Catalog of 3.5.7 subgroup rank two temperaments

Todo: merge articles Merge into No-twos subgroup temperaments

Table

Name	Comma ratio	Comma n/d	Comma c	Comma name	a&b (3)	a&b (2)	Complexity	Damage	Mapping	TE gen1	TE gen2	Per/3	MOS
Izar	[-11 -7 12⟩	13841287201/13839609375	0.210		b271 & b1071	171p & 676cd	11.675	0.003	[⟨271 397 480] ⟨1071 1569 1897]⟩	1901.9584	877.2825	1	2*,3,5,7,9,11*,13*,24,37,50,63,76,...258*,271*
Canopus	[3 4 -5⟩	16875/16807	6.990	small BP diesis, mirkwai	b13 & b101	8d & 64cd	4.866	0.249	[⟨13 19 23] ⟨101 148 179]⟩	1901.7828	583.9055	1	2,3*,4,7,10*,13*,23,36,49,62,75,88,101,114*
*Procyon	[-8 -3 7⟩	823543/820125	7.200		b13 & b144	8d & 91p	6.810	0.183	[⟨13 19 23] ⟨144 211 255]⟩	1902.198	145.4124	1	...13*,14,27,40,53,66,79,92,105,118,131,144,157*
*Gacrux	[6 8 -10⟩	284765625/282475249	13.981
BPS (Bohlen-Pierce-Stearns)	[-5 1 2⟩	245/243	14.191	minor BP diesis, sensamagic	b13 & b17	8d & 11cd	2.749	0.895	[⟨13 19 23] ⟨17 25 30]⟩	1903.7424	440.902	1	2,3,4*,5,9,13*,17,30,43,56,69,82*,95*
Sirius	[-2 5 -3⟩	3125/3087	21.181	major BP diesis, gariboh	b13 & b19	8d & 12p	4.021	0.913	[⟨13 19 23] ⟨19 28 34]⟩	1902.4482	293.7397	1	2,3,4,5,6*,7,13*,19,32,45,58,71,84,97,110,123,136*
*Betelgeuse	[-13 -2 9⟩	40353607/39858075	21.391		b13 & b148	8d & 93bccd	8.754	0.423	[⟨13 19 23] ⟨148 217 262]⟩	1902.5991	732.4139	1	2*,3*,5*,8,13*,...226*
*Miaplacidus	[1 9 -8⟩	5859375/5764801	28.171		b13 & b94d	8d & 59ccdd	7.788	0.627	[⟨13 19 23] ⟨94 138 167]⟩	1901.88	585.8431	1	2,3*,4,7,10,13*,16,29,42,55,68,81,94,...224*
Arcturus	[-7 6 -1⟩	15625/15309	35.371	great BP diesis	b13 & b2	8d & 1cdd	4.823	1.271	[⟨13 19 23] ⟨2 3 4]⟩	1903.8685	878.9253	1	2*,3,5,7,9,11,13*
*Pollux	[-18 -1 11⟩	1977326743/1937102445	35.581		b13 & b139	8d & 88dd	10.697	0.576	[⟨13 19 23] ⟨139 204 246]⟩	1902.8625	438.6389	1	2,3,4*,5,9*,13
*Castor	[-1 14 -11⟩	6103515625/5931980229	49.352		b13 & b113d	8d & 71ccddd	11.259	0.760	[⟨13 19 23] ⟨113 166 201]⟩	1902.0166	438.5094	1	2,3,4*,5,9*,13
*Muphrid	[-12 7 1⟩	546875/531441	49.562		b13 & b2d	8d & 1c	6.599	1.302	[⟨13 19 23] ⟨2 3 3]⟩	1904.3123	879.0503	1	2*,3,5,7,9,11,13*
*Rigel	[-9 11 -4⟩	48828125/47258883	56.552		b13 & b21d	8d & 5d	8.844	1.108	[⟨13 19 23] ⟨21 31 38]⟩	1903.2571	731.7183	1	2*,3*,5*,8*,13*
*Mirzam	[-17 8 3⟩	133984375/129140163	63.752		b13 & b32d	8d & 20c	9.347	1.182	[⟨13 19 23] ⟨32 47 56]⟩	1904.3391	293.1889	1	2,3,4,5,6*,7,13*
