Landscape microtemperaments: Difference between revisions

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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]]

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

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

* ''[[Chromat]]'' (10976/10935) → [[~~Hemimage temperaments~~ #Chromat|~~Hemimage temperaments~~]]

* ''[[Chromat]]'' (+10976/10935) → [[Amity family #Chromat|Amity family]]

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

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

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, and ~~chromium~~ in the order of increasing [[badness]].

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

== Septichrome ==

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Comma list: 9801/9800, 151263/151250, 234375/234256

~~Mapping:~~ {{~~mapping~~| 6 1 -15 -24 -32 | 0 5 17 24 31 }}

: mapping generators: ~55/49, ~375/308

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Comma list: 1716/1715, 2080/2079, 34398/34375, 85293/85184

~~Mapping:~~ {{~~mapping~~| 6 1 -15 -24 -32 -68 | 0 5 17 24 31 53 }}

Optimal tunings:

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Comma list: 936/935, 1701/1700, 1716/1715, 2025/2023, 61965/61952

~~Mapping:~~ {{~~mapping~~| 6 1 -15 -24 -32 -68 -1 | 0 5 17 24 31 53 15 }}

{{Mapping|legend=0| 6 1 -15 -24 -32 -68 -1 | 0 5 17 24 31 53 15 }}

Optimal tunings:

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Comma list: 936/935, 1701/1700, 1716/1715, 2025/2023, 2376/2375, 23409/23408

~~Mapping:~~ {{~~mapping~~| 6 1 -15 -24 -32 -68 -1 34 | 0 5 17 24 31 53 15 -5 }}

{{Mapping|legend=0| 6 1 -15 -24 -32 -68 -1 34 | 0 5 17 24 31 53 15 -5 }}

Optimal tunings:

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Comma list: 936/935, 1701/1700, 1716/1715, 1863/1862, 2024/2023, 2025/2023, 2376/2375

~~Mapping:~~ {{~~mapping~~| 6 1 -15 -24 -32 -68 -1 34 -12 | 0 5 17 24 31 53 15 -5 23 }}

{{Mapping|legend=0| 6 1 -15 -24 -32 -68 -1 34 -12 | 0 5 17 24 31 53 15 -5 23 }}

Optimal tunings:

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Comma list: 3025/3024, 102487/102400, {{monzo| 39 -4 -11 -5 2 }}

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

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

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Comma list: 3025/3024, 4096/4095, 14641/14625, 85750/85683

~~Mapping:~~ {{~~mapping~~| 21 4 39 98 58 107 | 0 6 2 -8 3 -6 }}

Optimal tunings:

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Comma list: 2601/2600, 3025/3024, 4096/4095, 8624/8619, 14641/14625

~~Mapping:~~ {{~~mapping~~| 21 4 39 98 58 107 120 | 0 6 2 -8 3 -6 -7 }}

Optimal tunings:

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Comma list: 2376/2375, 2601/2600, 2926/2925, 3025/3024, 3213/3211, 4096/4095

~~Mapping:~~ {{~~mapping~~| 21 4 39 98 58 107 120 16 | 0 6 2 -8 3 -6 -7 15 }}

{{Mapping|legend=0| 21 4 39 98 58 107 120 16 | 0 6 2 -8 3 -6 -7 15 }}

Optimal tunings:

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Comma list: 1496/1495, 2376/2375, 2601/2600, 2646/2645, 2926/2925, 3025/3024, 3213/3211

~~Mapping:~~ {{~~mapping~~| 21 4 39 98 58 107 120 16 95 | 0 6 2 -8 3 -6 -7 15 0 }}

{{Mapping|legend=0| 21 4 39 98 58 107 120 16 95 | 0 6 2 -8 3 -6 -7 15 0 }}

Optimal tunings:

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Comma list: 9801/9800, 151263/151250, 184549376/184528125

~~Mapping:~~ {{~~mapping~~| 12 0 161 338 517 | 0 1 -7 -16 -25 }}

Optimal tunings:

