Ennealimmal notation

I was writing email to Joe, when Windows crashed and killed all
aboard. I took this as a portent, and am posting this here so all can
listen in.

Let us represent 7-limit notes by means of what I've taken to
calling "monzos"--row vectors of integers representing the exponents
of 2, 3, 5, and 7 respectively. 1/1, which I take to be middle C, is
represented by the monzo [0, 0, 0, 0], and is given the white space
between the bass and treble clefs. Of notes without accidentals, only
one (middle C) is allowed in this space. The white space above the
treble clef is C an octave up, and below the bass clef C an octave
down, and so forth. It might make more sense to choose A as the place
to center on, and in any case to use ABCDEFGHI as the nine nominals;
I'd like opinions on that.

Let [a, b, c, d] be a monzo. The number of steps up or down from
middle C--the staff line or space on which the note is located--is
given by 9a + 13b + 19c + 24d. (This is an example of what I call a
val.) The number of sharp symbols (if positive) or flat symbols (if
negative) is given by 2b + 3c + 2d (another val.) The sharp is a
sharp of reasonable size, being about the size of the 43-et sharp. In
terms of cents, we can take it to be 253/3 cents; together with 400/3
cents for 1/9 of an octave, this gives us in effect a 3600-et version
of ennealimmal, which happens to be a very good one.

This is the basic system, but I presume in practice it will work
better to use the symbols for two or three flats and sharps, along
with step adjustments. The double sharp symbol could be given the job
of representing two sharps, down a step, or 2*(253/3)-400/3 = 35.33
cents. The triple sharp symbol could be given the job of representing
three flats *down*, and two steps up, of size therefore 2*(400/3)-3*
(253/3) = 13.67 cents.

If we take the octave starting at middle C to be C, D, E, F, G, H, I,
A, B, C', then 5/4 is represented as D###, which can be rendered more
perspicuouly as F "triple flat", or an F of 400 cents, down 13.67
cents to 386.33 cents. 3/2 becomes four steps up plus two sharps, or
G##; which is a G of 533.33 cents plus two sharps totaling 168.67
cents, giving 702 cents; but we can also call it H "double sharp", or
an H of 666.67 cents up 35.33 cents to 702 cents. 7/4 is represented
by I##, but again we may call that A "double sharp"; an A of 933.33
cents up 35.33 cents to 968.67 cents. The C major tetrad is now
C - F "triple flat" - H "double sharp" - A "double sharp". If you
compare the figures above to JI values, you will see that we are
very, very close--this is, effectively, 7-limit JI.