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). (Note that these are not true Latin ordinals, unlike the corresponding Italian notation of ottava (see staff notation).)

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), and allow for the convenient and analogous notation of a scale with any number of notes.

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.

An example of VGQDMN that hopefully uses the right scale this time

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. 9na for oneirotonic, or 10ma for gramitonic. It is read as the Italian ordinal for the given number, and the last two letters also come from that (with the ending changed to -a if necessary). (This follows from the use of 15ma in Western music.) It can be called an equava in general.

Key signatures are notated as you would expect given the principle of generalizing from diatonic.

Tables and other resources:

Equave names

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. Note that unlike the equava markings which use Italian ordinals like ottava, these do not use true Latin ordinals, but instead just the -ave suffix, for recognizability as an interval name:

Equave names:

Steps (1-indexed)	Name	Equava marking
2	Biave	2da "seconda"
3	Triave	3za "terza"
4	Quadrave	4ta "quarta"
5	Quintave	5ta "quinta"
6	Sextave	6ta "sesta"
7	Septave	7ma "settima"
8	Octave	8va "ottava"
9	Nonave	9na "nona"
10	Decave	10ma "decima"
11	Undecave	11ma "undicesima"
12	Duodecave	12ma "dodicesima"
13	Tredecave	13ma "tredicesima"
14	Quattuordecave	14ma "quattordicesima"
15	Quindecave	15ma "quindicesima"
16	Sexdecave	16ma "sedicesima"
17	Septendecave	17ma "diciassettesima"
18	Octodecave	18ma "diciottesima"
19	Novemdecave	19ma "diciannovesima"
20	Vigintave	20ma "ventesima"
21	Unvigintave	21ma "ventunesima"
22	Duovigintave	22ma "ventiduesima"
23	Tresvigintave	23ma "ventitreesima"
24	Quattuorvigintave	24ma "ventiquattresima"
25	Quinvigintave	25ma "venticinquesima"

Optimal clefs

All clefs used in VGQDMN. They all resemble their corresponding letters, and are all shown on the middle staff line. H and J clefs are from Bohlen-Pierce notation.

This is the table of optimal clef layouts to be analogous to the treble and bass clef for scales with different sizes. This assumes that A3 is the top line of the bass clef. Preferably, the second line from the bottom of the staff is used as the treble clef, and the second line from the top is used as the bass clef, except when that would cause a clef with an equave up/down which could be avoided by using a different line for the clef indicator.

Scale size	Staff lines	Treble clef	Bass clef
3	3	A (quarta up) on 2nd line	B on 2nd line
4	3	A (quinta up) on 1st line	A on 3rd line
5	4	E on 1st line	D on 3rd line
6	4	A (settima up) on 2nd line	E on 3rd line
7	5	G on 2nd line	F on 4th line
8	5	E on 1st line	G on 4th line
9	6	G on 2nd line	H on 5th line
10	6	E on 1st line	J on 5th line
11	7	G on 2nd line	K on 6th line
12	7		L on 6th line
13	8		M on 7th line
14	8		N on 7th line
15	9		O on 8th line
16	9		P on 8th line
17	10		Q on 9th line
18	10		R on 9th line
19	11		S on 10th line
20	11		T on 10th line

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.