John Chambers wrote:
>
> Bruce Olson writes:
> | Why so awkward? I've already shown how to do this quite simply with
> | J:<key sig>, [<tonic>] and in the K:<tonic><mode> you still have the
> | logic flaw. It's going to be a developer's nightmare to resolve any
> | inconsistanies in the triple K:spec.
>
> The main reason is that I, for one, didn't follow the description of
> the J: line, and I don't understand the supposed "logic flaw" that
> you're talking about. Can you explain it so dummies like me can
> understand? If not, we'll just continue in our erroneous ways.
>
> I'm not trying to be sarcastic or anything; I read your entire
> message with curiosity, and frankly, I didn't understand more than
> one or two sentences in it. I think you were writing about some sort
> of musical topic, but I'm not even sure of that, as the language was
> so far outside anything that I'm familiar with. What's a pi1? I've
> never heard of it. Or maybe I have and it went out the other ear.
> Some education is in order here.
>
> (I've played a lot of kinds of music, but obviously not enough. ;-)
>
Thank to Phil Taylor for explaining pi1. See the rest of Bronson's
system and the earlier (and poorer) Gilchrist system in the text file on
keys and modes on my website. Jack Campin used neither of these in his
mini-treatise on modes on his website. Bronson's only drawback is
getting Greek pi into recognizable simple ASCII.
Sorry I'm so late, this and finding and ordering an oscilloscope
to see what the BASIC 'SOUND' command in my ABC program is actually
doing at my computer's speaker has taken a bit of time (And it's
behavior leaves something to be desired). Groan, trying to get the
logic straight, simple and complete, has taken a long time here,
and it think this is about the 5th draft, and hope that it's
intelligible.
What we have for the situation key sig/tonic/scoring mode is
practically trivial algebra. [Simple minded Gramm-Schmidt
procedure to get an orthonormal set of basis vectors that span
the space.]
The SFMODE.GIF on my website shows the linear dependence among
the three vectors: key sig., tonic, and scoring mode; and that
there are only two independent vectors. Key sig. is the obvious
practical #1, because no knowledge of tonic or scoring modes is
needed to write out the tune in music notation or -play it or
sing a song to it. J:<key sig.> in my program does that, and is
directly the unspecified mode option.
Nothing else is required unless you want to put in something
about the structure of the tune. I do, because I can't
stressed note code without it. [Not really true, but using
anything, like tonic (origin of scale of tune), that subdivides a
large file of coded tunes into smaller blocks for searching for
the likes (any name) of a given tune (any name) is a great time
saver. (Like giving the state in your address, so I only need
search your state map for the city, and don't have to look
through a whole USA map for city, and then having to weed out the
accidental coincidences on like named cities.]
What second? No real choice for me but <tonic>, because <scoring
mode> doesn't necessarily have anything to do with tune mode.
[Some editors in the past just used major and minor scoring modes
and used 'accidentals' to correct to proper mode, so key sig. and
final don't work there. But my program will tell you both the
scoring mode and real tune mode. Normally the same, but sometimes
very different.] Remaining,<scoring mode>, is a dependent
variable, easily calculated in an ABC program, for which there is
no need of any specification.
K:<tonic><[scoring] mode><key sig.> puts top priority last
instead of first. And, and anyhow, is redundant because
K:<tonic><scoring mode> has already determined <key sig.>, but
unfortunately it hasn't really told us much else, because no one
has to give it correctly to get <key sig.> to come out right.
The options for <tonic><scoring mode> are quickly obtained from
SFMODE.GIF.
J:<key sig.><tonic>, is complete, and there no ambiguities,
inconsistancies, or redundancies. K:<key sig.><tonic> would be
fine, but it's way to late to change K: to be given that way now.
All previously coded tunes wouldn't work. That's why I used J:.
k: would also work, but obviously lead to confusion.
There's one hitch, those odd modes like pi1; they can be scored
in three modes, all with different key sigs., but always gets the
right key sig. for the scoring mode, and since none of the modes
are the real tune mode, it makes no difference which scoring it
is (my program will tell you what the scoring mode is, anyhow).
My program will figure out the true tune mode no matter how it's
scored. [If it's circular mode you need to, as alway specify
<tonic> in my J:spec, it's simply J:<key. sig><tonic>.
[If you want a copy of SFMODE.GIF download it soon, because the
numbers there proved inconvenient for the 35 note just intonation
scale I've started working on. The new GIF is ready and waiting
to prove itself useful, but I've only gotten the scale part
rewritten and there are a lot of subroutines to be revised for
the new program. The starting numbers for the series in the new
version are different. The linear dependence is always the same,
whatever starting numbers one chooses. Too bad one can't do
chords in BASIC, because I'll have all the notes to get that
diminished 7th right (1 3b 5b 7bb. The 6# (458 1/3 Hz) of the 21
note just intonation scale for 7bb (456.192) isn't too bad, but
12TET is poor whether you use 6 or 6# for 7bb. The 'right' note
is close to the mid-point between them. 'Right' here is a bit
fuzzy. It's 'right' if the base note, 1, is your sole
consideration.]
[This brings me to a pet peeve. It seems ridiculous to define
chords in 12TET; you only get approximations to the classical
chord ratios in 12TET. Getting that last note, the 6th, of a
diminished 7th in 12TET back to 7bb takes more than trivial
math. It's usually fairly easy to compact/reduce/map big N to
little M, but without special constraints you can't go backwards]
Bruce Olson
--
Old English, Irish and, Scots: popular songs, tunes, broadside
ballads at my website (no advs-spam, etc)- www.erols.com/olsonw
or click below <A href="http://www.erols.com/olsonw"> Click </a>
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