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, quintuple or sextuple fourth (minor seventh, tenth, thirteenth or sixteenth or diminished nineteenth), 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]; the bastonic chromatic scale, a minor sixteenth which is the Phrygian mode of Hyperionic[10L 5s] or a diminished nineteenth which is the Locrian mode of Subsextal[12L 6s]. Since there are exactly 9 naturals in triple fourth notation, 12 in quadruple fourth, 15 in quintuple fourth and 18 in sextuple fourth notation, letters A-G plus J, Q or Q, S (GJABCQDEF or GABCQDSEF, flats written F molle) or dozenal, hex or duohex digits (0123456789XE0 or E1234567GABDE with flats written D molle or 123456789ABCDEF1 or 0123456789XɜABCDEF0 with flats written F molle) may be used.

Cents

Notation		Supersoft	Soft	Semisoft	Basic	Semihard	Hard	Superhard
Fourth	Seventh	~11ed4/3	~8ed4/3	~13ed4/3	~5ed4/3	~12ed4/3	~7ed4\3	~9ed4/3
Do#, Sol#	Sol#	1\11, 46.154	1\8, 63.158	2\13, 77.419	1\5, 100	3\12, 124.138	2\7, 141.176	3\9, 163.63
Reb, Lab	Lab	3\11, 138.462	2\8, 126.316	3\13, 116.129		2\12, 82.759	1\7, 70.588	1\9, 54.54
Re, La	La	4\11, 184.615	3\8, 189.474	5\13, 193.548	2\5, 200	5\12, 206.897	3\7, 211.765	4\9, 218.18
Re#, La#	La#	5\11, 230.769	4\8, 252.632	7\13, 270.967	3\5, 300	8\12, 331.034	5\7, 352.941	7\9, 381.81
Mib, Sib	Sib	7\11, 323.077	5\8, 315.789	8\13, 309.677		7\12, 289.655	4\7, 282.353	5\9, 272.72
Mi, Si	Si	8\11, 369.231	6\8, 378.947	10\13, 387.097	4\5, 400	10\12, 413.793	6\7, 423.529	8\9, 436.36
Mi#, Si#	Si#	9\11, 415.385	7\8, 442.105	12\13, 464.516	5\5, 500	13\12, 537.069	8\7, 564.705	11\9, 600
Dob, Solb	Dob	10\11, 461.538		11\13, 425.806	4\5, 400	9\12, 372.414	5\7, 352.941	6\9, 327.27
Do, Sol	Do	11\11, 507.692	8\8, 505.263	13\13, 503.226	5\5, 500	12\12, 496.552	7\7, 494.118	9\9, 490.90
Do#, Sol#	Do#	12\11, 553.846	9\8, 568.421	15\13, 580.645	6\5, 600	15\12, 620.690	9\7, 635.294	12\9, 654.54
Reb, Lab	Reb	14\11, 646.154	10\8, 631.579	16\13, 619.355		14\12, 579.310	8\7, 564.706	10\9, 545.45
Re, La	Re	15\11, 692.308	11\8 694.737	18\13, 696.774	7\5, 700	17\12, 703.448	10\7, 705.882	13\9, 709.09
Re#, La#	Re#	16\11, 738.462	12\8, 757.895	20\13, 774.294	8\5, 800	20\12, 827.586	12\7, 847.059	16\9, 872.72
Mib, Sib	Mib	18\11, 830.769	13\8, 821.053	21\13, 812.903		19\12, 786.207	11\7, 776.471	14\9, 763.63
Mi, Si	Mi	19\11, 876.923	14\8, 884.211	23\13, 890.323	9\5, 900	22\12, 910.345	13\7, 917.647	17\9, 927.27
Mi#, Si#	Mi#	20\11, 923.077	15\8, 947.378	25\13, 967.742	10\5, 1000	25\12, 1034.483	15\7, 1058.824	20\9, 1090.90
Dob, Solb	Solb	21\11, 969.231		24\13, 929.033	9\5, 900	21\12, 868.966	11\7, 776.471	15\9, 818.18
Do, Sol	Sol	22\11, 1015.385	16\8, 1010.526	26\13, 1006.452	10\5, 1000	24\12, 993.103	14\7, 988.235	18\9, 981.81

