User:Moremajorthanmajor/3L 1s (fifth equivalent)

3L 1s<3/2>, is a fifth-repeating MOS scale. The notation "<3/2>" means the period of the MOS is 3/2, disambiguating it from octave-repeating 3L 1s. The name of the period interval is called the sesquitave (by analogy to the tritave). 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 fifth complement (480 to 514.3 cents).

In the fifth-repeating version of the diatonic scale, each tone has a 3/2 perfect fifth above it. The scale has two major chords and two minor chords.

Basic Angel is in 7edf, which is a very good fifth-based equal tuning similar to 12edo.

Notation

There are 4 main ways to notate the angel scale. One method uses a simple sesquitave (fifth) repeating notation consisting of 4 naturals (eg. Do Re Mi Fa, Sol La Si Do). Given that 1-5/4-5/3 is fifth-equivalent to a tone cluster of 1-10/9-5/4, it may be more convenient to notate angel scales as repeating at the double, triple or quadruple sesquitave (major ninth, thirteenth or seventeenth i. e. ~pentave), however it does make navigating the genchain harder. This way, 5/3 is its own pitch class, distinct from 10/9. Notating this way produces a major ninth which is the Aeolian mode of Napoli[6L 2s], a major thirteenth which is the Dorian mode of Bijou[9L 3s] or an ~pentave which is the Mixolydian mode of Hextone[12L 4s]. Since there are exactly 8 naturals in double sesquitave notation, 12 in triple sesquitave notation and 16 in quadruple sesquitave notation, letters A-H (FGABHCDEF) or dozenal or hex digits (0123456789XE0 or D1234567FGACD with flats written C molle or 0123456789ABCDEF0 or G123456789ABCDEFG with flats written F molle) may be used.

