Yahoo Tuning Groups Ultimate Backup tuning 612-tet and 665-tet sagittal notation?

--- In tuning@yahoogroups.com, "Danny Wier" <dawiertx@s...> wrote:
> Are there symbols yet for multiples of one-twelfth comma (or a
schisma) not
> covered by 217-tone sagittal notation?

Hi Danny,

Perhaps surprisingly, there are a number of possibilities. Maybe you
can help us settle on standard sets. Can you tell us what you intend
to use them for. This may affect the choice of symbols.

In both 612-tET and 665-tET we would need to use 5-schisma accent
marks placed immediately to the left of shafted symbols, to raise or
lower their pitch by a schisma. These are similar in appearance to
acute (up) and grave (down) accents in text.

1/612th octave is essentially an eleventh of a 5-comma (syntonic or
Dydimus), or a twelfth of a 3-comma (Pythagorean), or a 5-schisma
(plain old schisma), as you say. 1/665th of an octave is essentially a
twelfth of a syntonic comma. And 665-tET has exactly 3 times as many
divisions per apotome (sharp or flat) as 217-ET which is essentially
quarter-5-commas.

Unfortunately we shouldn't simply make the 217-tET symbols stand for
every third step of 665-tET and then add schisma-up and schisma-down
accented versions on either side of these, because the increased
resolution of 665-tET means that in a few cases these degrees are no
longer the best approximation to the same ratio as they were in
217-tET. And it is the ratio approximations that are the constant
meanings of the symbols across all tunings, just as a sharp or flat
has the constant meaning of representing a chain of 7 approximate 2:3s
in all tunings.

It is however possible to find an unaccented symbol that is valid in
its primary comma role for all multiples of 3 degrees of 665-tET, if
this is important. And most of them _are_ the same as the
corresponding 217-tET symbol. Here are the single shaft ones, in the
ASCII longhand:

|( )~| |~ /| |) (| (|( //| /|) /|\ (|) (|\

So the corresponding 665-tET notation could be:
'| .)~| )~| ')~| .|~ |~ '|~ etc.

Will you be wanting the multishaft symbols too, or are you planning to
use the conventional sharps and flats?

Unfortunately 612-tET doesn't work out quite as neatly as the above,
with unaccented symbols on every third degree.

Here's one proposed notation for it.

'| )| |( ~| )|( )~| ~|( |~ '|~ ./| /| '/| )/| |) '|) |\
(| ~|) .(|( (|( .//| //| '//| ./|) /|) '/|) /|\ (/| '(/|
|\) (|) .(|\ (|\ '(|\

🔗Dave Keenan <d.keenan@bigpond.net.au>

🔗kraig grady <kraiggrady@anaphoria.com>

🔗Dave Keenan <d.keenan@bigpond.net.au>

--- In tuning@yahoogroups.com, kraig grady <kraiggrady@a...> wrote:
> The only thing i would like to throw into the mix here , is that it
is better to have most differention between symbols as possible to
make it read easier. The great thing about sharps and flats is that
don't look anything like each other
>

Yes. I totally agree. We have tried to maintain that principle as much
as possible with sagittal. But you would appreciate that when we come
to notating something as extreme as degrees of 612 or 665-tET where
there are up to 126 divisions _between_ a sharp and a flat it starts
to get a little difficult to find symbols which look sufficiently
different from one another (and from all the other myriad symbols one
may find on a music staff) and yet which form some kind of orderly
progression.

We figure that if two symbols are likely to be confused with each
other they had better be close together in pitch so the result isn't
too disastrous. e.g. missing an accent mark that represents a schisma
(about 2 cents) isn't going to bother too many listeners in most contexts.

We are definitely still open to suggestions for improving sagittal. We
think we've done a reasonable job, although you can't tell this from
the attempted ASCII representation of the symbols. Looking at the
actual graphical symbols on Scala's Chromatic Clavier or Staff window
will give a better idea. Unfortunately Scala doesn't yet have all the
symbols required to do 612 or 665. Also you'll probably get an error
message if you try to generate the full 612 or 665-tET in Scala,
although you can set up a scale with the pitches from from say C to C#
without any problem.

I'd also like to point out that, although someone may be able to come
up with a set of symbols that are more differentiated than the
sagittal ones for any _particular_ tuning, they are unlikely to form
part of a _universal_ notation system where they have uniform meanings
across all tunings. We believe we have come up with a system that has
maximum differentiation for the simpler tunings, with differentiation
degrading gracefully as tuning complexity increases.