	[15 -9 -1⟩	14348907/13671875	83.676		b17 & b32	11cd & 20cd	8.228	1.762	[⟨17 25 30] ⟨32 47 57]⟩	1898.8326	891.5018	1	2*,3,5,7,9,11,13,15*,17*,32,49*,66,115,164*
*Capella	[10 -8 1⟩	413343/390625	97.866	small link	b17 & b19	12p & 11cd	6.452	2.629	[⟨17 25 30] ⟨19 28 34]⟩	1897.8856	895.415	1	2*,3,5,7,9,11,13,15,17*,19,36*,53*,89,142*,195*
	[13 -4 -4⟩	1594323/1500625	104.857		b4 & b32	3bcdd & 20cd	7.126	2.550	[⟨4 6 7] ⟨32 47 57]⟩	474.1446	55.0036	4	...32*,36*,68*,104*,172*,276*
	[16 0 -9⟩	43046721/40353607	111.847		b9 & b36	6bcd & 23d	8.773	2.209	[⟨9 13 16] ⟨36 53 64]⟩	210.9385	44.1126	9	18,27,36*,45*,81,126,171*,216*,387*
Toliman	[5 -7 3⟩	83349/78125	112.057	minor link	b6 & b17	4p & 11cd	5.649	3.437	[⟨6 9 11] ⟨17 25 30]⟩	1898.4178	333.298	1	2,3,4,5*,6*,11,17*,23,40,57*,74,131*
Vega	[8 -3 -2⟩	6561/6125	119.047	major link	b4 & b15	3bcdd & 10bccdd	4.377	4.713	[⟨4 6 7] ⟨15 22 27]⟩	1892.0204	494.8658	1	2,3*,4*,7,11,15,19*,23*,42*,65*
*Achernar	[0 -6 5⟩	16807/15625	126.247		b7 & b17	4bcd & 11cd	4.847	4.514	[⟨7 10 12] ⟨17 25 30]⟩	1901.955	559.351	1	2,3*,4,7*,10,17*
%	[3 -2 0⟩	27/25	133.238	large limma, BP small semitone	b4 & b6	3bcdd & 4p	1.629	14.176	[⟨4 6 7] ⟨6 9 11]⟩	939.6121	549.9897	2	4*,6,10*,14,24*,34,58,82*
	[6 2 -5⟩	18225/16807	140.228	minimal BP chroma	b9 & b10	6bcd & 6ccdd	4.885	4.974	[⟨9 13 16] ⟨10 15 18]⟩	1895.1156	201.762	1	...9*,10,19*,28*,47*
%	[-2 -1 2⟩	49/45	147.428	BP minor semitone, swetismic neutral second	b4 & b7	3bcdd & 4bcd	1.925	13.274	[⟨4 6 7] ⟨7 10 12]⟩	1917.7266	516.1077	1	2,3*,4*,7,11*,15*,26*
	[1 3 -3⟩	375/343	154.418	BP major semitone, minor BP chroma	b3 & b6	2cd & 4p	2.941	9.098	[⟨3 4 5] ⟨6 9 11]⟩	632.9248	234.1367	3	6*,9*,15,24*,33,57*,81*
	[-7 0 4⟩	2401/2187	161.619		b4 & b40cd	3bcdd & 25p	3.868	7.240	[⟨4 6 7] ⟨40 58 70]⟩	478.34	41.8631	4	...44*,48,92*,136,228*,320*
	[-4 4 -1⟩	625/567	168.609	BP great semitone, major BP chroma	b2 & b7	1cdd & 4bcd	3.195	9.146	[⟨2 3 4] ⟨7 10 12]⟩	1914.567	1069.8876	1	2*,3,5,7*,9*,16,25,34*
	[-9 5 1⟩	21875/19683	182.799	maximal BP chroma	b9 & b11	6bcd & 7d	4.970	6.373	[⟨9 13 16] ⟨11 16 19]⟩	1913.8948	858.1831	1	2*,3,5,7,9*,11,20*,29*
%	[9 0 -5⟩	19683/16807	273.465		b5 & b10	3d & 6ccdd	4.904	9.663	[⟨5 7 9] ⟨10 15 18]⟩	377.3036	145.1888	5	10*,15*,25*,40,65*

names: * = proposed

names: % = not shown on PTS plots

MOS: * = maximally even

complexity = ln(n*d)/4

damage = 1200 *log(n/d) / log(n*d)

(complexity and damage are calculated as in the "Middle Path" tables)