30th-octave temperaments: Difference between revisions
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== Zinc == | == 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 [[10th-octave temperaments#Neon|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. | ''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 [[10th-octave temperaments#Neon|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. | ||
Zinc has mos scales of size 60 and 90. 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]]. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
Revision as of 17:03, 24 September 2023
Template:Fractional-octave navigation 30edo is not a harmonically notable temperament, but some of its multiples are.
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.
Zinc has mos scales of size 60 and 90. 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.
Subgroup: 2.3.5.7
Comma list: 250047/250000, [-45 -24 14 18⟩
Mapping: [⟨30 2 15 66], ⟨0 5 6 2]]
Optimal tuning (CTE): ~53747712/52521875 = 1\30, ~216/175 = 364.389
Optimal ET sequence: 270, 1380, 1650, 1920, 2190, 4650
Badness: 0.0742
11-limit
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 250047/250000, 97869261875/97844723712
Mapping: [⟨30 2 15 66 122], ⟨0 5 6 2 -2]]
Optimal tuning (CTE): ~18865/18432 = 1\30, ~216/175 = 364.389
Optimal ET sequence: 270, 1110, 1380, 1650, 1920, 2190
Badness: 0.0220
13-limit
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 123201/123200, 250047/250000, 1990656/1990625
Mapping: [⟨30 2 15 66 122 193], ⟨0 5 6 2 -2 -9]]
Optimal tuning (CTE): ~351/343 = 1\30, ~216/175 = 364.389
Optimal ET sequence: 270, 1380, 1650, 1920, 2190, 4650, 6840e, 11490de
Badness: 0.0150