30th-octave temperaments: Difference between revisions

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30edo is 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.

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.

== 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 [[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]].~~

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.

~~[[Subgroup]]: 2.3.5~~.7

~~[[Comma list]]: 250047/250000~~, ~~{{monzo| -45 -24 14 18 }}~~

~~{{Mapping|legend=1| 30~~ 2 ~~15 66 | 0 5 6 2 }}~~

~~[[Optimal tuning]] ([[CTE]]): ~53747712/52521875 = 1\30, ~216/175 = 364.389~~

~~{{Optimal ET sequence|legend=1| 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: {{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|legend=1| 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: {{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|legend=1| 270~~, ~~1380~~, ~~1650~~, ~~1920, 2190, 4650, 6840e, 11490de }}~~

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.

~~Badness: 0.0150~~

@@ Line 1: / Line 1: @@
-{{Fractional-octave navigation|30}}
+{{Technical data page}}
-edo is 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.
+{{Infobox fractional-octave|30}}
+edo 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.
 == 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 [[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]].
+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.
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 250047/250000, {{monzo| -45 -24 14 18 }}
-{{Mapping|legend=1| 30 2 15 66 | 0 5 6 2 }}
-[[Optimal tuning]] ([[CTE]]): ~53747712/52521875 = 1\30, ~216/175 = 364.389
-{{Optimal ET sequence|legend=1| 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: {{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|legend=1| 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: {{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|legend=1| 270, 1380, 1650, 1920, 2190, 4650, 6840e, 11490de }}
+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.
-Badness: 0.0150
+{{Navbox fractional-octave}}