@@ Line 1: / Line 1: @@
+{{Flat}}{{natural}}{{sharp}}
+&#x266D;&#x266E;&#x266F;
+<span class="bravura">&#xE260;</span>
+<span class="bravura">&#xE261;</span>
+<span class="bravura">&#xE262;</span>
+<span class="heji">n</span>
+== Template: Temperament data ==
 {{User:FloraC/Temperament data
 | Subgroup = 2.3.5.7
@@ Line 140: / Line 152: @@
 |}
-== Tunings to be reviewed ==
+== Tunings ==
 {| class="wikitable mw-collapsible mw-collapsed"
 |+style=white-space:nowrap | 5-limit Prime-Optimized Tunings
 |-
-! Weight-skew\Order !! Chebyshevian !! Euclidean !! Manhattan
+! rowspan="2" |
+! rowspan="2" | Manhattan
+! colspan="2" | Euclidean
+! rowspan="2" | Chebyshevian
 |-
-| Tenney || CTC<br>~3/2 = 696.5784¢<br>Eigenmonzo basis: 2.5 (1/4-comma tuning) || CTE<br>~3/2 = 697.2143¢ || CTOP<br>~3/2 = 698.0197¢
+! Unskewed
+! Skewed
 |-
-| Tenney-Weil || CTWC<br>~3/2 = 696.5784¢<br>Eigenmonzo basis: 2.5 (1/4-comma tuning) || CTWE<br>~3/2 = 696.6512¢ || CTWOP<br>~3/2 = 696.5784¢<br>Eigenmonzo basis: 2.5 (1/4-comma tuning)
+! Equilateral
+| CEOP: ~3/2 = 697.654¢<br>(1/5-comma)
+| CEE: ~3/2 = 696.895¢<br>(4/17-comma)
+| CSEE: ~3/2 = 696.453¢<br>(11/43-comma)
+| CEC: ~3/2 = 696.578¢<br>(1/4-comma)
 |-
-| Equilateral || CEC<br>~3/2 = 696.5784¢<br>Eigenmonzo basis: 2.5 (1/4-comma tuning) || CEE<br>~3/2 = 696.8947¢<br>Eigenmonzo basis: 2.1875 (4/17-comma tuning) || CEOP<br>~3/2 = 697.6537¢<br>Eigenmonzo basis: 2.15 (1/5-comma tuning)
+! Tenney
+| CTOP: ~3/2 = 698.020¢
+| CTE: ~3/2 = 697.214¢
+| CWE: ~3/2 = 696.651¢
+| CTC: ~3/2 = 696.578¢<br>(1/4-comma)
 |-
-| Equilateral-Weil || CEWC<br>~3/2 = 696.5784¢<br>Eigenmonzo basis: 2.5 (1/4-comma tuning) || CEWE<br>~3/2 = 696.4534¢<br>Eigenmonzo basis: 2.48828125/3 (11/43-comma tuning) || CEWOP<br>~3/2 = 696.5784¢<br>Eigenmonzo basis: 2.5 (1/4-comma tuning)
+! Benedetti, <br>Wilson
-|-
+| CBOP: ~3/2 = 698.160¢<br>(3/17-comma)
-| Benedetti || CBC<br>~3/2 = 696.5784¢<br>Eigenmonzo basis: 2.5 (1/4-comma tuning) || CBE<br>~3/2 = 697.3738¢<br>Eigenmonzo basis: 2.{{monzo| 0 25 36 }} (36/169-comma tuning) || CBOP<br>~3/2 = 698.1598¢<br>Eigenmonzo basis: 2.30375 (3/17-comma tuning)
+| CBE: ~3/2 = 697.374¢<br>(36/169-comma)
-|-
+| CSBE: ~3/2 = 696.787¢<br>(31/129-comma)
-| Benedetti-Weil || CBWC<br>~3/2 = 696.5784¢<br>Eigenmonzo basis: 2.5 (1/4-comma tuning) || CBWE<br>~3/2 = 696.7868¢<br>Eigenmonzo basis: 2.{{monzo| 0 5 31 }} (31/129-comma tuning) || CBWOP<br>~3/2 = 696.5784¢<br>Eigenmonzo basis: 2.5 (1/4-comma tuning)
+| CBC: ~3/2 = 696.578¢<br>(1/4-comma)
 |}
@@ Line 162: / Line 186: @@
 |+style=white-space:nowrap | 7-limit Prime-Optimized Tunings
 |-
-! Weight-skew\Order !! Chebyshevian !! Euclidean !! Manhattan
+! rowspan="2" |
+! rowspan="2" | Manhattan