The sagittal system of symbols has something in common with chinese
characters. Each sagittal symbol is a different combination of a few
common strokes, where the strokes themselves look as different as
possible from one another.

🔗Danny Wier <dawiertx@sbcglobal.net>

From: "Dave Keenan" <d.keenan@bigpond.net.au>

> Yes. I totally agree. We have tried to maintain that principle as much
> as possible with sagittal. But you would appreciate that when we come
> to notating something as extreme as degrees of 612 or 665-tET where
> there are up to 126 divisions _between_ a sharp and a flat it starts
> to get a little difficult to find symbols which look sufficiently
> different from one another (and from all the other myriad symbols one
> may find on a music staff) and yet which form some kind of orderly
> progression.

What I'm thinking, is using a mixed notation that can use up to three
symbols per note. The first would be a sharp, flat, natural, double sharp or
double flat; a sharp or flat raises or lowers a note one apotome. A second
symbol would be used to raise or lower a note a number of commas, and the
third symbol indicates fractions of a comma or schismas. Since in 612-tone
twelve steps make a Pythagorean comma (thirteen in 665-tone) the twelve
sagittal symbols could represent those fractions of a comma, added to the
existing diagonal slash-like marks for commas. I wouldn't see the need for
126 distinct symbols for each multiple of a twelfth-comma (or "schisma" as
the case may be; that's a better term for a stem in 612- or 665-tone).

> We are definitely still open to suggestions for improving sagittal. We
> think we've done a reasonable job, although you can't tell this from
> the attempted ASCII representation of the symbols. Looking at the
> actual graphical symbols on Scala's Chromatic Clavier or Staff window
> will give a better idea. Unfortunately Scala doesn't yet have all the
> symbols required to do 612 or 665. Also you'll probably get an error
> message if you try to generate the full 612 or 665-tET in Scala,
> although you can set up a scale with the pitches from from say C to C#
> without any problem.

Not if you change the maximum scale size in params.par file. I successfully
generated a 4296-tet scale once!

> I'd also like to point out that, although someone may be able to come
> up with a set of symbols that are more differentiated than the
> sagittal ones for any _particular_ tuning, they are unlikely to form
> part of a _universal_ notation system where they have uniform meanings
> across all tunings. We believe we have come up with a system that has
> maximum differentiation for the simpler tunings, with differentiation
> degrading gracefully as tuning complexity increases.

That's okay; even in Turkish music there are three notation symbols in use
(Arel-Ezgi, Yekta Bey, one other I can't remember). Even Arabic
quarter-tones are marked differently depending on who's printing the sheet
music.

> The sagittal system of symbols has something in common with chinese
> characters. Each sagittal symbol is a different combination of a few
> common strokes, where the strokes themselves look as different as
> possible from one another.

I'm thinking the rebus principle myself! Korean does that with Hangul
phonetic script; consonant and vowel symbols are arranged in a square-shaped
cell for each syllable; each cell may contain anywhere from two to five
distinct symbols.

🔗Dave Keenan <d.keenan@bigpond.net.au>

Hi Danny,

It seems you saw my reply to Kraig Grady, but may have missed my
earlier reply to you, at
/tuning/topicId_46887.html#46919
and the small correction to it at
/tuning/topicId_46887.html#46924

--- In tuning@yahoogroups.com, "Danny Wier" <dawiertx@s...> wrote:
> From: "Dave Keenan" <d.keenan@b...>
> What I'm thinking, is using a mixed notation that can use up to three
> symbols per note. The first would be a sharp, flat, natural, double
sharp or
> double flat; a sharp or flat raises or lowers a note one apotome. A
second
> symbol would be used to raise or lower a note a number of commas,
and the
> third symbol indicates fractions of a comma or schismas. Since in
612-tone
> twelve steps make a Pythagorean comma (thirteen in 665-tone) the twelve
> sagittal symbols could represent those fractions of a comma, added
to the
> existing diagonal slash-like marks for commas. I wouldn't see the
need for
> 126 distinct symbols for each multiple of a twelfth-comma (or
"schisma" as
> the case may be; that's a better term for a stem in 612- or 665-tone).

This is somewhat uncanny if you haven't read those messages, since you
can in fact do something very much like this in sagittal. Yes you can
use standard sharps, flats and their doubles for apotomes. And yes we
have separate symbols for schismas (although we like to think of their
combination with the arrow-like symbols as being a single accented
arrow-like symbol, but that's neither-here-nor-there). The rest is
only slightly different to what you suggested. You would use 12
distinct arrow-like symbols (and their inversions) for the
quarter-syntonic-commas and add schisma up and down symbols (which
look like miniature versions of the comma slash symbols) to those, to
fill in the gaps.

