Landscape microtemperaments: Difference between revisions

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* ''[[Sextile]]'' (+33554432/33480783) → [[Garischismic clan #Sextile|Garischismic clan]]

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

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

* ''[[Terture]]'' (+359661568/358722675) → [[Vulture family #Terture|Vulture family]]

* ''[[Pentadecal]]'' (+875/864) → [[Keemic temperaments #Pentadecal|Keemic temperaments]]

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* ''[[Trivish]]'' (+134217728/133984375) → [[Vishnu family #Trivish|Vishnu family]]

* ''[[Domain (temperament)|Domain]]'' (+645700815/645657712) → [[Minortone family #Domain|Minortone family]]

* ''[[Aemilic]]'' (+{{monzo|-84 53}}) → [[~~159th-octave temperaments~~ #Aemilic|~~159th-octave temperaments~~]]

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

* ''[[Aemilic]]'' (+{{monzo|-84 53}}) → [[Mercator family #Aemilic|Mercator family]]

Considered below are septichrome, akjayland, pnict, atomic, slendscape, avicenna, zinc, magnesium, poe, chromium, and phosphorus in the order of increasing [[badness]].

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==== Hafnium ====

Hafnium (1224 & 4320), named after the 72nd element, splits the 1/12-octave period into six 1/72-octave parts. Since 4320edo and 5544edo have good 31st and 37th harmonics, addition of these primes are also prescribed. In the add-37 version, [[37/22]] is mapped to exact 3\4.

Hafnium (1224 & 4320), named after the 72nd element, splits the 1/12-octave period into six 1/72-octave parts. Since 4320edo and 5544edo have good 31st and 37th harmonics, addition of these primes are also prescribed. In the add-37 version, [[37/22]] is mapped to exact 3\4 (see also [[Berylic]]).

Subgroup: 2.3.5.7.11.13

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== Zinc ==

~~{{See also| 10th-octave temperaments #Neon }}~~

Zinc maybe described as the {{nowrap| 270 & 2190 }} temperament, and is a [[weak extension]] of [[miscellaneous 5-limit temperaments #Neon|neon]]. It was named by [[Eliora]] in 2023 after the 30th element for having a 30th-octave period.

Zinc maybe described as the {{nowrap| 270 & 2190 }} temperament. It was named by [[Eliora]] in 2023 after the 30th element for having a 30th-octave period.

[[Subgroup]]: 2.3.5.7

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Badness (Sintel): 0.640

==== 2.3.5.7.11.13.19 subgroup ~~(neozinc)~~ ====

==== 2.3.5.7.11.13.19 subgroup ====

A 2.7.11.19 restriction worth considering is [[30th-octave temperaments#Oyster|oyster]].

Subgroup: 2.3.5.7.11.13.19

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: mapping generators: ~{{monzo| -21 34 4 -15 }}, ~210827008/199290375

[[Optimal tuning]] ([[~~CTE~~]]): ~{{monzo|-21 34 4 -15}} = 80.~~0000~~, ~28/27 = 62.~~9267~~

[[Optimal tuning]]s:

* [[WE]]: ~{{monzo|-21 34 4 -15}} = 80.000039{{c}}, ~210827008/199290375 = 97.073339{{c}}

: [[error map]]: {{val| +0.0006 -0.0013 +0.0330 -0.0392 }}

* [[CWE]]: ~{{monzo|-21 34 4 -15}} = 80.000000{{c}}, ~210827008/199290375 = 97.073314{{c}}

: error map: {{val| 0.0000 -0.0019 +0.0323 -0.0400 }}

[[Badness]]: 0.~~381587~~

[[Badness]] (Sintel): 9.66

[[Category:Landscape microtemperaments| ]]

[[Category:Temperament collections]]

[[Category:~~Landscape microtemperaments| ]] <!~~-~~- main article -->~~

[[Category:Catalogs of rank-2 temperaments]]

~~[[Category:Rank~~ 2]]

