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).

WBN is intended to be used with the assumption of just octaves.

Example

As WBN (not WBM, sorry, I'm bad at acronyms) is not a rigid system, an example scale is probably the best way to explain how it works:

WBN 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.

WBN 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, this one would be called 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 - Vector has 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 was 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 this has been done 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 it could be called a mean tone.

You could also refer to the fifths by the scales they generate - mavila and diatonic - however, this will likely not be very helpful as neither of these fifths are actually being used to generate scales.

What about accidentals?

This system does not specify accidentals. A recommendation is to 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 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.

Examples applied to actual scales

12edo is the same as normal:

Degree	Cents	Name
0	0	unison
1	100	minor second
2	200	major second
3	300	minor third
4	400	major third
5	500	perfect fourth
6	600	tritone
7	700	perfect fifth
8	800	minor sixth
9	900	major sixth
10	1000	minor seventh
11	1100	major seventh
12	1200	octave

So is 17edo, due to its lack of common major and minor thirds:

Degree	Cents	Name
0	0.00	unison
1	70.59	minor second
2	141.18	neutral second
3	211.76	major second
4	282.35	minor third
5	352.94	neutral third
6	423.53	major third
7	494.12	fourth
8	564.71	small tritone
9	635.29	large tritone
10	705.88	fifth
11	776.47	minor sixth
12	847.06	neutral sixth
13	917.65	major sixth
14	988.24	harmonic seventh
15	1058.82	neutral seventh
16	1129.41	major seventh
17	1200.00	octave

However, 27edo is noticeably different from ups-and-downs naming.

Degree	Cents	Name	Name (Ups and downs)
0	0.00	unison	perfect unison
1	44.44	diesis	minor 2nd
2	88.89	minor second	upminor 2nd
3	133.33	neutral second	mid 2nd
4	177.78	small major second	downmajor 2nd
5	222.22	large major second	major 2nd
6	266.67	subminor third	minor 3rd
7	311.11	minor third	upminor 3rd
8	355.56	neutral third	mid 3rd
9	400.00	major third	downmajor 3rd
10	444.44	supermajor third	major 3rd
11	488.89	fourth	perfect 4th
12	533.33	superfourth	up 4th
13	577.78	small tritone	mid 4th
14	622.22	large tritone	mid 5th
15	666.67	subfifth	down 5th
16	711.11	fifth	perfect 5th
17	755.56	subminor sixth	minor 6th
18	800.00	minor sixth	upminor 6th
19	844.44	neutral sixth	mid 6th
20	888.89	major sixth	downmajor 6th
21	933.33	supermajor sixth	major 6th
22	977.78	harmonic seventh	minor 7th
23	1022.22	large minor seventh	upminor 7th
24	1066.67	neutral seventh	mid 7th
25	1111.11	major seventh	downmajor 7th
26	1155.56	supermajor seventh	major 7th
27	1200.00	octave	8ve

The notation works in tunings without a diatonic scale:

Degree	Cents	Name
0	0	unison
1	75	minor second
2	150	neutral second
3	225	major second
4	300	minor third
5	375	major third
6	450	semisixth
7	525	fourth
8	600	tritone
9	675	fifth
10	750	semitenth
11	825	minor sixth
12	900	major sixth
13	975	harmonic seventh
14	1050	neutral seventh
15	1125	major seventh
16	1200	octave

And in tunings where the diatonic scale is degenerate:

Degree	Cents	Name
0	0	unison
1	80	minor second
2	160	neutral second
3	240	major second
4	320	minor third
5	400	major third
6	480	fourth
7	560	small tritone
8	640	large tritone
9	720	fifth
10	800	minor sixth
11	880	major sixth
12	960	harmonic seventh
13	1040	neutral seventh
14	1120	major seventh
15	1200	octave

Here is an example for 13edo:

Degree	Cents	Name
0	0.00	unison
1	92.31	minor second
2	184.62	major second
3	276.92	minor third
4	369.23	major third
5	461.54	fourth
6	553.85	small tritone
7	646.15	large tritone
8	738.46	fifth
9	830.77	minor sixth
10	923.08	major sixth
11	1015.38	minor seventh
12	1107.69	major seventh
13	1200.00	octave

This major third is extremely flat, however it still falls into the submajor range, so it is still reasonable to call it major.

Here is a table of interval names for 72edo up to the tritone:

Degree	Cents	Name
0	0.000	unison
1	16.667	comma
2	33.333	small diesis
3	50.000	large diesis
4	66.667	subminor second
5	83.333	small semitone
6	100.000	medium semitone
7	116.667	large semitone
8	133.333	sup[er|ra]minor second
9	150.000	neutral second
10	166.667	submajor second
11	183.333	ptolemaic tone
12	200.000	pythagorean tone
13	216.667	large tone
14	233.333	supermajor second
15	250.000	inframinor third
16	266.667	small subminor third
17	283.333	large subminor third
18	300.000	common minor third
19	316.667	just minor third
20	333.333	sup[er|ra]minor third
21	350.000	neutral third
22	366.667	submajor third
23	383.333	just major third
24	400.000	common major third
25	416.667	small supermajor third
26	433.333	large supermajor third
27	450.000	ultramajor third
28	466.667	subfourth
29	483.333	small fourth
30	500.000	perfect fourth
31	516.667	small superfourth
32	533.333	large superfourth
33	550.000	ultrafourth
34	566.667	subtritone
35	583.333	small tritone
36	600.000	medium tritone

Note that "ultrafourth" has been used to align the use of "superfourth" with other "super-" intervals. Alternatively, one could use "acute" in this case and reserve "superfourth" for the intervals around 550c. The system fits rather nicely into 53edo:

Degree	Cents	Name
0	0.00	unison
1	22.64	comma
2	45.28	diesis
3	67.92	subminor second
4	90.57	small minor second
5	113.21	large minor second
6	135.85	sup[er|ra]minor second
7	158.49	submajor second
8	181.13	ptolemaic tone
9	203.77	pythagorean tone
10	226.42	supermajor second
11	249.06	inframinor third
12	271.70	subminor third
13	294.34	pythagorean minor third
14	316.98	just minor third
15	339.62	sup[er|ra]minor third
16	362.26	submajor third
17	384.91	just major third
18	407.55	pythagorean major third
19	430.19	supermajor third
20	452.83	ultramajor third
21	475.47	subfourth
22	498.11	fourth
23	520.75	superfourth
24	543.40	ultrafourth
25	566.04	subtritone
26	588.68	small tritone