no consensus on what group etiquette is or ought to be,
and that is the most important thing which could come out of this.

Hmmm. No, that doesn't work....

________________________________

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf
Of Cornell III, Howard M
Sent: Friday, March 09, 2007 12:33 PM
To: tuning@yahoogroups.com
Subject: RE: [tuning] Re: Sagittal info spreadsheet now available

How about simply: "Post unto others as you would have them reply."

________________________________

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf
Of Gene Ward Smith
Sent: Friday, March 09, 2007 11:42 AM
To: tuning@yahoogroups.com
Subject: [tuning] Re: Sagittal info spreadsheet now available

--- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com> , "monz"
<monz@...> wrote:

> Guys, i know it's important to air grievances about behavior
> and to discuss group etiquette here when it seems to have
> been breached. But after a certain point, this kind of stuff
> should be migrated to private email correspondence. Let's
> try to keep posts here more on-topic.

We have reached no consensus on what group etiquette is or ought to be,
and that is the most important thing which could come out of this.

--- In tuning@yahoogroups.com, "Cornell III, Howard M"
<howard.m.cornell.iii@...> wrote:
>
> How about simply: "Post unto others as you would have them reply."

What if you want a flame-war?

If you play rough, expect it to be tough.

Oz.

----- Original Message -----
From: Cornell III, Howard M
To: tuning@yahoogroups.com
Sent: 09 Mart 2007 Cuma 20:36
Subject: RE: [tuning] Re: Sagittal info spreadsheet now available

Hmmm. No, that doesn't work....

------------------------------------------------------------------------------
From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of Cornell III, Howard M
Sent: Friday, March 09, 2007 12:33 PM
To: tuning@yahoogroups.com
Subject: RE: [tuning] Re: Sagittal info spreadsheet now available

How about simply: "Post unto others as you would have them reply."

------------------------------------------------------------------------------
From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of Gene Ward Smith
Sent: Friday, March 09, 2007 11:42 AM
To: tuning@yahoogroups.com
Subject: [tuning] Re: Sagittal info spreadsheet now available

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

> Guys, i know it's important to air grievances about behavior
> and to discuss group etiquette here when it seems to have
> been breached. But after a certain point, this kind of stuff
> should be migrated to private email correspondence. Let's
> try to keep posts here more on-topic.

We have reached no consensus on what group etiquette is or ought to be,
and that is the most important thing which could come out of this.

If you play rough, expect it to be tough.

Oz.

I disagree. I think unnecessary jeering and attempts at embarrassment are
contrary to the purpose of this List. I would prefer giving each
correspondent a fair listen and response. The medium itself puts us all at a
disadvantage because we cannot hear and see each other for greater meaning.

But when it is too rough, it takes the form of censorship.

Johnny

<BR><BR><BR>**************************************<BR> AOL now offers free
email to everyone. Find out more about what's free from AOL at
http://www.aol.com.

> > [TD] In my numerical 1/3-comma notation that would go
> >
> > F Ab^3 F#_4 A_1
> >
> > commentary: 6/5 times 7/4 times 3/5 'equals' (via tempering out the
> > 'tertiadec') 81/64 reduced by 1/3 comma; which is 1/3 schisma away
> > from an ET third.
>
> [GWS] Yike! In pontiac/schismatic, that's E\, that is, E flat by a
225/224
> symbol. In the 1/3 comma meantone/19-et system, it's E sharp by a
> comma.
>

... I started from F, thus A\ relative to schismatic or A/// (?)
relative to 1/3 comma meantone.

The notation is that superscript numbers ^x are the number of
"1/3-comma" steps to raise a note above the Pythagorean sequence;
subscript numbers _x are the reverse. Same as Dave's 1G, 2G, etc. on
the sharp and flat sides respectively.

