Thank You for Saggital Notation

I'd like to thank George Secor and Dave Keenan, along with a host of
others, for Saggital notation, and to thank Manuel Op Coul for its
implementation in Scala.

I thought it wasn't worth my time to look at notation. Not really my
problem, after all -- I don't have a xen instrument except my computer. I
map Dutch note names to cent values in Lilypond, and that's good enough.
Nobody's going to play my stuff, either, so what difference does *notation*
make?

Quite a bit, as it turns out.

I forget why it came up, but I started reading about Saggital while on
vacation a few weeks ago. I had thought that it was primarily for JI, but
it turns out it's supposed to be useful for EDOs, too, and that -- along
with the linkage between EDOs and JI -- is where it's really, really smart.

It's so much easier to think in terms of note names and accidentals than in
the numbers or scordatura or what have you that I've been using. "C E\! G"
builds on what I already know about C, E, and G in 12 EDO / Pythagorean,
letting me instantly recognize that this is a C major chord with an
approximately just major third. E\!/ G\!/ B\!/ is an E minor chord. E\!/
means I'm getting something like a neutral third -- the single (or triple)
stem makes me think of prime eleven.

Relationships of accidentals in a scale matter, too. For instance, seeing
the sequence C E\!!!/ E\!!/ E\!/ E G\!/ G in Wurschmidt[13] shows me that I
have nothing that looks much like a second or fourth, and lots of choices
of thirds.

Those relationships can tell me about the "patent temperament"[1] of the
EDO I'm using[2]: When I see an "E" and no "E\!" in 31 EDO, that means that
31 tempers out 81/80; seeing both "E" and "E\!" in 53 EDO means that 53
doesn't temper out 81/80.

[1] Is that a term? I mean the temperament given using the patent val.
[2] Though not necessarily the temperament I'm using, if I'm not using the
patent val.

Seriously, who wouldn't love that?

Don't get me wrong: I'm sure I haven't grokked it in any kind of detail.
But that's part of the beauty of the system. I don't have to grok all the
detail to find it useful. And now, although I *could* generate a complete
set of accidentals for, say, 31 EDO, I don't have to, because Scala does it
for me. (Thank you again, Manuel!)

So, thank you to all those involved in making Saggital notation, especially
the ringleaders, and if you haven't tried Saggital yet, I recommend it.

Regards,
Jake

Hi Jake,

> I had thought that it was primarily for JI, but it turns out it's supposed to
be useful for

> EDOs, too, and that -- along with the linkage between EDOs and JI -- is where
it's really,

> really smart.

> It's so much easier to think in terms of note names and accidentals than in
the numbers

> or scordatura or what have you that I've been using. "C E\! G" builds on what
I already

> know about C, E, and G in 12 EDO / Pythagorean, letting me instantly recognize
that

> this is a C major chord with an approximately just major third.

Well, any notation that works for JI can be used for any regular temperament, or
for an

EDO if the val mapping is specified. The idea to use conventional notation and
microtonal

accidentals to notate just intonation is nothing new, and dates back at least to
Helmholtz.

However, from what I think I remember having read about Sagittal notation, much
thought

was put in the choice of accidentals, commas that can usually be ignored, and
for which

EDO the patent val or a subgroup mapping is used. So I think the special thing
about

Sagittal is not what it accomplishes (supporting JI and EDOs), but how well it
does, and

the amount of work that went into the design.

I'm wasn't sure if this is what you meant, and I'm sorry if this sounds like
criticism.

> E\!/ G\!/ B\!/ is an E minor chord.

I suppose there's a typo? Or did you mean a pythagorean minor chord?

> Relationships of accidentals in a scale matter, too. For instance, seeing the
sequence

> C E\!!!/ E\!!/ E\!/ E G\!/ G in Wurschmidt[13] shows me that I have nothing
that looks

> much like a second or fourth, and lots of choices of thirds.

Hm ... while using the diatonic scale as a notation basis works, I'd recommend
to use a

7-, 10- or 13-note Würschmidt MOS as a basis scale, and an accidental for the
chroma

instead, if you really want to *think* in this temperament.

(especially if you're going to do modulations, or use MODMOS scales)

You can even do this with Sagittal notation if you specify a tuning, and

use two key signatures:

One that uses Sagittal accidentals to get Würschmidt[7], and a second key
signature

that contains Würschmidt[7] chroma accidentals in case you want to modulate.

> [...] and if you haven't tried Saggital yet, I recommend it.

You'll laugh, but that's what I wanted to do starting yesterday. :)

I finally* finished programming my microtonal Vocaloid 3 plugin to the point
that it reliably

supports 13-limit JI, or any EDO I want. Now I'm going to become more familiar
with

Sagittal notation, and think about a good way to implement it. Then I'll be back
to ask for

feedback. ;)

* the manual for implementing those plugins is only available in Japanese, and
it took

me some time to translate it

Best regards

- Geddy

Oh, and another thing I noticed:

> [...] seeing the sequence C E\!!!/ E\!!/ E\!/ E G\!/ G in Wurschmidt[13] [...]

You seem to use 31-EDO notation here, since Wuerschmidt[13] has no pythagorean

major third C - E, and Wuerschmidt temperament itself does not temper out the
syntonic

comma. I didn't check if the other notes are correct.

