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Walker Brightness Notation is a way of naming intervals "invented" by Jay Walker / [[User:VectorGraphics|VectorGraphics]]. It names intervals purely based on their sizes, ignoring [[just intonation]] and [[MOS|MOS scales]] almost entirely (though it takes names from them, specifically [[5L 2s|diatonic]], for the sake of recognizability).  
[[File:Imageeqt.png|thumb|e]]
'''Walker brightness notation''' is a way of naming intervals "invented" by Jay Walker / [[User:VectorGraphics|VectorGraphics]]. It names intervals purely based on their sizes, ignoring [[just intonation]] and [[MOS scale]]s almost entirely (though it takes names from them, specifically [[5L 2s|diatonic]], for the sake of recognizability).  


== Example ==
WBN is intended to be used with the assumption of just octaves.
As WBM is not a rigid system, an example scale is probably the best way to explain how it works:
 
{| class="wikitable"
WBN uses increasing levels of detail to specify intervals more or less precisely. For example, 435c is a supermajor third, and "supermajor third", "major third", and "third" are all valid descriptions. WBN can be simply used to refer to the sizes of intervals.
|+WBM Exemplary Scale
 
!Degree
However, it can also name the intervals in a scale as follows:
![[Cents]]
 
!Name
== Steps to name the intervals in a scale: ==
|-
Note: Intervals at the boundary always go in the category closer to the octave or unison, so that all octave complements work.
|0
 
|0
=== 1. Give each interval in the scale its base label ===
|
 
|-
* Label the unison and the octave at 0 and 1200 cents.
|1
* Label any intervals between 650 and 750 cents "fifth".
|53
* Label any intervals between 450 and 550 cents "fourth".
|
* Label any intervals between 550 and 650 cents "tritone".
|-
* Label any intervals between 50 and 250 cents "second".
|2
* Label any intervals between 250 and 450 cents "third".
|134
* Label any intervals between 750 and 950 cents "sixth".
|
* Label any intervals between 950 and 1150 cents "seventh".
|-
* Label any intervals between 1150 and 1200 cents (but not 1200 cents exactly) "suboctave".
|3
* Label any intervals between 0 and 50 cents (but not 0 cents exactly) "comma".
|156
 
|
=== 2. Resolve ambiguities (stage 1: major and minor) ===
|-
 
|4
==== If there are multiple intervals labeled "third": ====
|188
 
|
* Label any intervals between 250 and 340 cents "minor third".
|-
* Label any intervals between 360 and 450 cents "major third".
|5
* Label any intervals between 340 and 360 cents "neutral third".
|206
 
|
==== If there are multiple intervals labeled "second": ====
|-
 
|6
* Label any intervals between 50 and 140 cents "minor second".
|220
* Label any intervals between 160 and 250 cents "major second".
|
* Label any intervals between 140 and 160 cents "neutral second"
|-
 
|7
==== If there are multiple intervals labeled "tritone": ====
|248
 
|
* Label any intervals between 550 and 600 cents "narrow tritone".
|-
* If an interval is 600 cents exactly, label it "mid tritone".
|8
 
|266
Do this for the octave complements of these interval ranges, changing the qualities and interval sizes respectively, for example 860 to 950 is a major sixth.
|
 
|-
=== 3. Resolve ambiguities (stage 2: supermajor and subminor) ===
|9
 
|300
==== If there are multiple intervals labeled "fourth": ====
|
 
|-
* Label any intervals between 450 and 480 cents "subfourth".
|10
* Label any intervals between 520 and 550 cents "superfourth".
|315
* Continue to call any intervals between 480 and 520 cents "fourth".
|
 
|-
==== If there are multiple intervals labeled "major third": ====
|11
 
|366
* Label any intervals between 425 and 450 cents "supermajor third".
|
* Continue to call any intervals between 360 and 425 cents "major third".
|-
 
|12
==== If there are multiple intervals labeled "minor third": ====
|435
 
|
* Label any intervals between 250 and 280 cents "subminor third".
|-
* Continue to call any intervals between 280 and 340 cents "minor third".
|13
 
|542
==== If there are multiple intervals labeled "major second": ====
|
 
|-
* Label any intervals between 220 and 250 cents "supermajor second".
|14
* Continue to call any intervals between 160 and 220 cents "major second".
|588
 
|
==== If there are multiple intervals labeled "minor second": ====
|-
 
|15
* Label any intervals between 50 and 80 cents "subminor second".
|611
* Continue to call any intervals between 80 and 140 cents "minor second".
|
 
|-
==== If there are multiple intervals labeled "comma": ====
|16
 
|684
* Label any intervals between 30 and 50 cents "diesis".
|
* Continue to call any intervals smaller than 30 cents "comma".
|-
 
|17
==== If there are multiple intervals labeled "narrow tritone": ====
|688
 
|
* Label any intervals between 550 and 575 cents "subtritone".
|-
* Continue to call any intervals between 575 and 600 cents "narrow tritone".
|18
 
|969
Do this for the octave complements of these interval ranges. Note that 1150-1170c becomes an infraoctave, due to "diesis" not having a well-defined octave complement, and that the octave complement of a narrow tritone is a wide tritone.
|
 
