User:Ganaram inukshuk/Sandbox

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

Mos intervals

The intervals of SCALESIG are named after the number of steps subtended and, apart from the unison (0-step) and octave (STEPCOUNT-step), appear in two varieties or sizes each. Interval varieties are named major and minor, or augmented, perfect, and diminished for the generators of SCALESIG.

Intervals of 5L 3s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-oneirostep	Perfect 0-oneirostep	P0oneis	0	0.0 ¢
1-oneirostep	Minor 1-oneirostep	m1oneis	s	0.0 ¢ to 150.0 ¢
	Major 1-oneirostep	M1oneis	L	150.0 ¢ to 240.0 ¢
2-oneirostep	Minor 2-oneirostep	m2oneis	L + s	240.0 ¢ to 300.0 ¢
	Major 2-oneirostep	M2oneis	2L	300.0 ¢ to 480.0 ¢
3-oneirostep	Diminished 3-oneirostep	d3oneis	L + 2s	240.0 ¢ to 450.0 ¢
	Perfect 3-oneirostep	P3oneis	2L + s	450.0 ¢ to 480.0 ¢
4-oneirostep	Minor 4-oneirostep	m4oneis	2L + 2s	480.0 ¢ to 600.0 ¢
	Major 4-oneirostep	M4oneis	3L + s	600.0 ¢ to 720.0 ¢
5-oneirostep	Perfect 5-oneirostep	P5oneis	3L + 2s	720.0 ¢ to 750.0 ¢
	Augmented 5-oneirostep	A5oneis	4L + s	750.0 ¢ to 960.0 ¢
6-oneirostep	Minor 6-oneirostep	m6oneis	3L + 3s	720.0 ¢ to 900.0 ¢
	Major 6-oneirostep	M6oneis	4L + 2s	900.0 ¢ to 960.0 ¢
7-oneirostep	Minor 7-oneirostep	m7oneis	4L + 3s	960.0 ¢ to 1050.0 ¢
	Major 7-oneirostep	M7oneis	5L + 2s	1050.0 ¢ to 1200.0 ¢
8-oneirostep	Perfect 8-oneirostep	P8oneis	5L + 3s	1200.0 ¢

Mos genchain

Generator chain of 10L 5s

Bright gens	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.
4	Augmented 1-mosdegree	A1md	Augmented 4-mosdegree	A4md	Augmented 7-mosdegree	A7md	Augmented 10-mosdegree	A10md	Augmented 13-mosdegree	A13md
3	Augmented 0-mosdegree	A0md	Augmented 3-mosdegree	A3md	Augmented 6-mosdegree	A6md	Augmented 9-mosdegree	A9md	Augmented 12-mosdegree	A12md
2	Augmented 2-mosdegree	A2md	Augmented 5-mosdegree	A5md	Augmented 8-mosdegree	A8md	Augmented 11-mosdegree	A11md	Augmented 14-mosdegree	A14md
1	Perfect 1-mosdegree	P1md	Perfect 4-mosdegree	P4md	Perfect 7-mosdegree	P7md	Perfect 10-mosdegree	P10md	Perfect 13-mosdegree	P13md
0	Perfect 0-mosdegree Perfect 3-mosdegree	P0md P3md	Perfect 3-mosdegree Perfect 6-mosdegree	P3md P6md	Perfect 6-mosdegree Perfect 9-mosdegree	P6md P9md	Perfect 9-mosdegree Perfect 12-mosdegree	P9md P12md	Perfect 12-mosdegree Perfect 15-mosdegree	P12md P15md
−1	Perfect 2-mosdegree	P2md	Perfect 5-mosdegree	P5md	Perfect 8-mosdegree	P8md	Perfect 11-mosdegree	P11md	Perfect 14-mosdegree	P14md
−2	Diminished 1-mosdegree	d1md	Diminished 4-mosdegree	d4md	Diminished 7-mosdegree	d7md	Diminished 10-mosdegree	d10md	Diminished 13-mosdegree	d13md
−3	Diminished 3-mosdegree	d3md	Diminished 6-mosdegree	d6md	Diminished 9-mosdegree	d9md	Diminished 12-mosdegree	d12md	Diminished 15-mosdegree	d15md
−4	Diminished 2-mosdegree	d2md	Diminished 5-mosdegree	d5md	Diminished 8-mosdegree	d8md	Diminished 11-mosdegree	d11md	Diminished 14-mosdegree	d14md