Could it be simpler - at least on the surface? (Beneath lurks the
complexity of Term Temperament...)

~~~T~~~

Jon,

I appreciate your concern, but Gene is a moderator of this list and it
is part of a moderator's duty to remind list members of the standards
we expect in our treatment of each other.

I have always found this list to have fairly high standards. I just
came across a thread in sci.math where some poor guy had to put up
with the following from another poster.

"You just have an inferiority complex in it."

"Whiner."

"paranoid."

"you are emotionally stuck."

"Everybody is wize to your con game, little boy."

"Go buy a maths book, my chigger, and pretend to read it."

The recipient of these personal attacks snd insults was admirably
restrained in response.

I'm glad we don't have stuff like that here. I think anyone who posted
stuff like that ought to be banned if he didn't desist after a
warning. But on sci.math I couldn't even find where he was cautioned!

Sure, I've "lost it" on occasion myself, but I've apologised in short
order.

Another behaviour that might be deserving of banning would be to
continually post things that really belong on a different list,
despite many repeated reminders.

I've had to consider these things carefully as I am owner and
moderator of two yahoo groups myself.

Gene,

I do apologise for any hurt caused by my description of how you come
across to me on this, and other, lists.

I found it quite helpful when you let me know that I came across to
you as an unsmiling policemen for the "one true notation system" [my
interpretation]. I'd prefer to just be a smiling evangelist (and
customer service agent) for a damn good one. But maybe I should leave
that to George. :-)

I though you might similarly benefit from knowing how you come across
to me. And if an unfamiliar word might have sent a few people off to
google it and in the process learn about NPD and other personality
disorders then that could only lead to better understanding -- heaven
knows I've probably got a few myself. And better understanding can
only lead to more harmony. And harmony is something we all take
seriously on this list. :-)

Now, back on topic
------------------

George Secor helped me to realise I'd done something inadvertently
that must have indeed been frustrating for you, and I apologise for
that too. When you wrote:

"Now, how would this best work in Sagittal? Using ">" for 225/224 and
"/" for 81/80, the C otonal tetrad would be C-E>-G>-A#/."

I thought that this was a rhetorical question followed by its answer!

I assumed that you were willing to use just those two pairs of
accidentals (the < > pair being user-definables) and stack them to get
other numbers of generators. You had seemed to prefer that sort of
thing in the past. Hence my answer.

"It's valid ..."

But I recall now that you recently said something to someone else to
the effect that there are plenty of Sagittals so why stack them. Now I
realise you were asking for symbol pairs for the remaing degrees. My
most humble apologies for what must have been terribly frustrating.

George tried to answer, but he in fact gave several commas (and one
symbol) that were valid for 171-EDO, but not for enneadecal.

It turns out that George's and my disagreement over the 8G symbol was
because George was notating 171-ET while I was notating Tom's planar
1/3-comma temperament. Neither symbol is valid for 8G of enneadecal
but when you drop the accents, all those we gave for other numbers of
generators are valid for enneadecal.

I applied the 7-limit enneadecal mapping [[19, 30, 44, 53], [0, 1, 1,
3]] to every 7-limit comma on my list and found the following.

Sagittal accidentals (in long ASCII form) for Gene's enneadecal notation:

gen. up comma
--- ----- -----------
1G '|( 225/224
2G ~|(. 245/243
and ~|(.. 126/125
3G /| 81/80
4G '|) 3645/3584
5G ~|) 49/48
6G //| 6561/6400
7G '/|) 59049/57344

I couldn't find any reasonable 7-limit comma for 8G of enneadecal but
that doesn't really matter because, as you point out, we only need 4
pairs to notate its 171-MOS/DE.

However the 11-limit mapping turned up the following
8G '/|\ 1082565/1048576

Now, when you drop the accents you have the following pairs of single
ASCII characters. These are the same ones George gave, except for 8G.

Sagittal accidentals (in short ASCII form) for Gene's enneadecal notation:

gen. down up
--- ---- --
1G c r
2G a g
3G \ /
4G t f
5G h p
6G _ =
7G u n
8G v ^

It must also be frustrating that we haven't finished the list of
accented Sagittal so you can do this processing yourself. Don't worry,
it's frustrating for us too.

But you could actually help us here, by taking the values given for
the accents in the Sagiital-2 spreadsheet and looking at possible