> Not if you change the maximum scale size in params.par file. I
successfully
> generated a 4296-tet scale once!

OK! Thanks for that tip. By the way, the biggest ET notatable with
sagittal is 1171. So we have essentially one cent resolution relative
to Pythagorean. It's funny to think that if you had a piano tuned to
consecutive steps of 1171-tET and started with C at the low end, you
still wouldn't have reached C# by the time you got to the high end. On
an 88-keyer you'd be one step short of Db (in Pythagorean terms).

But I recently met a woman who teaches music in Germany, who had in
her office for some time, a specially made 97-key acoustic piano with
consecutive steps of 96-ET on it. I had to tell her that 72-tET would
have been better value for money since it has better JI
approximations, and I was able to demonstrate that for her on my
laptop using Scala. She was very interested in the just thirds and
sixths, but I think she found the ratios of 7 a bit freaky. :-)

I mentioned resolution relative to Pythagorean. I should mention that
we've also catered for folks who want to notate everything relative to
12-tET-sized fifths (In Scala, SET NOTATION SA12R) although we
recommend doing this only for scales that actually _have_ some
12-tET-sized fifths. It gives mutually-consistent notations for all
multiples of 12-ET up to 192-ET (excluding 180-ET). This notation
_only_ :-) has a resolution of about 6 cents (i.e. max errors of about
+-3 cents). However this could be extended to 2 cent resolution, by
using the schisma symbols in a false manner to mean 2 cents. I say
"false" because from the ratio-approximation point-of-view the
5-schisma is actually negative relative to 12-ET-sized fifths.

> > The sagittal system of symbols has something in common with chinese
> > characters. Each sagittal symbol is a different combination of a few
> > common strokes, where the strokes themselves look as different as
> > possible from one another.
>
> I'm thinking the rebus principle myself! Korean does that with Hangul
> phonetic script; consonant and vowel symbols are arranged in a
square-shaped
> cell for each syllable; each cell may contain anywhere from two to five
> distinct symbols.

All right! I'd never heard of the Rebus principle before. A quick
Google search has furthered my education in this regard, thanks. It
makes so much sense!
http://www-rohan.sdsu.edu/dept/chinese/aspect/rebus.html

Here's my summary of the Rebus Principle:
Written symbols which initially represent meanings directly (e.g. via
simple pictures) are subsequently borrowed to represent new words that
have the same _sounds_, regardless of the meaning. This occurs because
if you have to make a new symbol for every new _meaning_, you will
soon run out of distinguishable symbols, whereas there are far fewer
_sounds_ to be represented.

However it isn't totally clear to me how this relates to notating
pitch, since, in this case, the sound _is_ the meaning. Ah but which
aspect of the sound is to be _meant_ by a symbol, the size of the
melodic step, or the sonority of the harmony? We have chosen to favour
harmony since experiments have shown that small errors in pitch have a
much greater effect on perception of harmony than melody. But we have
not ignored melody either, since whenever possible, we ensure that
symbols do not represent widely different melodic distances in
different tunings.

So in this case we could say that different ratios which are very
close together constitute different meanings for the same sound. And
we do indeed use the same symbol to represent nearby ratios other than
the one that is represented directly in the strokes making up the
symbol, and just as with natural languages, sometimes the original
direct ratio meaning of the symbol is completely squeezed out because
the other ratios are far more common. And, just like the chinese who
then add "semantic radicals" to distinguish the meaning of same-sound
words, we then allow those who feel the need, to add schisma accent
marks (or sometimes whole new symbols) to distinguish these ratios.

I find this parallel with the evolution of natural languages to be
uncanny. But instead of taking hundred or thousands of years, this
evolution took place over about 18 months! If you have the patience to
go thru the archives of tuning-math in the "Common notation for JI and
ETs" thread, you can see it happening. Extraordinary!

Thanks for pointing that out.

612-tet and 665-tet sagittal notation?

🔗Danny Wier <dawiertx@sbcglobal.net>

🔗Dave Keenan <d.keenan@bigpond.net.au>

🔗Dave Keenan <d.keenan@bigpond.net.au>

🔗kraig grady <kraiggrady@anaphoria.com>

🔗Dave Keenan <d.keenan@bigpond.net.au>

🔗Danny Wier <dawiertx@sbcglobal.net>

🔗Dave Keenan <d.keenan@bigpond.net.au>

🔗Paul Erlich <perlich@aya.yale.edu>

🔗Gene Ward Smith <gwsmith@svpal.org>