User:Ganaram inukshuk/Sandbox

This is a sandbox page for me (Ganaram) to test out a few things before deploying things. (Expect some mess.)

Sandbox for proposed templates

MOS characteristics

Scale degrees of the modes of 5L 2s

UDP	Cyclic order	Step pattern	Scale degree (diadegree)
			0	1	2	3	4	5	6	7
6|0	1	LLLsLLs	Perf.	Maj.	Maj.	Aug.	Perf.	Maj.	Maj.	Perf.
5|1	5	LLsLLLs	Perf.	Maj.	Maj.	Perf.	Perf.	Maj.	Maj.	Perf.
4|2	2	LLsLLsL	Perf.	Maj.	Maj.	Perf.	Perf.	Maj.	Min.	Perf.
3|3	6	LsLLLsL	Perf.	Maj.	Min.	Perf.	Perf.	Maj.	Min.	Perf.
2|4	3	LsLLsLL	Perf.	Maj.	Min.	Perf.	Perf.	Min.	Min.	Perf.
1|5	7	sLLLsLL	Perf.	Min.	Min.	Perf.	Perf.	Min.	Min.	Perf.
0|6	4	sLLsLLL	Perf.	Min.	Min.	Perf.	Dim.	Min.	Min.	Perf.

Intervals of 5L 2s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-diastep	Perfect 0-diastep	P0dias	0	0.0 ¢
1-diastep	Minor 1-diastep	m1dias	s	0.0 ¢ to 171.4 ¢
	Major 1-diastep	M1dias	L	171.4 ¢ to 240.0 ¢
2-diastep	Minor 2-diastep	m2dias	L + s	240.0 ¢ to 342.9 ¢
	Major 2-diastep	M2dias	2L	342.9 ¢ to 480.0 ¢
3-diastep	Perfect 3-diastep	P3dias	2L + s	480.0 ¢ to 514.3 ¢
	Augmented 3-diastep	A3dias	3L	514.3 ¢ to 720.0 ¢
4-diastep	Diminished 4-diastep	d4dias	2L + 2s	480.0 ¢ to 685.7 ¢
	Perfect 4-diastep	P4dias	3L + s	685.7 ¢ to 720.0 ¢
5-diastep	Minor 5-diastep	m5dias	3L + 2s	720.0 ¢ to 857.1 ¢
	Major 5-diastep	M5dias	4L + s	857.1 ¢ to 960.0 ¢
6-diastep	Minor 6-diastep	m6dias	4L + 2s	960.0 ¢ to 1028.6 ¢
	Major 6-diastep	M6dias	5L + s	1028.6 ¢ to 1200.0 ¢
7-diastep	Perfect 7-diastep	P7dias	5L + 2s	1200.0 ¢

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MOS intervals (using large/small instead of MmAPd)

Intervals of 5L 2s

Interval	Size(s)	Steps	Range in cents	Abbrev.
0-diastep (root)	Perfect 0-diastep	0	0.0¢	P0ms
1-diastep	Small 1-diastep	s	0.0¢ to 171.4¢	s1ms
	Large 1-diastep	L	171.4¢ to 240.0¢	L1ms
2-diastep	Small 2-diastep	L + s	240.0¢ to 342.9¢	s2ms
	Large 2-diastep	2L	342.9¢ to 480.0¢	L2ms
3-diastep	Small 3-diastep	2L + s	480.0¢ to 514.3¢	s3ms
	Large 3-diastep	3L	514.3¢ to 720.0¢	L3ms
4-diastep	Small 4-diastep	2L + 2s	480.0¢ to 685.7¢	s4ms
	Large 4-diastep	3L + s	685.7¢ to 720.0¢	L4ms
5-diastep	Small 5-diastep	3L + 2s	720.0¢ to 857.1¢	s5ms
	Large 5-diastep	4L + s	857.1¢ to 960.0¢	L5ms
6-diastep	Small 6-diastep	4L + 2s	960.0¢ to 1028.6¢	s6ms
	Large 6-diastep	5L + s	1028.6¢ to 1200.0¢	L6ms
7-diastep (octave)	Perfect 7-diastep	5L + 2s	1200.0¢	P7ms

