Kalismic temperaments: Difference between revisions

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__FORCETOC__

~~These are~~ [[rank-3 temperament]]s tempering out [[9801/9800]]. Temperaments discussed elsewhere are:

This is a collection of [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] that [[tempering out|temper out]] the kalisma, [[9801/9800]]. These temperaments always split the octave into halves.

* ''[[~~Jubilee~~]]'' (+50/49 ~~or 99/98~~) → [[Jubilismic family #~~Jubilee~~|Jubilismic family]]

Temperaments discussed elsewhere are:

* ''[[Jubilismic]]'' (+50/49) → [[Jubilismic family #Undecimal jubilismic|Jubilismic family]]

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

* ''[[Bisector]]'' (+121/120 or 245/243) → [[Sensamagic family #Bisector|Sensamagic family]]

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* ''[[Baldur]]'' (+2401/2400) → [[Breed family #Baldur|Breed family]]

* ''[[Thor]]'' (+3025/3024 or 4375/4374) → [[Ragismic family #Thor|Ragismic family]]

* ''[[Semihemimean]]'' (+3136/3125) → [[Hemimean family #Semihemimean|Hemimean family]]

* ''[[Semiporwell]]'' (+6144/6125) → [[Porwell family #Semiporwell|Porwell family]]

* ''[[Semicanou]]'' (+14641/14580) → [[Canou family #Semicanou|Canou family]]

* ''[[Odin]]'' (+151263/151250) → [[Landscape family #Odin|Landscape family]]

Considered below are ~~odin,~~ lycoris, van gogh, sif, loki, pessoal, and linus. For the rank-4 temperament, see [[Rank-4 temperament #Kalismic (9801/9800)]].

Considered below are lycoris, van gogh, sif, loki, pessoal, and linus, in the order of increasing [[badness]]. For the rank-4 temperament, see [[Rank-4 temperament #Kalismic (9801/9800)]].

== ~~Odin~~ ==

== Lycoris ==

~~{{See also| Landscape family }}~~

Lycoris tempers out the [[parimo]] in addition to the kalisma, and splits the [[syntonic comma]] into three equal parts, one for [[121/120]], and two for [[243/242]]. It is therefore [[support]]ed by third-comma equal temperaments. [[342edo]] shows an excellent example of this, but it can be tuned much more accurate.

[[~~Subgroup~~]]~~: 2~~.~~3.5.7.11~~

It was named by [[Flora Canou]] in 2023 after the flower associated with afterlife in Japanese culture, under the impression that a temperament with such intricacy will never be fully explored in a lifetime.

~~[[Comma list]]: 9801/9800, 151263/151250~~

~~{{Mapping|legend=1| 6 0 0 8 17 | 0 1 0 -2 -4 | 0 0 1 2 3 }}~~

~~: mapping generators: ~55/49, ~3, ~5~~

~~{{Optimal ET sequence|legend=1| 12, 42, 48dee, 54c, 60e, 72, 198, 270, 342, 612, 954, 1236, 1506, 1578, 1848, 3426, 4038, 5616, 7464, 17118e, 18966e }}~~

~~[[Badness]]: 0.116 × 10-3~~

~~== Lycoris ==~~

[[Subgroup]]: 2.3.5.7.11

[[Comma list]]: 9801/9800, 1771561/1771470

: mapping generators: ~99/70, ~3, ~11/9

: ~~mapping generators~~: ~99/70, ~3, ~81/70

[[Optimal tuning]]s:

* [[WE]]: ~99/70 = 600.0018{{c}}, ~3/2 = 701.9411{{c}}, ~11/9 = 347.3976{{c}}

[[~~Optimal tuning~~]] ([[~~CTE~~]]): ~99/70 = ~~1\2~~, ~3/2 = 701.~~9439~~, ~81/70 = ~~252~~.~~6028~~