Generator chain of 2L 5s

Bright gens	Scale degree	Abbrev.
8	Augmented 3-peldegree	A3peld
7	Augmented 0-peldegree	A0peld
6	Augmented 4-peldegree	A4peld
5	Major 1-peldegree	M1peld
4	Major 5-peldegree	M5peld
3	Major 2-peldegree	M2peld
2	Major 6-peldegree	M6peld
1	Perfect 3-peldegree	P3peld
0	Perfect 0-peldegree Perfect 7-peldegree	P0peld P7peld
−1	Perfect 4-peldegree	P4peld
−2	Minor 1-peldegree	m1peld
−3	Minor 5-peldegree	m5peld
−4	Minor 2-peldegree	m2peld
−5	Minor 6-peldegree	m6peld
−6	Diminished 3-peldegree	d3peld
−7	Diminished 7-peldegree	d7peld
−8	Diminished 4-peldegree	d4peld

Generator chain of 5L 2s

Bright gens	Scale degree	Abbrev.
11	Augmented 2-diadegree	A2diad
10	Augmented 5-diadegree	A5diad
9	Augmented 1-diadegree	A1diad
8	Augmented 4-diadegree	A4diad
7	Augmented 0-diadegree	A0diad
6	Augmented 3-diadegree	A3diad
5	Major 6-diadegree	M6diad
4	Major 2-diadegree	M2diad
3	Major 5-diadegree	M5diad
2	Major 1-diadegree	M1diad
1	Perfect 4-diadegree	P4diad
0	Perfect 0-diadegree Perfect 7-diadegree	P0diad P7diad
−1	Perfect 3-diadegree	P3diad
−2	Minor 6-diadegree	m6diad
−3	Minor 2-diadegree	m2diad
−4	Minor 5-diadegree	m5diad
−5	Minor 1-diadegree	m1diad
−6	Diminished 4-diadegree	d4diad
−7	Diminished 7-diadegree	d7diad
−8	Diminished 3-diadegree	d3diad
−9	Diminished 6-diadegree	d6diad
−10	Diminished 2-diadegree	d2diad
−11	Diminished 5-diadegree	d5diad

5L 2s modes and modmos modes

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.

Scale degrees of the modes of 5L 2s (LsLLsAs)

UDP and alterations	Cyclic order	Step pattern	Scale degree (diadegree)
			0	1	2	3	4	5	6	7
2|4 M6md	1	LsLLsAs	Perf.	Maj.	Min.	Perf.	Perf.	Min.	Maj.	Perf.
0|6 M5md	2	sLLsAsL	Perf.	Min.	Min.	Perf.	Dim.	Maj.	Min.	Perf.
5|1 A4md	3	LLsAsLs	Perf.	Maj.	Maj.	Perf.	Aug.	Maj.	Maj.	Perf.
3|3 A3md	4	LsAsLsL	Perf.	Maj.	Min.	Aug.	Perf.	Maj.	Min.	Perf.
1|5 M2md	5	sAsLsLL	Perf.	Min.	Maj.	Perf.	Perf.	Min.	Min.	Perf.
6|0 A1md	6	AsLsLLs	Perf.	Aug.	Maj.	Aug.	Perf.	Maj.	Maj.	Perf.
0|6 d3md d6md	7	sLsLLsA	Perf.	Min.	Min.	Dim.	Dim.	Min.	Dim.	Perf.

Scale degrees of the modes of 5L 2s (LsLLLLs)

UDP and alterations	Cyclic order	Step pattern	Scale degree (diadegree)
			0	1	2	3	4	5	6	7
5|1 m2md 3|3 M6md	1	LsLLLLs	Perf.	Maj.	Min.	Perf.	Perf.	Maj.	Maj.	Perf.
3|3 m1md 1|5 M5md	2	sLLLLsL	Perf.	Min.	Min.	Perf.	Perf.	Maj.	Min.	Perf.
6|0 A4md	3	LLLLsLs	Perf.	Maj.	Maj.	Aug.	Aug.	Maj.	Maj.	Perf.
6|0 m6md 4|2 A3md	4	LLLsLsL	Perf.	Maj.	Maj.	Aug.	Perf.	Maj.	Min.	Perf.
4|2 m5md 2|4 M2md	5	LLsLsLL	Perf.	Maj.	Maj.	Perf.	Perf.	Min.	Min.	Perf.
2|4 d4md 0|6 M1md	6	LsLsLLL	Perf.	Maj.	Min.	Perf.	Dim.	Min.	Min.	Perf.
0|6 d3md	7	sLsLLLL	Perf.	Min.	Min.	Dim.	Dim.	Min.	Min.	Perf.