MOS mode degrees (using large/small instead of MmAPd)

Scale degree qualities of 5L 2s modes

Mode names		Ordering		Step pattern	Scale degree
Default	Names	Bri.	Rot.		0	1	2	3	4	5	6	7
5L 2s 6|0	Lydian	1	1	LLLsLLs	Perf.	Lg.	Lg.	Lg.	Lg.	Lg.	Lg.	Perf.
5L 2s 5|1	Ionian (major)	2	5	LLsLLLs	Perf.	Lg.	Lg.	Sm.	Lg.	Lg.	Lg.	Perf.
5L 2s 4|2	Mixolydian	3	2	LLsLLsL	Perf.	Lg.	Lg.	Sm.	Lg.	Lg.	Sm.	Perf.
5L 2s 3|3	Dorian	4	6	LsLLLsL	Perf.	Lg.	Sm.	Sm.	Lg.	Lg.	Sm.	Perf.
5L 2s 2|4	Aeolian (minor)	5	3	LsLLsLL	Perf.	Lg.	Sm.	Sm.	Lg.	Sm.	Sm.	Perf.
5L 2s 1|5	Phrygian	6	7	sLLLsLL	Perf.	Sm.	Sm.	Sm.	Lg.	Sm.	Sm.	Perf.
5L 2s 0|6	Locrian	7	4	sLLsLLL	Perf.	Sm.	Sm.	Sm.	Sm.	Sm.	Sm.	Perf.

MOS mode degrees (proposed encoding scheme)

Encoding scheme

Value	Encoded		Decoded
	Intervals with 2 sizes	Intervals with 1 size	Nonperfectable intervals	Bright gen	Dark gen	Period intervals
2	Large plus 2 chromas	Perfect plus 2 chromas	2× Augmented	2× Augmented	3× Augmented	2× Augmented
1	Large plus 1 chroma	Perfect plus 1 chroma	Augmented	Augmented	2× Augmented	Augmented
0	Large	Perfect	Major	Perfect	Augmented	Perfect
-1	Small	Perfect minus 1 chroma	Minor	Diminished	Perfect	Diminished
-2	Small minus 1 chroma	Perfect minus 2 chromas	Diminished	2× Diminished	Diminished	2× Diminished
-3	Small minus 2 chromas	Perfect minus 3 chromas	2× Diminished	3× Diminished	2× Diminished	3× Diminished

Rationale:

• Easy to translate values to number of chromas for mos notation. Best done with notation assigned to the brightest mode, but can be adapted for arbitrary notations by adjusting the approprite chroma offsets.

Examples of encodings for 5L 2s

Interval encodings for 5L 2s

Interval in mossteps	Encoding		Decoding	Standard notation in the key of F
	Mossteps	Chroma
0	0	0	Perfect 0-diastep	F
s	1	-1	Minor 1-diastep	Fb
L	1	0	Major 1-diastep	G
L + s	2	-1	Minor 2-diastep	Gb
2L	2	0	Major 2-diastep	A
2L + s	3	-1	Perfect 3-diastep	Ab
3L	3	0	Augmented 3-diastep	B
2L + 2s	4	-1	Diminished 4-diastep	Bb
3L + s	4	0	Perfect 4-diastep	C
3L + 2s	5	-1	Minor 5-diastep	Cb
4L + s	5	0	Major 5-diastep	D
4L + 2s	6	-1	Minor 6-diastep	Db
5L + s	6	0	Major 6-diastep	E
5L + 2s	7	0	Perfect 7-diastep	F

Mode names		Ordering		Step pattern	Scale degree (encoded)
Default	Names	Bri.	Rot.		0	1	2	3	4	5	6	7
5L 2s 6|0	Lydian	1	1	LLLsLLs	0	1	1	1	1	1	1	0
5L 2s 5|1	Ionian (major)	2	5	LLsLLLs	0	1	1	0	1	1	1	0
5L 2s 4|2	Mixolydian	3	2	LLsLLsL	0	1	1	0	1	1	0	0
5L 2s 3|3	Dorian	4	6	LsLLLsL	0	1	0	0	1	1	0	0
5L 2s 2|4	Aeolian (minor)	5	3	LsLLsLL	0	1	0	0	1	0	0	0
5L 2s 1|5	Phrygian	6	7	sLLLsLL	0	0	0	0	1	0	0	0
5L 2s 0|6	Locrian	7	4	sLLsLLL	0	0	0	0	0	0	0	0