Cents

Notation				Supersoft	Soft	Semisoft	Basic	Semihard	Hard	Superhard
Diatonic	Napoli	Bijou	Hextone	~15edf	~11edf	~18edf	~7edf	~17edf	~10edf	~13edf
Do#, Sol#	F#	0#, D#	0#, G#	1\15 46; 6.5	1\11 63: 6.3	2\18 77; 2, 2.6	1\7 100	3\17 124; 7.25	2\10 141; 5.6	3\13 163.63
Reb, Lab	Gb	1b, 1c	1f	3\15 138; 3.25	2\11 126; 3.16	3\18 116; 7.75		2\17 82; 1.318	1\10 70; 1.7	1\13 54.54
Re, La	G	1	1	4\15 184; 1.625	3\11 189; 2.1	5\18 193; 1, 1, 4.6	2\7 200	5\17 206; 1, 8.6	3\10 211; 1, 3.25	4\13 218.18
Re#, La#	G#	1#	1#	5\15 230; 1.3	4\11 252; 1.583	7\18 270; 1.03	3\7 300	8\17 331; 29	5\10 352; 1.0625	7\13 381.81
Mib, Sib	Ab	2b, 2c	2f	7\15 323; 13	5\11 315; 1.26	8\18 309; 1, 2.1		7\17 289; 1, 1.9	4\10 282; 2.83	5\13 272.72
Mi, Si	A	2	2	8\15 369; 4.3	6\11 378; 1.05	10\18 387; 10.3	4\7 400	10\17 413; 1, 3.83	6\10 423; 1.8	8\13 436.36
Mi#, Si#	A#	2#	2#	9\15 415; 2.6	7\11 442; 9.5	12\18 464; 1.0625	5\7 500	13\17 537; 14.5	8\10 564; 1.416	11\13 600
Fab, Dob	Bbb	3b, 3c	3f	10\15 461; 1, 1.16		11\18 425; 1.24	4\7 400	9\17 372; 2.416	5\10 352; 1.0625	6\13 327.27
Fa, Do	Bb	3	3	11\15 507; 1.4	8\11 505; 3.8	13\18 503; 4, 2.3	5\7 500	12\17 496; 1.8125	7\10 494; 8.5	9\13 490.90
Fa#, Do#	B	3#	3#	12\15 553; 1.18	9\11 568; 2.375	15\18 580; 1.55	6\7 600	15\17 620; 1.45	9\10 635; 3.4	12\13 654.54
Fax, Dox	B#	3x	3x	13\15 600	10\11 631; 1.72	17\18 658; 15.5	7\7 700	18\17 744; 1.2083	11\10 776; 2.125	15\13 818.18
Dob, Solb	Hb	4b, 4c	4f	14\15 646; 6.5		16\18 619; 2.81	6\7 600	14\17 579; 3.2	8\10 564; 1.416	10\13 545.45
Do, Sol	H	4	4	15\15 692; 3.25	11\11 694; 1, 2.8	18\18 696; 1.2916	7\7 700	17\17 703; 2, 2.16	10\10 705; 1.13	13\13 709.09
Do#, Sol#	Η#	4#	4#	16\15 738; 2.16	12\11 757; 1, 8.5	20\18 774; 5, 6	8\8 800	20\17 827; 1, 1.416	12\10 847; 17	16\13 872.72
Reb, Lab	Cb	5b, 5c	5	18\15 830; 1.3	13\11 821; 19	21\18 812; 1, 9.3		19\17 786; 4.83	11\10 776; 2.125	14\13 763.63
Re, La	C	5	5	19\15 876; 1.083	14\11 884; 4.75	23\18 890; 3.1	9\5 900	22\17 910; 2.9	13\10 917; 1.54	17\13 927.27
Re#, La#	C#	5#	5#	20\15 923: 13	15\11 947; 2, 1.4	25\18 967; 1, 2.875	10\7 1000	25\17 1034; 2, 14	15\10 1058; 1, 4.6	20\13 1090.90
