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:
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.
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 |