@@ Line 6: / Line 6: @@
 * ''[[Flattie]]'' (+21/20) → [[Dicot family #Flattie|Dicot family]]
 * ''[[Opossum]]'' (+28/27) → [[Trienstonic clan #Opossum|Trienstonic clan]]
-* [[Diminished (temperament)|Diminished]] (+36/35) → [[Dimipent family #Diminished|Dimipent family]]
+* [[Diminished (temperament)|Diminished]] (+36/35) → [[Diminished family #Septimal diminished|Diminished family]]
 * [[Keemun]] (+49/48) → [[Kleismic family #Keemun|Kleismic family]]
 * [[Augene]] (+64/63) → [[Augmented family #Augene|Augmented family]]
@@ Line 12: / Line 12: @@
 * [[Mavila]] (+135/128) → [[Pelogic family #Mavila|Pelogic family]]
 * [[Sensi]] (+245/243), [[Sensipent family #Sensi|Sensipent family]]
-* ''[[Gilead]]'' (+343/324) → [[Shibboleth family #Gilead|Shibboleth family]]
 * [[Muggles]] (+525/512) → [[Magic family #Muggles|Magic family]]
 * [[Valentine]] (+1029/1024) → [[Gamelismic clan #Valentine|Gamelismic clan]]
-* ''[[Diaschismic]]'' (+2048/2025) → [[Diaschismic family #Diaschismic|Diaschismic family]]
+* ''[[Diaschismic]]'' (+2048/2025) → [[Diaschismic family #Septimal diaschismic|Diaschismic family]]
 * ''[[Wollemia]]'' (+2240/2187) → [[Tetracot family #Wollemia|Tetracot family]]
 * ''[[Unicorn]]'' (+10976/10935) → [[Unicorn family #Unicorn|Unicorn family]]
@@ Line 21: / Line 20: @@
 * ''[[Grackle]]'' (+32805/32768) → [[Schismatic family #Grackle|Schismatic family]]
 * ''[[Worschmidt]]'' (+33075/32768) → [[Würschmidt family #Worschmidt|Würschmidt family]]
+* ''[[Thuja]]'' (+65536/64827) → [[Buzzardsmic clan #Thuja|Buzzardsmic clan]]
 * ''[[Passionate]]'' (+131072/127575) → [[Passion family #Passionate|Passion family]]
 * ''[[Vishnean]]'' (+540225/524288) → [[Vishnuzmic family #Vishnean|Vishnuzmic family]]
@@ Line 32: / Line 32: @@
 {{Main| Myna }}
-In addition to 126/125, myna tempers out [[1728/1715]], the orwell comma, and [[2401/2400]], the breedsma. It can also be described as the {{nowrap|27 &amp; 31}} temperament. It has 6/5 as a generator, and [[58edo]] can be used as a tuning, with [[89edo]] being a better one, and fans of round amounts in cents may like [[120edo]]. It is also possible to tune myna with pure fifths by taking 6<sup>1/10</sup> as the generator. Myna extends naturally but with much increased complexity to the 11 and 13 limits.
+-limit myna is naturally found by establishing a structure of thirds, by making [[7/6]] - [[6/5]] - [[49/40]] - [[5/4]] - [[9/7]] all equidistant (the distances between which are [[36/35]], [[49/48]], and [[50/49]]). 11-limit myna then arises from equating this neutral third to [[11/9]]. Myna's characteristic feature is that the pental thirds are tuned outwards so that the chroma between them ([[25/24]]) is twice the size of the interval between the pental and septimal thirds ([[36/35]]), leaving space for a neutral third in between. In that sense, it is opposed to [[keemic temperaments]], where the chroma between the pental thirds is the same as the distance between the pental and septimal thirds.
+In terms of commas tempered, in addition to 126/125, myna adds [[1728/1715]], the orwell comma, and [[2401/2400]], the breedsma. It can also be described as the {{nowrap|27 &amp; 31}} temperament. It has 6/5 as a generator, and [[58edo]] can be used as a tuning, with [[89edo]] being a better one, and fans of round amounts in cents may like [[120edo]]. It is also possible to tune myna with pure fifths by taking 6<sup>1/10</sup> as the generator. Myna extends naturally but with much increased complexity to the 11 and 13 limits.