: [[error map]]: {{val| +0.004 -0.010 +0.013 -0.018 -0.031 }}

* [[CWE]]: ~99/70 = 600.0000{{c}}, ~3/2 = 701.9414{{c}}, ~11/9 = 347.3969{{c}}

: error map: {{val| 0.000 -0.014 +0.009 +0.014 -0.038 }}

{{Optimal ET sequence|legend=1| 152, 328, 342, 836, 1178, 1354, 1506, 1848, 2684, 4038, 4190, 4532, 11254, 15786e }}

[[Badness]]: 0.~~249 × 10-3~~

[[Badness]] (Sintel): 0.299

=== Higanbana ===

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Comma list: 9801/9800, 10648/10647, 1399680/1399489

Mapping: {{mapping| 2 1 5 -~~3 3 8~~ | 0 2 2 6 4 1 | 0 0 -6 5 -1 4 }}

Mapping: {{mapping| 2 1 -1 2 2 4 | 0 2 2 6 4 1 | 0 0 6 -5 1 4 }}

: mapping generators: ~99/70, ~1458/1001, ~81/70

Optimal ~~tuning (CTE)~~: ~99/70 = ~~1\2~~, ~1458/1001 = 650.~~9715~~, ~81/70 = ~~252~~.~~6037~~

Optimal tunings:

* WE: ~99/70 = 599.9996{{c}}, ~1458/1001 = 650.9717{{c}}, ~11/9 = 347.3963{{c}}

* CWE: ~99/70 = 600.0000{{c}}, ~1458/1001 = 650.9718{{c}}, ~11/9 = 347.3964{{c}}

{{Optimal ET sequence|legend=1| 166, 190, 304d, 328, 494, 684, 1012, 1178, 1506, 2190, 2684, 4190, 6380, 9064, 15938 }}

{{Optimal ET sequence|legend=0| 166, 190, 304d, 328, 494, 684, 1012, 1178, 1506, 2190, 2684, 4190, 6380, 9064, 15938 }}

Badness: 0.~~416 × 10-3~~

Badness (Sintel): 0.389

== Van gogh ==

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: mapping generators: ~99/70, ~3, ~11/10

: ~~mapping generators~~: ~99/70, ~3, ~9/7

[[Optimal tuning]]s:

* [[WE]]: ~99/70 = 600.0022{{c}}, ~3/2 = 701.9464{{c}}, ~11/9 = 164.9319{{c}}

: [[error map]]: {{val| +0.004 -0.004 +0.022 +0.005 -0.046 }}

* [[CWE]]: ~99/70 = 600.0000{{c}}, ~3/2 = 701.9469{{c}}, ~11/9 = 164.9316{{c}}

: error map: {{val| 0.000 -0.008 +0.018 -0.000 -0.055 }}

{{Optimal ET sequence|legend=1| 22, 58, 80, 138cde, 204cde, 226ce, 240d, 262d, 284, 320, 342, 742, 764, 1084, 1106, 1448, 1506, 1848, 4038, 4802, 5144, 6992 }}

[[Badness]]: 0.~~297 × 10-3~~

[[Badness]] (Sintel): 0.358

== Sif ==

Sif tempers out 2097152/2096325, and extends to a strong [[13-limit]] temperament by virtue of the identity 2097152/2096325 = ([[4096/4095]])⋅([[6656/6655]]). It was named by [[Flora Canou]] in 2023 as a sharp-tending counterpart of [[thor]].

