User:FloraC/Sandbox

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Subgroup: 2.3.5.7

Comma list: 81/80, 126/125

Mapping: [⟨1 0 -4 -13], ⟨0 1 4 10]]

Mapping generators: ~2, ~3

Wedgie: ⟨⟨1 4 10 4 13 12]]

Optimal tuning (CTE): ~3/2 = 696.9521

Optimal GPV sequence: 12, 19, 31, 81, 112b, 143b

Badness: 0.0137

Tunings to be reviewed

5-limit Prime-Optimized Tunings
Weight-skew\Order Chebyshevian Euclidean Manhattan
Tenney CTC
~3/2 = 696.5784¢
Eigenmonzo basis: 2.5 (1/4-comma tuning)		 CTE
~3/2 = 697.2143¢		 CTOP
~3/2 = 698.0197¢
Tenney-Weil CTWC
~3/2 = 696.5784¢
Eigenmonzo basis: 2.5 (1/4-comma tuning)		 CTWE
~3/2 = 696.6512¢		 CTWOP
~3/2 = 696.5784¢
Eigenmonzo basis: 2.5 (1/4-comma tuning)
Equilateral CEC
~3/2 = 696.5784¢
Eigenmonzo basis: 2.5 (1/4-comma tuning)		 CEE
~3/2 = 696.8947¢
Eigenmonzo basis: 2.1875 (4/17-comma tuning)		 CEOP
~3/2 = 697.6537¢
Eigenmonzo basis: 2.15 (1/5-comma tuning)
Equilateral-Weil CEWC
~3/2 = 696.5784¢
Eigenmonzo basis: 2.5 (1/4-comma tuning)		 CEWE
~3/2 = 696.4534¢
Eigenmonzo basis: 2.48828125/3 (11/43-comma tuning)		 CEWOP
~3/2 = 696.5784¢
Eigenmonzo basis: 2.5 (1/4-comma tuning)
Benedetti CBC
~3/2 = 696.5784¢
Eigenmonzo basis: 2.5 (1/4-comma tuning)		 CBE
~3/2 = 697.3738¢
Eigenmonzo basis: 2.[0 25 36⟩ (36/169-comma tuning)		 CBOP
~3/2 = 698.1598¢
Eigenmonzo basis: 2.30375 (3/17-comma tuning)
Benedetti-Weil CBWC
~3/2 = 696.5784¢
Eigenmonzo basis: 2.5 (1/4-comma tuning)		 CBWE
~3/2 = 696.7868¢
Eigenmonzo basis: 2.[0 5 31⟩ (31/129-comma tuning)		 CBWOP
~3/2 = 696.5784¢
Eigenmonzo basis: 2.5 (1/4-comma tuning)
7-limit Prime-Optimized Tunings
Weight-skew\Order Chebyshevian Euclidean Manhattan
Tenney CTC
~3/2 = 696.8826¢
Eigenmonzo basis: 2.7		 CTE
~3/2 = 696.9521¢		 CTOP
~3/2 = 696.6458¢
Tenney-Weil CTWC
~3/2 = 696.8826¢
Eigenmonzo basis: 2.7		 CTWE
~3/2 = 696.6562¢		 CTWOP
~3/2 = 696.8826¢
Eigenmonzo basis: 2.7
Equilateral CEC
~3/2 = 696.8826¢
Eigenmonzo basis: 2.7		 CEE
~3/2 = 696.8843¢
Eigenmonzo basis: 2.[0 1 4 10⟩		 CEOP
~3/2 = 697.3437¢
Eigenmonzo basis: 2.21
Equilateral-Weil CEWC
~3/2 = 696.8826¢
Eigenmonzo basis: 2.7		 CEWE
~3/2 = 696.7248¢
Eigenmonzo basis: 2.4117715/9		 CEWOP
~3/2 = 696.8826¢
Eigenmonzo basis: 2.7
Benedetti CBC
~3/2 = 696.8826¢
Eigenmonzo basis: 2.7		 CBE
~3/2 = 697.0147¢
Eigenmonzo basis: 2.[0 1225 1764 2250⟩		 CBOP
~3/2 = 697.8422¢
Eigenmonzo basis: 2.750141
Benedetti-Weil CBWC
~3/2 = 696.8826¢
Eigenmonzo basis: 2.7		 CBWE
~3/2 = 696.6306¢
Eigenmonzo basis: 2.[0 -3290 3171 7215⟩		 CBWOP
~3/2 = 696.8826¢
Eigenmonzo basis: 2.7

