Ploidacot/Omega-pentacot

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Omega-pentacot is a temperament archetype where the generator is a semitone, five of which stack to form a perfect fourth of 4/3, and the period is a 2/1 octave. Omega-pentacot temperaments usually generate the 1L 11s and 12L 1s MOS structures. Regular temperaments of omega-pentacot are cluster temperaments with 12 clusters of notes in an octave.

Omega-pentacot
Pergen [P8, P4/5]
Numeral form 4-sheared 5-cot
Pure generator size 99.61 ¢
Pure period size 1200 ¢
Forms 12, 13, 25, 37
Characteristic multival entry 5

Temperament interpretations

Quinticular

Omega-pentacot temperaments are generally interpretated as quinticular temperaments; the generator is 18/17, five of them gives 4/3, so the quinticular comma (1419857/1417176) is tempered out.

Quindromeda

In quindromeda, the generator is 18/17, three generators make 19/16, five make 4/3, and 28 make 5th harmonic in the 2.3.5.17.19 subgroup, so 1216/1215, 1445/1444, and 6144/6137 are tempered out. This temperament is supported by 12, 169, 181, 193, 205, 217, 229, and 241 edos.

Equating 225/224 with 256/255 leads to quintakwai (12 & 193), which tempers out 400/399 (also equating 20/19 and 21/20) in the 2.3.5.7.17.19 subgroup, and 361/360 with 400/399 leads to quintagar (12 & 217), which tempers out 476/475 (also equating 19/17 with 28/25) in the 2.3.5.7.17.19 subgroup.

Quintaleap

In quintaleap, the generator is 18/17, three generators make 19/16, five make 4/3, and 16 make 5/2 in the 2.3.5.17.19 subgroup, so 256/255, 361/360, and 4624/4617 are tempered out. This temperament is supported by 12, 109, 121, 133, 145, and 157 edos.

In the 2.3.5.7.17.19 subgroup, tempering out 400/399 (equating 20/19 and 21/20) leads to quintupole (12 & 121), and tempering out 476/475 (equating 19/17 with 28/25) leads to quinticosiennic (12 & 145).

Passion

In passion, the generator is 16/15, four generators make 5/4, and five make 4/3. It is best tuned with a slightly flat generator of about 98.7 ¢, and follows that both 3 and 5 should be tuned sharp. The canonical mapping of 7 places 7/4 at 10 generators, and follows that the generator should be tuned flatter (about 98.1 ¢).