Mib, Sib	Db	6b, 6c	6f	22\15 1015; 2.6	16\11 1010; 1.9	26\18 1006; 2, 4.6		24\17 993; 9.6	14\10 988; 4.25	18\13 981.81
Mi, Si	D	6	6	23\15 1061; 1, 1.16	17\11 1073; 1, 2.16	28\18 1083; 1.148	11\7 1100	27\17 1117; 4, 7	16\10 1129; 2, 2.3	21\9 1145.45
Mi#, Si#	D#	6#	6#	24\15 1107; 1.4	18\11 1136; 1.1875	30\18 1161; 3.4	12\7 1200	30\17 1241; 2.63	18\10 1270; 1.7	24\13 1309.09
Fab, Dob	Ebb	7b, 7c	7f	25\15 1153; 1.18		29\18 1121; 1, 1, 2.6	11\7 1100	26\17 1075; 1.16	15\10 1058; 1, 4.6	19\13 1036.36
Fa, Do	Eb	7	7	26\15 1200	19\11 1200	31\18 1200	12\7 1200	29\17 1200	17\10 1200	22\13 1200
Fa#, Do#	E	7#	7#	27\15 1246; 6.5	20\11 1263; 6.3	33\18 1277; 2, 2.6	13\7 1300	32\17 1324; 7.25	19\10 1341; 5.6	25\13 1363.63
Fax, Dox	E#	7x	7x	28\15 1292; 3.25	21\11 1326; 3.16	35\18 1354; 1, 5.2	14\7 1400	35\17 1448; 3.625	21\10 1482; 2.83	28\13 1527.27
Dob, Solb	Fb	8b, Fc	8f	29\15 1338; 2.16		34\18 1316; 7.75	13\7 1300	31\17 1282; 1.318	18\10 1270; 1.7	23\13 1254.54
Do, Sol	F	8, F	8	30\15 1384; 1.625	22\11 1389; 2.1	36\18 1393; 1, 1, 4.6	14\7 1400	34\17 1406; 1, 8.6	20\10 1411; 1, 3.25	26\13 1418.18
Do#, Sol#	F#	8#, F#	8#	31\15 1430; 1.3	23\11 1452; 1.583	38\18 1470; 1.03	15\7 1500	37\17 1531; 29	22\10 1552; 1.0625	29\13 1581.81
Reb, Lab	Gb	9b, Gc	9f	33\15 1523; 13	24\11 1515; 1.26	39\18 1509; 1, 2.1		36\17 1489; 1, 1.9	21\10 1482; 2.83	27\13 1472.72
Re, La	G	9, G	9	34\15 1569; 4.3	25\11 1578; 1.05	41\18 1587; 10.3	16\7 1600	39\17 1613; 1, 3.83	23\10 1623; 1.8	30\13 1636.36
Re#, La#	G#	9#, G#	9#	35\15 1615; 2.6	26\11 1642; 9.5	43\18 1664; 1.0625	17\7 1700	42\17 1737; 14.5	25\10 1764; 1.416	33\13 1800
Mib, Sib	Ab	Xb, Ac	Af	37\15 1707; 1.4	27\11 1705; 3.8	44\18 1703; 4, 2.3		41\17 1696; 1.8125	24\10 1694; 8.5	31\13 1690.90
Mi, Si	A	X, A	A	38\15 1753; 1.18	28\11 1768; 2.375	46\18 1780; 1.55	18\7 1800	44\17 1820; 1.45	26\10 1835; 3.4	34\13 1854.54
Mi#, Si#	A#	X#, A#	A#	39\15 1800	29\11 1831; 1.72	48\18 1858; 15.5	19\7 1900	47\17 1944; 1.2083	28\10 1976; 2.125	37\13 2018.18
Fab, Dob	Bbb	Ebb, Ccc	Bf	40\15 1846; 6.5		47\18 1819; 2.81	18\7 1800	43\17 1779; 3.2	25\10 1764; 1.416	32\13 1745.45
Fa, Do	Bb	Eb, Cc	B	41\15 1892; 3.25	30\11 1894; 1, 2.8	49\18 1896; 1.2916	19\7 1900	46\17 1903; 2.16	27\10 1905; 1.13	35\13 1909.09