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Comma list: 9801/9800, 151263/151250, 371293/371250, 184549376/184528125

~~Mapping:~~ {{~~mapping~~| 60 0 805 1690 2585 1173 | 0 1 7 -16 -25 -10 }}

{{Mapping|legend=0| 60 0 805 1690 2585 1173 | 0 1 7 -16 -25 -10 }}

: mapping generators: ~2704/2673, ~3

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Comma list: 9801/9800, 12376/12375, 28561/28560, 151263/151250, 11275335/11275264

~~Mapping:~~ {{~~mapping~~| 60 0 805 1690 2585 1173 1957 | 0 1 7 -16 -25 -10 -18 }}

{{Mapping|legend=0| 60 0 805 1690 2585 1173 1957 | 0 1 7 -16 -25 -10 -18 }}

Optimal tunings:

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Comma list: 9801/9800, 12376/12375, 12636/12635, 23409/23408, 28561/28560, 151263/151250

~~Mapping:~~ {{~~mapping~~| 60 60 385 730 1085 573 877 -61 | 0 1 7 -16 -25 -10 -18 9 }}

{{Mapping|legend=0| 60 60 385 730 1085 573 877 -61 | 0 1 7 -16 -25 -10 -18 9 }}

Optimal tunings:

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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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Comma list: 9801/9800, 151263/151250, 184549376/184528125, 308915776/308828625

~~Mapping:~~ {{~~mapping~~| 72 0 966 2028 3102 2777 | 0 1 -7 -16 -25 -22 }}

{{Mapping|legend=0| 72 0 966 2028 3102 2777 | 0 1 -7 -16 -25 -22 }}

: mapping generators: ~105/104, ~3

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Comma list: 9801/9800, 12376/12375, 151263/151250, 1713660/1713481, 97144749/97140736

~~Mapping:~~ {{~~mapping~~| 72 0 966 2028 3102 2777 979 | 0 1 -7 -16 -25 -22 -6 }}

{{Mapping|legend=0| 72 0 966 2028 3102 2777 979 | 0 1 -7 -16 -25 -22 -6 }}

: mapping generators: ~105/104, ~3

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Comma list: 9801/9800, 10881/10880, 12376/12375, 57629/57624, 179712/179707, 61456384/61448625

~~Subgroup-val mapping:~~ {{~~mapping~~| 72 0 966 2028 3102 2777 979 -328 | 0 1 -7 -16 -25 -22 -6 6 }}

{{Mapping|legend=2| 72 0 966 2028 3102 2777 979 -328 | 0 1 -7 -16 -25 -22 -6 6 }}

Optimal tunings:

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Comma list: 9801/9800, 10881/10880, 12376/12375, 16576/16575, 57629/57624, 93093/93092, 179712/179707

~~Subgroup-val mapping:~~ {{~~mapping~~| 72 0 966 2028 3102 2777 979 -328 3228 | 0 1 -7 -16 -25 -22 -6 6 -25 }}

{{Mapping|legend=2| 72 0 966 2028 3102 2777 979 -328 3228 | 0 1 -7 -16 -25 -22 -6 6 -25 }}

Optimal tunings:

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Comma list: 3025/3024, 102487/102400, 180224/180075

~~Mapping:~~ {{~~mapping~~| 15 0 17 54 40 | 0 4 3 -2 2 }}

Optimal tunings:

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Comma list: 1716/1715, 3025/3024, 4096/4095, 14641/14625

~~Mapping:~~ {{~~mapping~~| 15 0 17 54 40 109 | 0 4 3 -2 2 -9 }}

Optimal tunings:

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Comma list: 3025/3024, 5632/5625, 102487/102400

~~Mapping:~~ {{~~mapping~~| 3 2 8 16 9 | 0 8 -3 -22 4 }}

Optimal tunings:

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Comma list: 676/675, 1001/1000, 3025/3024, 4096/4095

~~Mapping:~~ {{~~mapping~~| 3 2 8 16 9 8 | 0 8 -3 -22 4 9 }}

Optimal tunings:

