Gamelismic and portent

Gamelismic; portent

Subgroups	2.3.5.7, 2.3.5.7.11
Comma basis	1029/1024 (7-limit); 385/384, 441/440 (11-limit)
Reduced mapping	⟨1; 3 0 -1 4; 0 1 0 -1]
ET join	15 & 26 & 31
Generators (CWE)	~8/7 = 233.8 ¢, ~5/4 = 385.3 ¢
MOS scales	n/a
Ploidacot	n/a
Minimax error	9-odd-limit: 2.41 ¢; 11-limit 21-odd-limit: 2.81 ¢
Target scale size	9-odd-limit: ? notes; 11-limit 21-odd-limit: ? notes

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).

See Gamelismic family #Gamelismic and Gamelismic family #Portent for technical data.

Interval lattice

• 
  11-limit portent

Chords

Portent enables essentially tempered chords of gamelismic, keenanismic, and werckismic.

Scales

• Portent11tri – 11-tone trivalent scale in 190edo tuning
• Portent26 – 26-tone hobbit scale in 11-odd-limit minimax tuning
• Penslen

Tunings

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 ¢