Landscape microtemperaments: Difference between revisions

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VisualWikitext

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 * [[Misty]] (+3136/3125 or 5120/5103) → [[Misty family]]
 * ''[[Term (temperament)|Term]]'' (+32805/32768) → [[Schismatic family #Term|Schismatic family]]
+* ''[[Sextile]]'' (+33554432/33480783) → [[Garischismic clan #Sextile|Garischismic clan]]
 * ''[[Tritricot]]'' (+{{monzo| 35 -23 -3 3 }}) → [[Alphatricot family #Tritricot|Alphatricot family]]
 * [[Compton]] (+225/224) → [[Compton family #Compton|Compton family]]
-* ''[[Terture]]'' (+359661568/358722675) → [[Vulture family #Domain|Vulture family]]
+* ''[[Terture]]'' (+359661568/358722675) → [[Vulture family #Terture|Vulture family]]
-* ''[[Chromat]]'' (10976/10935) → [[Hemimage temperaments #Chromat|Hemimage temperaments]]
+* ''[[Pentadecal]]'' (+875/864) → [[Keemic temperaments #Pentadecal|Keemic temperaments]]
+* ''[[Chromat]]'' (+10976/10935) → [[Amity family #Chromat|Amity family]]
 * ''[[Tritikleismic]]'' (+1029/1024) → [[Kleismic family #Tritikleismic|Kleismic family]]
 * [[Ennealimmal]] (+2401/2400 or 4375/4374) → [[Septiennealimmal clan #Ennealimmal|Septiennealimmal clan]]
@@ Line 18: / Line 20: @@
 * ''[[Triquart]]'' (+117649/116640) → [[Quartonic family #Triquart|Quartonic family]]
 * ''[[Stearnscape]]'' (+118098/117649) → [[Stearnsmic clan #Stearnscape|Stearnsmic clan]]
-* ''[[Domain (temperament)|Domain]]'' (+645700815/645657712) → [[Minortonic family #Domain|Minortonic family]]
+* ''[[Trivish]]'' (+134217728/133984375) → [[Vishnu family #Trivish|Vishnu family]]
+* ''[[Domain (temperament)|Domain]]'' (+645700815/645657712) → [[Minortone family #Domain|Minortone family]]
 * ''[[Aemilic]]'' (+{{monzo|-84 53}}) → [[159th-octave temperaments #Aemilic|159th-octave temperaments]]
-Considered below are septichrome, akjayland, pnict, atomic, slendscape, avicenna, sextile, zinc, magnesium, poe, and chromium in the order of increasing [[badness]].
+Considered below are septichrome, akjayland, pnict, atomic, slendscape, avicenna, zinc, magnesium, poe, chromium, and phosphorus in the order of increasing [[badness]].
 == Septichrome ==
@@ Line 73: / Line 76: @@
 ==== 17-limit ====
-Subgroup: 2.3.5.7.11.13
+Subgroup: 2.3.5.7.11.13.17
 Comma list: 936/935, 1701/1700, 1716/1715, 2025/2023, 61965/61952
@@ Line 510: / Line 513: @@
 Badness (Sintel): 0.928
-== Sextile ==
-: ''For the 5-limit version, see [[Schismic–commatic equivalence continuum #Sextile (5-limit)]].''
-Sextile tempers out the [[garischisma]] with a 1/6-octave period and is the {{nowrap| 12 & 270 }} temperament.
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 250047/250000, 33554432/33480783
-{{Mapping|legend=1| 6 0 71 150 | 0 1 -6 -14 }}
-: mapping generators: ~4096/3645, ~3
-[[Optimal tuning]]s:
-* [[WE]]: ~4096/3645 = 199.9828{{c}}, ~3/2 = 702.1521{{c}}
-: [[error map]]: {{val| -0.103 +0.094 +0.173 -0.088 }}
-* [[CWE]]: ~4096/3645 = 200.0000{{c}}, ~3/2 = 702.2187{{c}}
-: error map: {{val| 0.000 +0.264 +0.374 +0.112 }}
-{{Optimal ET sequence|legend=1| 12, …, 258, 270, 1362c, 1632c, …, 2442bc, 2712bc }}
-[[Badness]] (Sintel): 1.77
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 5632/5625, 9801/9800, 151263/151250
-Mapping: {{mapping| 6 0 71 150 230 | 0 1 -6 -14 -22 }}
-Optimal tunings:
-* WE: ~55/49 = 199.9817{{c}}, ~3/2 = 702.1383{{c}}
-* CWE: ~55/49 = 200.0000{{c}}, ~3/2 = 702.2080{{c}}
-{{Optimal ET sequence|legend=0| 12, …, 258e, 270, 822, 1092, 1362c }}
-Badness (Sintel): 0.981
-=== 13-limit ===
-Subgroup: 2.3.5.7.11.13
-Comma list: 1716/1715, 2080/2079, 5632/5625, 10648/10647
-Mapping: {{mapping| 6 0 71 150 230 279 | 0 1 -6 -14 -22 -27 }}
