Quasi-diatonic MOS notation
Quasi-diatonic MOS notation (Vector's version) is nearly identical to what has been described of CompactStar's take on quasi-diatonic MOS notation. Credit to User:CompactStar for the system for choosing the default mode, and for some other ideas. Namely, the following:
Note names
The root is A (A4), fixed to 440Hz by default. Starting from B, the notes of the darkest mode of the MOS are labelled until A an equave up (thanks User:CompactStar!), where the nominals repeat. So nominals in order are always A, B, C, D, E, F, G, etc. with the darkest mode being on B. For example, in 5L3s, the darkest mode is sLsLLsLL, so the notes ABCDEFGH represent the scale LsLsLLsL on A. This is done to make it backwards-compatible with existing diatonic notation, which starts on B for its darkest mode, Locrian. I is skipped, as in Bohlen-Pierce, to avoid confusion, and V is skipped as well.
Note that this is incompatible with conventional Bohlen-Pierce notation itself, as it refers to BP's note "C" as A.
Accidentals are # and b, which raise and lower by a chroma (the difference between a large and small step, L-s) respectively. Double sharp and double flat work as expected.
So, in 13edo, the notes of 5L3s are:
A, A#/Bb, B, C, C#/Db, D, E, E#/Fb, F, F#/Gb, G, H, H#/Ab, and A an octave higher.
MODMOSes are notated using the MOS's base notation.
Interval names
Intervals are named analogously to diatonic: interval size classes are named with ordinal numbers starting from the scale step as the 2nd (i.e. they are 1-indexed). So a 2-step would be a third, a 3-step would be a fourth, etc. The exceptions are the 0-step (which is called the unison), and the equave (which takes the -ave suffix following a Latin number root indicating the scale step, to indicate that it is the equave - note that in a 2-note MOS, it is called the triave, which is distinct from the tritave (a ratio of 3/1). A table of equave names will be available at the bottom of the page).
Generators are perfect, other intervals are major and minor (where major refers to the larger of the two interval sizes, and minor refers to the smaller of the two). Augmented and diminished, for interval names, function as # and b do for note names respectively. So in 5L3s (and in fact, in any MOS with >3 notes that is not an edo, due to the way the position of A in the scale is defined), A-C is a minor third, A-C# is a major third, and A-Cx is an augmented third. Augmented and diminished are also used to name the 1 imperfect generator interval of each class, depending on its size relative to the perfect generator. As such, in 5L3s, there are 7 perfect sixths and one augmented sixth.
Staves
The number of staff lines is equal to half the number of scale steps plus 1 (rounding up). So a scale with 8 notes would have 5 lines, a scale with 9 notes would have 6 lines, and a scale of 11 notes would have 7 lines. A3 is always on a staff line.
New clefs need to be introduced to refer to arbitrary notes, in order to bridge the gap between the A clef (introduced specifically for this notation) and the C, F, and G clefs (shared with diatonic). Other clefs can just use blackletter/fraktur or cursive versions of the Latin letter until a standard clef is chosen (the Bohlen-Pierce H and J clefs are recommended for H and J).
Note that it is recommended to use conventional clefs where possible, including (primarily) the C, G, and F clefs, and (secondarily) the H and J clefs.
A clef refers to the closest note on a staff line with that name to A3 (an equave below A4). For example, in diatonic, the G clef refers to the G above middle C, because that's the closest G staff line to A3. Similarly, the F clef refers to the F below middle C, because that's the closest F staff line to A3.(So of course, a clef is only valid where such a staff line exists, i.e. in an octatonic scale where all the staff lines are A, C, E, and G, an F clef would not be valid. A J clef would also not be valid, because there is no note named J.)
Additionally, if two of the same note on a staff line are equally close to A3, such as with an E clef in an octatonic scale, it refers to the note above A3.
The MOS is always specified with text above the beginning of the score (for example, "oneirotonic", "5L3s", or "LLsLLsLs").
8va markings work as normal, though the number is changed to match the number of steps in the equave, i.e. 9va for oneirotonic, or 10va for gramitonic.
Key signatures are notated as you would expect given the principle of generalizing from diatonic.
Tables and other resources:
A table of what the equave is called based on how many steps it contains, using number prefixes analogous to the Latin numbers used to name -illions. This is distinct from the Greek numbers used to name harmonics, as the term "octave" comes from Latin:
| Steps (1-indexed) | Name |
|---|---|
| 2 | Biave |
| 3 | Triave |
| 4 | Quadrave |
| 5 | Quintave |
| 6 | Sextave |
| 7 | Septave |
| 8 | Octave |
| 9 | Nonave |
| 10 | Decave |
| 11 | Undecave |
| 12 | Duodecave |
| 13 | Tredecave |
| 14 | Quattuordecave |
| 15 | Quindecave |
| 16 | Sexdecave |
| 17 | Septendecave |
| 18 | Octodecave |
| 19 | Novemdecave |
| 20 | Vigintave |
| 21 | Unvigintave |
| 22 | Duovigintave |
| 23 | Tresvigintave |
| 24 | Quattuorvigintave |
| 25 | Quinvigintave |
Extension to other scales
For ternary systems, sharps and flats can be given subscripts or superscripts indicating what diesis is being sharpened or flattened by.