User:Moremajorthanmajor/2L 1s (perfect fourth-equivalent)

2L 1s<perfect fourth>, is a perfect fourth-repeating MOS scale. The notation "<perfect fourth>" means the period of the MOS is a perfect fourth, disambiguating it from octave-repeating 2L 1s.

The generator range is 171.4 to 240 cents, placing it near the diatonic major second, usually representing a major second of some type. The dark (chroma-negative) generator is, however, its fourth complement (240 to 342.9 cents).

In the fourth-repeating version of the diatonic scale, each tone has a 4/3 perfect fourth above it. The scale has one major chord and two minor chords.

Basic diatonic is in 5ed4/3, which is a very good fourth-based equal tuning similar to 12edo.

Notation

There are 4 main ways to notate this scale. One method uses a simple fourth repeating notation consisting of 3 naturals (eg. Do Re Mi, Sol La Si). Given that 1-5/4-3/2 is fourth-equivalent to a tone cluster of 1-9/8-5/4, it may be more convenient to notate diatonic scales as repeating at the double, triple, quadruple or quintuple fourth (minor seventh, tenth, thirteenth or sixteenth), however it does make navigating the genchain harder. This way, 3/2 is its own pitch class, distinct from 9/8. Notating this way produces a minor tenth which is the Dorian mode of Middletown[6L 3s], also known as the Mahur scale in Persian/Arabic music, a minor thirteenth which is the Aeolian mode of Bijou[8L 4s] or a minor sixteenth which is the Phrygian mode of Hyperionic. Since there are exactly 9 naturals in triple fourth notation, 12 in quadruple fourth and 15 in quintuple fourth notation, letters A-G plus J, Q or Q, S (GJABCQDEF or GABCQDSEF, flats written F molle) or dozenal or hex digits (0123456789XE0 or E1234567GABDE with flats written D molle or 123456789ABCDEF1 with flats written F molle) may be used.

