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 intro

First sentence:

• Single-period 2/1-equivalent: xL ys (TAMNAMS name tamnams-name), also called other-name, is an octave-repeating moment of symmetry scale that divides the octave (2/1) into x large and y small steps.
• Multi-period 2/1-equivalent: nxL nys (TAMNAMS name tamnams-name), also called other-name, is an octave-repeating moment of symmetry scale that divides the octave (2/1) into nx large steps and ny small steps, with n periods of c cents containing x large and y small steps each.
• Single-period 3/1-equivalent: 3/1-equivalent xL ys, also called other-name, is a twelfth-repeating moment of symmetry scale that divides the tritave or perfect 12th (3/1, c cents) into x large and y small steps.
• Multi-period 3/1-equivalent: 3/1-equivalent nxL nys, also called other-name, is a twelfth-repeating moment of symmetry scale that divides the tritave or perfect 12th (3/1, nc cents) into nx large steps and ny small steps, with n periods of c cents containing x large and y small steps each.
• Single-period 3/2-equivalent: 3/2-equivalent xL ys, also called other-name, is a fifth-repeating moment of symmetry scale that divides the perfect 5th (3/2, c cents) into x large and y small steps.
• Multi-period 3/2-equivalent: 3/2-equivalent nxL nys, also called other-name, is a fifth-repeating moment of symmetry scale that divides the perfect 5th (3/2, nc cents) into nx large steps and ny small steps, with n periods of c cents containing x large and y small steps each.

Second sentence:

• Generators that produce this scale range from g1 cents to g2 cents, or from d1 cents to d2 cents.

Octave-equivalent relational info:

• Parents of mosses with 6-10 steps: xL ys is the parent scale of both child-soft and child-hard.
• Children of mosses with 6-10 steps: xL ys expands parent-scale by adding step-count-difference tones.

Rothenprop:

• Single-period: Scales of this form are always proper because there is only one small step.
• Multi-period: Scales of this form, where every period is the same, are proper because there is only one small step per period.

MOS tunings

Soft Tuning of 10L 4s⟨4/1⟩

Scale degree	Abbrev.	Soft (3:2) 38ed4
		Steps	¢
Perfect 0-mosdegree	P0md	0\38	0.0
Minor 1-mosdegree	m1md	2\38	126.3
Major 1-mosdegree	M1md	3\38	189.5
Minor 2-mosdegree	m2md	5\38	315.8
Major 2-mosdegree	M2md	6\38	378.9
Perfect 3-mosdegree	P3md	8\38	505.3
Augmented 3-mosdegree	A3md	9\38	568.4
Diminished 4-mosdegree	d4md	10\38	631.6
Perfect 4-mosdegree	P4md	11\38	694.7
Minor 5-mosdegree	m5md	13\38	821.1
Major 5-mosdegree	M5md	14\38	884.2
Minor 6-mosdegree	m6md	16\38	1010.5
Major 6-mosdegree	M6md	17\38	1073.7
Perfect 7-mosdegree	P7md	19\38	1200.0
Minor 8-mosdegree	m8md	21\38	1326.3
Major 8-mosdegree	M8md	22\38	1389.5
Minor 9-mosdegree	m9md	24\38	1515.8
Major 9-mosdegree	M9md	25\38	1578.9
Perfect 10-mosdegree	P10md	27\38	1705.3
Augmented 10-mosdegree	A10md	28\38	1768.4
Diminished 11-mosdegree	d11md	29\38	1831.6
Perfect 11-mosdegree	P11md	30\38	1894.7
Minor 12-mosdegree	m12md	32\38	2021.1
Major 12-mosdegree	M12md	33\38	2084.2
Minor 13-mosdegree	m13md	35\38	2210.5
Major 13-mosdegree	M13md	36\38	2273.7
Perfect 14-mosdegree	P14md	38\38	2400.0