Fa#, Do#	B	E, C	B#	42\15 1938; 2.16	31\11 1957; 1, 8.5	51\18 1974; 5.16	20\7 2000	49\17 2027; 1, 1.416	29\10 2047; 17	38\13 2072.72
Fax, Dox	B#	Ex, Cx	Bx	43\15 1984; 1.625	32\11 2021; 19	53\18 2051; 1, 1, 1, 1.4	21\7 2100	52\17 2151; 2.625	31\10 2188; 4.25	41\13 2236.36
Dob, Solb	Hb	0b, Dc	Cf	44\15 2030; 1.3		52\18 2012; 1, 9,3	20\7 2000	48\17 1986; 4.83	28\10 1976; 2.125	36\13 1963.63
Do, Sol	H	0, D	C	45\15 2076; 1.083	33\11 2084; 4.75	54\18 2090; 3.1	21\7 2100	51\17 2110; 2.9	30\10 2117; 1.54	39\13 2127.27
Do#, Sol#	Η#	0#, D#	C#	46\15 2123; 13	34\11 2147; 2, 1.4	56\18 2167; 1, 2.875	22\7 2200	54\17 2234; 2, 14	32\10 2258; 1, 4.6	42\13 2090.90
Reb, Lab	Cb	1b, 1c	Df	48\15 2215; 2.6	35\11 2210; 1.9	57\18 2206; 2, 4.6		53\17 2193; 9.6	31\10 2188; 4.25	40\13 2181.81
Re, La	C	1	D	49\15 2261; 1, 1.16	36\11 2273; 1, 2.16	59\18 2283; 1.148	23\7 2300	56\17 2317; 4, 7	33\10 2329; 2, 2.3	43\13 2245.45
Re#, La#	C#	1#	D#	50\15 2307; 1.4	37\11 2336; 1.1875	61\18 2361; 3.4	24\7 2400	59\17 2441; 2.63	35\10 2470; 1.7	46\13 2509.09
Mib, Sib	Db	2b, 2c	Ef	52\15 2400	38\11 2400	62\18 2400		58\17 2400	34\10 2400	44\13 2400
Mi, Si	D	2	E	53\15 2446; 6.5	39\11 2463; 6.3	64\18 2477; 2, 2.6	25\7 2500	61\17 2524; 7.25	36\10 2541; 5.6	47\13 2563.63
Mi#, Si#	D#	2#	E#	54\15 2492; 3.25	40\11 2526; 3.1	66\18 2554; 1, 5.2	26\7 2600	64\17 2648; 2.625	38\10 2682; 2.83	50\13 2727.27
Fab, Dob	Ebb	3b, 3c	Fff	55\15 2538; 2.16		65\18 2516; 7.75	25\7 2500	60\17 2482; 1.318	35\10 2470; 1.7	45\13 2454.54
Fa, Do	Eb	3	Ff	56\15 2584; 1.625	41\11 2589; 2.1	67\18 2593; 1, 1, 4.6	26\7 2600	63\17 2606; 1, 8.6	37\10 2611; 1, 3.25	48\13 2618.18
Fa#, Do#	E	3#	F	57\15 2630; 1.3	42\11 2652; 1.583	69\18 2670; 1.03	27\7 2700	66\17 2731; 29	39\10 2752; 1.0625	51\13 2781.81
Fax, Dox	E#	3x	F#	58\15 2676; 1.083	43\11 2715; 1.26	71\18 2748; 2.583	28\7 2800	69\17 2855; 4.8	41\10 2894; 8.5	54\13 2945.45
Dob, Solb	Fb	4b, 4c	0f, Gf	59\15 2723; 13		70\18 2709; 1, 2.1	27\7 2700	65\17 2689; 1, 1.9	38\10 2682; 2.83	49\13 2672.72
Do, Sol	F	4	0, G	60\15 2769; 4.3	44\11 2778; 1.05	72\18 2787; 3.1	28\7 2800	68\17 2813; 1, 3.83	40\10 2823; 1.8	52\13 2836.36