[[Subgroup]]: 2.3.5.7.11

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: mapping generators: ~99/70, ~3

[[Optimal tuning]] ([[~~CTE~~]]): ~99/70 = 1\2, ~3/2 = 701.~~9492~~, ~48/35 = 546.~~6041~~

[[Optimal tuning]]s:

* [[WE]]: ~99/70 = 599.9863{{c}}, ~3/2 = 701.9658{{c}}, ~48/35 = 546.5930{{c}}

: [[error map]]: {{val| -0.027 -0.017 +0.045 +0.052 +0.000 }}

* [[CWE]]: ~99/70 = 600.0000{{c}}, ~3/2 = 701.9755{{c}}, ~48/35 = 546.6052{{c}}

: error map: {{val| 0.000 +0.021 +0.107 +0.124 +0.101 }}

{{Optimal ET sequence|legend=1| 22, 46, 68, 114, 134, 156, 178, 202, 224, 270, 494, 742, 764, 966, 1236, 1506, 2742, 3236, 3506, 4742d, 10990ccdde, 15732ccdddee }}

[[Badness]]: 0.~~423 × 10-3~~

[[Badness]] (Sintel): 0.508

=== 13-limit ===

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Mapping: {{mapping| 2 0 1 7 11 16 | 0 1 0 1 -1 -3 | 0 0 4 -5 -1 1 }}

Optimal ~~tuning (CTE)~~: ~99/70 = 1\2, ~3/2 = 701.~~9902~~, ~48/35 = 546.~~6064~~

Optimal tunings:

* WE: ~99/70 = 599.9857{{c}}, ~3/2 = 701.9705{{c}}, ~48/35 = 546.5927{{c}}

* CWE: ~99/70 = 600.0000{{c}}, ~3/2 = 701.9877{{c}}, ~48/35 = 546.6058{{c}}

{{Optimal ET sequence|legend=1| 22, 46, 156f, 178, 202f, 224, 270, 494, 764, 1012, 1236, 1506, 3236, 3506, 4742df, 6248cdf, 8248cdef, 12990ccddeff, 14496ccdddeeff }}

{{Optimal ET sequence|legend=0| 22, 46, 156f, 178, 202f, 224, 270, 494, 764, 1012, 1236, 1506, 3236, 3506, 4742df, 6248cdf, 8248cdef, 12990ccddeff, 14496ccdddeeff }}

Badness: 0.~~339 × 10-3~~

Badness (Sintel): 0.317

== Loki ==

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: mapping generators: ~99/70, ~3, ~5

: ~~mapping generators~~: ~99/70, ~3, ~5

[[Optimal tuning]]s:

* [[WE]]: ~99/70 = 599.9481{{c}}, ~3/2 = 702.1195{{c}}, ~5/4 = 386.7636{{c}}

: [[error map]]: {{val| -0.104 +0.061 +0.242 -0.005 -0.128 }}

* [[CWE]]: ~99/70 = 600.0000{{c}}, ~3/2 = 702.1647{{c}}, ~5/4 = 386.7768{{c}}

: error map: {{val| 0.000 +0.210 +0.463 +0.163 +0.119 }}

{{Optimal ET sequence|legend=1| 12, 22, 34d, 56d, 74d, 84de, 96d, 118, 130, 152, 248, 270, 670, 822, 940, 1092, 1362c, 2032c, 2302c }}

[[Badness]]: 0.~~493 × 10-3~~

[[Badness]] (Sintel): 0.592

== Pessoal ==

Pessoal tempers out the [[olympia]]. It was named by [[Aura]] in 2023, meaning [[Wiktionary: pessoal #Portuguese|"personal"]], for the fact that it is associated with [[abigail]], which is in turn a person's name.

[[Subgroup]]: 2.3.5.7.11

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: mapping generators: ~99/70, ~3, ~32/21

[[Optimal tuning]] ([[~~CTE~~]]): ~99/70 = 1\2, ~3/2 = 702.~~0759~~, ~32/21 = 728.~~7910~~

[[Optimal tuning]]s:

