30th-octave temperaments
30edo is by many metrics not a harmonically notable temperament, but some of its multiples are. Due to plenty of divisors of number 30, these temperaments are also difficult to catalog due to their belonging in multiple temperament families, and this page is designed to accommodate that.
Due to landscape comma being a notable comma that divides the octave in 3, many temperaments whose wheel is a multiple of 3 (such as 12, 15, 24, etc.), end up belonging in the landscape microtemperaments. This page therefore describes theoretical interest specific to 30edo, beyond just belonging in that group.
Zinc is a prominent 30th-octave temperament, see Landscape microtemperaments#Zinc for technical details. From a fractional-octave perspective, MOS scales of zinc are significantly distinct from either landscape rank-3 scales or the 10th-octave mos scales that produce neon or its descendant temperaments like deca. The 120-tone mos has 65/64 within reach. Poe is another temperament of interest.
Considered below is oyster.
Oyster
Oyster is a 2.7.11.19 weak restriction of zinc of reasonably low badness and contains all the harmonics within the reach of a standard MIDI 128-note keyboard ― 120 notes is sufficient to cover all the temperament for the subgroup. Furthermore, 7/4 is the generator. As harmonics 3 and 5 are not used, oyster is neither a landscape nor neon temperament.
Overall, this temperament is a simple augmentation of 30edo with harmonics 7, 11, and 19 that is unique and of decent badness.
Named so because oysters are the biggest source of the element zinc, the namesake of the temperament it is derived of.
Subgroup: 2.7.11.19
Comma list: 184877/184832, 2.7.11.19 [-67 0 12 6⟩
Subgroup-val mapping: [⟨30 60 128 79], ⟨0 1 -1 2]]
Optimal tunings:
- WE: ~102760448/100422619 = 40.000 ¢, ~7/4 = 968.757 ¢
- CWE: ~102760448/100422619 = 40.000 ¢, ~7/4 = 968.750 ¢
Supporting ETs: 30, 120, 150, 270, 390, 420, 570, 660, 690, 960, 1110, 1230, 1500, 1650
Badness (Sintel): 0.499