Relative cents

Notation				Supersoft	Soft	Semisoft	Basic	Semihard	Hard	Superhard
Diatonic	Napoli	Bijou	Hextone	~15edf	~11edf	~18edf	~7edf	~17edf	~10edf	~13edf
Do#, Sol#	F#	0#, D#	0#, G#	1\15 46.6	1\11 63.63	2\18 77.7̄	1\7 100	3\17 123; 1.8	2\10 140	3\13 161; 1, 1.16
Reb, Lab	Gb	1b, 1c	1f	3\15 140	2\11 127.27	3\18 116.6		2\17 82; 2.83	1\10 70	1\13 53; 1.18
Re, La	G	1	1	4\15 186.6	3\11 190.90	5\18 194.4	2\7 200	5\17 205; 1.13	3\10 210	4\13 215; 2.6
Re#, La#	G#	1#	1#	5\15 233.3	4\11 254.54	7\18 272.2̄	3\7 300	8\17 329; 2, 2.3	5\10 350	7\13 376; 1.083
Mib, Sib	Ab	2b, 2c	2f	7\15 326.6	5\11 318.18	8\18 311.1		7\17 288; 4.25	4\10 280	5\13 269; 4.3
Mi, Si	A	2	2	8\15 373.3	6\11 381.81	10\18 388.8	4\7 400	10\17 411; 1, 3.25	6\10 420	8\13 430; 1.3
Mi#, Si#	A#	2#	2#	9\15 420	7\11 445.45	12\18 466.6	5\7 500	13\17 535; 3.4	8\10 560	11\13 592; 3.25
Fab, Dob	Bbb	3b, 3c	3f	10\15 466.6		11\18 427.7	4\7 400	9\17 370; 1.7	5\10 350	6\13 323; 13
Fa, Do	Bb	3	3	11\15 513.3	8\11 509.09	13\18 505.5	5\7 500	12\17 494; 8.5	7\10 490	9\13 484; 1.625
Fa#, Do#	B	3#	3#	12\15 560	9\11 572.72	15\18 583.3	6\7 600	15\17 617; 1.416	9\10 630	12\13 646; 6.5
Fax, Dox	B#	3x	3x	13\15 606.6	10\11 636.36	17\18 661.1	7\7 700	18\17 741; 5.6	11\10 770	15\13 807; 1.4
Dob, Solb	Hb	4b, 4c	4f	14\15 653.3		16\18 622.2	6\7 600	14\17 576; 2.125	8\10 560	10\13 538; 2.16
Do, Sol	H	4	4	700
Do#, Sol#	Η#	4#	4#	16\15 746.6	12\11 763.63	20\18 777.7	8\7 800	20\17 823; 1.8	12\10 840	16\13 861; 1, 1.16
Reb, Lab	Cb	5b, 5c	5	18\15 840	13\11 827.27	21\18 816.6		19\17 782; 2.83	11\10 770	14\13 753; 1.18
Re, La	C	5	5	19\15 886.6	14\11 890.90	23\18 894.4	9\7 900	22\17 905; 1.13	13\10 910	17\13 915; 2.6
Re#, La#	C#	5#	5#	20\15 933.3	15\11 954.54	25\18 972.2	10\7 1000	25\17 1029; 2, 2.3	15\10 1050	20\13 1076; 1.083
Mib, Sib	Db	6b, 6c	6f	22\15 1026.6	16\11 1018.18	26\18 1011.1		24\17 988; 4.25	14\10 980	18\13 969; 4.3
Mi, Si	D	6	6	23\15 1073.3	17\11 1081.81	28\18 1088.8	11\7 1100	27\17 1111; 1, 3.25	16\10 1120	21\13 1130; 1.3
Mi#, Si#	D#	6#	6#	24\15 1120	18\11 1145.45	30\18 1166.6	12\7 1200	30\17 1235; 3.4	18\10 1260	24\13 1292; 3.25
Fab, Dob	Ebb	7b, 7c	7f	25\15 1166.6		29\18 1127.7	11\7 1100	26\17 1070; 1.7	15\10 1050	19\13 1023; 13
Fa, Do	Eb	7	7	26\15 1213.3	19\11 1209.09	31\18 1205.5	12\7 1200	29\17 1194; 8.5	17\10 1190	22\13 1184; 1.625
Fa#, Do#	E	7#	7#	27\15 1260	20\11 1272.72	33\18 1283.3	13\7 1300	32\17 1317; 1.416	19\10 1330	25\13 1346; 6.5
Fax, Dox	E#	7x	7x	28\15 1306.6	21\11 1336.36	35\18 1361.1	14\7 1400	35\17 1441; 5.6	21\10 1470	28\13 1507; 1.4
Dob, Solb	Fb	8b, Fc	8f	29\15 1333.3		34\18 1322.2	13\7 1300	31\17 1276; 2.125	18\10 1260	23\13 1238; 2.16
Do, Sol	F	8, F	8	1400