* [[WE]]: ~99/70 = 599.9711{{c}}, ~3/2 = 702.0265{{c}}, ~32/21 = 728.7942{{c}}

: [[error map]]: {{val| -0.058 +0.014 +0.040 +0.122 -0.040 }}

* [[CWE]]: ~99/70 = 600.0000{{c}}, ~3/2 = 702.0635{{c}}, ~32/21 = 728.8214{{c}}

: error map: {{val| 0.000 +0.109 +0.150 +0.289 +0.134 }}

{{Optimal ET sequence|legend=1| 36, 46, 84, 94, 130, 224, 270, 494, 764, 1164, 1658, 3586cd, 5244cdde, 6008bcdde }}

[[Badness]]: 0.~~499 × 10-3~~

[[Badness]] (Sintel): 0.599

=== 13-limit ===

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Mapping: {{mapping| 2 0 1 10 14 13 | 0 1 0 -1 -3 -1 | 0 0 3 -1 2 -2 }}

Optimal ~~tuning (CTE)~~: ~99/70 = 1\2, ~3/2 = 702.~~0637~~, ~32/21 = 728.~~7786~~

Optimal tunings:

* WE: ~99/70 = 599.9835{{c}}, ~3/2 = 702.0253{{c}}, ~32/21 = 728.7700{{c}}

* CWE: ~99/70 = 600.0000{{c}}, ~3/2 = 702.0477{{c}}, ~32/21 = 728.7882{{c}}

{{Optimal ET sequence|legend=1| 36, 46, 84, 94, 130, 224, 270, 494, 764, 1258, 1882d, 2152d }}

{{Optimal ET sequence|legend=0| 36, 46, 84, 94, 130, 224, 270, 494, 764, 1258, 1882d, 2152d }}

Badness: 0.~~391 × 10-3~~

Badness (Sintel): 0.366

== Linus ==

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: ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #Linus]].''

Linus [[tempering out|tempers out]] the [[linus comma]], {{monzo| 11 -10 -10 10 }} in the 7-limit and can be described as the 80 & 130 & 270 temperament. It tempers out 9801/9800 and 391314/390625 in the 11-limit; 1001/1000, 4225/4224, and 4459/4455 in the 13-limit. The 1/10-octave period interval represents 15/14, three of which represents 16/13, and five of which represents both 99/70 and 140/99.

Linus [[tempering out|tempers out]] the [[linus comma]], {{monzo| 11 -10 -10 10 }} in the 7-limit and can be described as the {{nowrap| 80 & 130 & 270 }} temperament. It tempers out 9801/9800 and 391314/390625 in the 11-limit; 1001/1000, 4225/4224, and 4459/4455 in the 13-limit. The 1/10-octave period interval represents 15/14, three of which represents 16/13, and five of which represents both 99/70 and 140/99.

[[Subgroup]]: 2.3.5.7.11

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[[Optimal tuning]] ([[~~CTE~~]]): ~15/14 = ~~1\10~~, ~3/2 = 702.~~0010~~, ~5/4 = 386.~~5927~~

[[Optimal tuning]]s:

* [[WE]]: ~15/14 = 119.9975{{c}}, ~3/2 = 702.0188{{c}}, ~5/4 = 386.6399{{c}}

: [[error map]]: {{val| -0.025 +0.039 +0.276 -0.215 -0.143 }}

* [[CWE]]: ~15/14 = 120.0000{{c}}, ~3/2 = 702.0181{{c}}, ~5/4 = 386.6218{{c}}

: error map: {{val| 0.000 +0.063 +0.308 -0.186 -0.092 }}

{{Optimal ET sequence|legend=1| 50, 60e, 80, 130, 190, 270, 670, 940, 1130, 1400, 1800c, 2070c, 2340c }}

[[Badness]]: 1.~~12 × 10-3~~

[[Badness]] (Sintel): 1.34

=== 13-limit ===

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Mapping: {{mapping| 10 0 0 -11 4 37 | 0 1 0 1 -1 0 | 0 0 1 1 2 0 }}

Optimal ~~tuning (CTE)~~: ~15/14 = ~~1\10~~, ~3/2 = ~~702~~.~~0010~~, ~5/4 = 386.~~5928~~

Optimal tunings:

* WE: ~15/14 = 120.0054{{c}}, ~3/2 = 701.9625{{c}}, ~5/4 = 386.4910{{c}}

* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 701.9533{{c}}, ~5/4 = 386.5119{{c}}

~~Optimal ET sequence:~~ {{Optimal ET sequence| 50, 60e, 80, 130, 190, 270, 590, 730, 860, 1130, 1590df, 1860def }}

{{Optimal ET sequence|legend=0| 50, 60e, 80, 130, 190, 270, 590, 730, 860, 1130, 1590df, 1860def }}

Badness: 0.~~771 × 10-3~~

Badness (Sintel): 0.721

[[Category:Temperament collections]]

[[Category:Kalismic temperaments| ]]

~~[[Category:Kalismic| ]] ~~

[[Category:Rank 3]]

@@ Line 1: / Line 1: @@
 __FORCETOC__
 {{Technical data page}}
-These are [[rank-3 temperament]]s tempering out [[9801/9800]]. Temperaments discussed elsewhere are:
+This is a collection of [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] that [[tempering out|temper out]] the kalisma, [[9801/9800]]. These temperaments always split the octave into halves.
-* ''[[Jubilee]]'' (+50/49 or 99/98) → [[Jubilismic family #Jubilee|Jubilismic family]]
+Temperaments discussed elsewhere are:
+* ''[[Jubilismic]]'' (+50/49) → [[Jubilismic family #Undecimal jubilismic|Jubilismic family]]
 * ''[[Fantastic]]'' (+225/224) → [[Marvel family #Fantastic|Marvel family]]
 * ''[[Bisector]]'' (+121/120 or 245/243) → [[Sensamagic family #Bisector|Sensamagic family]]
@@ Line 13: / Line 15: @@
 * ''[[Baldur]]'' (+2401/2400) → [[Breed family #Baldur|Breed family]]
 * ''[[Thor]]'' (+3025/3024 or 4375/4374) → [[Ragismic family #Thor|Ragismic family]]
+* ''[[Semihemimean]]'' (+3136/3125) → [[Hemimean family #Semihemimean|Hemimean family]]
 * ''[[Semiporwell]]'' (+6144/6125) → [[Porwell family #Semiporwell|Porwell family]]
 * ''[[Semicanou]]'' (+14641/14580) → [[Canou family #Semicanou|Canou family]]
+* ''[[Odin]]'' (+151263/151250) → [[Landscape family #Odin|Landscape family]]
-Considered below are odin, lycoris, van gogh, sif, loki, pessoal, and linus. For the rank-4 temperament, see [[Rank-4 temperament #Kalismic (9801/9800)]].
+Considered below are lycoris, van gogh, sif, loki, pessoal, and linus, in the order of increasing [[badness]]. For the rank-4 temperament, see [[Rank-4 temperament #Kalismic (9801/9800)]].
-== Odin ==
+== Lycoris ==
-{{See also| Landscape family }}
+Lycoris tempers out the [[parimo]] in addition to the kalisma, and splits the [[syntonic comma]] into three equal parts, one for [[121/120]], and two for [[243/242]]. It is therefore [[support]]ed by third-comma equal temperaments. [[342edo]] shows an excellent example of this, but it can be tuned much more accurate.