Quasisoft Tunings of 5L 3s⟨11/5⟩

Scale degree	Abbrev.	Soft (3:2) 21ed11/5		Semisoft (5:3) 34ed11/5
		Steps	¢	Steps	¢
Perfect 0-mosdegree	P0md	0\21	0.0	0\34	0.0
Minor 1-mosdegree	m1md	2\21	130.0	3\34	120.4
Major 1-mosdegree	M1md	3\21	195.0	5\34	200.7
Minor 2-mosdegree	m2md	5\21	325.0	8\34	321.2
Major 2-mosdegree	M2md	6\21	390.0	10\34	401.5
Diminished 3-mosdegree	d3md	7\21	455.0	11\34	441.6
Perfect 3-mosdegree	P3md	8\21	520.0	13\34	521.9
Minor 4-mosdegree	m4md	10\21	650.0	16\34	642.4
Major 4-mosdegree	M4md	11\21	715.0	18\34	722.6
Perfect 5-mosdegree	P5md	13\21	845.0	21\34	843.1
Augmented 5-mosdegree	A5md	14\21	910.0	23\34	923.4
Minor 6-mosdegree	m6md	15\21	975.0	24\34	963.5
Major 6-mosdegree	M6md	16\21	1040.0	26\34	1043.8
Minor 7-mosdegree	m7md	18\21	1170.0	29\34	1164.3
Major 7-mosdegree	M7md	19\21	1235.0	31\34	1244.6
Perfect 8-mosdegree	P8md	21\21	1365.0	34\34	1365.0

Superhard Tuning of 5L 3s⟨11/5⟩

Scale degree	Abbrev.	Superhard (4:1) 23ed11/5
		Steps	¢
Perfect 0-mosdegree	P0md	0\23	0.0
Minor 1-mosdegree	m1md	1\23	59.3
Major 1-mosdegree	M1md	4\23	237.4
Minor 2-mosdegree	m2md	5\23	296.7
Major 2-mosdegree	M2md	8\23	474.8
Diminished 3-mosdegree	d3md	6\23	356.1
Perfect 3-mosdegree	P3md	9\23	534.1
Minor 4-mosdegree	m4md	10\23	593.5
Major 4-mosdegree	M4md	13\23	771.5
Perfect 5-mosdegree	P5md	14\23	830.9
Augmented 5-mosdegree	A5md	17\23	1008.9
Minor 6-mosdegree	m6md	15\23	890.2
Major 6-mosdegree	M6md	18\23	1068.3
Minor 7-mosdegree	m7md	19\23	1127.6
Major 7-mosdegree	M7md	22\23	1305.7
Perfect 8-mosdegree	P8md	23\23	1365.0

Hypohard Tunings of 5L 3s⟨11/5⟩

Scale degree	Abbrev.	Basic (2:1) 13ed11/5		Semihard (5:2) 31ed11/5		Hard (3:1) 18ed11/5
		Steps	¢	Steps	¢	Steps	¢
Perfect 0-mosdegree	P0md	0\13	0.0	0\31	0.0	0\18	0.0
Minor 1-mosdegree	m1md	1\13	105.0	2\31	88.1	1\18	75.8
Major 1-mosdegree	M1md	2\13	210.0	5\31	220.2	3\18	227.5
Minor 2-mosdegree	m2md	3\13	315.0	7\31	308.2	4\18	303.3
Major 2-mosdegree	M2md	4\13	420.0	10\31	440.3	6\18	455.0
Diminished 3-mosdegree	d3md	4\13	420.0	9\31	396.3	5\18	379.2
Perfect 3-mosdegree	P3md	5\13	525.0	12\31	528.4	7\18	530.8
Minor 4-mosdegree	m4md	6\13	630.0	14\31	616.5	8\18	606.7
Major 4-mosdegree	M4md	7\13	735.0	17\31	748.6	10\18	758.3
Perfect 5-mosdegree	P5md	8\13	840.0	19\31	836.6	11\18	834.2
Augmented 5-mosdegree	A5md	9\13	945.0	22\31	968.7	13\18	985.8
Minor 6-mosdegree	m6md	9\13	945.0	21\31	924.7	12\18	910.0
Major 6-mosdegree	M6md	10\13	1050.0	24\31	1056.8	14\18	1061.7
Minor 7-mosdegree	m7md	11\13	1155.0	26\31	1144.8	15\18	1137.5
Major 7-mosdegree	M7md	12\13	1260.0	29\31	1276.9	17\18	1289.2
Perfect 8-mosdegree	P8md	13\13	1365.0	31\31	1365.0	18\18	1365.0