Cents

Notation					Supersoft	Soft	Semisoft	Basic	Semihard	Hard	Superhard
Diatonic		Mahur	Bijou	Hyperionic	~11ed4/3	~8ed4/3	~13ed4/3	~5ed4/3	~12ed4/3	~7ed4\3	~9ed4/3
Fourth	Seventh
Do#, Sol#	Sol#	G#	0#, D#	1#	1\11 46; 6.5	1\8 63; 6.3	2\13 77; 2, 2.6	1\5 100	3\12 124; 7.25	2\7 141; 5.6	3\9 163.63
Reb, Lab	Lab	Jf, Af	1b, 1d	2f	3\11 138; 3.25	2\8 126; 3.16	3\13 116; 7.75		2\12 82; 1.318	1\7 70; 1.7	1\9 54.54
Re, La	La	J, A	1	2	4\11 184; 1.625	3\8 189; 2.1	5\13 193; 1, 1, 4.6	2\5 200	5\12 206; 1, 8.6	3\7 211; 1, 3.25	4\9 218.18
Re#, La#	La#	J#, A#	1#	2#	5\11 230; 1.3	4\8 252; 1.583	7\13 270; 1.03	3\5 300	8\12 331; 29	5\7 352; 1.0625	7\9 381.81
Mib, Sib	Sib	Af, Bf	2b, 2d	3f	7\11 323; 13	5\8 315; 1.26	8\13 309; 1, 2.1		7\12 289; 1, 1.9	4\7 282; 2.83	5\9 272.72
Mi, Si	Si	A, B	2	3	8\11 369; 4.3	6\8 378; 1.05	10\13 387; 10.3	4\5 400	10\12 413; 1, 3.83	6\7 423; 1.8	8\9 436.36
Mi#, Si#	Si#	A#, B#	2#	3#	9\11 415; 2.6	7\8 442; 9.5	12\13 464; 1.9375	5\5 500	13\12 537; 14.5	8\7 564; 1.416	11\9 600
Dob, Solb	Dob	Bb, Cf	3b, 3d	4f	10\11 461; 1, 1.16		11\13 425; 1.24	4\5 400	9\12 372; 2.416	5\7 352; 1.0625	6\9 327.27
Do, Sol	Do	B, C	3	4	11\11 507; 1.4	8\8 505; 3.8	13\13 503; 4, 2.3	5\5 500	12\12 496; 1.8125	7\7 494; 8.5	9\9 490.90
Do#, Sol#	Do#	B#, C#	3#	4#	12\11 553; 1.18	9\8 568; 2.375	15\13 580; 1.55	6\5 600	15\12 620; 1.45	9\7 635; 3.4	12\9 654.54
Reb, Lab	Reb	Cf, Qf	4b, 4d	5f	14\11 646; 6.5	10\8 631; 1.72	16\13 619; 2.81		14\12 579; 3.2	8\7 564; 1.416	10\9 545.45
Re, La	Re	C, Q	4	5	15\11 692; 3.25	11\8 694; 1, 2.8	18\13 696; 1.2916	7\5 700	17\12 703; 2, 2.16	10\7 705; 1.13	13\9 709.09
Re#, La#	Re#	C#, Q#	4#	5#	16\11 738; 2.16	12\8 757; 1, 8.5	20\13 774; 5.16	8\5 800	20\12 827; 1, 1.416	12\7 847; 17	16\9 872.72
Mib, Sib	Mib	Qf, Df	5b, 5d	6f	18\11 830; 1.3	13\8 821; 19	21\13 812; 1, 9.3		19\12 786; 4.83	11\7 776; 2.125	14\9 763.63
Mi, Si	Mi	Q, D	5	6	19\11 876; 1.083	14\8 884; 4.75	23\13 890; 3.1	9\5 900	22\12 910; 2.9	13\7 917; 1.54	17\9 927.27
Mi#, Si#	Mi#	Q#, D#	5#	6#	20\11 923: 13	15\8 947; 2, 1.4	25\13 967; 1, 2.875	10\5 1000	25\12 1034; 2, 14	15\7 1058; 1, 4.6	20\9 1090.90
Dob, Solb	Solb	Df, Sf	6b, 6d	7f	21\11 969; 4.3		24\13 929; 31	9\5 900	21\12 868; 1, 28	11\7 776; 2.125	15\9 818.18
Do, Sol	Sol	D, S	6	7	22\11 1015; 2.6	16\8 1010; 1.9	26\13 1006; 2, 4.6	10\5 1000	24\12 993; 9.6	14\7 988; 4.25	18\9 981.81
Do#, Sol#	Sol#	D#, S#	6#	7#	23\11 1061; 1, 1.16	17\8 1073; 1, 2.16	28\13 1083; 1.148	11\5 1100	27\12 1117; 4, 7	16\7 1129; 2, 2.3	24\9 1309.09
Reb, Lab	Lab	Ef	7b, 7d	8f	25\11 1153; 1.18	18\8 1136; 1.1875	29\13 1122; 1.72		26\12 1075; 1.16	15\7 1058; 1, 4.6	19\9 1036.36
Re, La	La	E	7	8	26\11 1200	19\8 1200	31\13 1200	12\5 1200	29\12 1200	17\7 1200	22\9 1200
Re#, La#	La#	E#	7#	8#	27\11 1246; 6,5	20\8 1263; 6.3	33\13 1277; 2, 2.6	13\5 1300	32\12 1324; 7.25	19\7 1341; 5.6	25\9 1363.63
Mib, Sib	Sib	Ff	8b, Fd	9f	29\11 1338; 3.25	21\8 1326; 3.16̄	34\13 1316; 7.75		31\12 1282; 1.318	18\7 1270; 1.7	23\9 1254.54