Scale degrees of the modes of 5L 2s (LLsLsAs)

UDP and alterations	Cyclic order	Step pattern	Scale degree (diadegree)
			0	1	2	3	4	5	6	7
5|1 m5md	1	LLsLsAs	Perf.	Maj.	Maj.	Perf.	Perf.	Min.	Maj.	Perf.
3|3 d4md	2	LsLsAsL	Perf.	Maj.	Min.	Perf.	Dim.	Maj.	Min.	Perf.
1|5 d3md	3	sLsAsLL	Perf.	Min.	Min.	Dim.	Perf.	Min.	Min.	Perf.
6|0 m2md	4	LsAsLLs	Perf.	Maj.	Min.	Aug.	Perf.	Maj.	Maj.	Perf.
4|2 m1md	5	sAsLLsL	Perf.	Min.	Maj.	Perf.	Perf.	Maj.	Min.	Perf.
6|0 A1md A4md	6	AsLLsLs	Perf.	Aug.	Maj.	Aug.	Aug.	Maj.	Maj.	Perf.
0|6 d6md	7	sLLsLsA	Perf.	Min.	Min.	Perf.	Dim.	Min.	Dim.	Perf.

Scale degrees of the modes of 5L 2s (AAdAdAd)

UDP and alterations	Cyclic order	Step pattern	Scale degree (diadegree)
			0	1	2	3	4	5	6	7
6|0 A1md AA2md AA4md A6md	1	AAdAdAd	Perf.	Aug.	2× Aug.	Aug.	2× Aug.	Maj.	Aug.	Perf.
6|0 A1md m2md d4md d6md 0|6 A1md A3md M5md d6md	2	AdAdAdA	Perf.	Aug.	Min.	Aug.	Dim.	Maj.	Dim.	Perf.
0|6 d1md dd3md dd5md d6md	3	dAdAdAA	Perf.	Dim.	Min.	2× Dim.	Dim.	2× Dim.	Dim.	Perf.
6|0 A1md m2md d4md A6md 0|6 A1md A3md M5md A6md	4	AdAdAAd	Perf.	Aug.	Min.	Aug.	Dim.	Maj.	Aug.	Perf.
3|3 d1md dd3md d4md d6md 0|6 d1md dd3md M5md d6md	5	dAdAAdA	Perf.	Dim.	Min.	2× Dim.	Dim.	Maj.	Dim.	Perf.
6|0 A1md m2md AA4md A6md 3|3 A1md A3md AA4md A6md	6	AdAAdAd	Perf.	Aug.	Min.	Aug.	2× Aug.	Maj.	Aug.	Perf.
6|0 d1md m2md d4md d6md 0|6 d1md A3md M5md d6md	7	dAAdAdA	Perf.	Dim.	Min.	Aug.	Dim.	Maj.	Dim.	Perf.

Scale degrees of the modes of 5L 2s (LLLLLLd)

UDP and alterations	Cyclic order	Step pattern	Scale degree (diadegree)
			0	1	2	3	4	5	6	7
6|0 A4md A5md A6md	1	LLLLLLd	Perf.	Maj.	Maj.	Aug.	Aug.	Aug.	Aug.	Perf.
6|0 A4md A5md m6md 4|2 A3md A4md A5md	2	LLLLLdL	Perf.	Maj.	Maj.	Aug.	Aug.	Aug.	Min.	Perf.
6|0 A4md m5md m6md 2|4 M2md A3md A4md	3	LLLLdLL	Perf.	Maj.	Maj.	Aug.	Aug.	Min.	Min.	Perf.
6|0 d4md m5md m6md 0|6 M1md M2md A3md	4	LLLdLLL	Perf.	Maj.	Maj.	Aug.	Dim.	Min.	Min.	Perf.
4|2 d3md d4md m5md 0|6 M1md M2md d3md	5	LLdLLLL	Perf.	Maj.	Maj.	Dim.	Dim.	Min.	Min.	Perf.
2|4 d2md d3md d4md 0|6 M1md d2md d3md	6	LdLLLLL	Perf.	Maj.	Dim.	Dim.	Dim.	Min.	Min.	Perf.
0|6 d1md d2md d3md	7	dLLLLLL	Perf.	Dim.	Dim.	Dim.	Dim.	Min.	Min.	Perf.