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Comma list: 676/675, 715/714, 936/935, 1001/1000, 4096/4095

~~Mapping:~~ {{~~mapping~~| 3 2 8 16 9 8 4 | 0 8 -3 -22 4 9 24 }}

Optimal tunings:

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Comma list: 676/675, 715/714, 936/935, 1001/1000, 1216/1215, 1729/1728

~~Mapping:~~ {{~~mapping~~| 3 2 8 16 9 8 4 0 | 0 8 -3 -22 4 9 24 37 }}

Optimal tunings:

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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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Comma list: 9801/9800, 151263/151250, {{monzo| -27 -6 4 6 3 }}

~~Mapping:~~ {{~~mapping~~| 30 2 15 66 122 | 0 5 6 2 -2 }}

Optimal tunings:

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Comma list: 9801/9800, 10648/10647, 105644/105625, 196625/196608

~~Mapping:~~ {{~~mapping~~| 30 2 15 66 122 193 | 0 5 6 2 -2 -9 }}

Optimal tunings:

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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

Comma list: 5929/5928, 6860/6859, 9801/9800, 10241/10240, 89376/89375

~~Mapping:~~ {{~~mapping~~| 30 2 15 66 122 193 91 | 0 5 6 2 -2 -9 4 }}

Optimal tunings:

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Comma list: 9801/9800, 10648/10647, 31213/31212, 105644/105625, 196625/196608

~~Mapping:~~ {{~~mapping~~| 60 4 30 132 244 386 391 | 0 5 6 2 -2 -9 -8 }}

{{Mapping|legend=0| 60 4 30 132 244 386 391 | 0 5 6 2 -2 -9 -8 }}

: mapping generators: ~612/605, ~216/175

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Comma list: 5929/5928, 6860/6859, 9801/9800, 10241/10240, 23409/23408, 89376/89375

~~Mapping:~~ {{~~mapping~~| 60 4 30 132 244 386 391 182 | 0 5 6 2 -2 -9 -8 4 }}

{{Mapping|legend=0| 60 4 30 132 244 386 391 182 | 0 5 6 2 -2 -9 -8 4 }}

Optimal tunings:

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Comma list: 9801/9800, 19712/19683, 151263/151250

~~Mapping:~~ {{~~mapping~~| 30 0 -73 -106 -134 | 0 1 3 4 5 }}

Optimal tunings:

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Comma list: 1001/1000, 4225/4224, 4459/4455, 19712/19683

~~Mapping:~~ {{~~mapping~~| 30 0 -73 -106 -134 111 | 0 1 3 4 5 0 }}

Optimal tunings:

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Comma list: 9801/9800, 46656/46585, 151263/151250

~~Mapping:~~ {{~~mapping~~| 24 1 -6 18 46 | 0 3 5 4 3 }}

Optimal tunings:

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Comma list: 1716/1715, 2080/2079, 34398/34375, 39366/39325

~~Mapping:~~ {{~~mapping~~| 24 1 -6 18 46 -47 -13 | 0 3 5 4 3 11 }}

Optimal tunings:

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Comma list: 936/935, 1701/1700, 1716/1715, 2025/2023, 11016/11011

~~Mapping:~~ {{~~mapping~~| 24 1 -6 18 46 -47 -13 | 0 3 5 4 3 11 9 }}

Optimal tunings:

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Badness (Sintel): 1.06

== Phosphorus ==

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 250047/250000, {{monzo| 60 -96 1 32 }}

[[Mapping]]: {{mapping| 15 8 -4 -4 | 0 13 32 38 }}

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

[[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]] (Sintel): 9.66

[[Category:Landscape microtemperaments| ]]

[[Category:Landscape| ]]