combinations of left accents and single or double right accents with
at least the Athenian (green background) symbols and telling us what
23-limit commas you think they should represent. Best do it on
tuning-math though, not here.

Regards,
-- Dave Keenan

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

Thanks, Dave. Yahoo destroyed my long response to this, so I will need
to try again later.

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

> I appreciate your concern, but Gene is a moderator of this list and
it
> is part of a moderator's duty to remind list members of the
standards
> we expect in our treatment of each other.

I apologize for being annoying, and will try to be less so. And I'm
glad to see you have not taken yourself off in dudgeon high or low.

> The recipient of these personal attacks snd insults was admirably
> restrained in response.

If by admirably restrained you mean accusing people of conspiracy and
massive fraud. By the way, if you are looking for someone to exercise
your abilities as a psychiatric diagnositician on, James Harris looks
an awful lot like--wait for it--Narcissistic Personality Disorder.
This has even been pointed out to him, though of course utterly
without theraputic benefit.

Here's the crank.net web page on Harris:

http://www.crank.net/harris.html

Blogspot:

http://jstevh.blogspot.com/

Sorry about the off-topic, but you brought it up.

> I'm glad we don't have stuff like that here. I think anyone who
posted
> stuff like that ought to be banned if he didn't desist after a
> warning. But on sci.math I couldn't even find where he was
cautioned!

If sci.math were a moderated group like sci.math.research, it is
James Harris who would have been banned. Trust me.

> I though you might similarly benefit from knowing how you come
across
> to me.

Tossing out amateur diagnoses from the DSM-IV list is not helpful to
this list. You are not a trained psychologist, you are not board
certified, and you have not interviewed me. Even if you are correct
in your conclusion that someone on this list has Borderline
Personality Disorder or Antisocial Personality Disorder, please keep
it to yourself. I just don't see how it could possibly be helpful to
say so.

> I applied the 7-limit enneadecal mapping [[19, 30, 44, 53], [0, 1,
1,
> 3]] to every 7-limit comma on my list and found the following.

Thanks. Between 245/243 and 126/125, do you have a preference? I seem
to recall 126/125 was not regarded in a very good light as something
to notate for some reason.

> Sagittal accidentals (in short ASCII form) for Gene's enneadecal
notation:
>
> gen. down up
> --- ---- --
> 1G c r
> 2G a g
> 3G \ /
> 4G t f
> 5G h p
> 6G _ =
> 7G u n
> 8G v ^

Looks good. Could this be used in microabc, I wonder?

> But you could actually help us here, by taking the values given for
> the accents in the Sagiital-2 spreadsheet and looking at possible
> combinations of left accents and single or double right accents with
> at least the Athenian (green background) symbols and telling us what
> 23-limit commas you think they should represent. Best do it on
> tuning-math though, not here.

I no longer have much of a clue what you are looking for in 23-limit
commas; long, long ago and far, fae away in another galaxy we were
considering JI when looking at those.

> Tossing out amateur diagnoses from the DSM-IV list is not helpful
> to this list. You are not a trained psychologist, you are not
> board certified, and you have not interviewed me. Even if you are
> correct in your conclusion that someone on this list has
> Borderline Personality Disorder or Antisocial Personality
> Disorder, please keep it to yourself. I just don't see how it
> could possibly be helpful to say so.

I must have missed the offending message.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > Tossing out amateur diagnoses from the DSM-IV list is not helpful
> > to this list. You are not a trained psychologist, you are not
> > board certified, and you have not interviewed me. Even if you are
> > correct in your conclusion that someone on this list has
> > Borderline Personality Disorder or Antisocial Personality
> > Disorder, please keep it to yourself. I just don't see how it
> > could possibly be helpful to say so.
>
> I must have missed the offending message.
>
> -Carl

Hi Carl,

No, you didn't miss it, because there never was any such message.

Gene has made this accusation up out of whole cloth.

-- Dave K

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

> No, you didn't miss it, because there never was any such message.
>
> Gene has made this accusation up out of whole cloth.

I was going to let the whole thing drop, but apparently you don't
want that.

First you said this:

"But you should know that you've been
