99-et in Sagittal (for Gene)

Gene,

Dave Keenan and I have had a very productive discussion about how to
notate 99-ET (using conventional staff notation with 7 nominals in a
sequence of 5ths), and here's what we've finally agreed on:

99: |~ /| ~|) //| )/|\ )||( ~~|| ||\ /||~ /||\

Note the presence of )/|\ -- our new (3-flag) semi-apotome symbol.

This symbol sequence is the same as what we have for every other
symbol of 198-ET:

198: )|( |~ ~~| /| |\ ~|) (|( //| /|\ )/|\ (|)
)||( ~||( ~~|| /|| ||\ ~||) /||~ //|| /||\

)|( is 891:896 (7:11k)
|~ is taken as 243:245 (245C, a secondary role), but is also valid as
729:736 (23C, its primary role)
~~| is valid as both 98:99 (11:49C) and 99:100 (11:25C)
/| is 80:81 (5C)
|\ is 54:55 (55C)
~|) is 48:49 (49S)
(|( is 44:45 (5:11S), and also valid as 1664:1701 (7:13S)
//| is 6400:6561 (25S)
/|\ is 32:33 (11M)
)/|\ is 392:405 (5:49M)
(|) is 704:729 (11L)

The double-shaft symbols are apotome-complements of the single-shaft
symbols taken in reverse order, beginning with //|

The 99-ET symbol semantics is such that pairs of symbols two degrees
apart differ by a 5-comma (5C):

1 |~ 245C, i.e. 49C – 5C
2 /| 5C
3 ~|) 49C
4 //| 25C, i.e. 5C + 5C
5 )/|\ 5:49M, i.e. 49C + 5C

--George

--- In tuning-math@yahoogroups.com, "George D. Secor" <gdsecor@...> wrote:
>
>
> Gene,
>
> Dave Keenan and I have had a very productive discussion about how to
> notate 99-ET (using conventional staff notation with 7 nominals in a
> sequence of 5ths), and here's what we've finally agreed on:
>
> 99: |~ /| ~|) //| )/|\ )||( ~~|| ||\ /||~ /||\

What would you suggest as single ascii character shorthand for this
symbol set?

I get that

245/243: 1 step
81/80: 2 steps
49/48: 3 steps
6561/6400: 4 steps
405/392: 5 steps

This seems pretty good. In comparison, the Tenney reductions would be

126/125: 1 step
81/80: 2 steps
49/48: 3 steps
525/512: 4 steps
28/27: 5 steps

--- In tuning-math@yahoogroups.com, "Gene Ward Smith"
<genewardsmith@...> wrote:
>
> --- In tuning-math@yahoogroups.com, "George D. Secor" <gdsecor@>
wrote:
> >
> >
> > Gene,
> >
> > Dave Keenan and I have had a very productive discussion about how
to
> > notate 99-ET (using conventional staff notation with 7 nominals
in a
> > sequence of 5ths), and here's what we've finally agreed on:
> >
> > 99: |~ /| ~|) //| )/|\ )||( ~~|| ||\ /||~ /||\
>
> What would you suggest as single ascii character shorthand for this
> symbol set?

So glad you asked! Dave and I decided to make the shorthand more
useful by reassigning some of the characters to more popular ratios,
so we now have:

ASCII shorthand, with extended-character decimal codes
long down up Comma and extended-character description
----- ---- -- ----------------------------------------
|~ z ~ 23-comma, 729:736
/| \ / 5-comma, 80:81
~|) h p 49S-diesis, 48:49
//| _ = 25S-diesis, 6400:6561
)/|\ & % 5:49M-diesis, 392:405

Since shorthand is only for single-shaft symbols, the entire ASCII
sequence (up to an apotome) would be:

up: ~ / p = % #_ #h #\ #z #
dn: z \ h _ & b= bp b/ b~ b

--George