KB vis

Type	Visualization	Individual steps				Notes
		Start	Large step	Small step	End
Small vis	┌╥╥╥┬╥╥┬┐ │║║║│║║││ │││││││││ └┴┴┴┴┴┴┴┘	┌ │ │ └	╥ ║ │ ┴	┬ │ │ ┴	┐ │ │ ┘	Not enough room for note names.
Large vis	┌──┬─┬─┬─┬─┬─┬──┬──┬─┬─┬─┬──┬───┐ │░░│▒│░│▒│░│▒│░░│░░│▒│░│▒│░░│░░░│ │░░│▒│░│▒│░│▒│░░│░░│▒│░│▒│░░│░░░│ │░░└┬┘░└┬┘░└┬┘░░│░░└┬┘░└┬┘░░│░░░│ │░░░│░░░│░░░│░░░│░░░│░░░│░░░│░░░│ │░█░│░░░│░░░│░░░│░░░│░░░│░░░│░█░│ └───┴───┴───┴───┴───┴───┴───┴───┘	┌── │ │ │ │ │ X └──	┬─┬─ │ │ │ │ └┬┘ │ │ X ─┴──	─┬── │ │ │ │ │ X ─┴──	─┐ │ │ │ │ │ ─┘	Black squares indicate notes one equave apart. Contains shading characters, meant for spacing.

Type	Visualization	Individual steps							Notes
		Start	Size 1	Size 2	Size 3	Size 4	Size 5	End
Multisize vis (large)	┌────┬───┬──┬───┬──┬─┬─┬────┬────┬─┬─┬──┬─┬─┬────┬──────┐ │░░░░│▒▒▒│░░│▒▒▒│░░│▒│▒│░░░░│░░░░│▒│▒│░░│▒│▒│░░░░│░░░░░░│ │░░░░│▒▒▒│░░│▒▒▒│░░│▒│▒│░░░░│░░░░│▒│▒│░░│▒│▒│░░░░│░░░░░░│ │░░░░│▒▒▒│░░│▒▒▒│░░│▒│▒│░░░░│░░░░│▒│▒│░░├─┼─┤░░░░│░░░░░░│ │░░░░│▒▒▒│░░│▒▒▒│░░│▒│▒│░░░░│░░░░│▒│▒│░░│▒│▒│░░░░│░░░░░░│ │░░░░│▒▒▒│░░├───┤░░├─┴─┤░░░░│░░░░├─┼─┤░░│▒│▒│░░░░│░░░░░░│ │░░░░│▒▒▒│░░│▒▒▒│░░│▒▒▒│░░░░│░░░░│▒│▒│░░├─┴─┤░░░░│░░░░░░│ │░░░░│▒▒▒│░░│▒▒▒│░░│▒▒▒│░░░░│░░░░│▒│▒│░░│▒▒▒│░░░░│░░░░░░│ │░░░░└─┬─┘░░└─┬─┘░░└─┬─┘░░░░│░░░░└─┼─┘░░└─┬─┘░░░░│░░░░░░│ │░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│ │░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│ │░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│ │░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│ └──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┘	┌──── │░░░░ │░░░░ │░░░░ │░░░░ │░░░░ │░░░░ │░░░░ │░░░░ │░░░░ │░░░░ │░░░░ │░░░░ │░░░░ └────	────┬── ░░░░│░░ ░░░░│░░ ░░░░│░░ ░░░░│░░ ░░░░│░░ ░░░░│░░ ░░░░│░░ ░░░░│░░ ░░░░│░░ ░░░░│░░ ░░░░│░░ ░░░░│░░ ░░░░│░░ ────┴──	┬───┬── │▓▓▓│░░ │▓▓▓│░░ │▓▓▓│░░ │▓▓▓│░░ │▓▓▓│░░ │▓▓▓│░░ │▓▓▓│░░ │▓▓▓│░░ └─┬─┘░░ ░░│░░░░ ░░│░░░░ ░░│░░░░ ░░│░░░░ ──┴────	┬───┬── │▓▓▓│░░ │▓▓▓│░░ │▓▓▓│░░ │▓▓▓│░░ ├───┤░░ │▓▓▓│░░ │▓▓▓│░░ │▓▓▓│░░ └─┬─┘░░ ░░│░░░░ ░░│░░░░ ░░│░░░░ ░░│░░░░ ──┴────	┬─┬─┬── │▓│▓│░░ │▓│▓│░░ │▓│▓│░░ │▓│▓│░░ ├─┴─┤░░ │▓▓▓│░░ │▓▓▓│░░ │▓▓▓│░░ └─┬─┘░░ ░░│░░░░ ░░│░░░░ ░░│░░░░ ░░│░░░░ ──┴────	┬─┬─┬── │▓│▓│░░ │▓│▓│░░ │▓│▓│░░ │▓│▓│░░ ├─┼─┤░░ │▓│▓│░░ │▓│▓│░░ │▓│▓│░░ └─┼─┘░░ ░░│░░░░ ░░│░░░░ ░░│░░░░ ░░│░░░░ ──┴────	──┐ ░░│ ░░│ ░░│ ░░│ ░░│ ░░│ ░░│ ░░│ ░░│ ░░│ ░░│ ░░│ ░░│ ──┘	X's are placeholders for note names. Naturals only, as there is not enough room for accidentals. May not display correctly on some devices. Testing with unintrusive filler characters