coming across as a completely humorless narcissist ever since you've
been on the list. I try not to let it bother me. :-)"

And then you said this:

"I though you might similarly benefit from knowing how you come across
to me. And if an unfamiliar word might have sent a few people off to
google it and in the process learn about NPD and other personality
disorders then that could only lead to better understanding -- heaven
knows I've probably got a few myself."

In other words, Dave first characterized me as a narcissist, and then
he tells us the sort of narcissist he had in mind was NPD, which is
an acrosym for Nacissistic Personality Disorder. A personality
disorder is a psychiatric condition marked by extreme deviation of
the person with the disorder from the norm and what is considered
desirable. They are classifed by the American Psychiatric
Association, and probably in some way by the Austrialians also, or so
I would guess. NPD and other personality disorders are cataloged in
something called the Diagnostic and Statistical Manual of Mental
Disorders, and while by no means as serious as psychosis they are
highly impairing and not a matter to take lightly.

Legally, to claim claim someone has a personality disorder of this
type is very likely to constitute libel or defamation _per se_. _Per
se_ includes (quoting Wikipedia) "Allegations or imputations 'of
loathsome disease' (historically leprosy and sexually transmitted
disease, now also including mental illness.)" If the undesirability
of inciting flame wars is not a good enough reason to avoid armchair
diagnosis on this group, the fact that it is legally dubious to do
such a thing ought to provide a reason.

> NPD and other personality disorders are cataloged in
> something called the Diagnostic and Statistical Manual of Mental
> Disorders, and while by no means as serious as psychosis they are
> highly impairing and not a matter to take lightly.

I'm familiar with the DSM. But Gene, you know people do use
these things figuratively or even jokingly all the time.
"I'm obcessive-compulsive about ..." Given that Dave used a
smiley... That's not to say his remark *couldn't* have
been offensive, nor that it wasn't personal in nature.
But it doesn't seem to have been an ad hominem -- that is,
Dave wasn't trying to win an argument with it.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > NPD and other personality disorders are cataloged in
> > something called the Diagnostic and Statistical Manual of Mental
> > Disorders, and while by no means as serious as psychosis they are
> > highly impairing and not a matter to take lightly.
>
> I'm familiar with the DSM. But Gene, you know people do use
> these things figuratively or even jokingly all the time.
> "I'm obcessive-compulsive about ..." Given that Dave used a
> smiley... That's not to say his remark *couldn't* have
> been offensive, nor that it wasn't personal in nature.

It was hardly clear it was meant jokingly, and I think it's a bad
idea to leave the door widely open to the view that it was meant
entirely seriously.

> But it doesn't seem to have been an ad hominem -- that is,
> Dave wasn't trying to win an argument with it.

Does that matter?

> > I'm familiar with the DSM. But Gene, you know people do use
> > these things figuratively or even jokingly all the time.
> > "I'm obcessive-compulsive about ..." Given that Dave used a
> > smiley... That's not to say his remark *couldn't* have
> > been offensive, nor that it wasn't personal in nature.
>
> It was hardly clear it was meant jokingly, and I think it's a bad
> idea to leave the door widely open to the view that it was meant
> entirely seriously.

Sure.

> > But it doesn't seem to have been an ad hominem -- that is,
> > Dave wasn't trying to win an argument with it.
>
> Does that matter?

There was a time when we were all posting personality test
results here. I dunno. I think in a community like this,
you can't and shouldn't keep it 100% on-topic. Should
constrctive criticism of personalities be allowed in theory
(regardless of whether Dave's comments were of this type)?
I don't know.

-Carl

Just for the record, I don't know anything about NPD (and
don't want to), but from its name alone and having met you
I wouldn't think you have anything like it. (Just in case
my reply here could be read as supporting the 'diagnosis'.)

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
> > > I'm familiar with the DSM. But Gene, you know people do use
> > > these things figuratively or even jokingly all the time.
> > > "I'm obcessive-compulsive about ..." Given that Dave used a
> > > smiley... That's not to say his remark *couldn't* have
> > > been offensive, nor that it wasn't personal in nature.
> >
> > It was hardly clear it was meant jokingly, and I think it's a bad
