Landscape microtemperaments: Difference between revisions

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Landscape rank-2 temperaments discussed elsewhere are:

* [[Augene]] (+64/63 or 126/125) → [[Augmented family #Augene|Augmented family]]

* ''[[~~Waage~~]]'' (+225/224) → [[Compton family #Compton|Compton family]]

* ''[[Compton]]'' (+225/224) → [[Compton family #Compton|Compton family]]

* ''[[Tritikleismic]]'' (+1029/1024) → [[Kleismic family #Tritikleismic|Kleismic family]]

* ''[[Trisensory]]' (+1728/1715) → [[Sensipent family #Trisensory|Sensipent family]]

* ''[[Trisensory]]'' (+1728/1715) → [[Sensipent family #Trisensory|Sensipent family]]

* [[Ennealimmal]] (+2401/2400 or 4375/4374) → [[Ragismic microtemperaments #Ennealimmal|Ragismic microtemperaments]]

* ''[[Misty]]'' (+3136/3125 or 5120/5103) → [[Misty family]]

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* [[Mutt temperament|Mutt]] (+65625/65536) → [[Horwell temperaments #Mutt|Horwell temperaments]]

* ''[[Stearnscape]]'' (+118098/117649) → [[Stearnsmic clan #Stearnscape|Stearnsmic clan]]

* ''[[Tritricot]]'' (+~~11785390260224/11767897353375~~) → [[Tricot family #Tritricot|Tricot family]]

* ''[[Tritricot]]'' (+{{monzo| 35 -23 -3 3 }}) → [[Tricot family #Tritricot|Tricot family]]

Considered below are sextile, septichrome, pnict, domain, avicenna, terture, akjayland and terture.

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Mapping: {{mapping| 21 4 39 98 58 | 0 6 2 -8 3 3 }}

~~Mapping~~ generators: ~1323/1280, ~6615/5632

: mapping generators: ~1323/1280, ~6615/5632

Optimal tuning (CTE): ~1323/1280 = 1\21, ~6615/5632 = 278.8998

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: ''For the 5-limit version, see [[12th-octave temperaments#Magnesium (5-limit)]].

Magnesium is named after element 12 for being period 12, however, it's not an extension of the [[atomic]] - the associated comma is {{monzo|-157 -24 84}} in the 5-limit and the 7 generators together with [[12edo]] major second reach the just perfect fifth, [[3/2]].

Magnesium is named after element 12 for being period 12, however, it's not an extension of the [[atomic]] – the associated comma is {{monzo| -157 -24 84 }} in the 5-limit and the 7 generators together with [[12edo]] major second reach the just perfect fifth, [[3/2]].

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 250047/250000, ~~9234096523681640625/9223372036854775808~~

[[Comma list]]: 250047/250000, {{monzo| -59 2 18 5 }}

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Optimal tuning (CTE): ~138915/131072 = 1\12, ~3145728/2734375 = 243.130

{{Optimal ET sequence|legend=1| 84, 528, 612, ~~696~~, ~~1308~~, ~~1920~~, ~~2532~~ }}~~, ..~~.

{{Optimal ET sequence|legend=1| 84, 360d, 444, 528, 612, 1920, 2532, 10740cd, 13272bcdd, 15804bcdd, 18336bcddd }}

Badness: 0.0964

== Chromium ==

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

{{Optimal ET sequence|legend=1|270~~, 1110~~, 1380, 1650, 1920}}~~, ..~~.

{{Optimal ET sequence|legend=1| 270, 1380, 1650, 1920, 2190, 4650 }}

[[Badness]]: 0.0742

=== 11-limit ===

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Optimal tuning (CTE): ~18865/18432 = 1\30, ~216/175 = 364.389

{{Optimal ET sequence|legend=1|270~~, 840~~, 1110, 1380, 1650, 1920}}~~, ..~~.

{{Optimal ET sequence|legend=1| 270, 1110, 1380, 1650, 1920, 2190 }}

Badness: 0.0220

=== 13-limit ===

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Optimal tuning (CTE): ~351/343 = 1\30, ~216/175 = 364.389

{{Optimal ET sequence|legend=1|270, 1380, 1650, 1920}}~~, ..~~.