Simple Tunings of 4L 3s

Scale degree	Abbrev.	Basic (2:1) 11edo		Hard (3:1) 15edo		Soft (3:2) 18edo
		Steps	¢	Steps	¢	Steps	¢
Perfect 0-smidegree	P0smid	0\11	0.0	0\15	0.0	0\18	0.0
Minor 1-smidegree	m1smid	1\11	109.1	1\15	80.0	2\18	133.3
Major 1-smidegree	M1smid	2\11	218.2	3\15	240.0	3\18	200.0
Perfect 2-smidegree	P2smid	3\11	327.3	4\15	320.0	5\18	333.3
Augmented 2-smidegree	A2smid	4\11	436.4	6\15	480.0	6\18	400.0
Minor 3-smidegree	m3smid	4\11	436.4	5\15	400.0	7\18	466.7
Major 3-smidegree	M3smid	5\11	545.5	7\15	560.0	8\18	533.3
Minor 4-smidegree	m4smid	6\11	654.5	8\15	640.0	10\18	666.7
Major 4-smidegree	M4smid	7\11	763.6	10\15	800.0	11\18	733.3
Diminished 5-smidegree	d5smid	7\11	763.6	9\15	720.0	12\18	800.0
Perfect 5-smidegree	P5smid	8\11	872.7	11\15	880.0	13\18	866.7
Minor 6-smidegree	m6smid	9\11	981.8	12\15	960.0	15\18	1000.0
Major 6-smidegree	M6smid	10\11	1090.9	14\15	1120.0	16\18	1066.7
Perfect 7-smidegree	P7smid	11\11	1200.0	15\15	1200.0	18\18	1200.0