-[[Subgroup]]: 2.3.5.7.11
+It was named by [[Flora Canou]] in 2023 after the flower associated with afterlife in Japanese culture, under the impression that a temperament with such intricacy will never be fully explored in a lifetime.
-[[Comma list]]: 9801/9800, 151263/151250
-{{Mapping|legend=1| 6 0 0 8 17 | 0 1 0 -2 -4 | 0 0 1 2 3 }}
-: mapping generators: ~55/49, ~3, ~5
-{{Optimal ET sequence|legend=1| 12, 42, 48dee, 54c, 60e, 72, 198, 270, 342, 612, 954, 1236, 1506, 1578, 1848, 3426, 4038, 5616, 7464, 17118e, 18966e }}
-[[Badness]]: 0.116 × 10<sup>-3</sup>
-== Lycoris ==
 [[Subgroup]]: 2.3.5.7.11
 [[Comma list]]: 9801/9800, 1771561/1771470
-{{Mapping|legend=1| 2 0 4 -6 1 | 0 1 1 3 2 | 0 0 -6 5 -1 }}
+{{Mapping|legend=1| 2 0 -2 1 0 | 0 1 1 3 2 | 0 0 6 -5 1 }}
+: mapping generators: ~99/70, ~3, ~11/9
-: mapping generators: ~99/70, ~3, ~81/70
+[[Optimal tuning]]s:
+* [[WE]]: ~99/70 = 600.0018{{c}}, ~3/2 = 701.9411{{c}}, ~11/9 = 347.3976{{c}}
-[[Optimal tuning]] ([[CTE]]): ~99/70 = 1\2, ~3/2 = 701.9439, ~81/70 = 252.6028
+: [[error map]]: {{val| +0.004 -0.010 +0.013 -0.018 -0.031 }}
+* [[CWE]]: ~99/70 = 600.0000{{c}}, ~3/2 = 701.9414{{c}}, ~11/9 = 347.3969{{c}}
+: error map: {{val| 0.000 -0.014 +0.009 +0.014 -0.038 }}
 {{Optimal ET sequence|legend=1| 152, 328, 342, 836, 1178, 1354, 1506, 1848, 2684, 4038, 4190, 4532, 11254, 15786e }}
-[[Badness]]: 0.249 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.299
 === Higanbana ===
@@ Line 53: / Line 49: @@
 Comma list: 9801/9800, 10648/10647, 1399680/1399489
-Mapping: {{mapping| 2 1 5 -3 3 8 | 0 2 2 6 4 1 | 0 0 -6 5 -1 4 }}
+Mapping: {{mapping| 2 1 -1 2 2 4 | 0 2 2 6 4 1 | 0 0 6 -5 1 4 }}
 : mapping generators: ~99/70, ~1458/1001, ~81/70
-Optimal tuning (CTE): ~99/70 = 1\2, ~1458/1001 = 650.9715, ~81/70 = 252.6037
+Optimal tunings:
+* WE: ~99/70 = 599.9996{{c}}, ~1458/1001 = 650.9717{{c}}, ~11/9 = 347.3963{{c}}
+* CWE: ~99/70 = 600.0000{{c}}, ~1458/1001 = 650.9718{{c}}, ~11/9 = 347.3964{{c}}
-{{Optimal ET sequence|legend=1| 166, 190, 304d, 328, 494, 684, 1012, 1178, 1506, 2190, 2684, 4190, 6380, 9064, 15938 }}
+{{Optimal ET sequence|legend=0| 166, 190, 304d, 328, 494, 684, 1012, 1178, 1506, 2190, 2684, 4190, 6380, 9064, 15938 }}
-Badness: 0.416 × 10<sup>-3</sup>
+Badness (Sintel): 0.389
 == Van gogh ==
@@ Line 69: / Line 66: @@
 {{Mapping|legend=1| 2 0 8 0 11 | 0 1 1 2 1 | 0 0 -9 -1 -10 }}
+: mapping generators: ~99/70, ~3, ~11/10
-: mapping generators: ~99/70, ~3, ~9/7
+[[Optimal tuning]]s:
+* [[WE]]: ~99/70 = 600.0022{{c}}, ~3/2 = 701.9464{{c}}, ~11/9 = 164.9319{{c}}