Temperament pages

Note:

  1. Order: subgroup, comma list, (sval) mapping, (sval) mapping generators, gencom mapping, gencom, map to lattice, lattice basis, wedgie, POTE generator, minimax tuning, tuning ranges, algebraic generator, vals, badness, complexity spectrum, and others.
  2. Comma list should show the simplest commas sufficient to define the temperament, stated in Normal lists #Normal interval list.
  3. Mapping generators should show all the ratios as used in the mapping, including the period.
  4. Since minimax tuning are based on tonality diamond, it should explicitly state the odd limit, or a diamond function of ratios.
  5. Replace "EDOs" with Template:Val list.
  6. For subgroup temperaments, "mapping" becomes "sval mapping", add "gencom mapping" and "gencom". If TE is TE is TE (sic), simply show "POTE", otherwise show "POL2" or "POT2" instead of "POTE".

Get a family for:

  • Ripple (3 different 7-limit extensions) done
  • Smate (2 different 7-limit extensions) done
  • Passion (4 different 7-limit extensions, 3 strong and 1 weak) done
  • Parakleismic (2 different 7-limit extensions) canceled, not strong extensions
  • Superpyth (2 different 7-limit extensions) canceled, not strong extensions
  • Undim done
  • Quintaleap done
  • Quindromeda done

Who's next?

  • Meantone family
  • Archytas clan
  • Father family
  • Trienstonic clan
  • Septisemi temperaments
  • Archytas family
  • Slendro clan
  • Semiphore family
  • Marvel temperaments
  • Marvel family
  • Mint temperaments
  • Mint family
  • Gamelismic clan
  • Gamelismic family
  • Jubilismic clan
  • Jubilismic family
  • Didymus rank three family
  • Kleismic family
  • Kleismic rank three family
  • Shibboleth family
  • Keemic temperaments
  • Keemic family
  • Schismatic family
  • Hemimean clan
  • Hemimean family
  • Luna family
  • Canousmic temperaments
  • Canou family
  • Starling temperaments
  • Starling family
  • Sensipent family
  • Sensamagic clan
  • Sensamagic family
  • Magic family
  • Unicorn family
  • Trisedodge family
  • Sycamore family
  • Rastmic temperaments
  • Semicomma family
  • Orwellismic temperaments
  • Orwellismic family
  • Hemimage temperaments
  • Hemimage family
  • Porwell temperaments
  • Porwell family
  • Hemifamity temperaments
  • Hemifamity family
  • Porcupine family
  • Porcupine rank three family
  • Tetracot family
  • Misty family
  • Diaschismic family
  • Diaschismic rank three family
  • Amity family
  • Lehmerismic temperaments
  • Kalismic temperaments
  • Ragismic family
  • Ragismic microtemperaments
  • Landscape family
  • Landscape microtemperaments
  • Dimcomp family
  • Mirkwai family
  • Mirkwai clan
  • Breed family
  • Breedsmic temperaments
  • Escapade family
  • Gravity family
  • Cataharry family
  • Cataharry temperaments
  • Varunismic temperaments
  • Werckismic temperaments
  • Valinorsmic temperaments
  • Swetismic temperaments
  • Wizmic microtemperaments
  • Metric microtemperaments
  • Vulture family
  • Tricot family
  • Minortonic family
  • Gammic family
  • Mirwomo temperaments
  • Augmented family
  • Dimipent family
  • Dicot family
  • Bug family
  • Pelogic family
  • Horwell family
  • Horwell temperaments
  • Gariboh clan
  • Gariboh family
  • Octagar temperaments
  • Octagar family

Regular temperament properties

Subgroup Comma list Mapping Optimal
8ve stretch (¢) 		Tuning error
Absolute (¢) Relative (%)
2.3 [-49 31⟩ [⟨31 49]] +1.63 1.64 4.22
2.3.5 81/80, 393216/390625 [⟨31 49 72]] +0.98 1.63 4.20
2.3.5.7 81/80, 126/125, 1029/1024 [⟨31 49 72 87]] +0.83 1.43 3.70
2.3.5.7.11 81/80, 99/98, 121/120, 126/125 [⟨31 49 72 87 107]] +1.21 1.49 3.84