Tunings of 8L 3s⟨3/1⟩

Scale degree	Abbrev.	Supersoft (4:3) 41edt		Soft (3:2) 30edt		Semisoft (5:3) 49edt		Basic (2:1) 19edt		Semihard (5:2) 46edt		Hard (3:1) 27edt		Superhard (4:1) 35edt
		Steps	¢	Steps	¢	Steps	¢	Steps	¢	Steps	¢	Steps	¢	Steps	¢
Perfect 0-mosdegree	P0md	0\41	0.0	0\30	0.0	0\49	0.0	0\19	0.0	0\46	0.0	0\27	0.0	0\35	0.0
Minor 1-mosdegree	m1md	3\41	139.2	2\30	126.8	3\49	116.4	1\19	100.1	2\46	82.7	1\27	70.4	1\35	54.3
Major 1-mosdegree	M1md	4\41	185.6	3\30	190.2	5\49	194.1	2\19	200.2	5\46	206.7	3\27	211.3	4\35	217.4
Minor 2-mosdegree	m2md	7\41	324.7	5\30	317.0	8\49	310.5	3\19	300.3	7\46	289.4	4\27	281.8	5\35	271.7
Major 2-mosdegree	M2md	8\41	371.1	6\30	380.4	10\49	388.2	4\19	400.4	10\46	413.5	6\27	422.7	8\35	434.7
Minor 3-mosdegree	m3md	11\41	510.3	8\30	507.2	13\49	504.6	5\19	500.5	12\46	496.2	7\27	493.1	9\35	489.1
Major 3-mosdegree	M3md	12\41	556.7	9\30	570.6	15\49	582.2	6\19	600.6	15\46	620.2	9\27	634.0	12\35	652.1
Diminished 4-mosdegree	d4md	14\41	649.4	10\30	634.0	16\49	621.0	6\19	600.6	14\46	578.9	8\27	563.5	10\35	543.4
Perfect 4-mosdegree	P4md	15\41	695.8	11\30	697.4	18\49	698.7	7\19	700.7	17\46	702.9	10\27	704.4	13\35	706.4
Minor 5-mosdegree	m5md	18\41	835.0	13\30	824.2	21\49	815.1	8\19	800.8	19\46	785.6	11\27	774.9	14\35	760.8
Major 5-mosdegree	M5md	19\41	881.4	14\30	887.6	23\49	892.8	9\19	900.9	22\46	909.6	13\27	915.8	17\35	923.8
Minor 6-mosdegree	m6md	22\41	1020.6	16\30	1014.4	26\49	1009.2	10\19	1001.0	24\46	992.3	14\27	986.2	18\35	978.1
Major 6-mosdegree	M6md	23\41	1067.0	17\30	1077.8	28\49	1086.8	11\19	1101.1	27\46	1116.4	16\27	1127.1	21\35	1141.2
Perfect 7-mosdegree	P7md	26\41	1206.1	19\30	1204.6	31\49	1203.3	12\19	1201.2	29\46	1199.1	17\27	1197.5	22\35	1195.5
Augmented 7-mosdegree	A7md	27\41	1252.5	20\30	1268.0	33\49	1280.9	13\19	1301.3	32\46	1323.1	19\27	1338.4	25\35	1358.5
Minor 8-mosdegree	m8md	29\41	1345.3	21\30	1331.4	34\49	1319.7	13\19	1301.3	31\46	1281.8	18\27	1268.0	23\35	1249.9
Major 8-mosdegree	M8md	30\41	1391.7	22\30	1394.8	36\49	1397.4	14\19	1401.4	34\46	1405.8	20\27	1408.9	26\35	1412.9
Minor 9-mosdegree	m9md	33\41	1530.8	24\30	1521.6	39\49	1513.8	15\19	1501.5	36\46	1488.5	21\27	1479.3	27\35	1467.2
Major 9-mosdegree	M9md	34\41	1577.2	25\30	1585.0	41\49	1591.4	16\19	1601.6	39\46	1612.5	23\27	1620.2	30\35	1630.2
Minor 10-mosdegree	m10md	37\41	1716.4	27\30	1711.8	44\49	1707.9	17\19	1701.7	41\46	1695.2	24\27	1690.6	31\35	1684.6
Major 10-mosdegree	M10md	38\41	1762.8	28\30	1775.2	46\49	1785.5	18\19	1801.9	44\46	1819.3	26\27	1831.5	34\35	1847.6
Perfect 11-mosdegree	P11md	41\41	1902.0	30\30	1902.0	49\49	1902.0	19\19	1902.0	46\46	1902.0	27\27	1902.0	35\35	1902.0

