Lambda ups and downs notation

Lambda ups and downs notation is a nonoctave extension of ups and downs notation developed by CompactStar, for use in EDTs and no-twos rank-2 temperaments. It combines ups and downs notation with the preexisting notation for the Lambda scale in 13edt.

Explanation

The 5|3 mode of the Lambda MOS scale is written with 9 naturals CDEFGHJAB. Two modules of accidentals are used, #/b to raise and lower by one chroma (L − s), and ^/v to raise and lower by one EDTstep. Following the TAMNAMS convention for non-diatonic mosses, an interval that is k steps of lambda wide is referred to as a "k-mosstep" (e.g. a unison is a 0-mosstep and a tritave is a 9-mosstep). With the exception of the interval classes of ~7/3 and ~9/7 (the generators of the Lambda scale), large intervals use the "major" quality and small intervals use the "minor" quality. Additionally, "mid" is used for intervals halfway between major and minor, perfect and diminished, or perfect and augmented. "Up"/"down" can be prefixed to a quality to denote raising or lowering by 1 EDT-step.

Examples

9edt (L:s = 1:1)

0	1	2	3	4	5	6	7	8	9
C	D	E	F	G	H	J	A	B	C
P0ms	P1ms	P2ms	P3ms	P4ms	P5ms	P6ms	P7ms	P8ms	P9ms

13edt (L:s = 2:1)

0	1	2	3	4	5	6	7	8	9	10	11	12	13
C	C#, Db	D	E	F	F#, Gb	G	H	H#, Jb	J	A	A#, Bb	B	C
P0ms	A0ms, m1ms	M1ms	P2ms	m3ms	M3ms, m4ms	M4ms	m5ms	M5ms, m6ms	M6ms	P7ms	A7ms, m8ms	M8ms	P9ms

18edt (L:s = 2:2)

0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18
C	^C, vD	D	^D, vE	E	^E, vF	F	^F, vG	G	^G, vH	H	^H, vJ	J	^J, vA	A	^A, vB	B	^B, vC	C
P0ms	^0ms, v1ms	P1ms	^1ms, v2ms	P2ms	^2ms, v3ms	P3ms	^3ms, v4ms	P4ms	^4ms, v5ms	P5ms	^5ms, v6ms	P6	^6ms, v7ms	P7	^7ms, v8ms	P8	^8ms, v9ms	P9ms