If you really want to notate Wuerschmidt scales, you can't rely on the notation
that scala

suggests based on an EDO interpretation of that scale.

Hi Geddy,

> Well, any notation that works for JI can be used for any regular
temperament,
[snip]
> and dates back at least to Helmholtz.

Okay, I'm happy to give credit where it's due.

I was looking at Helmholtz-Ellis a little bit before I looked at Saggital,
and I thought H-E was mostly related to JI. Clearly, any JI notation can be
adjusted for any temperament or EDO by, say, dropping the Didymos
accidental for the third if you're playing in meantone (which is why the
major third C-E in 12 EDO has no accidentals), but the way it fell into
place for Saggital just seemed more natural to me.

That could have had to do with the explanation I was reading or where I was
coming from, too, of course. :)

> So I think the special thing about Sagittal is not what it accomplishes
(supporting
> JI and EDOs), but how well it does, and the amount of work that went into
the
> design.

Yes, all that. They've covered a ton of stuff that I usually don't care
about, and can understand quickly when I do.

> I'm wasn't sure if this is what you meant, and I'm sorry if this sounds
like criticism.

It's a mailing list. Criticize away! But no, I didn't take it badly.

> I suppose there's a typo? Or did you mean a pythagorean minor chord?

Sorry, I was still thinking about 31 EDO when I wrote that. E\!/ G\!/ B\!/
would be a pythagorean minor chord in a temperament that doesn't temper out
81/80.

> Hm ... while using the diatonic scale as a notation basis works, I'd
recommend to
> use a 7-, 10- or 13-note Würschmidt MOS as a basis scale, and an
accidental for
> the chroma instead, if you really want to *think* in this temperament.

Yes, I could do that, too, and that would make sense most of the time.
Wurschmidt is funny because it's *so* improper. In this case, I'm thinking
of using it for an idea I had a while back -- using the same basic chord
sequence, but with thirds shifting from subminor to supermajor as the piece
progresses.

> You can even do this with Sagittal notation if you specify a tuning, and
> use two key signatures:
> One that uses Sagittal accidentals to get Würschmidt[7], and a second key
signature
> that contains Würschmidt[7] chroma accidentals in case you want to
modulate.

Interesting, I hadn't considered that.

> You'll laugh, but that's what I wanted to do starting yesterday. :)

Synchronicity! I *am* laughing.

> I finally* finished programming my microtonal Vocaloid 3 plugin

Cool! Never used Vocaloid, but any tuning plug-ins for a voice synthesizer
would be pretty cool.

Regards,
Jake

On 09/05/2013 02:35 PM, gedankenwelt94@... wrote:

> However, from what I think I remember having read about Sagittal notation, much
> thought
> was put in the choice of accidentals, commas that can usually be ignored, and
> for which
> EDO the patent val or a subgroup mapping is used. So I think the special thing about
> Sagittal is not what it accomplishes (supporting JI and EDOs), but how well it
> does, and
> the amount of work that went into the design.

The shapes of the Sagittal accidentals relate to the sizes of the shifting intervals. You can roughly work out the size by counting the shafts and so read the pitch height without the harmony. The Helmholtz inspired notations take you straight to the prime factorization, but don't help you with the size of the shift that results. That's an even less useful balance when you move from JI to temperaments, because a given pitch may have different justifications.

Graham

> You can roughly work out the size by counting the
>
shafts and so read the pitch height without the harmony.

Yes, that's very helpful, and one reason that full-fledged Saggital (using
only arrows with various barbs on them, never the traditional sharp and
flat symbols) is easier for me to read and think through than mixed
Saggital (i.e., Saggital that incorporates traditional flats and sharps).

> The shapes of the Sagittal accidentals relate to the sizes of the
> shifting intervals. You can roughly work out the size by counting the
> shafts and so read the pitch height without the harmony.

Many thanks for the info, Graham, I'll keep that in mind! :)

And yes, it makes a huge difference whether a notation can be used for EDOs,

or if it is designed to work well with any EDO (which is indeed not the case for

the Helmholtz inspired notations I know).

> The Helmholtz inspired notations take you straight to the prime factorization,

> but don't help you with the size of the shift that results. That's an even
less

> useful balance when you move from JI to temperaments, because a given

> pitch may have different justifications.

I think when learning JI, it's a good thing if notes have a unique
representation,

and having too many ways to represent a note can be unnecessarily confusing.

But for practical purposes it's just as you mentioned, and it's completely
impractical

if everything is cluttered with accidentals.

For temperaments, it's invaluable to have a wide choice of accidentals,
especially

in the case of a high complexity temperament, and a base MOS scale with only a

few notes, s.th. stacks of chromas are common.

- Geddy

Thanks for your kind words, Jake. We did our best to avoid confustion. :-)

-- Dave Keenan

May I also add my thanks to both Jake & Geddy for their appreciation of Dave's &
my efforts, and to affirm that we did indeed manage to avoid confustion
(whatever that is). 8>}

--George

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

Thanks for your kind words, Jake. We did our best to avoid confustion. :-)

-- Dave Keenan