Scale degrees of the modes of 5L 2s (LALdLAd)

UDP and alterations	Cyclic order	Step pattern	Scale degree (diadegree)
			0	1	2	3	4	5	6	7
6|0 A2md AA3md A6md 3|3 A2md AA3md A6md	1	LALdLAd	Perf.	Maj.	Aug.	2× Aug.	Perf.	Maj.	Aug.	Perf.
4|2 A1md A2md A5md 1|5 A1md A2md A5md	2	ALdLAdL	Perf.	Aug.	Aug.	Perf.	Perf.	Aug.	Min.	Perf.
6|0 d2md d3md d5md d6md 2|4 d2md d3md d5md d6md	3	LdLAdLA	Perf.	Maj.	Dim.	Dim.	Perf.	Dim.	Dim.	Perf.
4|2 d1md d2md dd4md d5md 0|6 d1md d2md dd4md d5md	4	dLAdLAL	Perf.	Dim.	Dim.	Perf.	2× Dim.	Dim.	Min.	Perf.
5|1 A2md A5md A6md 2|4 A2md A5md A6md	5	LAdLALd	Perf.	Maj.	Aug.	Perf.	Perf.	Aug.	Aug.	Perf.
3|3 A1md A4md A5md 0|6 A1md A4md A5md	6	AdLALdL	Perf.	Aug.	Min.	Perf.	Aug.	Aug.	Min.	Perf.
5|1 d1md d2md d5md d6md 1|5 d1md d2md d5md d6md	7	dLALdLA	Perf.	Dim.	Dim.	Perf.	Perf.	Dim.	Dim.	Perf.

4L 4s modes and modmos modes

Scale degrees of the modes of 4L 4s

UDP	Cyclic order	Step pattern	Scale degree (tetrawddegree)
			0	1	2	3	4	5	6	7	8
4|0(4)	1	LsLsLsLs	Perf.	Maj.	Perf.	Maj.	Perf.	Maj.	Perf.	Maj.	Perf.
0|4(4)	2	sLsLsLsL	Perf.	Min.	Perf.	Min.	Perf.	Min.	Perf.	Min.	Perf.

Scale degrees of the modes of 4L 4s (LLssLLss)

UDP and alterations	Cyclic order	Step pattern	Scale degree (tetrawddegree)
			0	1	2	3	4	5	6	7	8
4|0(4) A2md A6md	1	LLssLLss	Perf.	Maj.	Aug.	Maj.	Perf.	Maj.	Aug.	Maj.	Perf.
4|0(4) m3md m7md 0|4(4) M1md M5md	2	LssLLssL	Perf.	Maj.	Perf.	Min.	Perf.	Maj.	Perf.	Min.	Perf.
0|4(4) d2md d6md	3	ssLLssLL	Perf.	Min.	Dim.	Min.	Perf.	Min.	Dim.	Min.	Perf.
4|0(4) m1md m5md 0|4(4) M3md M7md	4	sLLssLLs	Perf.	Min.	Perf.	Maj.	Perf.	Min.	Perf.	Maj.	Perf.

Scale degrees of the modes of 4L 4s (LLssLsLs)

UDP and alterations	Cyclic order	Step pattern	Scale degree (tetrawddegree)
			0	1	2	3	4	5	6	7	8
4|0(4) A2md	1	LLssLsLs	Perf.	Maj.	Aug.	Maj.	Perf.	Maj.	Perf.	Maj.	Perf.
0|4(4) M1md	2	LssLsLsL	Perf.	Maj.	Perf.	Min.	Perf.	Min.	Perf.	Min.	Perf.
0|4(4) d2md d4md d6md	3	ssLsLsLL	Perf.	Min.	Dim.	Min.	Dim.	Min.	Dim.	Min.	Perf.
0|4(4) M7md	4	sLsLsLLs	Perf.	Min.	Perf.	Min.	Perf.	Min.	Perf.	Maj.	Perf.
4|0(4) A6md	5	LsLsLLss	Perf.	Maj.	Perf.	Maj.	Perf.	Maj.	Aug.	Maj.	Perf.
0|4(4) M5md	6	sLsLLssL	Perf.	Min.	Perf.	Min.	Perf.	Maj.	Perf.	Min.	Perf.
4|0(4) A4md	7	LsLLssLs	Perf.	Maj.	Perf.	Maj.	Aug.	Maj.	Perf.	Maj.	Perf.
0|4(4) M3md	8	sLLssLsL	Perf.	Min.	Perf.	Maj.	Perf.	Min.	Perf.	Min.	Perf.

