Ennealimmal notation II

I haven't heard from Joe yet. Joe, did my previous make sense? Is
this helping?

Here's how to extend the notation to an 11-limit notation:

If [a, b, c, d, e] is an 11-limit monzo, then the number of steps is
given by 9a + 15b + 22c + 26d + 30.5e. If we end up with a half-step,
we tack a half-step symbol on. The appearance of these in a score
flags the presence of the 11-limit, which I think is kind of neat.
The formula for number of sharps is now 2b + 3c + 2d + e; this is
treated exactly as before. 11/8 over middle C would be
F "half-step" #.

It seems like it would just be easiest to have all accidentals (including naturals) carry
a ratio above them or to their left, allowing you to write in infinity-limit. It's only a
little bit more work. -Justin

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> I haven't heard from Joe yet. Joe, did my previous make sense? Is
> this helping?
>
> Here's how to extend the notation to an 11-limit notation:
>
> If [a, b, c, d, e] is an 11-limit monzo, then the number of steps is
> given by 9a + 15b + 22c + 26d + 30.5e. If we end up with a half-step,
> we tack a half-step symbol on. The appearance of these in a score
> flags the presence of the 11-limit, which I think is kind of neat.
> The formula for number of sharps is now 2b + 3c + 2d + e; this is
> treated exactly as before. 11/8 over middle C would be
> F "half-step" #.

>It seems like it would just be easiest to have all accidentals
>(including naturals) carry a ratio above them or to their left,
>allowing you to write in infinity-limit. It's only a little bit
>more work.

That's a *lot* more work, both for the printing and the reading.

-C.

But it disambiguates everything. I think all the worries about efficiency in notation
are...well, inefficient. -Justin

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >It seems like it would just be easiest to have all accidentals
> >(including naturals) carry a ratio above them or to their left,
> >allowing you to write in infinity-limit. It's only a little bit
> >more work.
>
> That's a *lot* more work, both for the printing and the reading.
>
> -C.

> -----Original Message-----
> From: Gene Ward Smith [mailto:gwsmith@svpal.org]
> Sent: Friday, August 01, 2003 12:51 PM
> To: tuning@yahoogroups.com
> Subject: [tuning] Ennealimmal notation II
>
>
> I haven't heard from Joe yet. Joe, did my previous make sense? Is
> this helping?

sorry, Gene ... i read your post to the list but
then got very busy since then.

> Here's how to extend the notation to an 11-limit notation:
>
> If [a, b, c, d, e] is an 11-limit monzo, then the number of steps is
> given by 9a + 15b + 22c + 26d + 30.5e. If we end up with a half-step,
> we tack a half-step symbol on. The appearance of these in a score
> flags the presence of the 11-limit, which I think is kind of neat.
> The formula for number of sharps is now 2b + 3c + 2d + e; this is
> treated exactly as before. 11/8 over middle C would be
> F "half-step" #.

i was creating an Excel spreadsheet to look at what
your accidentals were doing, but i had it wrong.

my initial response to your last post is that
i have strong misgivings about calling 386 cents
"D###" or "Fbbb" where zero cents is "C" -- that
note should be E, with or without an accidental,
unless the context very strongly implies Pythagorean
tuning and that it should be Fb.

as soon as i get time, i'll do the spreadsheet again,
with the correct formulas, then let you know what
i think. thanks!

-monz

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

> my initial response to your last post is that
> i have strong misgivings about calling 386 cents
> "D###" or "Fbbb" where zero cents is "C" -- that
> note should be E, with or without an accidental,
> unless the context very strongly implies Pythagorean
> tuning and that it should be Fb.

You can't use seven nominal thinking for a nine nominal system. It
might be better to go off to a different place in the alphabet. What
about naming the notes RST UVW XYZ?

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

> my initial response to your last post is that
> i have strong misgivings about calling 386 cents
> "D###" or "Fbbb" where zero cents is "C" -- that
> note should be E, with or without an accidental,
> unless the context very strongly implies Pythagorean
> tuning and that it should be Fb.

You can't use seven nominal thinking for a nine nominal system. It
might be better to go off to a different place in the alphabet. What
about naming the notes RST UVW XYZ?

h Justin,

> From: Justin Weaver [mailto:improvist@usa.net]
> Sent: Friday, August 01, 2003 1:34 PM
> To: tuning@yahoogroups.com
> Subject: [tuning] Re: Ennealimmal notation II
>
>
> It seems like it would just be easiest to have all
> accidentals (including naturals) carry
> a ratio above them or to their left, allowing you to write in
> infinity-limit. It's only a
> little bit more work. -Justin

this was essentially my initial attempt at a
new JI notation, except that instead of ratios
i much prefer a "monzo" (the prime-exponents vector),
which allows one to immediately visualize any
pitch on a lattice, and consequently to see how
it relates to all other notes in the system.

ratios allow that to some extent, but by including
all the useless exponents of 2 it complicates things
more than they need be, unless 8ve-register is an
important consideration in the analysis of the tuning.

i think "monzos" are far preferable, and i thought
that *long* before they were named after me.