Mi, Si	Si	F	8, F	9	30\11 1384; 1.625	22\8 1389; 2.1̄	36\13 1393; 1, 1, 4.6	14\5 1400	34\12 1406; 1, 8.6	20\7 1411; 1, 3.25	26\9 1418.18
Mi#, Si#	Si#	F#	8#, F#	9#	31\11 1430; 1.3	23\8 1452; 1.583	38\13 1470; 1.03	15\5 1500	37\12 1531; 29	22\7 1552; 1.0625	29\9 1581.81
Dob, Solb	Dob	Gf	9b, Gd	Af	32\11 1476; 1.083		37\13 1432: 3.875	14\5 1400	33\12 1365; 1.93	19\7 1341; 5.3	24\9 1309.09
Do, Sol	Do	G	9, G	A	33\11 1523; 13	24\8 1515; 1.26	39\13 1509; 1, 2.1	15\5 1500	36\12 1489; 1, 1.9	21\7 1482; 2.83	27\9 1472.72
Do#, Sol#	Do#	G#	9#, G#	A#	34\11 1569; 4.3	25\8 1578; 1.05̄	41\13 1587; 10.3	16\5 1600	39\12 1613; 1, 3.83	23\7 1623; 1.8	30\9 1636.36
Reb, Lab	Reb	Jf, Af	Xb, Ad	Bf	36\11 1661; 1, 1.16	26\8 1642; 9.5	42\13 1625; 1.24		38\12 1572; 29	22\7 1552; 1.0625	28\9 1527.27
Re, La	Re	J, A	X, A	B	37\11 1707; 1.4	27\8 1705; 3.8	44\13 1703; 4, 2.3̄	17\5 1700	41\12 1696; 1.8125	24\7 1694; 8.5	31\9 1690.90
Re#, La#	Re#	J#, A#	X#, A#	B#	38\11 1753; 1.18	28\8 1768; 2.375	46\13 1780; 1.55	18\5 1800	44\12 1820; 1.45	26\7 1835; 3,4	34\9 1854.54
Mib, Sib	Mib	Af, Bf	Eb, Bd	Cf	40\11 1846; 6.5	29\8 1831; 1.72	47\13 1819; 2.81		43\12 1779; 3.2	25\7 1764; 1, 3.25	32\9 1745.45
Mi, Si	Mi	A, B	E, B	C	41\11 1892; 3.25	30\8 1894; 1, 2.8	49\13 1896; 1.2916	19\5 1900	46\12 1903; 2, 2.16	27\7 1905; 1, 7.5	35\9 1909.09
Mi#, Si#	Mi#	A#, B#	E#, B#	C#	42\11 1938; 2.16	31\8 1957; 1, 8.5	51\13 1974; 5.16	20\5 2000	49\12 2027; 1, 1.416	29\7 2047; 17	38\9 2072.72
Dob, Solb	Solb	Bb, Cf	0b, Dd	Df	43\15 1984; 1.625		50\13 1935; 2.06	19\5 1900	45\12 1862; 14.5	26\7 1835; 3,4	33\9 1800
Do, Sol	Sol	B, C	0, D	D	44\11 2030; 1.3	32\8 2021; 19	52\13 2012; 1, 9.3	20\5 2000	48\12 1986; 4.83	28\7 1976; 2.125	36\9 1963.63
Do#, Sol#	Sol#	B#, C#	0#, D#	D#	45\11 2076; 1.083	33\8 2084; 4.75	54\13 2090; 3.1	21\5 2100	51\12 2110; 2.9	30\7 2117; 1.54	39\9 2127.27
Reb, Lab	Lab	Cf, Qf	1b, 1d	Ef	47\11 2169; 4.3	34\8 2147; 2, 1.4	55\13 2129; 31		50\12 2068; 1, 28	29\7 2047; 17	37\9 2018.18
Re, La	La	C, Q	1	E	48\11 2215; 2.6	35\8 2210; 1.9	57\13 2206; 2, 4.6	22\5 2200	53\12 2193; 9.6	31\7 2188; 4.25	40\9 2181.81
Re#, La#	La#	C#, Q#	1#	E#	49\11 2261; 1, 1.16	36\8 2273; 1, 2.16	59\13 2083; 1.148	23\5 2300	56\12 2327; 4, 7	33\7 2329; 2, 2.3	43\9 2345.45
Mib, Sib	Sib	Qf, Df	2b, 2d	Ff	51\11 2353; 1.18	37\8 2336; 1.1875	61\13 2322; 1.72		55\12 2275; 1.16	32\7 2258; 1, 4.6	41\9 2236.36
Mi, Si	Si	Q, D	2	F	52\11 2400	38\8 2400	62\13 2400	24\5 2400	58\12 2400	34\7 2400	44\9 2400
Mi#, Si#	Si#	Q#, D#	2#	F#	53\11 2446; 6.5	39\8 2463; 6.3	64\13 2477; 2, 2.6	25\5 2500	61\12 2524; 7.25	36\7 2541; 5.6	47/9 2563.63
Dob, Solb	Dob	Df, Sf	3b, 3d	1f	54\11 2492; 3.25		63\13 2438; 1.136	24\5 2400	57\12 2358; 1.61̄	33\7 2329; 2, 2.3	42\9 2390.90
Do, Sol	Do	D, S	3	1	55\11 2538; 2.16	40\8 2526; 3.16	65\13 2516; 7.75	25\5 2500	60\12 2482; 1.318	35\7 2470; 1.7	45\9 2454.54