Tunings of 9L 4s⟨7/2⟩

Scale degree	Abbrev.	Supersoft (4:3) 48ed7/2		Soft (3:2) 35ed7/2		Semisoft (5:3) 57ed7/2		Basic (2:1) 22ed7/2		Semihard (5:2) 53ed7/2		Hard (3:1) 31ed7/2		Superhard (4:1) 40ed7/2
		Steps	¢	Steps	¢	Steps	¢	Steps	¢	Steps	¢	Steps	¢	Steps	¢
Perfect 0-mosdegree	P0md	0\48	0.0	0\35	0.0	0\57	0.0	0\22	0.0	0\53	0.0	0\31	0.0	0\40	0.0
Minor 1-mosdegree	m1md	3\48	135.6	2\35	123.9	3\57	114.1	1\22	98.6	2\53	81.8	1\31	70.0	1\40	54.2
Major 1-mosdegree	M1md	4\48	180.7	3\35	185.9	5\57	190.2	2\22	197.2	5\53	204.6	3\31	209.9	4\40	216.9
Minor 2-mosdegree	m2md	7\48	316.3	5\35	309.8	8\57	304.4	3\22	295.7	7\53	286.4	4\31	279.8	5\40	271.1
Major 2-mosdegree	M2md	8\48	361.5	6\35	371.8	10\57	380.5	4\22	394.3	10\53	409.2	6\31	419.8	8\40	433.8
Perfect 3-mosdegree	P3md	11\48	497.0	8\35	495.7	13\57	494.6	5\22	492.9	12\53	491.1	7\31	489.7	9\40	488.0
Augmented 3-mosdegree	A3md	12\48	542.2	9\35	557.7	15\57	570.7	6\22	591.5	15\53	613.8	9\31	629.7	12\40	650.6
Minor 4-mosdegree	m4md	14\48	632.6	10\35	619.7	16\57	608.8	6\22	591.5	14\53	572.9	8\31	559.7	10\40	542.2
Major 4-mosdegree	M4md	15\48	677.8	11\35	681.6	18\57	684.9	7\22	690.1	17\53	695.7	10\31	699.6	13\40	704.9
Minor 5-mosdegree	m5md	18\48	813.3	13\35	805.6	21\57	799.0	8\22	788.7	19\53	777.5	11\31	769.6	14\40	759.1
Major 5-mosdegree	M5md	19\48	858.5	14\35	867.5	23\57	875.1	9\22	887.2	22\53	900.3	13\31	909.5	17\40	921.8
Minor 6-mosdegree	m6md	22\48	994.0	16\35	991.5	26\57	989.3	10\22	985.8	24\53	982.1	14\31	979.5	18\40	976.0
Major 6-mosdegree	M6md	23\48	1039.2	17\35	1053.4	28\57	1065.4	11\22	1084.4	27\53	1104.9	16\31	1119.4	21\40	1138.6
Minor 7-mosdegree	m7md	25\48	1129.6	18\35	1115.4	29\57	1103.4	11\22	1084.4	26\53	1064.0	15\31	1049.4	19\40	1030.2
Major 7-mosdegree	M7md	26\48	1174.8	19\35	1177.4	31\57	1179.5	12\22	1183.0	29\53	1186.7	17\31	1189.4	22\40	1192.9
Minor 8-mosdegree	m8md	29\48	1310.3	21\35	1301.3	34\57	1293.7	13\22	1281.6	31\53	1268.6	18\31	1259.3	23\40	1247.1
Major 8-mosdegree	M8md	30\48	1355.5	22\35	1363.3	36\57	1369.8	14\22	1380.2	34\53	1391.3	20\31	1399.2	26\40	1409.7
Minor 9-mosdegree	m9md	33\48	1491.1	24\35	1487.2	39\57	1483.9	15\22	1478.7	36\53	1473.2	21\31	1469.2	27\40	1464.0
Major 9-mosdegree	M9md	34\48	1536.3	25\35	1549.2	41\57	1560.0	16\22	1577.3	39\53	1595.9	23\31	1609.1	30\40	1626.6
Diminished 10-mosdegree	d10md	36\48	1626.6	26\35	1611.1	42\57	1598.1	16\22	1577.3	38\53	1555.0	22\31	1539.2	28\40	1518.2
Perfect 10-mosdegree	P10md	37\48	1671.8	27\35	1673.1	44\57	1674.2	17\22	1675.9	41\53	1677.8	24\31	1679.1	31\40	1680.8
Minor 11-mosdegree	m11md	40\48	1807.4	29\35	1797.0	47\57	1788.3	18\22	1774.5	43\53	1759.6	25\31	1749.1	32\40	1735.1
Major 11-mosdegree	M11md	41\48	1852.5	30\35	1859.0	49\57	1864.4	19\22	1873.1	46\53	1882.4	27\31	1889.0	35\40	1897.7
Minor 12-mosdegree	m12md	44\48	1988.1	32\35	1982.9	52\57	1978.6	20\22	1971.7	48\53	1964.2	28\31	1958.9	36\40	1951.9
Major 12-mosdegree	M12md	45\48	2033.3	33\35	2044.9	54\57	2054.7	21\22	2070.2	51\53	2087.0	30\31	2098.9	39\40	2114.6
Perfect 13-mosdegree	P13md	48\48	2168.8	35\35	2168.8	57\57	2168.8	22\22	2168.8	53\53	2168.8	31\31	2168.8	40\40	2168.8