 [[Subgroup]]: 2.3.5.7
@@ Line 41: / Line 43: @@
 : mapping generators: ~2, ~5/3
-{{Multival|legend=1| 10 9 7 -9 -17 -9 }}
 [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 310.146
@@ Line 49: / Line 49: @@
 * 7- and [[9-odd-limit]]: ~6/5 = {{monzo| 1/10 1/10 0 0}}
 : {{monzo list| 1 0 0 0 | 0 1 0 0 | 9/10 9/10 0 0 | 17/10 7/10 0 0 }}
-: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.3
+: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3
 {{Optimal ET sequence|legend=1| 27, 31, 58, 89 }}
@@ Line 61: / Line 61: @@
 Mapping: {{mapping| 1 9 9 8 22 | 0 -10 -9 -7 -25 }}
-{{Multival|legend=1| 10 9 7 25 -9 -17 5 -9 27 46 }}
 Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 310.144
@@ Line 147: / Line 145: @@
 : mapping generators: ~2, ~49/45
-{{Multival|legend=1| 11 13 17 -5 -4 3 }}
 [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~49/45 = 154.579
@@ Line 155: / Line 151: @@
 * [[7-odd-limit]]: ~49/45 = {{monzo| 4/13 0 -1/13 }}
 : {{monzo list| 1 0 0 0 | -5/13 0 11/13 0 | 0 0 1 0 | -3/13 0 17/13 0 }}
-: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.5
+: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5
 * [[9-odd-limit]]: ~49/45 = {{monzo| 3/11 -1/11 }}
 : {{monzo list| 1 0 0 0 | 0 1 0 0 | 5/11 13/11 0 0 | 4/11 17/11 0 0 }}
-: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.3
+: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3
 {{Optimal ET sequence|legend=1| 8d, 23d, 31, 101, 132c, 163c }}
@@ Line 176: / Line 172: @@
 * [[11-odd-limit]]: ~11/10 = {{monzo| 1/10 -1/5 0 0 1/10 }}
 : [{{monzo| 1 0 0 0 0 }}, {{monzo| 19/10 11/5 0 0 -11/10 }}, {{monzo| 27/10 13/5 0 0 -13/10 }}, {{monzo| 33/10 17/5 0 0 -17/10 }}, {{monzo| 19/5 12/5 0 0 -6/5 }}]
-: eigenmonzo (unchanged-interval) basis: 2.11/9
+: unchanged-interval (eigenmonzo) basis: 2.11/9
 Algebraic generator: positive root of 15''x''<sup>2</sup> - 10''x'' - 7, or (5 + sqrt (130))/15, at 154.6652 cents. The recurrence converges very quickly.
@@ Line 206: / Line 202: @@
 {{Mapping|legend=1| 1 6 7 8 | 0 -17 -18 -20 }}
-{{Multival|legend=1| 17 18 20 -11 -16 -4 }}
 [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 311.679
@@ Line 290: / Line 284: @@
 {{Mapping|legend=1| 1 4 4 3 | 0 -13 -9 -1 }}
-{{Multival|legend=1| 13 9 1 -16 -35 -23 }}
 [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~8/7 = 222.797
@@ Line 324: / Line 316: @@
 Badness: 0.028920
-== Thuja ==
-: ''For the 5-limit version of this temperament, see [[High badness temperaments #Thuja]].''
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 126/125, 65536/64827
-{{Mapping|legend=1| 1 -4 0 7 | 0 12 5 -9 }}
-{{Multival|legend=1| 12 5 -9 -20 -48 -35 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~175/128 = 558.605
-{{Optimal ET sequence|legend=1| 15, 43, 58 }}
-[[Badness]]: 0.088441
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 126/125, 176/175, 1344/1331
-Mapping: {{mapping| 1 -4 0 7 3 | 0 12 5 -9 1 }}
-Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 558.620
-{{Optimal ET sequence|legend=1| 15, 43, 58 }}
-Badness: 0.033078
-=== 13-limit ===
-Subgroup: 2.3.5.7.11.13
-Comma list: 126/125, 144/143, 176/175, 364/363
-Mapping: {{mapping| 1 -4 0 7 3 -7 | 0 12 5 -9 1 23 }}
-Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 558.589
-{{Optimal ET sequence|legend=1| 15, 43, 58 }}
-Badness: 0.022838
-=== 17-limit ===
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 126/125, 144/143, 176/175, 221/220, 256/255
-Mapping: {{mapping| 1 -4 0 7 3 -7 12 | 0 12 5 -9 1 23 -17 }}
-Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 558.509
-{{Optimal ET sequence|legend=1| 15, 43, 58 }}
-Badness: 0.022293
-=== 19-limit ===
-Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 96/95, 126/125, 144/143, 153/152, 176/175, 221/220
-Mapping: {{mapping| 1 -4 0 7 3 -7 12 1 | 0 12 5 -9 1 23 -17 7 }}
-Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 558.504
-{{Optimal ET sequence|legend=1| 15, 43, 58h }}
-Badness: 0.018938
-=== 23-limit ===
-Subgroup: 2.3.5.7.11.13.17.19.23
-Comma list: 96/95, 126/125, 144/143, 153/152, 176/175, 221/220, 231/230
-Mapping: {{mapping| 1 -4 0 7 3 -7 12 1 5 | 0 12 5 -9 1 23 -17 7 -1 }}
-Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 558.522
-{{Optimal ET sequence|legend=1| 15, 43, 58hi }}
-Badness: 0.016581
-=== 29-limit ===
-The ''raison d'etre'' of this entry is the simple and accurate approximation of factor twenty-nine, the 2.5.11.21.29 subgroup being of especially good accuracy and simplicity.
