Quasi-diatonic MOS notation

Quasi-diatonic MOS notation is a JI-agnostic notation system for MOS scales developed by User:CompactStar and User:VectorGraphics, which is designed as a natural extension of diatonic notation, instead of special-casing it as diamond-mos notation does. In diatonic, QDMN is identical to standard notation.

There were originally two versions, the original version by CompactStar and Vector's version, but they were nearly identical so they were simply merged into one. Credit to User:CompactStar for the system for choosing the default mode, and for the specification of the MOS name at the top of the sheet music.

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 is named after an Anglicized version of the Latin ordinal for the interval). 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 and no consecutive small steps 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.

Interval classes may be distinguished using TAMNAMS MOS prefixes. For example, the generator of armotonic might be called an armsixth to reduce ambiguity.

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.)

You may choose clefs based on the system provided in the next section, or, by CompactStar's preference, using only the C, G, and F clefs, and the nonstandard A clef if necessary (i.e. in 1L 1s).

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. This is distinct from the Greek numbers used to name harmonics, as the term "octave" comes from Latin. The -us ending is dropped from Latin numerals (as in second and quart) except where a final silent -e is kept to indicate a long vowel (as in octave), except where said -e would lead to confusion (as with non, where it would be confused with "none", also, the English pronunciation of the Latin non- root does not include a long vowel)

Equave names:

Steps (1-indexed)	Name	Equava marking
2	Second	2da "seconda"
3	Terce	3za "terza"
4	Quart	4ta "quarta"
5	Quint	5ta "quinta"
6	Sext	6ta "sesta"
7	Septim	7ma "settima"
8	Octave	8va "ottava"
9	Non	9na "nona"
10	Decim	10ma "decima"
11	Undecim	11ma "undicesima"
12	Duodecim	12ma "dodicesima"
13	Tertiodecim	13ma "tredicesima"
14	Quartodecim	14ma "quattordicesima"
15	Quintodecim	15ma "quindicesima"
16	Sextodecim	16ma "sedicesima"
17	Septimodecim	17ma "diciassettesima"
18	Duodevicesim	18ma "diciottesima"
19	Undevicesim	19ma "diciannovesima"
20	Vicesim	20ma "ventesima"
21	Vicesimoprime	21ma "ventunesima"
22	Vicesimosecond	22ma "ventiduesima"
23	Vicesimoterce	23ma "ventitreesima"
24	Vicesimoquart	24ma "ventiquattresima"
25	Vicesimoquint	25ma "venticinquesima"

Optimal clefs

All clefs used in VGQDMN. They all resemble their corresponding letters closely enough for their meanings to be intuitive (except for the standard C and G clefs and the semi-standard BP J clef), 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 (ᴸᵐ, ᵐˢ). In notation,, these are written in small text above or below the accidental.

Examples

Pentic

Interval	Steps subtended	Note name (from A = unison)	Soft tuning
perfect unison	-	A	0c
minor second	s	Bb	200c
major second	L	B	300c
diminished third	2s	Cb	400c
perfect third	L+s	C	500c
perfect fourth	L+2s	D	700c
augmented fourth	2L+s	D#	800c
minor fifth	1L+3s	Eb	900c
major fifth	2L+2s	E	1000c
perfect sext	2L+3s	A	1200c

Oneirotonic

Interval	Steps subtended	Note name (from A = unison)	Soft tuning
perfect unison	-	A	0c
minor second	s	Bb	114.29c
major second	L	B	171.43c
minor third	L+s	C	285.71c
major third	2L	C#	342.86c
diminished fourth	L+2s	Db	400.00c
perfect fourth	2L+s	D	457.14c
minor fifth	2L+2s	E	571.43c
major fifth	3L+s	E#	628.57c
perfect sixth	3L+2s	F	742.86c
augmented sixth	4L+s	F#	800.00c
minor seventh	3L+3s	Gb	857.14c
major seventh	4L+2s	G	914.29c
minor eighth	4L+3s	H	1028.57c
major eighth	5L+2s	H#	1085.71c
perfect non	5L+3s	A	1200c

Compatibility with German and fixed-do systems

German H system

As each interval in a MOS has one of two values, the note in the expected place of B is labelled H; the note that is the other size of second above A is labelled B. This note should usually be English B flat, as the last interval of the darkest mode of any MOS is always an L step. For notating edos as degenerate MOSes, the note name B is preferred over H, but H is still skipped after G. For scales with more than two sizes of second, the note a second above A that is furthest from H is labelled B. This means the German H system is only compatible with 23 notes, as opposed to the English system's 24.

Fixed do

Solfege follows a simple pattern, starts from the note two steps above A (this is "C" in scales with more than 2 pitch classes) and stops at the note before the next A, which is labeled "sol", then "la" and "si". The consonants chosen have been selected to be compatible with the phonology of many languages, and follow a cycle of 9 while the vowels follow a cycle of 5.

The vowels are the five-vowel system, the pronunciation of each consonant is as follows:

Consonant	IPA value	English example
d	/d/	door
r	/r/	water
m	/m/	man
f	/f/	fine
k	/k/	car
b	/b/	best
n	/n/	north
g	/g/	gate
t	/t/	tell
s	/s/	see
l	/l/	law

Alphabetic	German H	Solfege consonant	Solfege vowel	Full solfege
C	C	d	o	do
D	D	r	e	re
E	E	m	i	mi
F	F	f	a	fa
G	G	k	u	ku
H	J	b	o	bo
J	K	n	e	ne
K	L	g	i	gi
L	M	t	a	ta
M	N	d	u	du
N	O	r	o	ro
O	P	m	e	me
P	Q	f	i	fi
Q	R	k	a	ka
R	S	b	u	bu
S	T	n	o	no
T	U	g	e	ge
U	W	t	i	te
W	X	d	a	da
X	Y	r	u	ru
Y	Z	m	o	mo
(Last note)	(Last note)	-	-	sol
A	A	-	-	la
B flat	B	-	-	si bemol
B	H	-	-	si