[[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]]
-* ''[[Terture]]'' (+359661568/358722675) → [[Vulture family #Domain|Vulture family]]
+* ''[[Pentadecal]]'' (+875/864) → [[Keemic temperaments #Pentadecal|Keemic temperaments]]
-* ''[[Chromat]]'' (10976/10935) → [[Hemimage temperaments #Chromat|Hemimage temperaments]]
+* ''[[Chromat]]'' (+10976/10935) → [[Amity family #Chromat|Amity family]]
 * ''[[Tritikleismic]]'' (+1029/1024) → [[Kleismic family #Tritikleismic|Kleismic family]]
 * [[Ennealimmal]] (+2401/2400 or 4375/4374) → [[Septiennealimmal clan #Ennealimmal|Septiennealimmal clan]]
@@ Line 21: / 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, and chromium in the order of increasing [[badness]].
+Considered below are septichrome, akjayland, pnict, atomic, slendscape, avicenna, zinc, magnesium, poe, chromium, and phosphorus in the order of increasing [[badness]].
 == Septichrome ==
@@ Line 48: / Line 49: @@
 Comma list: 9801/9800, 151263/151250, 234375/234256
-Mapping: {{mapping| 6 1 -15 -24 -32 | 0 5 17 24 31 }}
+{{Mapping|legend=0| 6 1 -15 -24 -32 | 0 5 17 24 31 }}
 : mapping generators: ~55/49, ~375/308
@@ Line 64: / Line 65: @@
 Comma list: 1716/1715, 2080/2079, 34398/34375, 85293/85184
-Mapping: {{mapping| 6 1 -15 -24 -32 -68 | 0 5 17 24 31 53 }}
+{{Mapping|legend=0| 6 1 -15 -24 -32 -68 | 0 5 17 24 31 53 }}
 Optimal tunings:
@@ Line 79: / Line 80: @@
 Comma list: 936/935, 1701/1700, 1716/1715, 2025/2023, 61965/61952
-Mapping: {{mapping| 6 1 -15 -24 -32 -68 -1 | 0 5 17 24 31 53 15 }}
+{{Mapping|legend=0| 6 1 -15 -24 -32 -68 -1 | 0 5 17 24 31 53 15 }}
 Optimal tunings:
@@ Line 94: / Line 95: @@
 Comma list: 936/935, 1701/1700, 1716/1715, 2025/2023, 2376/2375, 23409/23408
-Mapping: {{mapping| 6 1 -15 -24 -32 -68 -1 34 | 0 5 17 24 31 53 15 -5 }}
+{{Mapping|legend=0| 6 1 -15 -24 -32 -68 -1 34 | 0 5 17 24 31 53 15 -5 }}
 Optimal tunings:
@@ Line 109: / Line 110: @@
 Comma list: 936/935, 1701/1700, 1716/1715, 1863/1862, 2024/2023, 2025/2023, 2376/2375
-Mapping: {{mapping| 6 1 -15 -24 -32 -68 -1 34 -12 | 0 5 17 24 31 53 15 -5 23 }}
+{{Mapping|legend=0| 6 1 -15 -24 -32 -68 -1 34 -12 | 0 5 17 24 31 53 15 -5 23 }}
 Optimal tunings:
@@ Line 148: / Line 149: @@
 Comma list: 3025/3024, 102487/102400, {{monzo| 39 -4 -11 -5 2 }}
-Mapping: {{mapping| 21 4 39 98 58 | 0 6 2 -8 3 3 }}
+{{Mapping|legend=0| 21 4 39 98 58 | 0 6 2 -8 3 3 }}
 : mapping generators: ~1323/1280, ~6615/5632
@@ Line 164: / Line 165: @@
 Comma list: 3025/3024, 4096/4095, 14641/14625, 85750/85683
-Mapping: {{mapping| 21 4 39 98 58 107 | 0 6 2 -8 3 -6 }}