Notation		Supersoft	Soft	Semisoft	Basic	Semihard	Hard	Superhard
Mahur	Bijou	~11ed4/3	~8ed4/3	~13ed4/3	~5ed4/3	~12ed4/3	~7ed4\3	~9ed4/3
G#	0#, E#	1\11, 46.154	1\8, 63.158	2\13, 77.419	1\5, 100	3\12, 124.138	2\7, 141.176	3\9, 163.63
Jf, Af	1b, 1d	3\11, 138.462	2\8, 126.316	3\13, 116.129		2\12, 82.759	1\7, 70.588	1\9, 54.54
J, A	1	4\11, 184.615	3\8, 189.474	5\13, 193.548	2\5, 200	5\12, 206.897	3\7, 211.765	4\9, 218.18
J#, A#	1#	5\11, 230.769	4\8, 252.632	7\13, 270.968	3\5, 300	8\12, 331.034	5\7, 352.941	7\9, 381.81
Af, Bf	2b, 2d	7\11, 323.077	5\8, 315.789	8\13, 309.677		7\12, 289.655	4\7, 282.353	5\9, 272.72
A, B	2	8\11, 369.231	6\8, 378.947	10\13, 387.097	4\5, 400	10\12, 413.793	6\7, 423.529	8\9, 436.36
A#, B#	2#	9\11, 415.385	7\8, 442.105	12\13, 464.516	5\5, 500	13\12, 537.069	8\7, 564.705	11\9, 600
Bb, Cf	3b, 3d	10\11, 461.538		11\13, 425.806	4\5, 400	9\12, 372.414	5\7, 352.941	6\9, 327.27
B, C	3	11\11, 507.692	8\8, 505.263	13\13, 503.226	5\5, 500	12\12, 496.552	7\7, 494.118	9\9, 490.90
B#, C#	3#	12\11, 553.846	9\8, 568.421	15\13, 580.645	6\5, 600	15\12, 620.690	9\7, 635.294	12\9, 654.54
Cf, Qf	4b, 4d	14\11, 646.154	10\8, 631.579	16\13, 619.355		14\12, 579.310	8\7, 564.706	10\9, 545.45
C, Q	4	15\11, 692.308	11\8 694.737	18\13, 696.774	7\5, 700	17\12, 703.448	10\7, 705.882	13\9, 709.09
C#, Q#	4#	16\11, 738.462	12\8, 757.895	20\13, 774.194	8\5, 800	20\12, 827.586	12\7, 847.059	16\9, 872.72
Qf, Df	5b, 5d	18\11, 830.769	13\8, 821.053	21\13, 812.903		19\12, 786.207	11\7, 776.471	14\9, 763.63
Q, D	5	19\11, 876.923	14\8, 884.211	23\13, 890.323	9\5, 900	22\12, 910.345	13\7, 917.647	17\9, 927.27
Q#, D#	5#	20\11, 923.077	15\8, 947.368	25\13, 967.742	10\5, 1000	25\12, 1034.483	15\7, 1058.824	20\9, 1090.90
Df, Sf	6b, 6d	21\11, 969.231		24\13, 929.033	9\5, 900	21\12, 868.966	11\7, 776.471	15\9, 818.18
D, S	6	22\11, 1015.385	16\8, 1010.526	26\13, 1006.452	10\5, 1000	24\12, 993.103	14\7, 988.235	18\9, 981.81