-monz

You'll have to point me to an example of this system in use as I find it hard to
conceptualize by the description alone. -Justin

--- In tuning@yahoogroups.com, <monz@a...> wrote:
> h Justin,
>
>
>
> > From: Justin Weaver [mailto:improvist@u...]
> > Sent: Friday, August 01, 2003 1:34 PM
> > To: tuning@yahoogroups.com
> > Subject: [tuning] Re: Ennealimmal notation II
> >
> >
> > It seems like it would just be easiest to have all
> > accidentals (including naturals) carry
> > a ratio above them or to their left, allowing you to write in
> > infinity-limit. It's only a
> > little bit more work. -Justin
>
>
>
> this was essentially my initial attempt at a
> new JI notation, except that instead of ratios
> i much prefer a "monzo" (the prime-exponents vector),
> which allows one to immediately visualize any
> pitch on a lattice, and consequently to see how
> it relates to all other notes in the system.
>
> ratios allow that to some extent, but by including
> all the useless exponents of 2 it complicates things
> more than they need be, unless 8ve-register is an
> important consideration in the analysis of the tuning.
>
> i think "monzos" are far preferable, and i thought
> that *long* before they were named after me.
>
>
>
> -monz

hi Gene,

> From: Gene Ward Smith [mailto:gwsmith@svpal.org]
> Sent: Friday, August 01, 2003 9:20 PM
> To: tuning@yahoogroups.com
> Subject: [tuning] Re: Ennealimmal notation II
>
>
> --- In tuning@yahoogroups.com, <monz@a...> wrote:
>
> > my initial response to your last post is that
> > i have strong misgivings about calling 386 cents
> > "D###" or "Fbbb" where zero cents is "C" -- that
> > note should be E, with or without an accidental,
> > unless the context very strongly implies Pythagorean
> > tuning and that it should be Fb.
>
> You can't use seven nominal thinking for a nine nominal system. It
> might be better to go off to a different place in the alphabet. What
> about naming the notes RST UVW XYZ?

OK, right, got it.

i think i'd prefer to follow Graham's "decimal notation"
example, and name them 0 1 2 3 4 5 6 7 8 and use the
accidentals with those (numeric) nominals.

for that matter, i believe that for non-"tonal" music
in 12edo tuning, such as Schoenberg-style free-atonality
or serialism, it's better to follow Forte's example and
name the notes 0 1 2 3 4 5 6 7 8 9 T E -- "T" and "E"
represent 10 and 11, respectively.

or perhaps 12edo could be labeled as dodecimal numbers,
like hexadecimal numbers, as 0 1 2 3 4 5 6 7 8 9 A B.
but since there is already an association of two notes
to A and B, and that association is different from this
one, T and E are better.

-monz

--- In tuning@yahoogroups.com, <monz@a...> wrote:
> hi Gene,
>
>
>
> > From: Gene Ward Smith [mailto:gwsmith@s...]
> > Sent: Friday, August 01, 2003 9:20 PM
> > To: tuning@yahoogroups.com
> > Subject: [tuning] Re: Ennealimmal notation II
> >
> >
> > --- In tuning@yahoogroups.com, <monz@a...> wrote:
> >
> > > my initial response to your last post is that
> > > i have strong misgivings about calling 386 cents
> > > "D###" or "Fbbb" where zero cents is "C" -- that
> > > note should be E, with or without an accidental,
> > > unless the context very strongly implies Pythagorean
> > > tuning and that it should be Fb.
> >
> > You can't use seven nominal thinking for a nine nominal system.
It
> > might be better to go off to a different place in the alphabet.
What
> > about naming the notes RST UVW XYZ?
>
>
>
> OK, right, got it.
>
> i think i'd prefer to follow Graham's "decimal notation"
> example, and name them 0 1 2 3 4 5 6 7 8 and use the
> accidentals with those (numeric) nominals.

first, wouldn't it be better to leave off the 0 and use 1-9?

second, graham's decimal notation example followed my decatonic
example from my paper, but i now regret it. numbers are already used
for way too many things in music theory, and when they refer to note
names too, things get hopelessly muddled. this is my experience from
working with ara on music in 22-tone equal temperament. i would now
return to the letter notation in the earlier, unpublished version of
my paper, which manuel has implemented in scala.