Do#, Sol#	F#	8#, F#	8#	31\15 1446.6	23\11 1463.63	38\18 1477.7̄	15\7 1500	37\17 1523; 1.8	22\10 1540	29\13 1561; 1, 1.16
Reb, Lab	Gb	9b, Gc	9f	33\15 1540	24\11 1527.27	39\18 1516.6		36\17 1482; 2.83	21\10 1470	27\13 1453; 1.18
Re, La	G	9, G	9	34\15 1586.6	25\11 1590.90	41\18 1594.4	16\7 1600	39\17 1605; 1.13	23\10 1610	30\13 1615; 2.6
Re#, La#	G#	9#, G#	9#	35\15 1633.3	26\11 1654.54	43\18 1672.2	17\7 1700	42\17 1729; 2, 2.3	25\10 1750	33\13 1776; 1.083
Mib, Sib	Ab	Xb, Ac	Af	37\15 1726.6	27\11 1718.18	44\18 1711.1		41\17 1688; 4.25	24\10 1680	31\13 1669; 4.3
Mi, Si	A	X, A	A	38\15 1773.3	28\11 1781.81	46\18 1788.8	18\7 1800	44\17 1811; 1, 3.25	26\10 1820	34\13 1830; 1.3
Mi#, Si#	A#	X#, A#	A#	39\15 1820	29\11 1845.45	48\18 1866.6	19\7 1900	47\17 1935; 3.4	28\10 1960	37\13 1992; 3.25
Fab, Dob	Bbb	Ebb, Ccc	Bf	40\15 1866.6		47\18 1827.7	18\7 1800	43\17 1770; 1.7	25\10 1750	32\13 1723; 13
Fa, Do	Bb	Eb, Cc	B	41\15 1913.3	30\11 1909.09	49\18 1905.5	19\7 1900	46\17 1894; 8.5	27\10 1890	35\13 1884; 1.625
Fa#, Do#	B	E, C	B#	42\15 1960	31\11 1972.72	51\18 1983.3	20\7 2000	49\17 2017; 1.416	29\10 2030	38\13 2046; 6.5
Fax, Dox	B#	Ex, Cx	Bx	43\15 2006.6	32\11 2036.36	53\18 2061.1	21\7 2100	52\17 2141; 5.6	31\10 2170	41\13 2207; 1.4
Dob, Solb	Hb	0b, Dc	Cf	44\15 2053.3		52\18 2022.2	20\7 2000	48\17 1976; 2.125	28\10 1960	36\13 1938; 2.16
Do, Sol	H	0, D	C	2100
Do#, Sol#	Η#	0#, D#	C#	46\15 2146.6	34\11 2163.63	56\18 2177.7	22\7 2200	54\17 2223; 1.8	32\10 2240	42\13 2261; 1, 1.16
Reb, Lab	Cb	1b, 1c	Df	48\15 2240	35\11 2227.27	57\18 2216.6		53\17 2182; 2.83	31\10 2170	40\13 2153; 1.18
Re, La	C	1	D	49\15 2286.6	36\11 2290.90	59\18 2294.4	23\7 2300	56\17 2305; 1.13	33\10 2310	43\13 2315; 2.6
Re#, La#	C#	1#	D#	50\15 2223.3	37\11 2354.54	61\18 2372.2	24\7 2400	59\17 2429; 2, 2.3	35\10 2450	46\13 2476; 1.083
Mib, Sib	Db	2b, 2c	Ef	52\15 2426.6	38\11 2418.18	62\18 2411.1		58\17 2388; 4.25	34\10 2380	44\13 2369; 4.3
Mi, Si	D	2	E	53\15 2473,3	39\11 2481.81	64\11 2488.8	25\7 2500	61\17 2511; 1, 3.25	36\10 2520	47\13 2530; 1.3
Mi#, Si#	D#	2#	E#	54\15 2520	40\11 2545.45	66\18 2566.6	26\7 2600	64\17 2635; 3.4	38\10 2660	50\13 2692; 3.25
Fab, Dob	Ebb	3b, 3c	Fff	55\15 2566.6		65\18 2527.7	25\7 2500	60\17 2470; 1.7	35\10 2450	45\13 2423; 13
Fa, Do	Eb	3	Ff	56\15 2613.3	41\11 2609.09	67\18 2605.5	26\7 2600	63\17 2594; 8.5	37\10 2590	48\13 2584; 1.625
Fa#, Do#	E	3#	F	57\15 2660	42\11 2672.72	69\18 2683.3	27\7 2700	66\17 2717; 1.416	39\10 2730	51\13 2746; 6.5
Fax, Dox	E#	3x	F#	58\15 2706.6	43\11 2736.36	71\18 2761.1	28\7 2800	69\17 2841; 5.6	41\10 2870	54\13 2907; 1.4
Dob, Solb	Fb	4b, 4c	0f, Gf	59\15 2753.3		70\18 2722.2	27\7 2700	65\17 2676; 2.125	38\10 2660	49\13 2638; 2.16
Do, Sol	F	4	0, G	2800