D#, S#	6#	23\11, 1061.538	17\8, 1073.684	28\13, 1083.871	11\5, 1100	27\12, 1117.241	16\7, 1129.412	21\9, 1145.45
Ef	7b, 7d	25\11, 1153.846	18\8, 1136.842	29\13, 1122.581		26\12, 1075.862	15\7, 1058.824	19\9, 1036.36
E	7	26\11, 1200	19\8, 1200	31\13, 1200	12\5, 1200	29\12, 1200	17\7, 1200	22\9, 1200
E#	7#	27\11, 1246.154	20\8, 1263.158	33\13, 1277.419	13\5, 1300	32\12, 1324.138	19\7, 1341.176	25\9, 1363.63
Ff	8b, Gd	29\11, 1338.462	21\8, 1326.316	34\13, 1316.129		31\12, 1282.759	18\7, 1270.588	23\9, 1254.54
F	8, G	30\11, 1384.615	22\8, 1389.474	36\13, 1393.548	14\5, 1400	34\12, 1406.897	20\7, 1411.765	26\9, 1418.18
F#	8#, G#	31\11, 1430.769	23\8, 1452.632	38\13, 1470.968	15\5, 1500	37\12, 1531.034	22\7, 1552.941	29\9, 1581.81
Gf	9b, Ad	32\11, 1476.923		37\13, 1432.258	14\5, 1400	33\12, 1365.517	19\7, 1341.176	24\9, 1309.09
G	9, A	33\11, 1523.077	24\8, 1515.789	39\13, 1509.677	15\5, 1500	36\12, 1489.655	21\7, 1482.353	27\9, 1472.72
G#	9#, A#	34\11, 1569.231	25\8, 1578.947	41\13, 1587.097	16\5, 1600	39\12, 1613.793	23\7, 1623.529	30\9, 1636.36
Jf, Af	Xb, Bd	36\11, 1661.538	26\8, 1642.105	42\13, 1625.806		38\12, 1572.034	22\7, 1552.941	28\9, 1527.27
J, A	X, B	37\11, 1707.692	27\8, 1705.263	44\13, 1703.226	17\5, 1700	41\12, 1696.552	24\7, 1694.118	31\9, 1690.90
J#, A#	X#, B#	38\11, 1753.846	28\8, 1768.421	46\13, 1780.645	18\5, 1800	44\12, 1820.690	26\7, 1835.294	34\9, 1854.54
Af, Bf	Eb, Dd	40\11, 1846.154	29\8, 1831.579	47\13, 1819.355		43\12, 1779.310	25\7, 1764.706	32\9, 1745.45
A, B	E, D	41\11, 1892.308	30\8, 1894.737	49\13, 1896.774	19\5, 1900	46\12, 1903.448	27\7, 1905.882	35\9, 1909.09
A#, B#	E#, D#	42\11, 1938.462	31\8, 1957.895	51\13, 1974.194	20\5, 2000	49\12, 2027.586	29\7, 2047.059	38\9, 2072.72
Bb, Cf	0b, Ed	43\11, 1984.615		50\13, 1935.484	19\5, 1900	45\12, 1862.069	26\7, 1835.294	33\9, 1800
B, C	0, E	44\11, 2030.769	32\8, 2021.053	52\13, 2012.903	20\5, 2000	48\12, 1986.207	28\7, 1976.471	36\9, 1963.63

