question regarding the use of sagittal notation

I have a piece I've written for an unmodified, microtonally-tuned
guitar. here's the tuning:

1: 1/1
2: 49/25
3: 7/5
4: 1/1
5: 8/5 = 110Hz
6: 1/1

The current is score is for the performer, everything is notated as if
it were in standard tuning. I want to make a score that someone could
analyze harmonically.

The thing with Sagittal is it's based around pythagorean tuning. All
the necessary pitch alterations required for the piece would just be
silly. What I have is four 12tet scales overlapping each other
microtonally. so if I use a notation based around 12tet, I only need
three new accidental markings, and five at the most for future tunings.

So what I was considering was using sagittal symbols that are closest
to the pitch alterations I'm using, and just explain myself in the notes.

Thoughts or suggestions?

For Monitorsrock:

I don't understand the way you listed the scale. Why is it not in ascending or descending order? And why is there 1/1 three times?

Petr

Those are what the guitar strings are tuned to, strings one through six

--- In tuning@yahoogroups.com, "monitorsrock" <12tone@...> wrote:
>
> I have a piece I've written for an unmodified, microtonally-tuned
> guitar. here's the tuning:
>
> 1: 1/1
> 2: 49/25
> 3: 7/5
> 4: 1/1
> 5: 8/5 = 110Hz
> 6: 1/1
>
> The current is score is for the performer, everything is notated as
if
> it were in standard tuning. I want to make a score that someone
could
> analyze harmonically.
>
> The thing with Sagittal is it's based around pythagorean tuning. All
> the necessary pitch alterations required for the piece would just be
> silly. What I have is four 12tet scales overlapping each other
> microtonally. so if I use a notation based around 12tet, I only need
> three new accidental markings, and five at the most for future
tunings.
>
> So what I was considering was using sagittal symbols that are
closest
> to the pitch alterations I'm using, and just explain myself in the
notes.
>
> Thoughts or suggestions?

Hmm, this is unusual in that your 8/5 is an "A", but okay. In that
case, the ratios can be notated:

8/5 as A
1/1 as C#\!
7/5 as G!)
49/25 as Db(! or C(|)

What are the future tunings?

--George

monitorsrock wrote:
> I have a piece I've written for an unmodified, microtonally-tuned
> guitar. here's the tuning:
> > 1: 1/1
> 2: 49/25
> 3: 7/5
> 4: 1/1
> 5: 8/5 = 110Hz
> 6: 1/1
> > The current is score is for the performer, everything is notated as if
> it were in standard tuning. I want to make a score that someone could
> analyze harmonically.
> > The thing with Sagittal is it's based around pythagorean tuning. All
> the necessary pitch alterations required for the piece would just be
> silly. What I have is four 12tet scales overlapping each other
> microtonally. so if I use a notation based around 12tet, I only need
> three new accidental markings, and five at the most for future tunings.

Sagittal is based around fifths and there's no problem with those fifths being tuned to 12tet.

> So what I was considering was using sagittal symbols that are closest
> to the pitch alterations I'm using, and just explain myself in the notes.
> > Thoughts or suggestions? Maybe it's either overkill or too imprecise, but you can use a 72tet notation. It's close enough to 7-limit JI that you can unify the fret-tuning with the string-tuning. And some people out there will be able to recognize the harmony.

Graham

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@...> wrote:
>
> --- In tuning@yahoogroups.com, "monitorsrock" <12tone@> wrote:
> >
> > I have a piece I've written for an unmodified, microtonally-tuned
> > guitar. here's the tuning:
> >
> > 1: 1/1
> > 2: 49/25
> > 3: 7/5
> > 4: 1/1
> > 5: 8/5 = 110Hz
> > 6: 1/1
> >
> > The current is score is for the performer, everything is notated
as if
> > it were in standard tuning. I want to make a score that someone
could
> > analyze harmonically.
> >
> > The thing with Sagittal is it's based around pythagorean tuning.
All
> > the necessary pitch alterations required for the piece would just
be
> > silly. What I have is four 12tet scales overlapping each other
> > microtonally. so if I use a notation based around 12tet, I only
need
> > three new accidental markings, and five at the most for future
tunings.
> >
> > So what I was considering was using sagittal symbols that are
closest
> > to the pitch alterations I'm using, and just explain myself in
the notes.
> >
> > Thoughts or suggestions?
>
> Hmm, this is unusual in that your 8/5 is an "A", but okay. In that
> case, the ratios can be notated:
>
> 8/5 as A
> 1/1 as C#\!
> 7/5 as G!)
> 49/25 as Db(! or C(|)

My reply (above) was spur-of-the moment, because I had only a few
minutes to write it. I have since had time to think about this more
carefully, and can now give a better reply.

In figure 10 (on p. 17) of the Sagittal paper:
http://dkeenan.com/sagittal/Sagittal.pdf
near the bottom there is a small chart showing the range of symbol
sizes, when the symbols are altering fifths of exactly 700 cents.

If you're using Scala, the command "set nota sa12r" will set the
symbol boundaries in this manner (as specified in the sag_12r.par
file). In order to see the accidental for each string, different
ratios would have to be entered in the "edit scale" option than what
you have here:

1: 1/1
2: 49/25
3: 7/5
4: 1/1
5: 8/5 = 110Hz
6: 1/1

Since string 5 is tuned to 110 Hz (two octaves below A=440 Hz), we'll
call that A, and all of the pitches on that string (including C) will
use 12-ET notation (with no Sagittal accidentals). Since Scala
displays a scale with C as 1/1, let's notate the ratios for the
pitches at the 3rd fret, where string 5 produces C. Since I want C
to be 1/1, in order to keep the same intervals between strings, I
would need to multiply each ratio by 5/8 (or 5/4, assuming octave
equivalence), so that:

1: 1/1 becomes 5/4
2: 49/25 becomes 49/40
3: 7/5 becomes 7/4
4: 1/1 becomes 5/4
5: 8/5 becomes 1/1
6: 1/1 becomes 5/4

If the ratios 1/1, 49/40, 5/4, and 7/4 are entered into the scale
(in "edit scale"), Scala shows:
C for 1/1
D#/|\ and E\!/ for 49/40
E\! for 5/4
B!!!) or Bb!) for 7/4

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> Maybe it's either overkill or too imprecise, but you can use
> a 72tet notation. It's close enough to 7-limit JI that you
> can unify the fret-tuning with the string-tuning. And some
> people out there will be able to recognize the harmony.

Yes, that's exactly what I got using 12-relative (12r) boundaries.
But "future tunings" may call for other accidentals, which can be
determined by following the steps outlined above.

--George