Sandbox for proposed templates

Cent ruler

50

50

50

50

50

50

50

50

50

50

50

50

50

50

50

50

50

50

50

50

50

50

50

50

L

L

L

s

L

L

s

MOS characteristics

NOTE: not suitable for displaying intervals or scale degrees. Repurpose for other content.

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 ¢

Tamnams suggests the name NAME for this scale, which comes from ORIGIN. Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.

4

5

6

7

8

9

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.

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

Encoding scheme for module:mos

Mossteps as a vector of L's and s's

For an arbitrary step sequence consisting of L's and s's, the sum of the quantities of L's and s's denotes what mosstep it is. EG, "LLLsL" is a 5-mosstep since it has 5 L's and s's total. This can be expressed as a vector denoting how many L's and s's there are. EG, "LLLsL" becomes { 4, 1 }, denoting 4 large steps and 1 small step.

Alterations by adding a chroma always adds one L and subtracts one s (or subtracts one L and adds one s, if lowering by a chroma), so the sum of L's and s's, even if one of the quantities is negative, will always denote what k-mosstep that interval is. EG, raising "LLLsL" by a chroma produces the vector { 5, 0 }, and raising it by another chroma produces the vector { 6, -1 }.

Through this, the "original size" of the interval can always be deduced.

EG, the vector { 6, -2 } is given, assuming a mos of 5L 2s. Adding 6 and -2 shows that the interval is a 4-mosstep. Taking the brightest mode of 5L 2s (LLLsLLs) and truncating it to the first 4 steps (LLLs), the corresponding vector is { 3, 1 }. This is the vector to compare to. Subtracting the given vector from the comparison vector ( as { 6-3, -2-1 }) produces the vector { 3, -3 }, meaning that { 6, -2 } is the large 4-mosstep raised by 3 chromas. (A shortcut can be employed by simply subtracting only the L-values.) The decoding scheme below shows how the "large 4-mosstep plus 3 chromas" can be decoded into more familiar terms. In this example, since the large 4-mosstep is the perfect bright generator, adding 3 chromas makes it triply augmented.

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:

• Vectors of L's and s's can always be translated back to the original k-mosstep, no matter how many chromas were added. The "unmodified" vector (the large k-mosstep, or perfect k-mosstep for period intervals) can be compared with the mosstep vector to produce the number of chromas.
  • Alterations by entire large steps or small steps is considered interval arithmetic.

• 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	Gb
L	1	0	Major 1-diastep	G
L + s	2	-1	Minor 2-diastep	Ab
2L	2	0	Major 2-diastep	A
2L + s	3	-1	Perfect 3-diastep	Bb
3L	3	0	Augmented 3-diastep	B
2L + 2s	4	-1	Diminished 4-diastep	Cb
3L + s	4	0	Perfect 4-diastep	C
3L + 2s	5	-1	Minor 5-diastep	Db
4L + s	5	0	Major 5-diastep	D
4L + 2s	6	-1	Minor 6-diastep	Eb
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	0	0	0	0	0	0	0
5L 2s 5|1	Ionian (major)	2	5	LLsLLLs	0	0	0	-1	0	0	0	0
5L 2s 4|2	Mixolydian	3	2	LLsLLsL	0	0	1	-1	0	0	-1	0
5L 2s 3|3	Dorian	4	6	LsLLLsL	0	0	-1	-1	0	0	-1	0
5L 2s 2|4	Aeolian (minor)	5	3	LsLLsLL	0	0	-1	-1	0	-1	-1	0
5L 2s 1|5	Phrygian	6	7	sLLLsLL	0	-1	-1	-1	0	-1	-1	0
5L 2s 0|6	Locrian	7	4	sLLsLLL	0	-1	-1	-1	-1	-1	-1	0