Notation		Supersoft	Soft	Semisoft	Basic	Semihard	Hard	Superhard
Hyperionic	Subsextal	~11ed4/3	~8ed4/3	~13ed4/3	~5ed4/3	~12ed4/3	~7ed4\3	~9ed4/3
1#	0#	1\11, 46.154	1\8, 63.158	2\13, 77.419	1\5, 100	3\12, 124.138	2\7, 141.176	3\9, 163.63
2f	1f	3\11, 138.462	2\8, 126.316	3\13, 116.129		2\12, 82.759	1\7, 70.588	1\9, 54.54
2	1	4\11, 184.615	3\8, 189.474	5\13, 193.548	2\5, 200	5\12, 206.897	3\7, 211.765	4\9, 218.18
2#	1#	5\11, 230.769	4\8, 252.632	7\13, 270.967	3\5, 300	8\12, 331.034	5\7, 352.941	7\9, 381.81
3f	2f	7\11, 323.077	5\8, 315.789	8\13, 309.677		7\12, 289.655	4\7, 282.353	5\9, 272.72
3	2	8\11, 369.231	6\8, 378.947	10\13, 387.098	4\5, 400	10\12, 413.793	6\7, 423.529	8\9, 436.36
3#	2#	9\11, 415.385	7\8, 442.105	12\13, 464.516	5\5, 500	13\12, 537.069	8\7, 564.705	11\9, 600
4f	3f	10\11, 461.538		11\13, 425.806	4\5, 400	9\12, 372.414	5\7, 352.941	6\9, 327.27
4	3	11\11, 507.692	8\8, 505.263	13\13, 503.226	5\5, 500	12\12, 496.552	7\7, 494.118	9\9, 490.90
4#	3#	12\11, 553.846	9\8, 568.421	15\13, 580.645	6\5, 600	15\12, 620.690	9\7, 635.294	12\9, 654.54
5f	4f	14\11, 646.154	10\8, 631.579	16\13, 619.355		14\12, 579.310	8\7, 564.706	10\9, 545.45
5	4	15\11, 692.308	11\8 694.737	18\13, 696.774	7\5, 700	17\12, 703.448	10\7, 705.882	13\9, 709.09
5#	4#	16\11, 738.462	12\8, 757.895	20\13, 774.194	8\5, 800	20\12, 827.586	12\7, 847.059	16\9, 872.72
6f	5f	18\11, 830.769	13\8, 821.053	21\13, 812.903		19\12, 786.207	11\7, 776.471	14\9, 763.63
6	5	19\11, 876.923	14\8, 884.211	23\13, 890.323	9\5, 900	22\12, 910.345	13\7, 917.647	17\9, 927.27
6#	5#	20\11, 923.077	15\8, 947.368	25\13, 967.742	10\5, 1000	25\12, 1034.483	15\7, 1058.824	20\9, 1090.90
7f	6f	21\11, 969.231		24\13, 929.032	9\5, 900	21\12, 868.966	11\7, 776.471	15\9, 818.18
7	6	22\11, 1015.385	16\8, 1010.526	26\13, 1006.452	10\5, 1000	24\12, 993.103	14\7, 988.235	18\9, 981.81
7#	6#	23\11, 1061.538	17\8, 1073.684	28\13, 1083.871	11\5, 1100	27\12, 1117.241	16\7, 1129.412	21\9, 1145.45
8f	7f	25\11, 1153.846	18\8, 1136.842	29\13, 1122.581		26\12, 1075.862	15\7, 1058.824	19\9, 1036.36
8	7	26\11, 1200	19\8, 1200	31\13, 1200	12\5, 1200	29\12, 1200	17\7, 1200	22\9, 1200
8#	7#	27\11, 1246.154	20\8, 1263.158	33\13, 1277.419	13\5, 1300	32\12, 1324.138	19\7, 1341.176	25\9, 1363.63
9f	8f	29\11, 1338.462	21\8, 1326.316	34\13, 1316.129		31\12, 1282.759	18\7, 1270.588	23\9, 1254.54
9	8	30\11, 1384.615	22\8, 1389.474	36\13, 1393.548	14\5, 1400	34\12, 1406.897	20\7, 1411.765	26\9, 1418.18
9#	8#	31\11, 1430.769	23\8, 1452.632	38\13, 1470.968	15\5, 1500	37\12, 1531.034	22\7, 1552.941	29\9, 1581.81
Af	9f	32\11, 1476.923		37\13, 1432.258	14\5, 1400	33\12, 1365.517	19\7, 1341.176	24\9, 1309.09
A	9	33\11, 1523.077	24\8, 1515.789	39\13, 1509.677	15\5, 1500	36\12, 1489.655	21\7, 1482.353	27\9, 1472.72