Mos intervals and mos interval HE

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 ¢

Harmonic entropy info for 5L 2s

Interval	Range in cents	Average of HE (from HE Calc)	Min of HE
Perfect 0-diastep	0.0 ¢	~2.4654 nats	~2.4654 nats
Minor 1-diastep	0.0 ¢ to 171.4 ¢	~4.6969 nats	~4.6333 nats
Major 1-diastep	171.4 ¢ to 240.0 ¢	~4.5872 nats	~4.5842 nats
Minor 2-diastep	240.0 ¢ to 342.9 ¢	~4.5596 nats	~4.5379 nats
Major 2-diastep	342.9 ¢ to 480.0 ¢	~4.5540 nats	~4.4846 nats
Perfect 3-diastep	480.0 ¢ to 514.3 ¢	~4.3841 nats	~4.3665 nats
Augmented 3-diastep	514.3 ¢ to 720.0 ¢	~4.6012 nats	~4.5615 nats
Diminished 4-diastep	480.0 ¢ to 685.7 ¢	~4.6013 nats	~4.5630 nats
Perfect 4-diastep	685.7 ¢ to 720.0 ¢	~4.1634 nats	~4.1224 nats
Minor 5-diastep	720.0 ¢ to 857.1 ¢	~4.5942 nats	~4.5711 nats
Major 5-diastep	857.1 ¢ to 960.0 ¢	~4.5145 nats	~4.4208 nats
Minor 6-diastep	960.0 ¢ to 1028.6 ¢	~4.5760 nats	~4.5502 nats
Major 6-diastep	1028.6 ¢ to 1200.0 ¢	~4.6377 nats	~4.6078 nats
Perfect 7-diastep	1200.0 ¢	~3.3273 nats	~3.3273 nats

Name

6-note mosses

TAMNAMS suggests the temperament-agnostic name antimachinoid as the name of 1L 5s. The name is based on being the opposite pattern of 5L 1s (machinoid).

TAMNAMS suggests the temperament-agnostic name malic as the name of 2L 4s. The name derives from Latin malus, since apples have two concave ends.

TAMNAMS suggests the temperament-agnostic name triwood as the name of 3L 3s. The name generalizes blackwood[10] and whitewood[14] to 3 periods.

TAMNAMS suggests the temperament-agnostic name citric as the name of 4L 2s. The name references its daughter scales 4L 6s (lime) and 6L 4s (lemon).

TAMNAMS suggests the temperament-agnostic name machinoid as the name of 5L 1s. The name derives from machine temperament. Although this name is directly based off of a temperament, tunings of machine cover the entire tuning range of 5L 1s see TAMNAMS/Appendix #Machinoid (5L 1s) for more information.

7-note mosses

TAMNAMS suggests the temperament-agnostic name onyx as the name of 1L 6s.

TAMNAMS suggests the temperament-agnostic name antidiatonic as the name of 2L 5s. The name is based on being the opposite pattern of 5L 2s (diatonic).

TAMNAMS suggests the temperament-agnostic name mosh as the name of 3L 4s. The name derives from "mohajira-ish", a name from Graham Breed's naming scheme.

TAMNAMS suggests the temperament-agnostic name smitonic as the name of 4L 3s. The name derives from "sharp minor third", referring to the generator's quality.

TAMNAMS suggests the temperament-agnostic name diatonic as the name of 5L 2s. The name commonly refers to a scale with 5 whole and 2 half steps, or 5 large and 2 small steps; see TAMNAMS/Appendix #On the term diatonic for more information.

TAMNAMS suggests the temperament-agnostic name archaeotonic as the name of 6L 1s. The name was originally used as a name for the 6L 1s scale in 13edo.

8-note mosses

TAMNAMS suggests the temperament-agnostic name antipine as the name of 1L 7s. The name is based on being the opposite pattern of 7L 1s (pine).

TAMNAMS suggests the temperament-agnostic name subaric as the name of 2L 6s. The name references to how 2L 6s is the parent scale (or subset scale) of 2L 8s (jaric) and 8L 2s (taric).

TAMNAMS suggests the temperament-agnostic name checkertonic as the name of 3L 5s. The name derives from the Kite guitar checkerboard scale.

TAMNAMS suggests the temperament-agnostic name tetrawood as the name of 4L 4s. The name generalizes blackwood[10] and whitewood[14] to 4 periods.

TAMNAMS suggests the temperament-agnostic name oneirotonic as the name of 5L 3s. The name was originally used as a name for the 5L 3s scale in 13edo.

