User:VectorGraphics/Walker brightness notation

e

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.

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.

However, it can also name the intervals in a scale as follows:

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.

1. Give each interval in the scale its base label

• Label the unison and the octave at 0 and 1200 cents.
• Label any intervals between 650 and 750 cents "fifth".
• 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".
• Label any intervals between 250 and 450 cents "third".
• 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".
• Label any intervals between 0 and 50 cents (but not 0 cents exactly) "comma".

2. Resolve ambiguities (stage 1: major and minor)

If there are multiple intervals labeled "third":

• Label any intervals between 250 and 340 cents "minor third".
• Label any intervals between 360 and 450 cents "major third".
• Label any intervals between 340 and 360 cents "neutral third".

If there are multiple intervals labeled "second":

• Label any intervals between 50 and 140 cents "minor second".
• Label any intervals between 160 and 250 cents "major second".
• Label any intervals between 140 and 160 cents "neutral second"

If there are multiple intervals labeled "tritone":

• Label any intervals between 550 and 600 cents "narrow tritone".
• If an interval is 600 cents exactly, label it "mid tritone".

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)

If there are multiple intervals labeled "fourth":

• Label any intervals between 450 and 480 cents "subfourth".
• Label any intervals between 520 and 550 cents "superfourth".
• Continue to call any intervals between 480 and 520 cents "fourth".

If there are multiple intervals labeled "major third":

• Label any intervals between 425 and 450 cents "supermajor third".
• Continue to call any intervals between 360 and 425 cents "major third".

If there are multiple intervals labeled "minor third":

• Label any intervals between 250 and 280 cents "subminor third".
• Continue to call any intervals between 280 and 340 cents "minor third".

If there are multiple intervals labeled "major second":

• Label any intervals between 220 and 250 cents "supermajor second".
• Continue to call any intervals between 160 and 220 cents "major second".

If there are multiple intervals labeled "minor second":

• Label any intervals between 50 and 80 cents "subminor second".
• Continue to call any intervals between 80 and 140 cents "minor second".

If there are multiple intervals labeled "comma":

• Label any intervals between 30 and 50 cents "diesis".
• Continue to call any intervals smaller than 30 cents "comma".

If there are multiple intervals labeled "narrow tritone":

• Label any intervals between 550 and 575 cents "subtritone".
• Continue to call any intervals between 575 and 600 cents "narrow tritone".

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)

If one of these steps resolves ambiguity, perform it:

• Seconds:
  • Label any intervals between 50 and 65 cents "inframinor second".
  • 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".
• Thirds:
  • Label any intervals between 250 and 260 cents "inframinor third".
  • Label any intervals between 325 and 340 cents "superminor third".
  • Label any intervals between 360 and 375 cents "submajor third".
  • Label any intervals between 440 and 450 cents "ultramajor third".
• Fourths:
  • Label any intervals between 450 and 460 cents "infrafourth".
  • Label any intervals between 535 and 550 cents "ultrafourth".
• Tritones:
  • Label any intervals between 550 and 560 cents "infratritone".

Do this for the octave complements of these interval ranges. Remember to do the octave complements for the tritones as well.

5. Resolve ambiguities (stage 4: arto and tendo)

If one of these steps resolves ambiguity, perform it:

• 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".

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:

• 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.

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:

- label the smallest and largest intervals in a region "small" and "large".

- 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.)

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

as an example:

Interval (cents)	Name
176	small artomajor second
178	over-small artomajor second
181	under-medium artomajor second
183	medium artomajor second
185	over-medium artomajor second
187	under-large artomajor second
189	large artomajor second
192	small major second
194	over-small major second
196	under-medium major second
198	over-medium major second
200	under-large major second
203	large major second
207	small tendomajor second
214	large tendomajor second