-Optimal tunings:
-* WE: ~55/49 = 199.9804{{c}}, ~3/2 = 702.1260{{c}}
-* CWE: ~55/49 = 200.0000{{c}}, ~3/2 = 702.2001{{c}}
-{{Optimal ET sequence|legend=0| 12f, …, 258ef, 270, 552, 822, 1092, 1914cde }}
-Badness (Sintel): 0.788
-==== 17-limit ====
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 936/935, 1701/1700, 1716/1715, 5632/5625, 7744/7735
-Mapping: {{mapping| 6 0 71 150 230 279 -4 | 0 1 -6 -14 -22 -27 3 }}
-Optimal tunings:
-* WE: ~55/49 = 199.9669{{c}}, ~3/2 = 702.0643{{c}}
-* CWE: ~55/49 = 200.0000{{c}}, ~3/2 = 702.1869{{c}}
-{{Optimal ET sequence|legend=0| 12f, 270, 552g }}
-Badness (Sintel): 1.06
-==== 19-limit ====
-Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 936/935, 1216/1215, 1701/1700, 1716/1715, 2376/2375, 4200/4199
-Mapping: {{mapping| 6 0 71 150 230 279 -4 35 | 0 1 -6 -14 -22 -27 3 -1 }}
-Optimal tunings:
-* WE: ~55/49 = 199.9711{{c}}, ~3/2 = 702.0829{{c}}
-* CWE: ~55/49 = 200.0000{{c}}, ~3/2 = 702.1890{{c}}
-{{Optimal ET sequence|legend=0| 12f, 270, 552g, 822gg }}
-Badness (Sintel): 0.948
-=== Sextilia ===
-Subgroup: 2.3.5.7.11.13
-Comma list: 1001/1000, 4096/4095, 4459/4455, 20449/20412
-Mapping: {{mapping| 6 0 71 150 230 -149 | 0 1 -6 -14 -22 18 }}
-Optimal tunings:
-* WE: ~55/49 = 199.9975{{c}}, ~3/2 = 702.2196{{c}}
-* CWE: ~55/49 = 200.0000{{c}}, ~3/2 = 702.2285{{c}}
-{{Optimal ET sequence|legend=0| 12, 258e, 270 }}
-Badness (Sintel): 1.62
-==== 17-limit ====
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 715/714, 1001/1000, 1701/1700, 4096/4095, 4459/4455
-Mapping: {{mapping| 6 0 71 150 230 -149 -4 | 0 1 -6 -14 -22 18 3 }}
-Optimal tunings:
-* WE: ~55/49 = 199.9862{{c}}, ~3/2 = 702.1714{{c}}
-* CWE: ~55/49 = 200.0000{{c}}, ~3/2 = 702.2207{{c}}
-{{Optimal ET sequence|legend=0| 12, 258e, 270 }}
-Badness (Sintel): 1.95
-==== 19-limit ====
-Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 715/714, 1001/1000, 1216/1215, 1701/1700, 1729/1728, 2912/2907
-Mapping: {{mapping| 6 0 71 150 230 -149 -4 35 | 0 1 -6 -14 -22 18 3 -1 }}
-Optimal tunings:
-* WE: ~55/49 = 199.9866{{c}}, ~3/2 = 702.1731{{c}}
-* CWE: ~55/49 = 200.0000{{c}}, ~3/2 = 702.2208{{c}}
-{{Optimal ET sequence|legend=0| 12, 258e, 270 }}
-Badness (Sintel): 1.53
 == Zinc ==
-{{See also| 10th-octave temperaments #Neon }}
+Zinc maybe described as the {{nowrap| 270 & 2190 }} temperament, and is a [[weak extension]] of [[miscellaneous 5-limit temperaments #Neon|neon]]. It was named by [[Eliora]] in 2023 after the 30th element for having a 30th-octave period.
-Zinc maybe described as the {{nowrap| 270 & 2190 }} temperament. It was named by [[Eliora]] in 2023 after the 30th element for having a 30th-octave period.
 [[Subgroup]]: 2.3.5.7
@@ Line 690: / Line 564: @@
 Badness (Sintel): 0.640
-==== 2.3.5.7.11.13.19 subgroup (neozinc) ====
+==== 2.3.5.7.11.13.19 subgroup ====
 Subgroup: 2.3.5.7.11.13.19
@@ Line 876: / Line 750: @@
 Badness (Sintel): 1.06
+== Phosphorus ==
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 250047/250000, {{monzo| 60 -96 1 32 }}
+[[Mapping]]: {{mapping| 15 8 -4 -4 | 0 13 32 38 }}
+: mapping generators: ~{{monzo| -21 34 4 -15 }}, ~210827008/199290375
+[[Optimal tuning]]s:
+* [[WE]]: ~{{monzo|-21 34 4 -15}} = 80.000039{{c}}, ~210827008/199290375 = 97.073339{{c}}
+: [[error map]]: {{val| +0.0006 -0.0013 +0.0330 -0.0392 }}
+* [[CWE]]: ~{{monzo|-21 34 4 -15}} = 80.000000{{c}}, ~210827008/199290375 = 97.073314{{c}}
+: error map: {{val| 0.0000 -0.0019 +0.0323 -0.0400 }}
+{{Optimal ET sequence|legend=1| 210, …, 1125, 1335, 2460 }}
+[[Badness]] (Sintel): 9.66
 [[Category:Temperament collections]]
 [[Category:Landscape microtemperaments| ]] <!-- main article -->
 [[Category:Rank 2]]