+! colspan="2" | Euclidean
+! rowspan="2" | Chebyshevian
 |-
-| Tenney || CTC<br>~3/2 = 696.8826¢<br>Eigenmonzo basis: 2.7 || CTE<br>~3/2 = 696.9521¢ || CTOP<br>~3/2 = 696.6458¢
+! Unskewed
+! Skewed
 |-
-| Tenney-Weil || CTWC<br>~3/2 = 696.8826¢<br>Eigenmonzo basis: 2.7 || CTWE<br>~3/2 = 696.6562¢ || CTWOP<br>~3/2 = 696.8826¢<br>Eigenmonzo basis: 2.7
+! Equilateral
+| CEOP: ~3/2 = 697.344¢
+| CEE: ~3/2 = 696.884¢
+| CSEE: ~3/2 = 696.725¢
+| CEC: ~3/2 = 696.883¢
 |-
-| Equilateral || CEC<br>~3/2 = 696.8826¢<br>Eigenmonzo basis: 2.7 || CEE<br>~3/2 = 696.8843¢<br>Eigenmonzo basis: 2.{{monzo| 0 1 4 10 }} || CEOP<br>~3/2 = 697.3437¢<br>Eigenmonzo basis: 2.21
+! Tenney
+| CTOP: ~3/2 = 696.646¢
+| CTE: ~3/2 = 696.952¢
+| CWE: ~3/2 = 696.656¢
+| CTC: ~3/2 = 696.883¢
 |-
-| Equilateral-Weil || CEWC<br>~3/2 = 696.8826¢<br>Eigenmonzo basis: 2.7 || CEWE<br>~3/2 = 696.7248¢<br>Eigenmonzo basis: 2.4117715/9 || CEWOP<br>~3/2 = 696.8826¢<br>Eigenmonzo basis: 2.7
+! Benedetti, <br>Wilson
-|-
+| CBOP: ~3/2 = 697.842¢
-| Benedetti || CBC<br>~3/2 = 696.8826¢<br>Eigenmonzo basis: 2.7 || CBE<br>~3/2 = 697.0147¢<br>Eigenmonzo basis: 2.{{monzo| 0 1225 1764 2250 }} || CBOP<br>~3/2 = 697.8422¢<br>Eigenmonzo basis: 2.750141
+| CBE: ~3/2 = 697.015¢
-|-
+| CSBE: ~3/2 = 696.631¢
-| Benedetti-Weil || CBWC<br>~3/2 = 696.8826¢<br>Eigenmonzo basis: 2.7 || CBWE<br>~3/2 = 696.6306¢<br>Eigenmonzo basis: 2.{{monzo| 0 -3290 3171 7215 }} || CBWOP<br>~3/2 = 696.8826¢<br>Eigenmonzo basis: 2.7
+| CBC: ~3/2 = 696.883¢
 |}
 == Temperament pages ==
 Note:
-# Order: [[subgroup]], [[comma list]], ([[sval]]) [[mapping]], (sval) mapping generators, gencom mapping, [[gencom]], lattice basis, [[wedgie]], [[optimal tuning]] ([[CTE]]), [[minimax tuning]], [[tuning ranges]], [[algebraic generator]], [[Optimal ET sequence]], [[badness]], [[complexity spectrum]], and others.
+# Order: [[subgroup]], [[comma list]], ([[sval]]) [[mapping]], (sval) mapping generators, gencom mapping, [[gencom]], lattice basis, [[wedgie]], [[optimal tuning]]s ([[CTE]], [[CWE]]/[[POTE]]), [[minimax tuning]], [[tuning ranges]], [[algebraic generator]], [[optimal ET sequence]], [[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 tunings are based on tonality diamond, it should explicitly state the ''odd'' limit, or a diamond function of ratios.
-# For subgroup temperaments, "mapping" becomes "sval mapping", add "gencom mapping" and "gencom". If TE is TE is TE (''sic''), simply show "CTE", otherwise show "subgroup CTE" or "inharmonic CTE" instead.
+# For subgroup temperaments, "mapping" becomes "sval mapping", add "gencom mapping" and "gencom". If TE is TE is TE (''sic''), simply show "CTE/CWE", otherwise show "subgroup/inharmonic CTE/CWE" instead.
