Gamelismic and portent: Difference between revisions

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-'''Portent''' is the [[Rank-3 temperament|rank-3]] [[temperament]] [[tempering out]] [[385/384]] and [[441/440]]. It is the most efficient [[11-limit]] [[extension]] to '''gamelismic''', the [[7-limit]] version tempering out [[1029/1024]].
+{{Infobox regtemp
+| Title = Gamelismic; portent
+| Subgroups = 2.3.5.7, 2.3.5.7.11
+| Comma basis = [[1029/1024]] (7-limit); <br>[[385/384]], [[441/440]] (11-limit)
+| Edo join 1 = 15 | Edo join 2 = 26 | Edo join 3 = 31
+| Mapping = 1; 3 0 -1 4; 0 1 0 -1
+| Generators = 8/7, 5/4
+| Generators tuning = 233.8, 385.3
+| Optimization method = CWE
+| Odd limit 1 = 9 | Mistuning 1 = 2.41 | Complexity 1 = ?
+| Odd limit 2 = 11-limit 21 | Mistuning 2 = 2.81 | Complexity 2 = ?
+}}
+'''Gamelismic''' is a [[rank-3 temperament|rank-3]] [[regular temperament|temperament]] [[generator|generated]] by a supermajor second of [[~]][[8/7]], three of them stacking to ~[[3/2]], and an independent dimension for [[prime interval|prime]] [[5/1|5]]. Thus it [[tempering out|tempers out]] [[1029/1024]], the gamelisma, in the [[7-limit]], which means it is an [[expansion]] of [[slendric]], the [[rank-2 temperament|rank-2]] [[2.3.7 subgroup|2.3.7-subgroup]] temperament that tempers out the same comma. It has an obvious [[extension]] to the [[11-limit]] tempering out [[385/384]] and [[441/440]], called '''portent''', as {{nowrap| 1029/1024 {{=}} (385/384)(441/440) }}.
-See [[Gamelismic family #Portent]] for more technical data.
+See [[Gamelismic family #Gamelismic]] and [[Gamelismic family #Portent]] for technical data.
 == Interval lattice ==
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 == Scales ==
-* [[Portent11tri]] – 11-tone trivalence scale in 190edo tuning
+* [[Portent11tri]] – 11-tone [[trivalent scale]] in 190edo tuning
-* [[Portent26]] – 26-tone hobbit scale in 11-odd-limit minimax tuning
+* [[Portent26]] – 26-tone [[hobbit scale]] in 11-odd-limit minimax tuning
+* [[Penslen]]
-[[Category:Temperaments]]
+== Tunings ==
+{| class="wikitable mw-collapsible mw-collapsed"
+|+ style="font-size: 105%; white-space: nowrap;" | 7-limit norm-based tunings
+|-
+! rowspan="2" |
+! colspan="3" | Euclidean
+|-
+! Constrained
+! Constrained & skewed
+! Destretched
+|-
+! Tenney
+| CTE: ~8/7 = 233.8889{{c}}, ~5/4 = 385.3137{{c}}
+| CWE: ~8/7 = 233.7474{{c}}, ~5/4 = 385.5205{{c}}
+| POTE: ~8/7 = 233.6875{{c}}, ~5/4 = 385.1853{{c}}
+|}
+{| class="wikitable mw-collapsible mw-collapsed"
+|+ style="font-size: 105%; white-space: nowrap;" | 11-limit norm-based tunings
+|-
+! rowspan="2" |
+! colspan="3" | Euclidean
+|-
+! Constrained
+! Constrained & skewed
+! Destretched
+|-
+! Tenney
+| CTE: ~8/7 = 233.9922{{c}}, ~5/4 = 385.7972{{c}}
+| CWE: ~8/7 = 233.7616{{c}}, ~5/4 = 385.3149{{c}}
+| POTE: ~8/7 = 233.6884{{c}}, ~5/4 = 385.1618{{c}}
+|}
+[[Category:Portent| ]] <!-- main article -->
+[[Category:Rank-3 temperaments]]
 [[Category:Gamelismic family]]
 [[Category:Keenanismic temperaments]]
 [[Category:Werckismic temperaments]]