+: [[error map]]: {{val| +0.004 -0.004 +0.022 +0.005 -0.046 }}
+* [[CWE]]: ~99/70 = 600.0000{{c}}, ~3/2 = 701.9469{{c}}, ~11/9 = 164.9316{{c}}
+: error map: {{val| 0.000 -0.008 +0.018 -0.000 -0.055 }}
 {{Optimal ET sequence|legend=1| 22, 58, 80, 138cde, 204cde, 226ce, 240d, 262d, 284, 320, 342, 742, 764, 1084, 1106, 1448, 1506, 1848, 4038, 4802, 5144, 6992 }}
-[[Badness]]: 0.297 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.358
 == Sif ==
+Sif tempers out 2097152/2096325, and extends to a strong [[13-limit]] temperament by virtue of the identity 2097152/2096325 = ([[4096/4095]])⋅([[6656/6655]]). It was named by [[Flora Canou]] in 2023 as a sharp-tending counterpart of [[thor]].
 [[Subgroup]]: 2.3.5.7.11
@@ Line 82: / Line 86: @@
 {{Mapping|legend=1| 2 0 1 7 11 | 0 1 0 1 -1 | 0 0 4 -5 -1 }}
 : mapping generators: ~99/70, ~3
-[[Optimal tuning]] ([[CTE]]): ~99/70 = 1\2, ~3/2 = 701.9492, ~48/35 = 546.6041
+[[Optimal tuning]]s:
+* [[WE]]: ~99/70 = 599.9863{{c}}, ~3/2 = 701.9658{{c}}, ~48/35 = 546.5930{{c}}
+: [[error map]]: {{val| -0.027 -0.017 +0.045 +0.052 +0.000 }}
+* [[CWE]]: ~99/70 = 600.0000{{c}}, ~3/2 = 701.9755{{c}}, ~48/35 = 546.6052{{c}}
+: error map: {{val| 0.000 +0.021 +0.107 +0.124 +0.101 }}
 {{Optimal ET sequence|legend=1| 22, 46, 68, 114, 134, 156, 178, 202, 224, 270, 494, 742, 764, 966, 1236, 1506, 2742, 3236, 3506, 4742d, 10990ccdde, 15732ccdddee }}
-[[Badness]]: 0.423 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.508
 === 13-limit ===
@@ Line 98: / Line 105: @@
 Mapping: {{mapping| 2 0 1 7 11 16 | 0 1 0 1 -1 -3 | 0 0 4 -5 -1 1 }}
-Optimal tuning (CTE): ~99/70 = 1\2, ~3/2 = 701.9902, ~48/35 = 546.6064
+Optimal tunings:
+* WE: ~99/70 = 599.9857{{c}}, ~3/2 = 701.9705{{c}}, ~48/35 = 546.5927{{c}}
+* CWE: ~99/70 = 600.0000{{c}}, ~3/2 = 701.9877{{c}}, ~48/35 = 546.6058{{c}}
-{{Optimal ET sequence|legend=1| 22, 46, 156f, 178, 202f, 224, 270, 494, 764, 1012, 1236, 1506, 3236, 3506, 4742df, 6248cdf, 8248cdef, 12990ccddeff, 14496ccdddeeff }}
+{{Optimal ET sequence|legend=0| 22, 46, 156f, 178, 202f, 224, 270, 494, 764, 1012, 1236, 1506, 3236, 3506, 4742df, 6248cdf, 8248cdef, 12990ccddeff, 14496ccdddeeff }}
-Badness: 0.339 × 10<sup>-3</sup>
+Badness (Sintel): 0.317
 == Loki ==
@@ Line 110: / Line 119: @@
 {{Mapping|legend=1| 2 0 0 -21 -18 | 0 1 0 4 2 | 0 0 1 3 4 }}
+: mapping generators: ~99/70, ~3, ~5
-: mapping generators: ~99/70, ~3, ~5
+[[Optimal tuning]]s:
+* [[WE]]: ~99/70 = 599.9481{{c}}, ~3/2 = 702.1195{{c}}, ~5/4 = 386.7636{{c}}
+: [[error map]]: {{val| -0.104 +0.061 +0.242 -0.005 -0.128 }}