A#	9#	34\11, 1569.231	25\8, 1578.947	41\13, 1587.097	16\5, 1600	39\12, 1613.793	23\7, 1623.529	30\9, 1636.36
Bf	Xb	36\11, 1661.538	26\8, 1642.105	42\13, 1625.806		38\12, 1572.034	22\7, 1552.941	28\9, 1527.27
B	X	37\11, 1707.692	27\8, 1705.263	44\13, 1703.226	17\5, 1700	41\12, 1696.552	24\7, 1694.118	31\9, 1690.90
B#	X#	38\11, 1753.846	28\8, 1768.421	46\13, 1780.645	18\5, 1800	44\12, 1820.690	26\7, 1835.294	34\9, 1854.54
Cf	ɛf	40\11, 1846.154	29\8, 1831.579	47\13, 1819.355		43\12, 1779.310	25\7, 1764.706	32\9, 1745.45
C	ɛ	41\11, 1892.308	30\8, 1894.737	49\13, 1896.774	19\5, 1900	46\12, 1903.448	27\7, 1905.882	35\9, 1909.09
C#	ɛ#	42\11, 1938.462	31\8, 1957.895	51\13, 1974.194	20\5, 2000	49\12, 2027.586	29\7, 2047.059	38\9, 2072.72
Df	Af	43\11, 1984.615		50\13, 1935.484	19\5, 1900	45\12, 1862.069	26\7, 1835.294	33\9, 1800
D	A	44\11, 2030.769	32\8, 2021.053	52\13, 2012.903	20\5, 2000	48\12, 1986.207	28\7, 1976.471	36\9, 1963.63
D#	A#	45\11, 2076.923	33\8, 2084.211	54\13, 2090.323	21\5, 2100	51\12, 2110.345	30\7, 2117.647	39\9, 2127.27
Ef	Bf	47\11, 2169.231	34\8, 2147.368	55\13, 2129.032		50\12, 2068.966	29\7, 2047.059	37\9, 2018.18
E	B	48\11, 2215.385	35\8, 2210.526	57\13, 2206.452	22\5, 2200	53\12, 2193.103	31\7, 2188.235	40\9, 2181.81
E#	B#	49\11, 2261.538	36\8, 2273.684	59\13, 2283.871	23\5, 2300	56\12, 2317.241	33\7, 2329.412	43\9, 2345.45
Ff	Cf	51\11, 2353.846	37\8, 2336.842	61\13, 2322.581		55\12, 2275.864	32\7, 2258.824	41\9, 2236.36
F	C	52\11, 2400	38\8, 2400	62\13, 2400	24\5, 2400	58\12, 2400	34\7, 2400	44\9, 2400
F#	C#	53\11, 2446.154	39\8, 2463.158	64\13, 2477.419	25\5, 2500	61\12, 2524.138	36\7, 2541.176	47/9, 2563.63
1f	Df	54\11, 2492.308		63\13, 2438.710	24\5, 2400	57\12, 2358.621	33\7, 2329.412	42\9, 2390.90
1	D	55\11, 2538.462	40\8, 2526.316	65\13, 2516.129	25\5, 2500	60\12, 2482.759	35\7, 2470.588	45\9, 2454.54
1#	D#	56\11, 2584.615	41\8, 2589.474	67\13, 2593.548	26\5, 2600	63\12, 2606.897	37\7, 2611.765	48\9, 2618.18
2f	Ef	58\11, 2676.923	42\8, 2652.632	69\13, 2670.968		62\12, 2565.517	36\7, 2541.176	46\9, 2509.09
2	E	59\11, 2723.077	43\8, 2715.789	70\13, 2709.677	27\5, 2700	65\12, 2689.655	38\7, 2682.353	49\9, 2672.72
2#	E#	60\11, 2769.231	44\8, 2778.947	72\13, 2787.097	28\5, 2800	68\12, 2813.793	40\7, 2823.529	52\9, 2836.36
3f	Ff	62\11, 2861.538	45\8, 2842.105	73\13, 2825.806		67\12, 2772.034	39\7, 2752.941	50\9, 2727.27
3	F	63\11, 2907.692	46\8, 2905.263	75\13, 2903.226	29\5, 2900	70\12, 2896.552	41\7, 2894.118	53\9, 2890.90
3#	F#	64\11, 2953.846	47\8, 2968.421	77\13, 2980.645	30\5, 3000	73\12, 3020.690	43\7, 3035.294	55\9, 3000
4f	0f	65\11, 3000		76\13, 2941.935	29\5, 2900	69\29, 2855.172	40\7, 2823.529	52\9, 2836.36
4	0	66\11, 3046.154	48\8, 3031.579	78\13, 3019.355	30\5, 3000	72\12, 2979.310	42\7, 2964.706	54\9, 2945.45