+{{Mapping|legend=0| 21 4 39 98 58 107 | 0 6 2 -8 3 -6 }}
 Optimal tunings:
@@ Line 179: / Line 180: @@
 Comma list: 2601/2600, 3025/3024, 4096/4095, 8624/8619, 14641/14625
-Mapping: {{mapping| 21 4 39 98 58 107 120 | 0 6 2 -8 3 -6 -7 }}
+{{Mapping|legend=0| 21 4 39 98 58 107 120 | 0 6 2 -8 3 -6 -7 }}
 Optimal tunings:
@@ Line 194: / Line 195: @@
 Comma list: 2376/2375, 2601/2600, 2926/2925, 3025/3024, 3213/3211, 4096/4095
-Mapping: {{mapping| 21 4 39 98 58 107 120 16 | 0 6 2 -8 3 -6 -7 15 }}
+{{Mapping|legend=0| 21 4 39 98 58 107 120 16 | 0 6 2 -8 3 -6 -7 15 }}
 Optimal tunings:
@@ Line 209: / Line 210: @@
 Comma list: 1496/1495, 2376/2375, 2601/2600, 2646/2645, 2926/2925, 3025/3024, 3213/3211
-Mapping: {{mapping| 21 4 39 98 58 107 120 16 95 | 0 6 2 -8 3 -6 -7 15 0 }}
+{{Mapping|legend=0| 21 4 39 98 58 107 120 16 95 | 0 6 2 -8 3 -6 -7 15 0 }}
 Optimal tunings:
@@ Line 263: / Line 264: @@
 Comma list: 9801/9800, 151263/151250, 184549376/184528125
-Mapping: {{mapping| 12 0 161 338 517 | 0 1 -7 -16 -25 }}
+{{Mapping|legend=0| 12 0 161 338 517 | 0 1 -7 -16 -25 }}
 Optimal tunings:
@@ Line 280: / Line 281: @@
 Comma list: 9801/9800, 151263/151250, 371293/371250, 184549376/184528125
-Mapping: {{mapping| 60 0 805 1690 2585 1173 | 0 1 7 -16 -25 -10 }}
+{{Mapping|legend=0| 60 0 805 1690 2585 1173 | 0 1 7 -16 -25 -10 }}
 : mapping generators: ~2704/2673, ~3
@@ Line 296: / Line 297: @@
 Comma list: 9801/9800, 12376/12375, 28561/28560, 151263/151250, 11275335/11275264
-Mapping: {{mapping| 60 0 805 1690 2585 1173 1957 | 0 1 7 -16 -25 -10 -18 }}
+{{Mapping|legend=0| 60 0 805 1690 2585 1173 1957 | 0 1 7 -16 -25 -10 -18 }}
 Optimal tunings:
@@ Line 311: / Line 312: @@
 Comma list: 9801/9800, 12376/12375, 12636/12635, 23409/23408, 28561/28560, 151263/151250
-Mapping: {{mapping| 60 60 385 730 1085 573 877 -61 | 0 1 7 -16 -25 -10 -18 9 }}
+{{Mapping|legend=0| 60 60 385 730 1085 573 877 -61 | 0 1 7 -16 -25 -10 -18 9 }}
 Optimal tunings:
@@ Line 322: / 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 328: / Line 329: @@
 Comma list: 9801/9800, 151263/151250, 184549376/184528125, 308915776/308828625
-Mapping: {{mapping| 72 0 966 2028 3102 2777 | 0 1 -7 -16 -25 -22 }}
+{{Mapping|legend=0| 72 0 966 2028 3102 2777 | 0 1 -7 -16 -25 -22 }}
 : mapping generators: ~105/104, ~3
@@ Line 344: / Line 345: @@
 Comma list: 9801/9800, 12376/12375, 151263/151250, 1713660/1713481, 97144749/97140736
-Mapping: {{mapping| 72 0 966 2028 3102 2777 979 | 0 1 -7 -16 -25 -22 -6 }}
+{{Mapping|legend=0| 72 0 966 2028 3102 2777 979 | 0 1 -7 -16 -25 -22 -6 }}
 : mapping generators: ~105/104, ~3
@@ Line 360: / Line 361: @@