Relative cents

Notation					Supersoft	Soft	Semisoft	Basic	Semihard	Hard	Superhard
Diatonic		Mahur	Bijou	Hyperionic	~11ed4/3	~8ed4/3	~13ed4/3	~5ed4/3	~12ed4/3	~7ed4\3	~9ed4/3
Fourth	Seventh
Do#, Sol#	Sol#	G#	0#, D#	1#	1\11 45.45	1\8 62.5	2\13 76; 1.083	1\5 100	3\12 125	2\7 142; 1.16	3\9 166.6
Reb, Lab	Lab	Jf, Af	1b, 1d	2f	3\11 136.36	2\8 125	3\13 115; 2.6		2\12 83.3	1\7 71; 2.3	1\9 55.5̄
Re, La	La	J, A	1	2	4\11 181.81	3\8 187.5	5\13 192; 3.25	2\5 200	5\12 208.3	3\7 214; 3.5	4\9 222.2
Re#, La#	La#	J#, A#	1#	2#	5\11 227.27	4\8 250	7\13 269; 4.3	3\5 300	8\12 333.3	5\7 357; 7	7\9 388.8
Mib, Sib	Sib	Af, Bf	2b, 2d	3f	7\11 318.18	5\8 312.5	8\13 307; 1.4		7\12 291.6̄	4\7 285; 1.4	5\9 277.7
Mi, Si	Si	A, B	2	3	8\11 363.63	6\8 375	10\13 384; 1.625	4\5 400	10\12 416.6	6\7 428; 1.75	8\9 444.4
Mi#, Si#	Si#	A#, B#	2#	3#	9\11 409.09	7\8 437.5	12\13 461; 1, 1.16	5\5 500	13\12 541.6	8\7 571; 2.3	11\9 611.1̄
Dob, Solb	Dob	Bb, Cf	3b, 3d	4f	10\11 454.54		11\13 423; 13	4\5 400	9\12 375	5\7 357; 7	6\9 333.3
Do, Sol	Do	B, C	3	4	500
Do#, Sol#	Do#	B#, C#	3#	4#	12\11 545.45	9\8 562.5	15\13 576; 1.083	6\5 600	15\12 625	9\7 642; 1.16	12\9 666.6
Reb, Lab	Reb	Cf, Qf	4b, 4d	5f	14\11 636.36	10\8 625	16\13 615; 2.6		14\12 583.3	8\7 571; 2.3	10\9 555.5̄
Re, La	Re	C, Q	4	5	15\11 681.81	11\8 687.5	18\13 692; 3.25	7\5 700	17\12 708.3	10\7 714; 3.5	13\9 722.2
Re#, La#	Re#	C#, Q#	4#	5#	16\11 727.27	12\8 750	20\13 769; 4.3	8\5 800	20\12 833.3	12\7 857; 7	16\9 888.8
Mib, Sib	Sib	Qf, Df	5b, 5d	6f	18\11 818.18	13\8 812.5	21\13 807; 1.4		19\12 791.6	11\7 785; 1.4	14\9 777.7
Mi, Si	Si	Q, D	5	6	19\11 863.63	14\8 875	23\13 884; 1.625	9\5 900	22\12 916.6	13\7 928; 1.75	17\9 944.4
Mi#, Si#	Si#	Q#, D#	5#	6#	20\11 909.09	15\8 937.5	25\13 961; 1, 1.16	10\5 1000	25\12 1041.6	15\7 1071; 2.3	20\9 1111.1̄
Dob, Solb	Solb	Df, Sf	6b, 6d	7f	21\11 954.54		24\13 923; 13	9\5 900	21\12 875	12\7 857; 7	15\9 833.3
Do, Sol	Sol	D, S	6	7	1000
Do#, Sol#	Sol#	D#, S#	6#	7#	23\11 1045.45	17\8 1062.5	28\13 1076; 1.083	11\5 1100	27\12 1125	16\7 1142; 1.16	21\9 1166.6
Reb, Lab	Lab	Ef	7b, 7d	8f	25\11 1136.36	18\8 1125	29\13 1115; 2.6		26\12 1083.3	22\7 1571; 2.3	19\9 1055.5̄
Re, La	La	E	7	8	26\11 1181.81	19\8 1187.5	31\13 1192; 3.25	12\5 1200	29\12 1208.3	17\7 1214; 3.5	22\9 1222.2
Re#, La#	La#	E#	7#	8#	27\11 1227.27	20\8 1250	33\13 1269; 4.3	13\5 1300	32\12 1333.3	19\7 1357; 7	25\9 1388.8