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 = 193.6725¢

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 = 216.7325¢

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
1\3	171.429	1	1	1.000	Equalised
6\17	180.000	6	5	1.200
5\14	181.81	5	4	1.250
14\39	182.609	14	11	1.273
9\25	183.051	9	7	1.286
4\11	184.615	4	3	1.333
11\30	185.915	11	8	1.375
7\19	186.6	7	5	1.400
10\27	187.500	10	7	1.429
13\35	187.952	13	9	1.444
16\43	188.253	16	11	1.4545
3\8	189.474	3	2	1.500	Mahuric-Meantone starts here
14\37	190.90	14	9	1.556
11\29	191.304	11	7	1.571
8\21	192.000	8	5	1.600
5\13	193.548	5	3	1.667
12\31	194.594	12	7	1.714
7\18	195.348	7	4	1.750
9\23	196.36	9	5	1.800
11\28	197.015	11	6	1.833
13\33	197.468	13	7	1.857
15\38	197.802	15	8	1.875
17\43	198.058	17	9	1.889
19\48	198.261	19	10	1.900
21\53	198.425	21	11	1.909
23\58	198.561	23	12	1.917
25\63	198.675	25	13	1.923
27\68	198.773	27	14	1.929
29\73	198.857	29	15	1.933
31\78	198.930	31	16	1.9375
33\83	198.995	33	17	1.941
35\88	199.052	35	18	1.944
2\5	200.000	2	1	2.000	Mahuric-Meantone ends, Mahuric-Pythagorean begins
17\42	201.9801	17	8	2.125
15\37	202.247	15	7	2.143
13\32	202.597	13	6	2.167
11\27	203.077	11	5	2.200
9\22	203.774	9	4	2.250
7\17	204.878	7	3	2.333
12\29	205.714	12	5	2.400
5\12	206.897	5	2	2.500	Mahuric-Neogothic heartland is from here…
18\43	207.693	18	7	2.571
13\31	208.000	13	5	2.600
8\19	208.696	8	3	2.667	…to here
11\26	209.524	11	4	2.750
14\33	210.000	14	5	2.800
3\7	211.755	3	1	3.000	Mahuric-Pythagorean ends, Mahuric-Superpyth begins
22\51	212.903	22	7	3.143
19\44	213.084	19	6	3.167
16\37	213.3	16	5	3.200
13\30	213.699	13	4	3.250
10\23	214.286	10	3	3.333
7\16	215.385	7	2	3.500
11\25	216.393	11	3	3.667
15\34	216.867	15	4	3.750
19\43	217.143	19	5	3.800
4\9	218.18	4	1	4.000
13\29	219.718	13	3	4.333
9\20	220.408	9	2	4.500
14\31	221.053	14	3	4.667
5\11	222.2	5	1	5.000	Mahuric-Superpyth ends
11\24	223.728	11	2	5.500
17\37	224.176	17	3	5.667
6\13	225.000	6	1	6.000
1\3	240.000	1	0	→ inf	Paucitonic

See also

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

4L 2s (7/4-equivalent) - Mixolydian Archytas temperament

4L 2s (39/22-equivalent) - Mixolydian Neogothic temperament

4L 2s (9/5-equivalent) - Mixolydian Meantone temperament

6L 3s (7/3-equivalent) - Mahuric-Archytas temperament

6L 3s (26/11-equivalent) - Mahuric-Neogothic temperament

6L 3s (12/5-equivalent) - Mahuric-Meantone temperament

8L 4s (28/9-equivalent)- Bijou Archytas temperament

8L 4s (22/7-equivalent) and 8L 4s ([math]π[/math]-equivalent) - Bijou Neogothic temperament

8L 4s (16/5-equivalent) - Bijou Meantone temperament

10L 5s (112/27-equivalent) - Hyperionic Archytas temperament

10L 5s (88/21-equivalent) - Hyperionic Neogothic temperament

10L 5s (30/7-equivalent) - Hyperionic Meantone temperament

12L 6s (11/2-equivalent) - Low undecimal Subsextal temperament

12L 6s (28/5-equivalent) - Low septimal Subsextal temperament

12L 6s (80/7-equivalent) - High septimal Subsextal temperament

12L 6s (64/11-equivalent) - High undecimal Subsextal temperament