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
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) |
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:
- 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.
- Comma list should show the simplest commas sufficient to define the temperament, stated in Normal lists #Normal interval list.
- Mapping generators should show all the ratios as used in the mapping, including the period.
- Since minimax tuning are based on tonality diamond, it should explicitly state the odd limit, or a diamond function of ratios.
- Replace "EDOs" with Template:Val list.
- 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)doneSmate (2 different 7-limit extensions)donePassion (4 different 7-limit extensions, 3 strong and 1 weak)doneParakleismic (2 different 7-limit extensions)canceled, not strong extensionsSuperpyth (2 different 7-limit extensions)canceled, not strong extensionsUndimdoneQuintaleapdoneQuindromedadone
Who's next?
Meantone familyArchytas clanFather familyTrienstonic clanSeptisemi temperamentsArchytas familySlendro clanSemiphore familyMarvel temperamentsMarvel familyMint temperamentsMint familyGamelismic clanGamelismic familyJubilismic clanJubilismic familyDidymus rank three familyKleismic familyKleismic rank three familyShibboleth familyKeemic temperamentsKeemic familySchismatic familyHemimean clanHemimean familyLuna familyCanousmic temperamentsCanou familyStarling temperamentsStarling familySensipent familySensamagic clanSensamagic familyMagic familyUnicorn familyTrisedodge familySycamore familyRastmic temperamentsSemicomma familyOrwellismic temperamentsOrwellismic familyHemimage temperamentsHemimage familyPorwell temperamentsPorwell familyHemifamity temperamentsHemifamity familyPorcupine familyPorcupine rank three familyTetracot familyMisty familyDiaschismic familyDiaschismic rank three familyAmity familyLehmerismic temperamentsKalismic temperamentsRagismic family- Ragismic microtemperaments
Landscape familyLandscape microtemperamentsDimcomp familyMirkwai familyMirkwai clanBreed familyBreedsmic temperamentsEscapade familyGravity familyCataharry familyCataharry temperamentsVarunismic temperamentsWerckismic temperamentsValinorsmic temperamentsSwetismic temperamentsWizmic microtemperamentsMetric microtemperamentsVulture familyTricot familyMinortonic familyGammic 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
- 7-tone
1L 6s,2L 5s,3L 4s,4L 3s,5L 2s,6L 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 |