Mib, Sib	Sib	Ff	8b, Fd	9f	29\11 1318.18	21\8 1312.5	34\13 1307; 1.4		31\12 1291.6	18\7 1285; 1.4	23\9 1277.7
Mi, Si	Si	F	8, F	9	30\11 1363.63	22\8 1375	36\13 1384; 1.625	14\5 1400	34\12 1416.6	20\7 1428; 1.75	26\9 1444.4
Mi#, Si#	Si#	F#	8#, F#	9#	31\11 1409.09	23\8 1437.5	38\13 1461; 1, 1.16	15\5 1500	37\12 1541.6	22\7 1571; 2.3	29\9 1611.1̄
Dob, Solb	Dob	Gf	9b, Gd	Af	32\11 1454.54		37\13 1423; 13	14\5 1400	33\12 1375	19\7 1357; 7	24\9 1333.3
Do, Sol	Do	G	9, G	A	1500
Do#, Sol#	Sol#	G#	9#, G#	A#	34\11 1545.45	25\8 1562.5	41\13 1576; 1.083	16\5 1600	39\12 1625	23\7 1642; 1.16	30\9 1666.6
Reb, Lab	Lab	Jf, Af	Xb, Ad	Bf	36\11 1636.36	26\8 1625	42\13 1615; 2.6		38\12 1583.3	22\7 1571; 2.3	28\9 1555.5̄
Re, La	La	J, A	X, A	B	37\11 1681.81	27\8 1687.5	44\13 1692; 3.25	17\5 1700	41\12 1708.3	24\7 1714; 3.5	31\9 1722.2
Re#, La#	La#	J#, A#	X#, A#	B#	38\11 1727.27	28\8 1750	46\13 1769; 4.3	18\5 1800	44\12 1833.3	26\7 1857; 7	34\9 1888.8
Mib, Sib	Sib	Af, Bf	Eb, Bd	Cf	40\11 1818.18	29\8 1812.5	47\13 1807; 1.4		43\12 1791.6	25\7 1785; 1.4	32\9 1777.7
Mi, Si	Si	A, B	E, B	C	41\11 1863.63	30\8 1875	49\13 1884; 1.625	19\5 1900	46\12 1916.6	27\7 1928; 1.75	35\9 1944.4
Mi#, Si#	Si#	A#, B#	E#, B#	C#	42\11 1909.09	31\8 1937.5	51\13 1961; 1, 1.16	20\5 2000	49\12 2041.6	29\7 2071; 2.3	38\9 2111.1̄
Dob, Solb	Dob	Bb, Cf	0b, Dd	Df	43\11 1954.54		50\13 1923; 13	19\5 1900	45\12 1875	26\7 1857; 7	33\9 1833.3
Do, Sol	Sol	B, C	0, D	D	2000
Do#, Sol#	Sol#	B#, C#	0#, D#	D#	45\11 2045.45	33\8 2062.5	54\13 2076; 1.083	21\5 2100	51\12 2125	30\7 2142; 1.16	39\9 2166.6
Reb, Lab	Lab	Cf, Qf	1b, 1d	Ef	47\11 2136.36	34\8 2125	55\13 2115; 2.6		50\12 2083.3	29\7 2071; 2.3	37\9 2055.5̄
Re, La	La	C, Q	1	E	48\11 2181.81	35\8 2187.5	57\13 2192; 3.25	22\5 2200	53\12 2208.3	31\7 2214; 3.5	40\9 2222.2
Re#, La#	La#	C#, Q#	1#	E#	49\11 2227.27	36\8 2250	59\13 2269; 4.3	23\5 2300	56\12 2333.3	33\7 2357; 7	43\9 2388.8
Mib, Sib	Sib	Qf, Df	2b, 2d	Ff	51\11 2318.18	37\8 2312.5	60\13 2307; 1.4		55\12 2291.6	32\7 2285; 1.4	41\9 2277.7
Mi, Si	Si	Q, D	2	F	52\11 2363.63	38\8 2375	62\13 2384; 1.625	24\5 2400	58\12 2416.6	34\7 2428; 1.75	44\9 2444.4
Mi#, Si#	Si#	Q#, D#	2#	F#	53\11 2409.09	39\8 2437.5	64\13 2461; 1, 1.16	25\5 2500	61\12 2541.6	36\7 2571; 2.3̄	47\9 2611.1̄
Dob, Solb	Dob	Df, Sf	3b, 3d	1f	54\11 2454.54		63\13 2423; 13	24\5 2400	57\12 2375	33\7 2357; 7	42\9 2333.3
Do, Sol	Do	D, S	3	1	2500