> > idea to leave the door widely open to the view that it was meant
> > entirely seriously.
>
> Sure.
>
> > > But it doesn't seem to have been an ad hominem -- that is,
> > > Dave wasn't trying to win an argument with it.
> >
> > Does that matter?
>
> There was a time when we were all posting personality test
> results here. I dunno. I think in a community like this,
> you can't and shouldn't keep it 100% on-topic. Should
> constrctive criticism of personalities be allowed in theory
> (regardless of whether Dave's comments were of this type)?
> I don't know.
>
> -Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> Just for the record, I don't know anything about NPD (and
> don't want to), but from its name alone and having met you
> I wouldn't think you have anything like it. (Just in case
> my reply here could be read as supporting the 'diagnosis'.)

Thanks, Carl. For the record, no one posting here at present strikes me
as psychologically disturbed. I suspect if someone was it wouldn't much
help to tell them so here.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@> wrote:
> ...
> > I applied the 7-limit enneadecal mapping [[19, 30, 44, 53], [0,
1, 1, 3]]
> > to every 7-limit comma on my list and found the following.
>
> Thanks. Between 245/243 and 126/125, do you have a preference? I
seem
> to recall 126/125 was not regarded in a very good light as
something
> to notate for some reason.

Hi, Gene. I believe that the 243:245 vs. 125:126 issue came up when
we were discussing symbols for ennealimmal. We've since decided that
the 17-comma (4096:4131) symbol ~|( that was one of those under
consideration for these ratios should be permitted in less-than-17-
limit tunings, regardless of whether it would be valid for notating
the 17-comma itself. Since the exact symbols for 243:245 and 125:126
are ~|(. and ~|(.. respectively (i.e., the 17C symbol with single-
and double-right accent marks), it's perfectly fine to omit the right-
accent marks if you don't need to make pitch distinctions as small as
0.4 cents, so that the unaccented symbol ~|( will represent either
one, or both. So you can use whichever ratio you choose.

The shorthand for ~|( is in the 2G line, below.

> > Sagittal accidentals (in short ASCII form) for Gene's enneadecal
notation:
> >
> > gen. down up
> > --- ---- --
> > 1G c r
> > 2G a g
> > 3G \ /
> > 4G t f
> > 5G h p
> > 6G _ =
> > 7G u n
> > 8G v ^
> ...
> > But you could actually help us here, by taking the values given
for
> > the accents in the Sagiital-2 spreadsheet and looking at possible
> > combinations of left accents and single or double right accents
with
> > at least the Athenian (green background) symbols and telling us
what
> > 23-limit commas you think they should represent. Best do it on
> > tuning-math though, not here.
>
> I no longer have much of a clue what you are looking for in 23-
limit
> commas; long, long ago and far, fae away in another galaxy we were
> considering JI when looking at those.

Never mind, then. I think Dave was just extending the courtesy of
inviting you to participate in our ongoing (and very detailed)
discussion about symbol definitions (which he's pretty much left to
me to finish up, since it's gotten to be so tedious). By the time
this is done, we expect to end up with separate symbols for perhaps
150 to 200 different ratios less than 1/2 apotome, and I expect that
just about anything you'll need will be covered.

One thing that would help is: if there's anything you can think of
that we might be likely to miss, then please let us know.

--George

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

> One thing that would help is: if there's anything you can think of
> that we might be likely to miss, then please let us know.

At one point it seemed you were not paying enough attention to low
prime limit commas, but I don't know what you'd be likely to miss these
days.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@> wrote:
>
> > One thing that would help is: if there's anything you can think
of
> > that we might be likely to miss, then please let us know.
>
> At one point it seemed you were not paying enough attention to low
> prime limit commas, but I don't know what you'd be likely to miss
these
> days.

Let me be more specific, then. It would be helpful if you were able
to generate a list of what you think are the 300 (or so) most
notationally useful commas less than half-apotome, in order of
decreasing usefulness, with the largest prime limit you think might
be useful (or say 31 limit) -- but only if it's not too much trouble.

--George

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

> Let me be more specific, then. It would be helpful if you were
able
> to generate a list of what you think are the 300 (or so) most