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

Badness: 0.0150

[[Category:Temperament collections]]

@@ Line 3: / Line 3: @@
 Landscape rank-2 temperaments discussed elsewhere are:
 * [[Augene]] (+64/63 or 126/125) → [[Augmented family #Augene|Augmented family]]
-* ''[[Waage]]'' (+225/224) → [[Compton family #Compton|Compton family]]
+* ''[[Compton]]'' (+225/224) → [[Compton family #Compton|Compton family]]
 * ''[[Tritikleismic]]'' (+1029/1024) → [[Kleismic family #Tritikleismic|Kleismic family]]
-* ''[[Trisensory]]' (+1728/1715) → [[Sensipent family #Trisensory|Sensipent family]]
+* ''[[Trisensory]]'' (+1728/1715) → [[Sensipent family #Trisensory|Sensipent family]]
 * [[Ennealimmal]] (+2401/2400 or 4375/4374) → [[Ragismic microtemperaments #Ennealimmal|Ragismic microtemperaments]]
 * ''[[Misty]]'' (+3136/3125 or 5120/5103) → [[Misty family]]
@@ Line 14: / Line 14: @@
 * [[Mutt temperament|Mutt]] (+65625/65536) → [[Horwell temperaments #Mutt|Horwell temperaments]]
 * ''[[Stearnscape]]'' (+118098/117649) → [[Stearnsmic clan #Stearnscape|Stearnsmic clan]]
-* ''[[Tritricot]]'' (+11785390260224/11767897353375) → [[Tricot family #Tritricot|Tricot family]]
+* ''[[Tritricot]]'' (+{{monzo| 35 -23 -3 3 }}) → [[Tricot family #Tritricot|Tricot family]]
 Considered below are sextile, septichrome, pnict, domain, avicenna, terture, akjayland and terture.
@@ Line 348: / Line 348: @@
 Mapping: {{mapping| 21 4 39 98 58 | 0 6 2 -8 3 3 }}
-Mapping generators: ~1323/1280, ~6615/5632
+: mapping generators: ~1323/1280, ~6615/5632
 Optimal tuning (CTE): ~1323/1280 = 1\21, ~6615/5632 = 278.8998
@@ Line 411: / Line 411: @@
 : ''For the 5-limit version, see [[12th-octave temperaments#Magnesium (5-limit)]].
-Magnesium is named after element 12 for being period 12, however, it's not an extension of the [[atomic]] - the associated comma is {{monzo|-157 -24 84}} in the 5-limit and the 7 generators together with [[12edo]] major second reach the just perfect fifth, [[3/2]].
+Magnesium is named after element 12 for being period 12, however, it's not an extension of the [[atomic]] – the associated comma is {{monzo| -157 -24 84 }} in the 5-limit and the 7 generators together with [[12edo]] major second reach the just perfect fifth, [[3/2]].
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: 250047/250000, 9234096523681640625/9223372036854775808
+[[Comma list]]: 250047/250000, {{monzo| -59 2 18 5 }}
 {{Mapping|legend=1| 12 2 23 58 | 0 7 2 -10 }}
@@ Line 423: / Line 423: @@
 Optimal tuning (CTE): ~138915/131072 = 1\12, ~3145728/2734375 = 243.130
-{{Optimal ET sequence|legend=1| 84, 528, 612, 696, 1308, 1920, 2532 }}, ...
+{{Optimal ET sequence|legend=1| 84, 360d, 444, 528, 612, 1920, 2532, 10740cd, 13272bcdd, 15804bcdd, 18336bcddd }}
+Badness: 0.0964
 == Chromium ==
@@ Line 492: / Line 494: @@
 [[Optimal tuning]] ([[CTE]]): ~53747712/52521875 = 1\30, ~216/175 = 364.389
-{{Optimal ET sequence|legend=1|270, 1110, 1380, 1650, 1920}}, ...
+{{Optimal ET sequence|legend=1| 270, 1380, 1650, 1920, 2190, 4650 }}
+[[Badness]]: 0.0742
 === 11-limit ===
@@ Line 503: / Line 507: @@
 Optimal tuning (CTE): ~18865/18432 = 1\30, ~216/175 = 364.389
-{{Optimal ET sequence|legend=1|270, 840, 1110, 1380, 1650, 1920}}, ...
+{{Optimal ET sequence|legend=1| 270, 1110, 1380, 1650, 1920, 2190 }}
+Badness: 0.0220
 === 13-limit ===
@@ Line 514: / Line 520: @@
 Optimal tuning (CTE): ~351/343 = 1\30, ~216/175 = 364.389
-{{Optimal ET sequence|legend=1|270, 1380, 1650, 1920}}, ...
+{{Optimal ET sequence|legend=1| 270, 1380, 1650, 1920, 2190, 4650, 6840e, 11490de }}
+Badness: 0.0150
 [[Category:Temperament collections]]