User:Moremajorthanmajor/7L 2s (major tenth-equivalent)

This page is about a MOS scale with a period of 5/2 and 7 large steps and 2 small steps arranged LLLsLLLLs (or any rotation of that, such as LLsLLLsLL).

Name

Temperaments

Terra Rubra-Meantone

Subgroup: 5/2.2.3

Comma list: 81/80

POL2 generator: ~3/2 = [[1]]

Mapping: [⟨1 1 1], ⟨0 -2 -1]]

Optimal ET sequence: 9ed5/2, 16ed5/2, 25ed5/2

Terra Rubra-Superpyth

Subgroup: 18/7.2.3

Comma list: 64/63

POL2 generator: ~3/2 = [[2]]

Mapping: [⟨1 1 1], ⟨0 -2 -1]]

Optimal ET sequence: 7ed18/7, 16ed18/7, 23ed18/7

Scale tree

Generator			Generator size	ed16\12 (→ed4\3)	L	s	Comments
4\7			960	914.285…	1	0
25\44			937.5	909.09	6	1
	71\125		936.263…	908.8	17	3
	46\81		935.593…	908.641…	11	2
	67\118		934.883…	908.474…	16	3
21\37			933.3	908.108	5	1
	80\141		932.038…	907.801…	19	4
	59\104		931.579…	907.692…	14	3
	38\67		930.612…	907.462…	9	2
	55\97		929.577…	907.216…	13	3
	72\127		929.032…	907.086…	17	4
	89\157		928.695…	907.006…	21	5
17\30			927.27	906.6	4	1
	115\203		926.174…	906.403…	27	7
	98\173		925.984…	906.358…	23	6
	81\143		925.714…	906.293…	19	5
	64\113		925.301…	906.194…	15	4
	47\83		924.591…	906.024…	11	3
	30\53		923.076…	905.660…	7	2
		73\129	922.105…	905.426…	17	5
	43\76		921.428…	905.263…	10	3
	56\99		920.547…	905.05	13	4
	69\122		920	904.918…	16	5
	82\145		919.626…	904.827…	19	6
	95\168		919.354…	904.761…	22	7
			919.340…	904.758…			L/s = π
	108\191		919.148…	904.712…	25	8
	121\214		918.987…	904.672…	28	9
	134\237		918.857…	904.642…	31	10
13\23			917.647…	904.347…	3	1
	100\177		916.030…	903.954…	23	8
	87\154		915.789…	903.896…	20	7
	74\131		915.463…	903.816…	17	6
	61\108		915	903.703	14	5
	48\85		914.286…	903.529…	11	4
			913.820…	903.415…			L/s = e
	35\62		913.043…	903.225…	8	3
			912.286…	903.040…			Split φ superdiatonic relation
		57\101	912	902.970…	13	5
		79\140	911.538…	902.857…	18	7
	22\39		910.344…	902.564…	5	2
		75\133	909.09	902.255…	17	7
		53\94	908.571…	902.127…	12	5
	31\55		907.317…	901.81	7	3
		71\126	906.382…	901.587…	16	7
	40\71		905.660…	901.408…	9	4
	49\87		904.615…	901.149…	11	5
	58\103		903.896…	900.970…	13	6
9\16			900	900	2	1	[BOUNDARY OF PROPRIETY: smaller generators are strictly proper]
	59\105		896.202…	899.047…	13	7
	50\89		895.522…	898.876…	11	6
	41\73		894.54	898.630…	9	5
	32\57		893.023…	898.245…	7	4	the 'Commatic' version of Terra Rubra, because its high accuracy of the 16/15 interval, the note '2b'
			892.459…	898.102…
		55\98	891.891	897.959…	12	7
	23\41		890.323…	897.560…	5	3	Golden Terra Rubra 1/5-tone
		83\148	889.285…	897.297	18	11
		60\107	888.8	897.196…	13	8	Golden Terra Rubra 1/13-tone
			888.643…	897.133…			GOLDEN Terra Rubra (L/s = φ)
	37\66		888	896.96	8	5	Golden Terra Rubra 1/8-tone
		88\157	887.394…	896.815…	19	12
	51\91		886.956…	896.703…	11	7
	65\116		886.36	896.551…	14	9
	79\141		885.981…	896.453…	17	11
	93\166		885.714…	896.385…	20	13
14\25			884.210…	896	3	2	Golden Terra Rubra 1/3-tone
	117\209		883.018…	895.693…	25	17
	103\184		882.857…	895.652…	22	15
	89\159		882.644…	895.579…	19	13
	75\134		882.353…	895.522…	16	11
	61\109		881.927…	895.412…	13	9
	47\84		881.25	895.238…	10	7
		80\143	880.733…	895.104…	17	12
	33\59		880	894.915…	7	5
		85\152	879.310…	894.736…	18	13
	52\93		878.873…	894.623…	11	8
	71\127		878.350…	894.488…	15	11
	90\161		878.048…	894.409…	19	14
	109\195		877.852…	894.358…	23	17
19\34			876.923…	894.117…	4	3
	62\111		875.294…	893.693	13	10
	43\77		874.576…	893.506…	9	7
	67\120		873.913…	893.3	14	11
24\43			872.72	893.023…	5	4
	53\95		871.232…	892.631…	11	9
29\52			870	892.307…	6	5
5\9			857.142…	888.8	1	0