Catalog of 3.5.7 subgroup rank two temperaments

Table

name	comma |>	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*
BP diatonic	| -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)

Graphs

357plot_cplx_damage.png

Complexity vs. damage plot. z<1 corresponds to the "Middle Path" inclusion criterion.

Projective tuning space diagrams

File:357ptslines1n.png

Temperaments with smaller commas, labeled by name

File:357ptslines1c.png

Temperaments with smaller commas, labeled by comma

File:357ptslines2n.png

Temperaments with larger commas, labeled by name

File:357ptslines2c.png

Temperaments with larger commas, labeled by comma

File:357ptslines12n.png

Both sets, labeled by name

File:357ptslines12c.png

Both sets, labeled by comma

11.675