> notationally useful commas less than half-apotome, in order of
> decreasing usefulness, with the largest prime limit you think might
> be useful (or say 31 limit) -- but only if it's not too much
trouble.

That would be a huge undertaking.

Things to look at: commas which arise from chains of a generator
interval coming close to a q-limit consonance. Generators might
include the fifth, major third, minor third, 7/6, 8/7, and half of
each of these; 1/3 of a fifth and etc.

Picking a generator, with the fifth given special promiance, look at:

(1) Coming close to a unison. For fifths, this gives the apotome and
the Pythagorean comma, etc. These can be found by continued fractions.

(2) Coming close to another interval, leading to a bridge comma for
that particular generator. For fifths, this gives us 81/80, 64/63,
5120/5103, 32805/32768, 33554432/33480783 (the septimal schisma) and
so forth.

Then, I think, just look at comas with a low badness figure in terms
of Hahn or Euclidean symmetrical distance. Now 2401/2400, for
example, fairly leaps out at you, and 49/48, 50/49, 126/125, 225/224
look interesting.

Gene,

First let me apologise for all that unpleasantness recently. I said
some stupid things and I'm sorry.

As George indicated, I really was offering an olive-branch in trying
to get you involved in Sagittal development again, with the accented
symbols. After all, you had a big part in not only determining the
best minimal set of 19-limit prime commas that got us started, but
also in regard to the right accents as generators of atomic temperament.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@> wrote:
>
> > Let me be more specific, then. It would be helpful if you were
> able
> > to generate a list of what you think are the 300 (or so) most
> > notationally useful commas less than half-apotome, in order of
> > decreasing usefulness, with the largest prime limit you think might
> > be useful (or say 31 limit) -- but only if it's not too much
> trouble.
>
> That would be a huge undertaking.

If anyone can do it, you can.

We've been struggling for years. George and I have been working so
closely for so long that we are probably just making all the same
mistakes.

If you didn't want to make such a huge undertaking, I'm guessing you
already have some list of commas that you can sort on some kind of
badness measure that would be relevant and select those under the
half-apotome. Anything like that would be a help.

-- Dave K

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

> As George indicated, I really was offering an olive-branch in trying
> to get you involved in Sagittal development again, with the accented
> symbols. After all, you had a big part in not only determining the
> best minimal set of 19-limit prime commas that got us started, but
> also in regard to the right accents as generators of atomic
temperament.

Thanks, Dave. I'm all for olive branches, and am known to say stupid
things also.

I'm not sure how much I could contribute to this project with a list
of 300 commas everyone should own, however. What's your opinion on
what is needed?

> If you didn't want to make such a huge undertaking, I'm guessing you
> already have some list of commas that you can sort on some kind of
> badness measure that would be relevant and select those under the
> half-apotome. Anything like that would be a help.

Oh sure, I could do that, but I thought the idea was to get
specifically notation-useful commas. You then end up pondering such
arcane questions as which of 225/224 or 5120/5103 is more useful.
225/224 is, in some sense, a more "powerful" comma, but 5120/5103 is
specifically suited to the use of fifths.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:

> You then end up pondering such
> arcane questions as which of 225/224 or 5120/5103 is more useful.
> 225/224 is, in some sense, a more "powerful" comma, but 5120/5103 is
> specifically suited to the use of fifths.

You can see it from the monzos:

225/224: |-5 2 2 -1>

5120/5103: |10 -6 1 -1>

The first number, the exponent for 2, we can ignore. But we can see how
heavily 5120/5103 is loaded along the 3 axis, and that it has +-1
(bridge property) to both 5 and 7. 225/224, by comparison, has the same
exponent for 3 and 5, and is loaded more along the 16/15 axis.
Generators like the secor or 9/7, which are not the first ones you want
to consider, are more in its line.

So how important are strongly 3-loaded commas? Well, unfortunately,
that depends. How important is it to notate by chains of fifths?

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@>
> wrote:
>
> > You then end up pondering such
> > arcane questions as which of 225/224 or 5120/5103 is more useful.
> > 225/224 is, in some sense, a more "powerful" comma, but 5120/5103 is
