From: jacob@max.cc.brandeis.edu ( )
Subject: Re: notation of accidentals [?]
Organization: Brandeis University Math Department
Date: Fri, 20 Nov 1992 01:30:19 GMT

In article <1992Nov19.003701.15474@news.cs.brandeis.edu> jacob@max.cc.brandeis.edu ( ) writes:

>The natural notation should be (to me) _relative_
>to the accidental at the clef, that is if the note
>is # at the clef then # --> x, natural --> # and
>b --> natural, if the note is b at the clef then
># --> natural, natural --> flat and b --> bb, and
>so on...

In article <1992Nov19.021846.22259@Princeton.EDU> roger@astro.princeton.edu (Roger Lustig) writes:

>There's a certain logic to that idea, but it also means that you have
>to read each note in light of what's gone before.  REmember that 
>accidentals are also used to cancel naturals.

I don't quite understand. Let's say you're in F major. Suppose you
want to say "b natural", then you'd write "b sharp".
Then suppose you want to cancel "b natural" and revert to "b flat".
You'd write "b natural".

This reverts you to what's at the clef signature. Everything should
be relative to the clef signature as long as that signature is in force.

But maybe I don't understand what you're saying.

Jacob:
>Besides being unnatural, the common notation also
>makes fast transposition a bit more awkward.

Roger:
>I'm not sure about that, given the cancellation function.

Here's an example. Let's say you have a piece in C major
with a chromatic F#.

Now say you want to transpose a 5th down. With my proposal
all you have to do is imagine you've got one flat at the clef
and read the piece in C-clef (2nd line) and you're done.
_Everything_ else stays the same. The F# transposed down one 5th
is _still_ written with a sharp.

With the current notation, you've got to do all of the above _and_
to imagine you're changing that sharp into a natural.

Roger:
>The accidentals # and b (natural is a very recent invention) were
>originally solmization instructions.  b meant "this is 'fa'"; #
>meant "this is mi."  In other words, one raised a note by giving it
>a sharp because that meant one had to sing the note above it as fa,
>and mi-fa is a half-step.

Funny. This is _almost_ how I used to think of flats and sharps when
I was a child. Actually I used to think of a flat as "this is fa" (F)
and a sharp as "this is si" (B), because of the upwards attraction
of a sharped note upwards (like si is attracted to do), and the downwards
attraction of the flat note downards (like fa is attracted to mi.)

Roger:
>Because singers knew the hexachord system, and knew not to sing tritones
>and other weird intervals without explicit markings, few accidentals 
>were needed.  In fact, one of the most remarkable pieces of the 16thC
>-- Willaert's "chromatic duo," Quidnam ebrietas, has but one flat in
>its tenor.  However, one has to add flats on the fly in order to avoid
>singing corrupt fourths and fifths, and one has to keep them, too! 
>The piece winds up on a written E that is sung Ebb.  Imagine using your
>system in a piece like that!  An accidental would have to be interpreted
>in light of all the music that had gone by so far.

I'm not sure why. I think I'd like an example where you'd need to know
anything beyond the clef signature to interpret an accidental. I assume
we're imagining that the musica ficta accidentals have been written in
(using my system) and that you're saying that to interpret an accidental
you'd need to know everything you've sung before. I really don't see why.

For example your E double-flat, if there's a E flat at the clef would be
written E flat, if there's no E flat at the clef, it would be written
E double-flat. I don't see where you'd need to know anything else to
interpret that E double-flat.

Jacob