SaLaTa dark vs. bright

[Dan Lindgren]

As an alternative to my previous SaLaTa proposals, I could
also have proposed something like this...

Like before, give twelve unique names to the 12 ET notes;
and for intervals, count the semitones. I would talk about how
notes and intervals could come in two different flavors:
dark (d) and bright (b), respectively. You would then make
noteheads in a chromatic notation either black (d) or white (b).
There would be one exception, though, and that would be the
note corresponding to D, which would be "darkbright" (db).

In the sequence of perfect fifths, you would have dark notes
to the left of D, and bright notes to the right. D's notehead
could be a circle with a dot in it. Then, without the need for any
key signatures, 25 notes (in the sequence of perfect fifths),
ranging from Ebb to Cx, could be described just by the color
of a notehead and its position on the chromatic stave.

Here are some examples of matching note names:

C/B# => dDo/bDo
Db/C# => dPa/bPa
Ebb/D/Cx => dRo/dbRo/bRo
Eb/D# => dNa/bNa
Fb/E => dMo/bMo
F/E# => dFa/bFa
Gb/F# => dVo/bVo
G/Fx => dSa/bSa
Ab/G# => dGo/bGo
Bbb/A => dLa/bLa
Bb/A# => dBo/bBo
Cb/B => dTa/bTa

If you would like to represent notes even further out on the
two extremities of the sequence/spiral of fifths, the
usual > and < signs could be used to push noteheads in
comma steps.

As for intervals, they too would be divided into dark and bright:

m2/+1 => d1/b1
-3/M2 => d2/b2
m3/+2 => d3/b3
-4/M3 => d4/b4
P4/+3 => d5/b5
-5/+4 => d6/b6
-6/P5 => d7/b7
m6/+5 => d8/b8
-7/M6 => d9/b9
m7/+6 => dX/bX
-8/M7 => dY/bY
-9/P8/+7 => d'0/db'0/b'0

(These intervals could also be modified with > and < signs.)

You could then say something like: "There are eight steps
between Do and Go" (The interval between C and G# is an
augmented fifth).

When you want to be more precise, you could instead say:
"There are eight dark steps between dark Do and dark Go"
(The interval between C and Ab is a minor sixth).

So SaLaTa effectively would have two levels of abstraction.

Not sure if I will ever pursue this scheme, but I just thought
that I would mention it anyway.

Dan

P.S. It would also be possible to just let D be dRo instead
of dbRo.

[Dan Lindgren]

Addendum:

If one would want to mark the "foreign" notes (that is, notes that
are not diatonic to the key signature), dots could be placed in
front of those noteheads. One would only have to mark the first
occurrence of a foreign note in a specific octave position within
a measure. Some sort of key signature would also be required.

Dan

[Dan Lindgren]

Here is a revised edition of my dark/bright SaLaTa:

Let the names be the same as before, but let Ro come out as
either dRo (Ebb) or bRo (D).

(This way, it puts the Pythagorean C closer to ET.)

Steps represent semitones as before; but at a finer level you
would measure intervals as a combination of dark and bright
steps. A dark step = m2, and a bright step = +1.

So, at the abstract level one could say that there are seven
steps between Do and Sa (there's a perfect fifth from C to
G). At the finer level one would say that there are four dark
and three bright steps between dark Do and dark Sa.

It doesn't actually matter in what order you take those steps
(it's akin to how you add vectors in mathematics).

If you like to verify this, look at the (RH) keyboard I propose
and try any combination of four dark steps (m2 = diagonally
down) and three bright steps (+1 = diagonally up), and you
should always land on the perfect fifth:

http://nydana.se/keyboard.pdf

But what should we call a note such as Cx, for instance?
I suggest xbRo, where x means extra; so, it's an extra bright
Ro. If you want to go even further out on the spiral, you just
add another x, for example: xxbRo, the extra extra bright Ro
(B###).

So, now you can name all notes and describe intervals - at
two different levels of abstraction.

Let me just say that you don't necessarily have to color the
noteheads black or white, it could suffice to use the "window
frames" I've talked about previously (simply apply the new
note names).

The black/white distinction could alternatively be expressed
in some other form - such as letting triangles have rounded
or sharp corners, or changing the slope of oval noteheads,
and so on.

Ideally, the black and white should be differentiated into a
grey scale (but that may not be convenient if you want a
thoroughly black/white notation). What you would see then,
is, for example, the C major scale with C as dark grey, D as
grey, E as a lighter shade of grey, F as a slightly darker
shade than C, and then increasingly brighter shades for
G, A and B. The whole sequence of perfect fifths would go
from very black to very white.

Then, when you play the piano, you may notice that the
brighter the color of a notehead, the more emphasis you
will generally give to that note.
 
Dan