30th-octave temperaments: Difference between revisions
doesn't show temperament data anymore as zinc got moved to landscape temps and this is just now a description of what makes zinc notable beyond belonging in landscape family |
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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. | 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. | ||
=== Oyster === | |||
Oyster is a 2.7.11.19 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 and it is of badness comparable to full-limit zinc variants. As harmonics 3 and 5 are not used, oyster is neither a landscape nor neon temperament. | |||
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 {{monzo|-67 0 12 6}} | |||
{{mapping|legend=2| 30 60 128 79 | 0 1 -1 2 }} | |||
Optimal tunings: | |||
* WE: ~102760448/100422619 = 40.000{{c}}, ~7/4 = 968.757{{c}} | |||
* CWE: ~102760448/100422619 = 40.000{{c}}, ~7/4 = 968.750{{c}} | |||
[[Support]]ing [[ET]]s: {{EDOs|30, 120, 150, 270, 390, 420, 570, 660, 690, 960, 1110, 1230, 1500, 1650}} | |||
Badness (Sintel): 0.499 | |||
{{Navbox fractional-octave}} | {{Navbox fractional-octave}} | ||
Revision as of 01:57, 5 August 2026
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.
Oyster
Oyster is a 2.7.11.19 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 and it is of badness comparable to full-limit zinc variants. As harmonics 3 and 5 are not used, oyster is neither a landscape nor neon temperament.
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