Scale tree

6-tone
1L 5s, 2L 4s, 3L 3s, 4L 2s, 5L 1s
7-tone
1L 6s, 2L 5s, 3L 4s, 4L 3s, 5L 2s, 6L 1s
8-tone
1L 7s, 2L 6s, 3L 5s, 4L 4s, 5L 3s, 6L 2s, 7L 1s
9-tone
1L 8s, 2L 7s, 3L 6s, 4L 5s, 5L 4s, 6L 3s, 7L 2s, 8L 1s
10-tone
1L 9s, 2L 8s, 3L 7s, 4L 6s, 5L 5s, 6L 4s, 7L 3s, 8L 2s, 9L 1s
11-tone
1L 10s, 2L 9s, 3L 8s, 4L 7s, 5L 6s, 6L 5s, 7L 4s, 8L 3s, 9L 2s, 10L 1s
12-tone
1L 11s, 2L 10s, 3L 9s, 4L 8s, 5L 7s, 6L 6s, 7L 5s, 8L 4s, 9L 3s, 10L 2s, 11L 1s

(Bounded by branch depth = 7)

Generator Cents L s L/s Comments
4\7 685.714 1 1 1.000
27\47 689.362 7 6 1.167
23\40 690.000 6 5 1.200
42\73 690.411 11 9 1.222
19\33 690.909 5 4 1.250
53\92 691.304 14 11 1.273
34\59 691.525 9 7 1.286
49\85 691.765 13 10 1.300
15\26 692.308 4 3 1.333
56\97 692.784 15 11 1.364
41\71 692.958 11 8 1.375
67\116 693.103 18 13 1.385
26\45 693.333 7 5 1.400
63\109 693.578 17 12 1.417
37\64 693.750 10 7 1.429
48\83 693.976 13 9 1.444
11\19 694.737 3 2 1.500 L/s = 3/2
51\88 695.455 14 9 1.556
40\69 695.652 11 7 1.571
69\119 695.798 19 12 1.583
29\50 696.000 8 5 1.600
66\131 696.183 21 13 1.615 Golden meantone
47\81 696.296 13 8 1.625
65\112 696.429 18 11 1.636
18\31 696.774 5 3 1.667 Meantone is in this region
61\105 697.143 17 10 1.700
43\74 697.297 12 7 1.714
68\117 697.436 19 11 1.727
25\43 697.674 7 4 1.750
57\98 697.959 16 9 1.778
32\55 698.182 9 5 1.800
39\67 698.507 11 6 1.833
7\12 700.000 2 1 2.000 Basic diatonic
(Generators smaller than this are proper)
38\65 701.539 11 5 2.200
31\53 701.887 9 4 2.250
55\94 702.128 16 7 2.286
24\41 702.409 7 3 2.333
65\111 702.703 19 8 2.375
41\70 702.857 12 5 2.400
58\99 703.030 17 7 2.428
17\29 703.448 5 2 2.500
61\104 703.846 18 7 2.571
44\75 704.000 13 5 2.600
71\121 704.132 21 8 2.625 Golden neogothic
27\46 704.348 8 3 2.667
64\109 704.587 19 7 2.714
37\63 704.762 11 4 2.750
47\80 705.000 14 5 2.800
10\17 705.882 3 1 3.000 L/s = 3/1
43\73 706.849 13 4 3.250
33\56 707.143 10 3 3.333
56\95 707.368 17 5 3.400
23\39 707.692 7 2 3.500
59\100 708.000 18 5 3.600
36\61 708.197 11 3 3.667
49\83 708.434 15 4 3.750
13\22 709.091 4 1 4.000 Archy is in this region
42\71 709.859 13 3 4.333
29\49 710.204 9 2 4.500
45\76 710.526 14 3 4.667
16\27 711.111 5 1 5.000
35\59 711.864 11 2 5.500
19\32 712.500 6 1 6.000
22\37 713.514 7 1 7.000
3\5 720.000 1 0 → inf
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