Intervals

Generators	Sesquitave notation	Interval category name	Generators	Notation of 3/2 inverse	Interval category name
The 4-note MOS has the following intervals (from some root):
0	Do, Sol	perfect unison	0	Do, Sol	sesquitave (just fifth)
1	Fa, Do	perfect fourth	-1	Re, La	perfect second
2	Mib, Sib	minor third	-2	Mi, Si	major third
3	Reb, Lab	diminished second	-3	Fa#, Do#	augmented fourth
The chromatic 7-note MOS also has the following intervals (from some root):
4	Dob, Solb	diminished sesquitave	-4	Do#, Sol#	augmented unison (chroma)
5	Fab, Dob	diminished fourth	-5	Re#, La#	augmented second
6	Mibb, Sibb	diminished third	-6	Mi#, Si#	augmented third

Genchain

The generator chain for this scale is as follows:

Mibb Sibb

Fab Dob

Dob Solb

Reb Lab

Mib Sib

Fa Do

Do Sol

Re La

Mi Si

Fa# Do#

Do# Sol#

Re# La#

Mi# Si#

d3

d4

d5

d2

m3

P4

P1

P2

M3

A4

A1

A2

A3

Modes

The mode names are based on the species of fifth:

Mode	Scale	UDP	Interval type
name	pattern	notation	2nd	3rd	4th
Lydian	LLLs	3|0	P	M	A
Major	LLsL	2|1	P	M	P
Minor	LLsL	1|2	P	m	P
Phrygian	sLLL	0|3	d	m	P

Temperaments

The most basic rank-2 temperament interpretation of angel is Napoli. The name "Napoli" comes from the “Neapolitan” sixth triad spelled root-(p-2g)-(2p-3g) (p = 3/2, g = the whole tone) which serves as its minor triad approximating 5:6:8 in pental interpretations or 18:21:28 in septimal ones. Basic ~7edf fits both interpretations.

Napoli-Meantone

Subgroup: 3/2.6/5.8/5

Comma list: 81/80

POL2 generator: ~9/8 = 192.6406

Mapping: [⟨1 1 2], ⟨0 -2 -3]]

Vals: ~(7edf, 11edf, 18edf)

Napoli-Superpyth

Subgroup: 3/2.7/6.14/9

Comma list: 64/63

POL2 generator: ~8/7 = 218.6371

Mapping: [⟨1 1 2], ⟨0 -2 -3]]

Vals: ~(7edf, 10edf, 13edf, 16edf)

Scale tree

The spectrum looks like this:

Generator (bright)			Cents		L	s	L/s	Comments
			Normalised	ed7\12
1\4			171; 2.3	175	1	1	1.000	Equalised
6\23			180	182; 1, 1.5	6	5	1.200
	11\42		180; 1.216	183.3	11	9	1.222
5\19			181.81	184; 4.75	5	4	1.250
	14\53		182; 1, 1.5	184; 1, 9.6	14	11	1.273
	9\34		183; 19.6	185; 3.4	9	7	1.286
4\15			184; 1.625	186.6	4	3	1.333
	11\41		185, 1, 10.83	187; 1.24	11	8	1.375
	7\26		186.6	188; 2.16	7	5	1.400
	10\37		187.5	189.189	10	7	1.429
	13\48		187; 1, 19.75	189.583	13	9	1.444
	16\59		188; 4.25	189; 1, 4.9	16	11	1.455
3\11			189; 2.1	190.90	3	2	1.500	Napoli-Meantone starts here
	17\62		190; 1, 1.12	191; 1, 14.5	17	11	1.545
	14\51		190.90	192; 8.375	14	9	1.556
	11\40		191; 3, 2.3	192.5	11	7	1.571
	8\29		192	193; 9.6	8	5	1.600
	5\18		193; 1, 1, 4.6	194.4	5	3	1.667
		12\43	194.594	195; 2.86	12	7	1.714
	7\25		195; 2.86	196	7	4	1.750
	9\32		196.36	196.875	9	5	1.800
	11\39		197; 67	197; 2, 3.4	11	6	1.833
	13\46		197; 2.135	197; 1, 4.75	13	7	1.857
	15\53		197; 1, 2, 1, 1.54	198; 8.83	15	8	1.875
	17\60		198; 17.16	198.3	17	9	1.889
	19\67		198: 3, 1, 28	198, 1, 1.03	19	10	1.900
	21\74		198; 2.3518	198.648	21	11	1.909
	23\81		198; 1, 3, 1.7	198; 1, 3, 3.8	23	12	1.917
	25\88		198; 1, 2, 12.25	198.863	25	13	1.923
	27\95		198; 1, 3.405	198; 1.05	27	14	1.929
	29\102		198; 1, 1.16	199; 51	29	15	1.933
2\7			200	200	2	1	2.000	Napoli-Meantone ends, Napoli-Pythagorean begins
	17\59		201.9801	201; 1, 2.27	17	8	2.125
	15\52		202; 4.045	201; 1.083	15	7	2.143
	13\45		202; 1, 1, 2.06	202.2	13	6	2.167
	11\38		203; 13	202; 1.583	11	5	2.200
	9\31		203; 1, 3.416	203; 4, 2.3	9	4	2.250
	7\24		204; 1. 7.2	204.16	7	3	2.333
		12\41	205; 1.4	204; 1. 7.2	12	5	2.400
	5\17		206; 1, 8.6	205; 1.13	5	2	2.500	Napoli-Neogothic heartland is from here…
		18\61	207; 1.4	206; 1.259	18	7	2.571
		13\44	208	206.81	13	5	2.600
	8\27		208; 1.4375	207.407	8	3	2.667	…to here
	11\37		209; 1.90	208.108	11	4	2.750
	14\47		210	208; 1.9583	14	5	2.800
	17\57		210; 3.23	208; 1.2954	17	6	2.833
	20\67		210; 1.9	208; 1, 21.3	20	7	2.857
	23\77		210; 1.45	209.09	23	8	2.875
3\10			211; 1, 3.25	210	3	1	3.000	Napoli-Pythagorean ends, Napoli-Superpyth begins
	22\73		212; 1, 9.3	210; 1, 23.3	22	7	3.143
	19\63		213; 11.8	211.1	19	6	3.167
	16\53		213.3	211; 3, 8.5	16	5	3.200
	13\43		213; 1, 2.318	211; 1.592	13	4	3.250
	10\33		214; 3.5	212.12	10	3	3.333
	7\23		215; 2.6	213; 23	7	2	3.500
	11\36		216; 2.5416	213.3	11	3	3.667
	15\49		216; 1.1527	214; 3.5	15	4	3.750
	19\62		217; 7	214; 1.9375	19	5	3.800
4\13			218.18	215; 2.6	4	1	4.000
	13\42		219; 1, 2.55	216.6	13	3	4.333
	9\29		220; 2.45	217; 4, 7	9	2	4.500
	14\45		221; 19	217.7	14	3	4.667
5\16			222.2	218.75	5	1	5.000	Napoli-Superpyth ends
	16\51		223; 3.90	219; 1, 1.55	16	3	5.333
	11\35		223; 1, 2.6875	220	11	2	5.500
	17\54		224; 5.72	220.370	17	3	5.667
6\19			225	221; 19	6	1	6.000
1\3			240	233.3	1	0	→ inf	Paucitonic