> > specifically suited to the use of fifths.
>
> You can see it from the monzos:
>
> 225/224: |-5 2 2 -1>
>
> 5120/5103: |10 -6 1 -1>
>
> The first number, the exponent for 2, we can ignore. But we can see how
> heavily 5120/5103 is loaded along the 3 axis, and that it has +-1
> (bridge property) to both 5 and 7. 225/224, by comparison, has the same
> exponent for 3 and 5, and is loaded more along the 16/15 axis.
> Generators like the secor or 9/7, which are not the first ones you want
> to consider, are more in its line.
>
> So how important are strongly 3-loaded commas? Well, unfortunately,
> that depends. How important is it to notate by chains of fifths?

Hi Gene,

If I told you what _I_ think, then I'd just be infecting you with the
same biases that George and I have built up. We really need an
independent opinion.

We want Sagittal to be usable with non chain-of-fifth nominals, but we
expect the vast majority of users will be using chain-of-fifth
nominals so there should be _some_ kind of weighting in their favour.

Given that we're talking about 300 commas under 57 cents I don't think
you have to worry too much about the exact weightings. Anything
reasonable should ensure that everyone's favourites are in there.

-- Dave K

> We want Sagittal to be usable with non chain-of-fifth nominals,
> but we expect the vast majority of users will be using
> chain-of-fifth nominals so there should be _some_ kind of
> weighting in their favour.
>
> Given that we're talking about 300 commas under 57 cents I don't
> think you have to worry too much about the exact weightings.
> Anything reasonable should ensure that everyone's favourites
> are in there.

Hi Dave,

I'll reply to this on tuning-math in a little bit (maybe
as late as tomorrow). I did some stuff in scheme with comma
lists. No way to 3-bias from what I've got, I don't think,
but perhaps it could be added.

Then again, I'm not sure what you want, because the stuff I
did is fairly easy stuff.

-Carl

> Then again, I'm not sure what you want, because the stuff I
> did is fairly easy stuff.

I meant, "maybe I don't understand what you're after".

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > We want Sagittal to be usable with non chain-of-fifth nominals,
> > but we expect the vast majority of users will be using
> > chain-of-fifth nominals so there should be _some_ kind of
> > weighting in their favour.
> >
> > Given that we're talking about 300 commas under 57 cents I don't
> > think you have to worry too much about the exact weightings.
> > Anything reasonable should ensure that everyone's favourites
> > are in there.
>
> Hi Dave,
>
> I'll reply to this on tuning-math in a little bit (maybe
> as late as tomorrow). I did some stuff in scheme with comma
> lists. No way to 3-bias from what I've got, I don't think,
> but perhaps it could be added.
>
> Then again, I'm not sure what you want, because the stuff I
> did is fairly easy stuff.

Email George whatever you've got.

That goes for anyone else with any kind of ranked comma list.

Thanks.

-- Dave K

Gene Ward Smith wrote:

> Oh sure, I could do that, but I thought the idea was to get > specifically notation-useful commas. You then end up pondering such > arcane questions as which of 225/224 or 5120/5103 is more useful. > 225/224 is, in some sense, a more "powerful" comma, but 5120/5103 is > specifically suited to the use of fifths.

I have some thoughts in that direction (finding notation-useful commas). I've got enough information to write a program to generate hundreds or thousands of possible rank-2 temperaments (of any specified limit), find a sensible generator mapping for each, find an optimal tuning (TOP or RMS-TOP), and find all the possible MOS of these up to a specified number of steps. While it's possible someone might want to notate a comma that's not an MOS step of one of these temperaments, with enough temperaments in the list, the more useful commas are likely to show up multiple times. Commas could be weighted by some combination of temperament accuracy, temperament complexity, generator complexity, and the number of temperaments each comma is useful for notating. Deciding how important each of these factors is will be the biggest issue influencing the order of the resulting comma list.

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:

> I have some thoughts in that direction (finding notation-useful
commas).
> I've got enough information to write a program to generate hundreds
or
> thousands of possible rank-2 temperaments (of any specified limit),
find
> a sensible generator mapping for each, find an optimal tuning (TOP or
> RMS-TOP), and find all the possible MOS of these up to a specified
> number of steps.

This is the sort of thing I meant by a huge undertaking. Are you
volunteering?