Sagittal accidental question

I am writing up a chart of chords spelled in Sagittal, and after banging my head a bit and getting bruised, perhaps some people on here who know more than I do might be able to clear things up:

I'm trying to write an inverted Ebm6 chord. Specifically, {1/1, 6/5, 3/2, 5/3}. With the sixth on C (being the universal reference pitch for my chart, kind of like writing a tonality diamond in a different way) this inverts to {1/1, 6/5, 36/25, 9/5}. Thus, C is 1/1. I figured out the 6/5 and the 9/5 pretty easily: use the so-named "flat 5-comma up" or "!!/" on the E and B. But what do I use to get to 36/25 on the G? Is it the "flat 25 s-diesis up", i.e., ")!!(" or is it something else?

That is really just a guess, based on page 10 of the "Sagittal: A Microtonal Notation System" PDF, which lists some approximate cent positions of the Athenian symbols. If I'm right, I'm not sure how this symbol breaks down.

Oh, by the way, in the chart on this page: http://sagittal.org/SagittalJI.gif

the 25C accidental, ,!/ is listed as 2048/2045. It should be 2048/2025. 2048/2045 is about 2.5 cents, and 2048/2025 is about 19.5 cents, per the chart.

Dear Andrew,

--- In tuning@yahoogroups.com, "bigAndrewM" <bigandrewm@...> wrote:
>
> But what do I use to get to 36/25 on the G? Is it the "flat 25 s-diesis up", i.e., ")!!(" or is it something else?
>
> That is really just a guess, based on page 10 of the "Sagittal: A Microtonal Notation System" PDF, which lists some approximate cent positions of the Athenian symbols. If I'm right, I'm not sure how this symbol breaks down.

I'm not very experienced with Sagittal notation, but I'm sure what you did was correct:

G is the 3/2 above C, and to get from 3/2 to 36/25 you need to multiply by 24/25.

If you take a look at the Sagittal-2 Character Map (available as PDF or Excel spreadsheet on the Sagittal homepage) on page 12, there's the accidental #112 with a numerator of 24 and a denominator of 25, which is exactly what we are looking for. On page 3, we can see that the pure long ASCII representation for #112 is ")!!(", and that it is called a "flat 25-S-diesis up".

Best
- Gedankenwelt

--- In tuning@yahoogroups.com, "bigAndrewM" <bigandrewm@...> wrote:
>
> I am writing up a chart of chords spelled in Sagittal, and after banging my head a bit and getting bruised, perhaps some people on here who know more than I do might be able to clear things up:
>
> I'm trying to write an inverted Ebm6 chord. Specifically, {1/1, 6/5, 3/2, 5/3}. With the sixth on C (being the universal reference pitch for my chart, kind of like writing a tonality diamond in a different way) this inverts to {1/1, 6/5, 36/25, 9/5}. Thus, C is 1/1. I figured out the 6/5 and the 9/5 pretty easily: use the so-named "flat 5-comma up" or "!!/" on the E and B. But what do I use to get to 36/25 on the G? Is it the "flat 25 s-diesis up", i.e., ")!!(" or is it something else?
>
> That is really just a guess, based on page 10 of the "Sagittal: A Microtonal Notation System" PDF, which lists some approximate cent positions of the Athenian symbols. If I'm right, I'm not sure how this symbol breaks down.

G)!!( is correct.

Andrew, an easy way to determine the notation for a tuning is with the Scala software, as follows.

First you'll set the notation to one of the Sagittal options. For an EDO, enter "set nota N" in the command line, where N is the division number of the EDO; for an EDO that's a multiple of 12, enter "set nota sa12r" to use the trojan symbol set. For JI, enter "set nota saji1" (for medium precision), "set nota saji2" (for high precision, no accents), "set nota saji3" (for high precision, with accents), or "set nota saji4" (for extreme precision). (Dave & I are in the process of changing the extreme-precision notation: "accents" will be called "diacritics", to avoid confusing them with symbols representing accent marks used for musical expression; in extreme precision, right-accents are being replaced with new 1- and 2-mina diacritics placed to the left of a Sagittal accidental.)

Next you'll need to get the tuning into memory. If the tuning is in a .scl file, then load it into Scala. For an EDO, enter "equal N" in the command line, where N is the division number of the EDO. (Although not all EDOs are currently supported, new ones may be added by editing the sag_et.par file in the Scala22 folder.) For JI ratios not in a file, enter "clear" in the command line before continuing.

Click on the Edit icon to view the scale currently in memory. If you entered "clear", you cleared the pitches from memory (except 1/1), which will allow you to enter pitches one at a time on the "New Pitch" line (if required, click on the Ascending box to sort them in order of pitch). Most pitches are notated two different ways, using different nominals.

--George

--- In tuning@yahoogroups.com, "bigAndrewM" <bigandrewm@...> wrote:
>
> Oh, by the way, in the chart on this page: http://sagittal.org/SagittalJI.gif
>
> the 25C accidental, ,!/ is listed as 2048/2045. It should be 2048/2025. 2048/2045 is about 2.5 cents, and 2048/2025 is about 19.5 cents, per the chart.

Thanks for spotting that!

That chart will require extensive revision very soon, due to the change in extreme-precision JI diacritics I mentioned in my previous message.

The chart currently shows a "7-limit Spartan" JI that's a sort of unofficial low-precision JI. I've been thinking about changing that to an official 13-limit low-precision Spartan JI that uses the entire Spartan symbol set:
|( /| |) //| /|) /|\ (|) (|\ )||( ||) ||\ /||) /||\

Note: |\ and /|| were originally in the Spartan set, but after Dave & I decided to include //| and )||( (for extended 5-limit JI and 53-EDO), we recently decided that these should replace |\ and /||, which we demoted to the Athenian level. (The Sagittal paper needs to be updated to reflect this change.)

--George

--- In tuning@yahoogroups.com, "gdsecor" <gdsecor@...> wrote:
> ...
> ... For an EDO, enter "set nota N" in the command line, where N is the division number of the EDO; ...

Oops! That should have been:
... For an EDO, enter "set nota saN" in the command line, where N is the division number of the EDO; ...

--George

Okay, thanks for the Scala info. I haven't dived into that aspect of that
software much yet.

And I look forward to seeing your Sagittal revisions.

I have arrived at a bit better understanding of this side of the Sagittal
notation system ,thanks to some input on the Facebook Xenharmonic page as well.
So, )!!( is the apotome complement of //! or, put another way, )!!( is \!!/
minus two syntonic commas. Which is exactly what I was looking for. I was just
thrown a bit because the tail-arcs (if that's the right phrase) of the )!!( look
similar to the arcs of )! and !( and )!( but not exactly, so I wasn't sure from
that angle if )!!( was a precise symbolic representation with 19-schismas, 5:7
kleismas, 7:11 kleismas, or something else.

Andrew

--- In tuning@yahoogroups.com, "gdsecor" <gdsecor@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "gdsecor" <gdsecor@> wrote:
> > ...
> > ... For an EDO, enter "set nota N" in the command line, where N is the division number of the EDO; ...
>
> Oops! That should have been:
> ... For an EDO, enter "set nota saN" in the command line, where N is the division number of the EDO; ...
>
> --George
>