|-
=== 4. Resolve ambiguities (stage 3: inframinor and ultramajor) ===
|19
 
|992
==== If one of these steps resolves ambiguity, perform it: ====
|
 
|-
* '''Seconds:'''
|20
** Label any intervals between 50 and 65 cents "inframinor second".
|1200
** Label any intervals between 125 and 140 cents "superminor second".
|
** Label any intervals between 160 and 175 cents "submajor second".
|}
** Label any intervals between 235 and 250 cents "ultramajor second".
So first, we name each interval according to its general interval class.
* '''Thirds:'''
{| class="wikitable"
** Label any intervals between 250 and 260 cents "inframinor third".
|+WBM Exemplary Scale
** Label any intervals between 325 and 340 cents "superminor third".
!Degree
** Label any intervals between 360 and 375 cents "submajor third".
!Cents
** Label any intervals between 440 and 450 cents "ultramajor third".
!Name
* '''Fourths:'''
|-
** Label any intervals between 450 and 460 cents "infrafourth".
|0
** Label any intervals between 535 and 550 cents "ultrafourth".
|0
* '''Tritones:'''
|unison
** Label any intervals between 550 and 560 cents "infratritone".
|-
 
|1
Do this for the octave complements of these interval ranges. Remember to do the octave complements for the tritones as well.
|53
 
|second
=== 5. Resolve ambiguities (stage 4: arto and tendo) ===
|-
 
|2
==== If one of these steps resolves ambiguity, perform it: ====
|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 [[1/1|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... [https://wiki.lspace.org/Pune harmonic reasons for calling it a seventh.]
* '''Seconds:'''
** Label any intervals between 80 and 95 cents "artominor second".
** Label any intervals between 110 and 125 cents "tendominor second".
** Label any intervals between 175 and 190 cents "artomajor second".
** Label any intervals between 205 and 220 cents "tendomajor second".
* '''Thirds:'''
** Label any intervals between 280 and 295 cents "artominor third".
** Label any intervals between 310 and 325 cents "tendominor third".
** Label any intervals between 375 and 390 cents "artomajor third".
** Label any intervals between 405 and 425 cents "tendomajor third".
* '''Fourths:'''
** Label any intervals between 480 and 495 cents "artofourth".
** Label any intervals between 510 and 520 cents "tendofourth".
* '''Tritones:'''
** Label any intervals between 575 and 585 cents "artotritone".


First of all, there are some special names to apply: [[7/4|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 [[81/80|comma]].)
Do this for the octave complements of these interval ranges. Remember to do the octave complements for the tritones as well. Though there are some notes to keep in mind:
{| class="wikitable"
!Degree
!Cents
!Name
|-
|0
|0
|unison
|-
|1
|53
|diesis
|-
|2
|134
|second
|}
{| class="wikitable"
!Degree
!Cents
!Name
|-
|17
|688
|fifth
|-
|18
|969
|[[7/4|harmonic seventh]]
|-
|19
|992
|seventh
|}
Note that "harmonic seventh" still requires other sevenths to be distinguished from it, unlike diesis and comma.


* If a pair of intervals ends up distinguished by ''arto'' vs. no stage 4 prefix, i.e. artomajor third and major third, the other interval can be labeled tendo, regardless of its actual size. The same applies in reverse, for if a pair of intervals is distinguished by ''tendo'' vs. no stage 4 prefix.
* If there is only one interval simply labelled ''fourth'', call it a "perfect fourth".
** Same with fifths.


So, we add qualifiers to distinguish intervals of the same general interval class.
=== 6. Resolve ambiguities (stage 5) ===
By this point, except for commas, the octave has been subdivided into 10-20c interval regions, suitable for notating edos as large as 71edo without any problems. Where intervals need to be named more precisely than this, however, intervals within a range can be described as follows:


{| class="wikitable"
- label the smallest and largest intervals in a region "small" and "large".
!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 [[9/7|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 [[Nominal-accidental chain|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.
- if there is an odd number of intervals in a region, label the middle one "medium". if there is an even number, label the middle two "under-medium" (for the lower note) and "over-medium" (for the higher one). (if there are only two intervals in a region, they keep the names small and large.)


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.
- "under" and "over" refer to the next smallest and largest intervals from a certain point, and can be stacked with exponents as a shorthand.


Also, there is a minor seventh but no major seventh.
as an example:
{| class="wikitable"
{| class="wikitable"
!Degree
|+
!Cents
!Interval (cents)
!Name
!Name
|-
|-
|0
|176
|0
|small artomajor second
|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
|178
|248
|over-small artomajor second
|semifourth
|-
|-
|8
|181
|266
|under-medium artomajor second
|subminor third
|-
|-
|9
|183
|300
|medium artomajor second
|common minor third
|-
|-
|10
|185
|315
|over-medium artomajor second
|just minor third
|-
|-
|11
|187
|366
|under-large artomajor second
|neutral third
|-
|-
|12
|189
|435
|large artomajor second
|major third
|-
|-
|13
|192
|542
|small major second
|fourth
|-
|-
|14
|194
|588
|over-small major second
|small tritone
|-
|-
|15
|196
|611
|under-medium major second
|large tritone
|-
|-
|16
|198
|684
|over-medium major second
|small fifth
|-
|-
|17
|200
|688
|under-large major second
|large fifth
|-
|-
|18
|203
|969
|large major second
|harmonic seventh
|-
|-
|19
|207
|992
|small tendomajor second
|minor seventh
|-
|-
|20
|214
|1200
|large tendomajor second
|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.
[[Category:Interval naming]]
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