TAMNAMS suggests the temperament-agnostic name ekic as the name of 6L 2s. The name is an abstraction of echidna and hedgehog temperaments.

TAMNAMS suggests the temperament-agnostic name pine as the name of 7L 1s. The name is an abstraction of porcupine temperament.

9-note mosses

TAMNAMS suggests the temperament-agnostic name antisubneutralic as the name of 1L 8s. The name is based on being the opposite pattern of 8L 1s (subneutralic).

TAMNAMS suggests the temperament-agnostic name balzano as the name of 2L 7s. The name was originally used as a name for the 2L 7s scale in 20edo.

TAMNAMS suggests the temperament-agnostic name tcherepnin as the name of 3L 6s. The name references Alexander Tcherepnin's nine-note scale, corresponding to to 3L 6s in 12edo.

TAMNAMS suggests the temperament-agnostic name gramitonic as the name of 4L 5s. The name derives from "grave minor third", referring to the generator's quality.

TAMNAMS suggests the temperament-agnostic name semiquartal as the name of 5L 4s. The name derives from "half-fourth", referring to the generator's quality.

TAMNAMS suggests the temperament-agnostic name hyrulic as the name of 6L 3s. The name is an abstraction of triforce temperament.

TAMNAMS suggests the temperament-agnostic name armotonic as the name of 7L 2s. The name references Armodue, a system of theory for the 7L 2s scale in 16edo.

TAMNAMS suggests the temperament-agnostic name subneutralic as the name of 8L 1s. The name derives from "subneutral", referring to the generator's quality.

10-note mosses

TAMNAMS suggests the temperament-agnostic name antisinatonic as the name of 1L 9s. The name is based on being the opposite pattern of 9L 1s (sinatonic).

TAMNAMS suggests the temperament-agnostic name jaric as the name of 2L 8s. The name is an abstraction of pajara, injera, and diaschismic temperaments.

TAMNAMS suggests the temperament-agnostic name sephiroid as the name of 3L 7s. The name derives from sephiroth temperament. Although this name is directly based off of a temperament, tunings of sephiroth cover the entire tuning range of 3L 7s; see TAMNAMS/Appendix #Sephiroid (3L 7s) for more information.

TAMNAMS suggests the temperament-agnostic name lime as the name of 4L 6s. The name references its parent scale 4L 2s (citric).

TAMNAMS suggests the temperament-agnostic name pentawood as the name of 5L 5s. The name generalizes blackwood[10] and whitewood[14] to 5 periods.

TAMNAMS suggests the temperament-agnostic name lemon as the name of 6L 4s. The name references its parent scale 4L 2s (citric), as well as indirectly referencing lemba temperament.

TAMNAMS suggests the temperament-agnostic name dicoid as the name of 7L 3s. The name derives from dichotic and dicot temperament. Although this name is directly based off of a temperament, tunings of dichotic and dicot cover the entire tuning range of 7L 3s; see TAMNAMS/Appendix #Dicoid (7L 3s) for more information.

TAMNAMS suggests the temperament-agnostic name taric as the name of 8L 2s. The name derives from Hindi aṭhārah for 18, in reference to 18edo containing a basic 8L 2s scale.

TAMNAMS suggests the temperament-agnostic name sinatonic as the name of 9L 1s. The name derives from the sinaic, referring to the generator's quality.

Scale data

User:MOS data is deprecated. Please use the following templates individually: MOS intervals, MOS genchain, and MOS mode degrees