 Comma list: 9801/9800, 10881/10880, 12376/12375, 57629/57624, 179712/179707, 61456384/61448625
-Subgroup-val mapping: {{mapping| 72 0 966 2028 3102 2777 979 -328 | 0 1 -7 -16 -25 -22 -6 6 }}
+{{Mapping|legend=2| 72 0 966 2028 3102 2777 979 -328 | 0 1 -7 -16 -25 -22 -6 6 }}
 Optimal tunings:
@@ Line 375: / Line 376: @@
 Comma list: 9801/9800, 10881/10880, 12376/12375, 16576/16575, 57629/57624, 93093/93092, 179712/179707
-Subgroup-val mapping: {{mapping| 72 0 966 2028 3102 2777 979 -328 3228 | 0 1 -7 -16 -25 -22 -6 6 -25 }}
+{{Mapping|legend=2| 72 0 966 2028 3102 2777 979 -328 3228 | 0 1 -7 -16 -25 -22 -6 6 -25 }}
 Optimal tunings:
@@ Line 410: / Line 411: @@
 Comma list: 3025/3024, 102487/102400, 180224/180075
-Mapping: {{mapping| 15 0 17 54 40 | 0 4 3 -2 2 }}
+{{Mapping|legend=0| 15 0 17 54 40 | 0 4 3 -2 2 }}
 Optimal tunings:
@@ Line 425: / Line 426: @@
 Comma list: 1716/1715, 3025/3024, 4096/4095, 14641/14625
-Mapping: {{mapping| 15 0 17 54 40 109 | 0 4 3 -2 2 -9 }}
+{{Mapping|legend=0| 15 0 17 54 40 109 | 0 4 3 -2 2 -9 }}
 Optimal tunings:
@@ Line 458: / Line 459: @@
 Comma list: 3025/3024, 5632/5625, 102487/102400
-Mapping: {{mapping| 3 2 8 16 9 | 0 8 -3 -22 4 }}
+{{Mapping|legend=0| 3 2 8 16 9 | 0 8 -3 -22 4 }}
 Optimal tunings:
@@ Line 473: / Line 474: @@
 Comma list: 676/675, 1001/1000, 3025/3024, 4096/4095
-Mapping: {{mapping| 3 2 8 16 9 8 | 0 8 -3 -22 4 9 }}
+{{Mapping|legend=0| 3 2 8 16 9 8 | 0 8 -3 -22 4 9 }}
 Optimal tunings:
@@ Line 488: / Line 489: @@
 Comma list: 676/675, 715/714, 936/935, 1001/1000, 4096/4095
-Mapping: {{mapping| 3 2 8 16 9 8 4 | 0 8 -3 -22 4 9 24 }}
+{{Mapping|legend=0| 3 2 8 16 9 8 4 | 0 8 -3 -22 4 9 24 }}
 Optimal tunings:
@@ Line 503: / Line 504: @@
 Comma list: 676/675, 715/714, 936/935, 1001/1000, 1216/1215, 1729/1728
-Mapping: {{mapping| 3 2 8 16 9 8 4 0 | 0 8 -3 -22 4 9 24 37 }}
+{{Mapping|legend=0| 3 2 8 16 9 8 4 0 | 0 8 -3 -22 4 9 24 37 }}
 Optimal tunings:
@@ Line 514: / 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 540: / Line 539: @@
 Comma list: 9801/9800, 151263/151250, {{monzo| -27 -6 4 6 3 }}
-Mapping: {{mapping| 30 2 15 66 122 | 0 5 6 2 -2 }}
+{{Mapping|legend=0| 30 2 15 66 122 | 0 5 6 2 -2 }}
 Optimal tunings:
@@ Line 555: / Line 554: @@
 Comma list: 9801/9800, 10648/10647, 105644/105625, 196625/196608
-Mapping: {{mapping| 30 2 15 66 122 193 | 0 5 6 2 -2 -9 }}
+{{Mapping|legend=0| 30 2 15 66 122 193 | 0 5 6 2 -2 -9 }}
 Optimal tunings:
@@ Line 565: / 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
 Comma list: 5929/5928, 6860/6859, 9801/9800, 10241/10240, 89376/89375
