Vishdelismic clan: Difference between revisions

VisualWikitext

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+{{Technical data page}}
 The '''vishdelismic clan''' of [[rank-3 temperament]]s [[tempering out|tempers out]] the [[vishdelisma]] ({{monzo|legend=1| 14 -3 -1 0 -2 }}, [[ratio]]: 5632/5625).
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 == Vishdelic ==
+The head of this clan is vishdelic, which finds [[11/9]] as a stack of four [[5/4]] major thirds minus an octave.
 [[Subgroup]]: 2.3.5.11
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 [[Badness]] (Sintel): 0.183
+=== Overview to extensions ===
+Temperaments discussed elsewhere are:
+* ''[[Minerva]]'' (+176/175) → [[Marvel family #Minerva|Marvel family]]
+* ''[[Zelda]]'' (+385/384) → [[Horwell family #Zelda|Horwell family]]
+* ''[[Belobog]]'' (+441/440) → [[Hemimean family #Belobog|Hemimean family]]
+* ''[[Jupiter]]'' (+540/539) → [[Porwell family #Jupiter|Porwell family]]
+* ''[[Mendel]]'' (+1375/1372) → [[Moctdelismic clan #Mendel|Moctdelismic clan]]
+* ''[[Zisa]]'' (+2401/2400) → [[Breed family #Zisa|Breed family]]
+The rest are considered below.
+== Ganesha ==
+: ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #Quasiorwellismic]].''
+[[Subgroup]]: 2.3.5.7.11
+[[Comma list]]: 3025/3024, 5632/5625
+{{Mapping|legend=1| 1 0 0 -22 -9 | 0 1 0 1 2 | 0 0 1 10 4 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9176{{c}}, ~3/2 = 702.1769{{c}}, ~5/4 = 386.6642{{c}}
+: [[error map]]: {{val| -0.082 +0.139 +0.186 +0.075 -0.390 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.1836{{c}}, ~5/4 = 386.6860{{c}}
+: error map: {{val| 0.000 +0.229 +0.372 +0.218 -0.207 }}
+{{Optimal ET sequence|legend=1| 31, 65d, 87, 118, 152, 239, 270, 962, 1232, 1502 }}
+[[Badness]] (Sintel): 0.469
+== Loki ==
+[[Subgroup]]: 2.3.5.7.11
+[[Comma list]]: 5632/5625, 9801/9800
+{{Mapping|legend=1| 2 0 0 -21 -18 | 0 1 0 4 2 | 0 0 1 3 4 }}
+: mapping generators: ~99/70, ~3, ~5
+[[Optimal tuning]]s:
+* [[WE]]: ~99/70 = 599.9481{{c}}, ~3/2 = 702.1195{{c}}, ~5/4 = 386.7636{{c}}
+: [[error map]]: {{val| -0.104 +0.061 +0.242 -0.005 -0.128 }}
+* [[CWE]]: ~99/70 = 600.0000{{c}}, ~3/2 = 702.1647{{c}}, ~5/4 = 386.7768{{c}}
+: error map: {{val| 0.000 +0.210 +0.463 +0.163 +0.119 }}
+{{Optimal ET sequence|legend=1| 12, 22, 34d, 56d, 74d, 84de, 96d, 118, 130, 152, 248, 270, 670, 822, 940, 1092, 1362c, 2032c, 2302c }}
+[[Badness]] (Sintel): 0.592
+== Baffin ==
+: ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #Decovulture]].''
+Baffin tempers out the [[olympia]] and the [[seascape comma]] in addition to the vishdelisma, so that the [[3/1|3rd]] [[harmonic]] is split in halves. This leads naturally to a [[13-limit]] temperament where [[676/675]], [[1001/1000]], [[2080/2079]] and [[4096/4095]] are all tempered out.
+It was named by [[Gene Ward Smith]] some time before 2011 for {{w|Baffin Island}}, as part of a series of island-themed names<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_96550.html#96556 Yahoo! Tuning Group | ''Madagascar<nowiki>[</nowiki>19<nowiki>]</nowiki>'']</ref>.
+[[Subgroup]]: 2.3.5.7.11
+[[Comma list]]: 5632/5625, 131072/130977
+{{Mapping|legend=1| 1 0 0 13 -9 | 0 2 0 -7 4 | 0 0 1 -2 4 }}
+: mapping generators: ~2, ~400/231, ~5
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9208{{c}}, ~400/231 = 950.9957{{c}}, ~5/4 = 386.7656{{c}}
+: [[error map]]: {{val| -0.079 +0.036 +0.293 -0.040 -0.193 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~400/231 = 951.0635{{c}}, ~5/4 = 386.7769{{c}}
+: error map: {{val| 0.000 +0.172 +0.463 +0.176 +0.044 }}
+{{Optimal ET sequence|legend=1| 34, 43, 53, 87, 130, 183, 270, 670, 940, 1210, 2063c }}
+[[Badness]] (Sintel): 1.17
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 676/675, 1001/1000, 4096/4095
+Mapping: {{mapping| 1 0 0 13 -9 1 | 0 2 0 -7 4 3 | 0 0 1 -2 4 1 }}
+Optimal tunings:
+* WE: ~2 = 1199.9633{{c}}, ~400/231 = 951.0591{{c}}, ~5/4 = 386.7388{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~400/231 = 951.0896{{c}}, ~5/4 = 386.7451{{c}}
+{{Optimal ET sequence|legend=0| 34, 43, 53, 87, 130, 183, 217, 270, 940, 1210f }}
+Badness (Sintel): 0.565
+Complexity spectrum: 15/13, 16/15, 13/12, 4/3, 16/13, 5/4, 18/13, 13/10, 6/5, 9/8, 11/10, 8/7, 7/5, 15/11, 10/9, 13/11, 15/14, 11/8, 7/6, 14/13, 12/11, 9/7, 11/9, 14/11
+== References ==
+[[Category:Vishdelismic clan| ]] <!-- main article -->
+[[Category:Vishdelismic| ]] <!-- key article -->
+[[Category:Temperament clans]]
+[[Category:Catalogs of rank-3 temperaments]]