TAMNAMS use

This article assumes TAMNAMS conventions for naming scale degrees, intervals, and step ratios.

Names for the scale degrees of xL ys, the position of the scales tones, are called mosdegrees, or prefixdegrees. Its intervals, the pitch difference between any two tones, are based on the number of large and small steps between them and are called mossteps, or prefixsteps. Both mosdegrees and mossteps use 0-indexed numbering, as opposed to using 1-indexed ordinals, such as mos-1st instead of 0-mosstep. The use of 1-indexed ordinal names is discouraged for nondiatonic MOS scales.

JI ratio intro

For general ratios: m/n, also called interval-name, is a p-limit just intonation ratio of exactly/about r¢.

For harmonics: m/1, also called interval-name, is a just intonation ration that represents the mth harmonic of exactly/about r¢.

MOS step sizes

3L 4s step sizes

Interval	Basic 3L 4s (10edo, L:s = 2:1)		Hard 3L 4s (13edo, L:s = 3:1)		Soft 3L 4s (17edo, L:s = 3:2)		Approx. JI ratios
	Steps	Cents	Steps	Cents	Steps	Cents
Large step	2	240¢	3	276.9¢	3	211.8¢	Hide column if no ratios given
Small step	1	120¢	1	92.3¢	2	141.2¢
Bright generator	3	360¢	4	369.2¢	5	355.6¢

Notes:

• Allow option to show the bright generator, dark generator, or no generator.
• JI ratios column only shows if there are any ratios to show

Mos ancestors and descendants

2nd ancestor	1st ancestor	Mos	1st descendants	2nd descendants
uL vs	zL ws	xL ys	xL (x+y)s	xL (2x+y)s
				(2x+y)L xs
			(x+y)L xs	(2x+y)L (x+y)s
				(x+y)L (2x+y)s

Navbox MOS

Moment-of-symmetry scales

6- to 10-note mosses	1L 5s (selenite) | 2L 4s ( | 3L 3s | 4L 2 | 5L 1s
Monolarge family	1L 5s (selenite) | 1L 6s (onyx) | 1L 7s (spinel) | 1L 8s (agate) | 1L 9s (olivine)
Diatonic mos family	Parent mos 5L 2s (diatonic) Chromatic scales 7L 5s (soft diatonic chromatic) | 5L 7s (hard diatonic chromatic) Enharmonic scales 7L 12s (soft diatonic enharmonic) | 12L 7s (hyposoft diatonic enharmonic) | 12L 5s (hypohard diatonic enharmonic) | 5L 12s (hard diatonic enharmonic) Subchromatic scales 7L 19s and 19L 7s | 19L 12s and 12L 19s | 12L 17s and 17L 12s | 17L 5s and 5L 17s