Intervals

Generators	Fourth notation	Interval category name	Generators	Notation of 4/3 inverse	Interval category name
The 3-note MOS has the following intervals (from some root):
0	Do, Sol	perfect unison	0	Do, Sol	perfect fourth
1	Mib, Sib	diminished third	-1	Re, La	perfect second
2	Reb, Lab	diminished second	-2	Mi, Si	perfect third
The chromatic 5-note MOS also has the following intervals (from some root):
3	Dob, Solb	diminished fourth	-3	Do#, Sol#	augmented unison (chroma)
4	Mibb, Sibb	doubly diminished third	-4	Re#, La#	augmented second

Genchain

The generator chain for this scale is as follows:

Mibb Sibb	Dob Solb	Reb Lab	Mib Sib	Do Sol	Re La	Mi Si	Do# Sol#	Re# La#	Mi# Si#
dd3	d4	d2	d3	P1	P2	P3	A1	A2	A3

Modes

The mode names are based on the species of fourth:

Mode	Scale	UDP	Interval type
name	pattern	notation	2nd	3rd
Major	LLs	2|0	P	P
Minor	LsL	1|1	P	d
Phrygian	LsLL	0|2	d	d

Temperaments

The most basic rank-2 temperament interpretation of diatonic is Mahuric. The name "Mahuric" comes from the “Mahur” scale in Persian and Arabic music. The major triad is spelled root-2g-(p+g) (p = 4/3, g = the whole tone) and approximates 4:5:6 in pental interpretations or 14:18:21 in septimal ones. Basic ~5ed4/3 fits both interpretations.

Mahuric-Meantone

Subgroup: 4/3.5/4.3/2

Comma list: 81/80

POL2 generator: ~9/8 = [[1]]

Mapping: [⟨1 0 1], ⟨0 2 1]]

Optimal ET sequence: ~(5ed4/3, 8ed4/3, 13ed4/3)

Mahuric-Superpyth

Subgroup: 4/3.9/7.3/2

Comma list: 64/63

POL2 generator: ~8/7 = [[2]]

Mapping: [⟨1 0 1], ⟨0 2 1]]

Optimal ET sequence: ~(5ed4/3, 7ed4/3, 9ed4/3, 11ed4/3)

Scale tree

The spectrum looks like this:

Generator (bright)			Cents		L	s	L/s	Comments
			Normalised	ed5\12
1\3			171; 2.3	166.6	1	1	1.000	Equalised
6\17			180	176; 2.125	6	5	1.200
	11\31		180; 1.216	177; 2, 2.6	11	9	1.222
5\14			181.81	178; 1.75	5	4	1.250
	14\39		182; 1, 1.5	179; 2, 19	14	11	1.273
	9\25		183; 19.6	180	9	7	1.286
4\11			184; 1.625	181.81	4	3	1.333
	15\41		185; 1.763	182; 1, 12.6	15	11	1.364
	11\30		185, 1, 10.83	183.3	11	8	1.375
	7\19		186.6	184; 4.75	7	5	1.400
	10\27		187.5	185.185	10	7	1.429
	13\35		187; 1, 19.75	185; 1.4	13	9	1.444
	16\43		188; 4.25	186; 21.5	16	11	1.4545
3\8			189; 2.1	187.5	3	2	1.500	Mahuric-Meantone starts here
	17\45		190; 1, 1.12	188.8	17	11	1.5455
	14\37		190.90	189.189	14	9	1.556
	11\29		191; 3, 2.3	189; 1, 1.9	11	7	1.571
	8\21		192	190; 2.1	8	5	1.600
		13\34	192.592	191; 5.6	13	8	1.625
	5\13		193; 1, 1, 4.6	192; 4.3	5	3	1.667
		12\31	194.594	193; 1, 1, 4.6	12	7	1.714
	7\18		195; 2.86	194.4	7	4	1.750
	9\23		196.36	195; 1.53	9	5	1.800
	11\28		197; 67	196; 2.3	11	6	1.833
	13\33		197; 2.135	196.96	13	7	1.857
	15\38		197; 1, 2, 1, 1.54	197; 2, 1.4	15	8	1.875
	17\43		198; 17.16	197; 1, 2, 14	17	9	1.889
	19\48		198: 3, 1, 28	197.916	19	10	1.900
	21\53		198; 2.3518	198; 8.83	21	11	1.909
	23\58		198; 1, 3, 1.7	198; 3.625	23	12	1.917
	25\63		198; 1, 2, 12.25	198; 2, 2.36	25	13	1.923
	27\68		198; 1, 3.405	198; 1.8	27	14	1.929
	29\73		198; 1, 1.16	198; 1, 1.703	29	15	1.933
	31\78		198; 1, 12, 2.8	198; 1, 2.54	31	16	1.9375
	33\83		198; 1.005	198; 1.257	33	17	1.941
	35\88		199; 19.18	198.863	35	18	1.944
2\5			200	200	2	1	2.000	Mahuric-Meantone ends, Mahuric-Pythagorean begins
	17\42		201.9801	202; 2.625	17	8	2.125
	15\37		202; 4.045	202.702	15	7	2.143
	13\32		202; 1, 1, 2.06	203.125	13	6	2.167
	11\27		203; 13	203.703	11	5	2.200
	9\22		203; 1, 3.416	204.54	9	4	2.250
	7\17		204; 1. 7.2	205; 1.13	7	3	2.333
		12\29	205; 1.4	206; 1, 8.6	12	5	2.400
		17\41	206.06	207; 3, 6.5	17	7	2.429
	5\12		206; 1, 8.6	208.3	5	2	2.500	Mahuric-Neogothic heartland is from here…
		18\43	207; 1.4	209; 3, 4.3	18	7	2.571
		13\31	208	209; 1, 2.1	13	5	2.600
	8\19		208; 1.4375	210; 1.9	8	3	2.667	…to here
	11\26		209; 1.90	211; 1, 1.16	11	4	2.750
	14\33		210	212.12	14	5	2.800
	17\40		210; 3.23	212.5	17	6	2.833
	20\47		210; 1.9	212; 1.30	20	7	2.857
	23\54		210; 1.45	212.962	23	8	2.875
	26\61		210.810	213; 8, 1.4	26	9	2.889
3\7			211; 1, 3.25	214; 3.5	3	1	3.000	Mahuric-Pythagorean ends, Mahuric-Superpyth begins
	22\51		212; 1, 9.3	215; 1, 2,1875	22	7	3.143
	19\44		213; 11.8	215.90	19	6	3.167
	16\37		213.3̄	216.216	16	5	3.200
	13\30		213; 1, 2.318	216.6	13	4	3.250
	10\23		214; 3.5	217; 5.75	10	3	3.333
	7\16		215; 2.6	218.75	7	2	3.500
		18\41	216	219; 1, 1.05	18	5	3.600
	11\25		216; 2.5416	220	11	3	3.667
	15\34		216; 1.1527	220; 1.7	15	4	3.750
	19\43		217; 7	220; 1, 7.6	19	5	3.800
	23\52		217; 3, 10.25	221; 6.5	23	6	3.833
4\9			218.18	222.2	4	1	4.000
	17\38		219; 1, 2.90	223; 1.583	17	4	4.250
	13\29		219; 1, 2.55	224; 7.25	13	3	4.333
	9\20		220; 2.45	225	9	2	4.500
	14\31		221; 19	225; 1.24	14	3	4.667
	19\42		221; 2.783	226; 4.2	19	4	4.750
5\11			222.2	227.27	5	1	5.000	Mahuric-Superpyth ends
	16\35		223; 3.90	228; 1.75	16	3	5.333
	11\24		223; 1, 2.6875	229.16	11	2	5.500
	17\37		224; 5.72	229.729	17	3	5.667
6\13			225	230; 1.3	6	1	6.000
1\3			240	250	1	0	→ inf	Paucitonic

See also

2L 1s (4/3-equivalent) - idealized tuning