-Mapping: {{mapping| 30 2 15 66 122 193 91 | 0 5 6 2 -2 -9 4 }}
+{{Mapping|legend=0| 30 2 15 66 122 193 91 | 0 5 6 2 -2 -9 4 }}
 Optimal tunings:
@@ Line 587: / Line 588: @@
 Comma list: 9801/9800, 10648/10647, 31213/31212, 105644/105625, 196625/196608
-Mapping: {{mapping| 60 4 30 132 244 386 391 | 0 5 6 2 -2 -9 -8 }}
+{{Mapping|legend=0| 60 4 30 132 244 386 391 | 0 5 6 2 -2 -9 -8 }}
 : mapping generators: ~612/605, ~216/175
@@ Line 603: / Line 604: @@
 Comma list: 5929/5928, 6860/6859, 9801/9800, 10241/10240, 23409/23408, 89376/89375
-Mapping: {{mapping| 60 4 30 132 244 386 391 182 | 0 5 6 2 -2 -9 -8 4 }}
+{{Mapping|legend=0| 60 4 30 132 244 386 391 182 | 0 5 6 2 -2 -9 -8 4 }}
 Optimal tunings:
@@ Line 660: / Line 661: @@
 Comma list: 9801/9800, 19712/19683, 151263/151250
-Mapping: {{mapping| 30 0 -73 -106 -134 | 0 1 3 4 5 }}
+{{Mapping|legend=0| 30 0 -73 -106 -134 | 0 1 3 4 5 }}
 Optimal tunings:
@@ Line 675: / Line 676: @@
 Comma list: 1001/1000, 4225/4224, 4459/4455, 19712/19683
-Mapping: {{mapping| 30 0 -73 -106 -134 111 | 0 1 3 4 5 0 }}
+{{Mapping|legend=0| 30 0 -73 -106 -134 111 | 0 1 3 4 5 0 }}
 Optimal tunings:
@@ Line 712: / Line 713: @@
 Comma list: 9801/9800, 46656/46585, 151263/151250
-Mapping: {{mapping| 24 1 -6 18 46 | 0 3 5 4 3 }}
+{{Mapping|legend=0| 24 1 -6 18 46 | 0 3 5 4 3 }}
 Optimal tunings:
@@ Line 727: / Line 728: @@
 Comma list: 1716/1715, 2080/2079, 34398/34375, 39366/39325
-Mapping: {{mapping| 24 1 -6 18 46 -47 -13 | 0 3 5 4 3 11 }}
+{{Mapping|legend=0| 24 1 -6 18 46 -47 -13 | 0 3 5 4 3 11 }}
 Optimal tunings:
@@ Line 742: / Line 743: @@
 Comma list: 936/935, 1701/1700, 1716/1715, 2025/2023, 11016/11011
-Mapping: {{mapping| 24 1 -6 18 46 -47 -13 | 0 3 5 4 3 11 9 }}
+{{Mapping|legend=0| 24 1 -6 18 46 -47 -13 | 0 3 5 4 3 11 9 }}
 Optimal tunings:
@@ Line 752: / Line 753: @@
 Badness (Sintel): 1.06
+== Phosphorus ==
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 250047/250000, {{monzo| 60 -96 1 32 }}
+[[Mapping]]: {{mapping| 15 8 -4 -4 | 0 13 32 38 }}
+: mapping generators: ~{{monzo| -21 34 4 -15 }}, ~210827008/199290375
+[[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| 210, …, 1125, 1335, 2460 }}
+[[Badness]] (Sintel): 9.66
+[[Category:Landscape microtemperaments| ]] <!-- main article -->
+[[Category:Landscape| ]] <!-- key article -->
 [[Category:Temperament collections]]
-[[Category:Landscape microtemperaments| ]] <!-- main article -->
+[[Category:Catalogs of rank-2 temperaments]]
-[[Category:Rank 2]]

Landscape microtemperaments: Difference between revisions

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