 Get a family for:
@@ Line 232: / Line 268: @@
 * <s>Kleismic family</s>
 * <s>Kleismic rank three family</s>
-* [[Hemimean clan]]
+* <s>Würschmidt family</s>
-* <s>Hemimean family</s>
 * <s>Unicorn family</s>
 * <s>Shibboleth family</s>
@@ Line 243: / Line 278: @@
 * <s>Sycamore family</s>
 * <s>Semicomma family</s>
-* [[Orwellismic temperaments]]
+* <s>Orwellismic temperaments</s>
 * <s>Orwellismic family</s>
-* [[Hemimage temperaments]]
+* <s>Hemimean clan</s>
+* <s>Hemimean family</s>
+* <s>Hemifamity temperaments</s>
+* <s>Hemifamity family</s>
+* <s>Porwell temperaments</s>
+* <s>Porwell family</s>
+* <s>Hemimage temperaments</s>
 * <s>Hemimage family</s>
-* [[Porwell temperaments]]
-* <s>Porwell family</s>
-* [[Hemifamity temperaments]]
-* <s>Hemifamity family</s>
 * <s>Porcupine family</s>
 * <s>Porcupine rank three family</s>
@@ Line 260: / Line 297: @@
 * <s>Misty family</s>
 * <s>Undim family</s>
-* [[Lehmerismic temperaments]]
+* <s>Lehmerismic temperaments</s>
-* [[Kalismic temperaments]]
+* <s>Kalismic temperaments</s>
-* [[Ragismic microtemperaments]]
+* <s>Ragismic microtemperaments</s>
 * <s>Ragismic family</s>
-* [[Landscape microtemperaments]]
+* <s>Landscape microtemperaments</s>
 * <s>Landscape family</s>
 * <s>Dimcomp family</s>
-* [[Mirkwai clan]]
+* <s>Mirkwai clan</s>
-* [[Mirkwai family]]
+* <s>Mirkwai family</s>
-* [[Breedsmic temperaments]]
+* <s>Quince clan</s>
-* [[Breed family]]
+* <s>Breedsmic temperaments</s>
+* <s>Breed family</s>
 * <s>Escapade family</s>
 * <s>Gravity family</s>
-* [[Cataharry temperaments]]
+* <s>Cataharry temperaments</s>
 * <s>Cataharry family</s>
-* [[Varunismic temperaments]]
+* <s>Varunismic temperaments</s>
 * <s>Rastmic rank three clan</s>
 * <s>Biyatismic clan</s>
-* [[Ptolemismic clan]]
+* <s>Ptolemismic clan</s>
 * <s>Valinorsmic clan</s>
 * <s>Pentacircle clan</s>
@@ Line 284: / Line 322: @@
 * <s>Werckismic temperaments</s>
 * <s>Swetismic temperaments</s>
-* [[Wizmic microtemperaments]]
+* <s>Wizmic microtemperaments</s>
-* [[Metric microtemperaments]]
+* <s>Metric microtemperaments</s>
+* <s>Horwell temperaments</s>
+* <s>Horwell family</s>
 * <s>Luna family</s>
 * <s>Vulture family</s>
@@ Line 291: / Line 331: @@
 * <s>Minortonic family</s>
 * <s>Gammic family</s>
+* <s>Vishnuzmic family</s>
 * <s>Garischismic clan</s>
 * <s>Canousmic temperaments</s>
@@ Line 298: / Line 339: @@
 * <s>Olympic clan</s>
 * <s>Alphaxenic rank three clan</s>
-* [[Mirwomo temperaments]]
+* <s>Mirwomo temperaments</s>
-* [[Horwell temperaments]]
+* <s>Gariboh clan</s>
-* [[Horwell family]]
+* <s>Gariboh family</s>
-* [[Gariboh clan]]
+* <s>Octagar temperaments</s>
-* [[Gariboh family]]
+* <s>Octagar family</s>
-* [[Octagar temperaments]]
+* <s>Wesley family</s>
-* [[Octagar family]]
+* <s>Apotome family</s>
+* [[Mabila family]]
+* [[Maquila family]]
+* [[Maja family]]
+* [[Ditonmic family]]
+* <s>Greenwoodmic temperaments</s>
+* <s>Avicennmic temperaments</s>
 == Regular temperament properties ==
@@ Line 367: / Line 414: @@
 ; 12-tone
 : [[1L 11s]], [[2L 10s]], [[3L 9s]], [[4L 8s]], <s>5L 7s</s>, <s>6L 6s</s>, <s>7L 5s</s>, [[8L 4s]], [[9L 3s]], [[10L 2s]], [[11L 1s]]
-(Bounded by branch depth = 7)
-{| class="wikitable center-all"
-! colspan="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<br>(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 ||
-|}

User:FloraC/Sandbox: Difference between revisions