@@ Line 8: / Line 8: @@
 * ''[[Sextile]]'' (+33554432/33480783) → [[Garischismic clan #Sextile|Garischismic clan]]
 * ''[[Tritricot]]'' (+{{monzo| 35 -23 -3 3 }}) → [[Alphatricot family #Tritricot|Alphatricot family]]
-* [[Compton]] (+225/224) → [[Compton family #Compton|Compton family]]
 * ''[[Terture]]'' (+359661568/358722675) → [[Vulture family #Terture|Vulture family]]
 * ''[[Pentadecal]]'' (+875/864) → [[Keemic temperaments #Pentadecal|Keemic temperaments]]
@@ Line 22: / Line 21: @@
 * ''[[Trivish]]'' (+134217728/133984375) → [[Vishnu family #Trivish|Vishnu family]]
 * ''[[Domain (temperament)|Domain]]'' (+645700815/645657712) → [[Minortone family #Domain|Minortone family]]
-* ''[[Aemilic]]'' (+{{monzo|-84 53}}) → [[159th-octave temperaments #Aemilic|159th-octave temperaments]]
+* [[Compton]] (+225/224) → [[Compton family #Compton|Compton family]]
+* ''[[Aemilic]]'' (+{{monzo|-84 53}}) → [[Mercator family #Aemilic|Mercator family]]
 Considered below are septichrome, akjayland, pnict, atomic, slendscape, avicenna, zinc, magnesium, poe, chromium, and phosphorus in the order of increasing [[badness]].
@@ Line 323: / Line 323: @@
 ==== Hafnium ====
-Hafnium (1224 & 4320), named after the 72nd element, splits the 1/12-octave period into six 1/72-octave parts. Since 4320edo and 5544edo have good 31st and 37th harmonics, addition of these primes are also prescribed. In the add-37 version, [[37/22]] is mapped to exact 3\4.
+Hafnium (1224 & 4320), named after the 72nd element, splits the 1/12-octave period into six 1/72-octave parts. Since 4320edo and 5544edo have good 31st and 37th harmonics, addition of these primes are also prescribed. In the add-37 version, [[37/22]] is mapped to exact 3\4 (see also [[Berylic]]).
 Subgroup: 2.3.5.7.11.13
@@ Line 515: / Line 515: @@
 == Zinc ==
-{{See also| 10th-octave temperaments #Neon }}
+Zinc maybe described as the {{nowrap| 270 & 2190 }} temperament, and is a [[weak extension]] of [[miscellaneous 5-limit temperaments #Neon|neon]]. It was named by [[Eliora]] in 2023 after the 30th element for having a 30th-octave period.
-Zinc maybe described as the {{nowrap| 270 & 2190 }} temperament. It was named by [[Eliora]] in 2023 after the 30th element for having a 30th-octave period.
 [[Subgroup]]: 2.3.5.7
@@ Line 566: / Line 564: @@
 Badness (Sintel): 0.640
-==== 2.3.5.7.11.13.19 subgroup (neozinc) ====
+==== 2.3.5.7.11.13.19 subgroup ====
+A 2.7.11.19 restriction worth considering is [[30th-octave temperaments#Oyster|oyster]].
 Subgroup: 2.3.5.7.11.13.19
@@ Line 761: / Line 761: @@
 : mapping generators: ~{{monzo| -21 34 4 -15 }}, ~210827008/199290375
-[[Optimal tuning]] ([[CTE]]): ~{{monzo|-21 34 4 -15}} = 80.0000, ~28/27 = 62.9267
+[[Optimal tuning]]s:
+* [[WE]]: ~{{monzo|-21 34 4 -15}} = 80.000039{{c}}, ~210827008/199290375 = 97.073339{{c}}
+: [[error map]]: {{val| +0.0006 -0.0013 +0.0330 -0.0392 }}
+* [[CWE]]: ~{{monzo|-21 34 4 -15}} = 80.000000{{c}}, ~210827008/199290375 = 97.073314{{c}}
+: error map: {{val| 0.0000 -0.0019 +0.0323 -0.0400 }}
-{{Optimal ET sequence|legend=1| 1125, 1335, 2460 }}
+{{Optimal ET sequence|legend=1| 210, …, 1125, 1335, 2460 }}
-[[Badness]]: 0.381587
+[[Badness]] (Sintel): 9.66
+[[Category:Landscape microtemperaments| ]] <!-- main article -->
 [[Category:Temperament collections]]
-[[Category:Landscape microtemperaments| ]] <!-- main article -->
+[[Category:Catalogs of rank-2 temperaments]]
-[[Category:Rank 2]]