Laka

Laka is a rank-3 temperament generated by a perfect fifth of ~3/2 and a step for the syntonic~septimal comma to reach the interval classes of 5, 7, and higher primes. Using an arrow to represent this comma step, we have 5/4 at the down major third (C–vE), 7/4 at the down minor seventh (C–vBb), and 11/8 at the up augmented third (C–^E#), tempering out 540/539, which makes it a member of swetismic temperaments.

The canonical extension to the 13-limit finds 13/8 at the up augmented fifth (C–^G#), tempering out 352/351, 640/637, 729/728 and 847/845, and a no-17 19-limit extension is available by recognizing 19/16 at the down augmented second (C–vD#), tempering out 400/399, 456/455 and 495/494. The lattice structure is very comparable to that of pele, but it is more complex as many of the simple divisive ratios are further away from the origin.

See Hemifamity family #Laka for technical details.

Interval lattice

• 
  13-limit laka
• 
  2.3.5.7.11.13.19-subgroup laka

These lattices show laka as generated by ~2, ~3/2, and ~7/4 for a direct comparison with pele.

Chords

Laka enables essentially tempered chords of swetismic in the 11-odd-limit, in addition to major minthmic, huntmic, squbemic and cuthbert in the 13-odd-limit.

Scales

• Dekany laka – a transversal scale