Pajara

Pajara, 22 & 32, is a regular temperament wherein the octave is split into two tritone periods, and the generator is a fifth (3/2). A fifth minus a tritone is 16/15 (diaschismic tempering), and therefore the 5/4 major third is found two generators below the tritone. Pajara makes the further equivalence of 5/4 plus a period to 7/4 (jubilismic tempering) and therefore twice 4/3 is 7/4 (archy tempering). The result is a 10-form system generated by a fifth tuned somewhere around 710 cents. There are five patent tunings of pajara: 12, 22, 54, 32, and 10 (which is also the 20edo val for the 7-limit).

Tuning considerations

Most optimization methods place the optimal tuning of pajara's perfect fifth at around 707 cents. However, pajara is usually not the best interpretation of those structures. EDOs with tunings of fifths flat of that of 22edo generally do not support pajara in the patent val, and those that do (or rank-2 pajara structures with that tuning) are generally extremely inaccurate in the 7-limit due to the fact that archy temperament forces 9/8 and 8/7 together.

Conversely, systems with fifths sharp of 32edo narrow the distinction between 5/4 and 6/5 considerably, detuning 6/5 to a neutral sound. Therefore, the tuning range of pajara can be considered to lie between about 709 to 712 cents.