User:VectorGraphics/Walker brightness notation

Walker Brightness Notation is a way of naming intervals "invented" by Jay Walker / VectorGraphics. It names intervals purely based on their sizes, ignoring just intonation and MOS scales almost entirely (though it takes names from them, specifically diatonic, for the sake of recognizability).

Example

As WBM is not a rigid system, an example scale is probably the best way to explain how it works:

WBM Exemplary Scale

Degree	Cents	Name
0	0
1	53
2	134
3	156
4	188
5	206
6	220
7	248
8	266
9	300
10	315
11	366
12	435
13	542
14	588
15	611
16	684
17	688
18	969
19	992
20	1200

So first, we name each interval according to its general interval class.

WBM Exemplary Scale

Degree	Cents	Name
0	0	unison
1	53	second
2	134	second
3	156	second
4	188	second
5	206	second
6	220	second
7	248	semifourth
8	266	third
9	300	third
10	315	third
11	366	third
12	435	third
13	542	fourth
14	588	tritone
15	611	tritone
16	684	fifth
17	688	fifth
18	969	seventh
19	992	seventh
20	1200	octave

Note that only 0c and 1200c (or the closest match to 1200c for non-octave scales) are called the unison and octave. Also, here 248c has been given the name "semifourth", we'll talk more about that later.

Also, note that the scale lacks a sixth entirely. This is in alignment with the sizes of "sixths" - there is no interval between ~750 to ~950 cents that could reasonably be called a sixth. 969c gets close, but along with it already being in the seventh range (albeit the lower end of it), there are... harmonic reasons for calling it a seventh.

First of all, there are some special names to apply: harmonic seventh for scale degree 18, and diesis for scale degree 1. (If there were a scale degree of around 10-30 cents, it would be called a comma.)

Degree	Cents	Name
0	0	unison
1	53	diesis
2	134	second

Degree	Cents	Name
17	688	fifth
18	969	harmonic seventh
19	992	seventh

Note that "harmonic seventh" still requires other sevenths to be distinguished from it, unlike diesis and comma.

So, we add qualifiers to distinguish intervals of the same general interval class.

Degree	Cents	Name
0	0	unison
1	53	diesis
2	134	minor second
3	156	neutral second
4	188	major second
5	206	major second
6	220	supermajor second
7	248	semifourth
8	266	subminor third
9	300	minor third
10	315	minor third
11	366	neutral third
12	435	major third
13	542	fourth
14	588	tritone
15	611	tritone
16	684	fifth
17	688	fifth
18	969	harmonic seventh
19	992	minor seventh
20	1200	octave

Note that there are some intricacies with the way I've named these, starting off with the minor second, which is considerably on the sharper end of the "minor second" range - had there been another smaller minor second, I would have called this one sup[er|ra]minor. Similarly with the major third, which is actually well into the supermajor range - however, there is no "normal" major third to distinguish it from, so "supermajor" is redundant. Onto the major seconds, you may notice there are two of them, along with the minor thirds. This will be resolved in the next step.

As for the semifourth, think of "semifourth" here as being a cover name for an interval with two names: 248c here serves as both an inframinor third and an ultramajor second, the same way a tritone can serve as both a diminished fifth and augmented fourth. (Side note - I have complaints about the way "diminished" and "augmented" are traditionally used. But that is beside the point...for now.) If another interval, say 242c, were in the scale, that would be the ultramajor second and 248c would be the inframinor third.

Here, the "minor thirds" closer to 6/5 have been given higher priority - 266c is subminor. Conversely, there is no major third close to 5/4, which I mentioned prior. Similarly with the fourth, which is considerably sharp.

Also, there is a minor seventh but no major seventh.

Degree	Cents	Name
0	0	unison
1	53	diesis
2	134	minor second
3	156	neutral second
4	188	minor tone
5	206	major tone
6	220	supermajor second
7	248	semifourth
8	266	subminor third
9	300	common minor third
10	315	just minor third
11	366	neutral third
12	435	major third
13	542	fourth
14	588	small tritone
15	611	large tritone
16	684	small fifth
17	688	large fifth
18	969	harmonic seventh
19	992	minor seventh
20	1200	octave

Here, the smaller and larger intervals have been named... "small" and "large", following the convention for tritones. There are a couple exceptions, which it is optional to include, but I have done so here:

The major seconds have been named "minor tone" and "major tone" - a reference to nicetone and zarlino, and to take advantage of the unique name for the major second - a tone. Note that the 220c is still called supermajor.

The minor thirds have been named based on which tunings of the minor third they approximate, which is an idea I've taken from Lumatone's 53edo naming scheme - "common" is used as a shorthand for 12edo. Similarly, if ~195c were in the scale I would refer to it as a mean tone.

You could also refer to the fifths by the scales they generate - mavila and diatonic - however, I don't believe this is very helpful as neither of these fifths are actually being used to generate scales. This is also why I try not to refer to fifths as wolf fifths unless they are in a tuning context where wolf fifths apply.

What about accidentals?

This system does not specify accidentals. I would personally use "sharp" and "flat" to cover the distances between some kind of minor third and some kind of major third (if not thirds, then seconds, sixths, or sevenths), preferably those close to either the common (300c and 400c) or just (315c and 386c) thirds, but I know the two are usually defined in terms of the circle of fifths (as in ups-and-downs notation and in Pythagorean tuning) and that can be used as well, where such systems are applicable.