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
- For technical data, see Landscape microtemperaments#Zinc.
Zinc temperament is named after the 30th element and in the 7-limit it can be described by tempering out the landscape comma and the neon comma. Tempering out the landscape comma divides the octave in 3, the neon comma in 10, and respectively zinc divides the octave into 3 x 10 = 30.
While the landscape comma is considered the "most important" comma of zinc, it can be played in ways that don't involve it. For example, it reaches the 11th harmonic in just 2 generators which can be found using the 90-tone mos.
Within the reach of a standard 128-note MIDI keyboard, zinc has mos scales of size 60, 90, and 120. These scales 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.