Gamelismic and portent: Difference between revisions

Revision as of 13:04, 11 November 2025

Gamelismic is a rank-3 temperament generated by a supermajor second of ~8/7, three of them stacking to ~3/2, and an independent dimension for prime 5. Thus it tempers out 1029/1024, the gamelisma, in the 7-limit, which means it is an expansion of slendric, the rank-2 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 1029/1024 = (385/384)(441/440).

7-limit norm-based tunings
	Euclidean
	Constrained	Constrained & skewed	Destretched
Tenney	CTE: ~8/7 = 233.8889 ¢, ~5/4 = 385.3137 ¢	CWE: ~8/7 = 233.7474 ¢, ~5/4 = 385.5205 ¢	POTE: ~8/7 = 233.6875 ¢, ~5/4 = 385.1853 ¢

11-limit norm-based tunings
	Euclidean
	Constrained	Constrained & skewed	Destretched
Tenney	CTE: ~8/7 = 233.9922 ¢, ~5/4 = 385.7972 ¢	CWE: ~8/7 = 233.7616 ¢, ~5/4 = 385.3149 ¢	POTE: ~8/7 = 233.6884 ¢, ~5/4 = 385.1618 ¢

@@ Line 14: / Line 14: @@
 * [[Portent11tri]] – 11-tone [[trivalent scale]] in 190edo tuning
 * [[Portent26]] – 26-tone [[hobbit scale]] in 11-odd-limit minimax tuning
+== 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 -->