5L 2s modes and modmos modes

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

UDP and alterations	Cyclic order	Step pattern	Scale degree (diadegree)
			0	1	2	3	4	5	6	7	8	9	10	11	12
6|0 A0md M1md A1md M2md A2md A3md P4md A4md M5md A5md M6md P7md 0|6 A0md M1md A1md M2md A2md A3md P4md A4md M5md A5md M6md P7md	1	cscscsscscss	Perf.	Aug.	Maj.	Aug.	Maj.	Aug.	Aug.	Perf.	Aug.	Maj.	Aug.	Maj.	Perf.
1|5 M1md m2md M2md P3md d4md P4md m5md M5md m6md d7md P7md 0|6 M1md m2md M2md P3md d4md P4md m5md M5md m6md d7md P7md	2	scscsscscssc	Perf.	Min.	Maj.	Min.	Maj.	Perf.	Dim.	Perf.	Min.	Maj.	Min.	Dim.	Perf.
6|0 A0md M1md A1md M2md P3md A3md P4md A4md M5md m6md M6md P7md 0|6 A0md M1md A1md M2md P3md A3md P4md A4md M5md m6md M6md P7md	3	cscsscscsscs	Perf.	Aug.	Maj.	Aug.	Maj.	Perf.	Aug.	Perf.	Aug.	Maj.	Min.	Maj.	Perf.
1|5 M1md m2md d3md P3md d4md P4md m5md d6md m6md d7md P7md 0|6 M1md m2md d3md P3md d4md P4md m5md d6md m6md d7md P7md	4	scsscscsscsc	Perf.	Min.	Maj.	Min.	Dim.	Perf.	Dim.	Perf.	Min.	Dim.	Min.	Dim.	Perf.
6|0 A0md M1md m2md M2md P3md A3md P4md m5md M5md m6md M6md P7md 0|6 A0md M1md m2md M2md P3md A3md P4md m5md M5md m6md M6md P7md	5	csscscsscscs	Perf.	Aug.	Maj.	Min.	Maj.	Perf.	Aug.	Perf.	Min.	Maj.	Min.	Maj.	Perf.
1|5 d2md m2md d3md P3md d4md d5md m5md d6md m6md d7md P7md 0|6 d2md m2md d3md P3md d4md d5md m5md d6md m6md d7md P7md	6	sscscsscscsc	Perf.	Min.	Dim.	Min.	Dim.	Perf.	Dim.	Dim.	Min.	Dim.	Min.	Dim.	Perf.
1|5 M1md m2md M2md P3md d4md P4md m5md M5md m6md M6md P7md 0|6 M1md m2md M2md P3md d4md P4md m5md M5md m6md M6md P7md	7	scscsscscscs	Perf.	Min.	Maj.	Min.	Maj.	Perf.	Dim.	Perf.	Min.	Maj.	Min.	Maj.	Perf.
6|0 A0md M1md A1md M2md P3md A3md P4md A4md M5md A5md M6md P7md 0|6 A0md M1md A1md M2md P3md A3md P4md A4md M5md A5md M6md P7md	8	cscsscscscss	Perf.	Aug.	Maj.	Aug.	Maj.	Perf.	Aug.	Perf.	Aug.	Maj.	Aug.	Maj.	Perf.
1|5 M1md m2md d3md P3md d4md P4md m5md M5md m6md d7md P7md 0|6 M1md m2md d3md P3md d4md P4md m5md M5md m6md d7md P7md	9	scsscscscssc	Perf.	Min.	Maj.	Min.	Dim.	Perf.	Dim.	Perf.	Min.	Maj.	Min.	Dim.	Perf.
6|0 A0md M1md m2md M2md P3md A3md P4md A4md M5md m6md M6md P7md 0|6 A0md M1md m2md M2md P3md A3md P4md A4md M5md m6md M6md P7md	10	csscscscsscs	Perf.	Aug.	Maj.	Min.	Maj.	Perf.	Aug.	Perf.	Aug.	Maj.	Min.	Maj.	Perf.
1|5 d2md m2md d3md P3md d4md P4md m5md d6md m6md d7md P7md 0|6 d2md m2md d3md P3md d4md P4md m5md d6md m6md d7md P7md	11	sscscscsscsc	Perf.	Min.	Dim.	Min.	Dim.	Perf.	Dim.	Perf.	Min.	Dim.	Min.	Dim.	Perf.
1|5 M1md m2md M2md P3md A3md P4md m5md M5md m6md M6md P7md 0|6 M1md m2md M2md P3md A3md P4md m5md M5md m6md M6md P7md	12	scscscsscscs	Perf.	Min.	Maj.	Min.	Maj.	Perf.	Aug.	Perf.	Min.	Maj.	Min.	Maj.	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.

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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 ¢

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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