-Subgroup: 2.3.5.7.11.13.17.19.23.29
-Comma list: 96/95, 116/115, 126/125, 144/143, 153/152, 176/175, 221/220, 231/230
-Mapping: {{mapping| 1 -4 0 7 3 -7 12 1 5 3 | 0 12 5 -9 1 23 -17 7 -1 4 }}
-Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 558.520
-{{Optimal ET sequence|legend=1| 15, 43, 58hi }}
-Badness: 0.013762
 == Cypress ==
@@ Line 430: / Line 325: @@
 {{Mapping|legend=1| 1 7 10 15 | 0 -12 -17 -27 }}
-{{Multival|legend=1| 12 17 27 -1 9 15 }}
 [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~135/98 = 541.828
@@ Line 471: / Line 364: @@
 {{Mapping|legend=1| 2 1 2 2 | 0 9 11 15 }}
-{{Multival|legend=1| 18 22 30 -7 -3 8 }}
 [[Optimal tuning]] ([[POTE]]): ~343/243 = 1\2, ~35/27 = 455.445
@@ Line 520: / Line 411: @@
 {{Mapping|legend=1| 1 12 10 5 | 0 -19 -14 -4 }}
-{{Multival|legend=1| 19 14 4 -22 -47 -30 }}
 [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~35/24 = 657.818
@@ Line 535: / Line 424: @@
 Mapping: {{mapping| 1 12 10 5 4 | 0 -19 -14 -4 -1 }}
-{{Multival|legend=1| 19 14 4 1 -22 -47 -64 -30 -46 -11 }}
 Optimal tuning (POTE): ~2 = 1\1, ~16/11 = 657.923
@@ Line 561: / Line 448: @@
 Mapping: {{mapping| 1 12 10 5 21 | 0 -19 -14 -4 -32 }}
-{{Multival|legend=1| 19 14 4 32 -22 -47 -15 -30 26 76 }}
 Optimal tuning (POTE): ~2 = 1\1, ~22/15 = 657.791
@@ Line 604: / Line 489: @@
 {{Mapping|legend=1| 1 -2 2 9 | 0 11 1 -19 }}
-{{Multival|legend=1| 11 1 -19 -24 -61 -47 }}
 [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~5/4 = 391.094
@@ Line 638: / Line 521: @@
 Badness: 0.030666
+== Gilead ==
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 126/125, 343/324
+{{Mapping|legend=1| 1 4 5 6 | 0 -9 -10 -12 }}
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1\1, ~6/5 = 321.109
+* [[POTE]]: ~2 = 1\1, ~6/5 = 321.423
+{{Optimal ET sequence|legend=1| 11cd, 15, 41dd, 56dd }}
+[[Badness]]: 0.115292
 == Supersensi ==
@@ Line 647: / Line 545: @@
 {{Mapping|legend=1| 1 -4 -4 -5 | 0 15 17 21 }}
-{{Multival|legend=1| 15 17 21 -8 -9 1 }}
 [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~343/270 = 446.568
@@ Line 804: / Line 700: @@
 [[Category:Temperament collections]]
+[[Category:Pages with mostly numerical content]]
 [[Category:Starling temperaments| ]] <!-- main article -->
 [[Category:Myna]]
 [[Category:Rank 2]]

Starling temperaments: Difference between revisions