+* [[CWE]]: ~99/70 = 600.0000{{c}}, ~3/2 = 702.1647{{c}}, ~5/4 = 386.7768{{c}}
+: error map: {{val| 0.000 +0.210 +0.463 +0.163 +0.119 }}
 {{Optimal ET sequence|legend=1| 12, 22, 34d, 56d, 74d, 84de, 96d, 118, 130, 152, 248, 270, 670, 822, 940, 1092, 1362c, 2032c, 2302c }}
-[[Badness]]: 0.493 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.592
 == Pessoal ==
 {{See also| Pessoalisma }}
+Pessoal tempers out the [[olympia]]. It was named by [[Aura]] in 2023, meaning [[Wiktionary: pessoal #Portuguese|"personal"]], for the fact that it is associated with [[abigail]], which is in turn a person's name.
 [[Subgroup]]: 2.3.5.7.11
@@ Line 125: / Line 141: @@
 {{Mapping|legend=1| 2 0 1 10 14 | 0 1 0 -1 -3 | 0 0 3 -1 2 }}
 : mapping generators: ~99/70, ~3, ~32/21
-[[Optimal tuning]] ([[CTE]]): ~99/70 = 1\2, ~3/2 = 702.0759, ~32/21 = 728.7910
+[[Optimal tuning]]s:
+* [[WE]]: ~99/70 = 599.9711{{c}}, ~3/2 = 702.0265{{c}}, ~32/21 = 728.7942{{c}}
+: [[error map]]: {{val| -0.058 +0.014 +0.040 +0.122 -0.040 }}
+* [[CWE]]: ~99/70 = 600.0000{{c}}, ~3/2 = 702.0635{{c}}, ~32/21 = 728.8214{{c}}
+: error map: {{val| 0.000 +0.109 +0.150 +0.289 +0.134 }}
 {{Optimal ET sequence|legend=1| 36, 46, 84, 94, 130, 224, 270, 494, 764, 1164, 1658, 3586cd, 5244cdde, 6008bcdde }}
-[[Badness]]: 0.499 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.599
 === 13-limit ===
@@ Line 141: / Line 160: @@
 Mapping: {{mapping| 2 0 1 10 14 13 | 0 1 0 -1 -3 -1 | 0 0 3 -1 2 -2 }}
-Optimal tuning (CTE): ~99/70 = 1\2, ~3/2 = 702.0637, ~32/21 = 728.7786
+Optimal tunings:
+* WE: ~99/70 = 599.9835{{c}}, ~3/2 = 702.0253{{c}}, ~32/21 = 728.7700{{c}}
+* CWE: ~99/70 = 600.0000{{c}}, ~3/2 = 702.0477{{c}}, ~32/21 = 728.7882{{c}}
-{{Optimal ET sequence|legend=1| 36, 46, 84, 94, 130, 224, 270, 494, 764, 1258, 1882d, 2152d }}
+{{Optimal ET sequence|legend=0| 36, 46, 84, 94, 130, 224, 270, 494, 764, 1258, 1882d, 2152d }}
-Badness: 0.391 × 10<sup>-3</sup>
+Badness (Sintel): 0.366
 == Linus ==
@@ Line 151: / Line 172: @@
 : ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #Linus]].''
-Linus [[tempering out|tempers out]] the [[linus comma]], {{monzo| 11 -10 -10 10 }} in the 7-limit and can be described as the 80 & 130 & 270 temperament. It tempers out 9801/9800 and 391314/390625 in the 11-limit; 1001/1000, 4225/4224, and 4459/4455 in the 13-limit. The 1/10-octave period interval represents 15/14, three of which represents 16/13, and five of which represents both 99/70 and 140/99.
+Linus [[tempering out|tempers out]] the [[linus comma]], {{monzo| 11 -10 -10 10 }} in the 7-limit and can be described as the {{nowrap| 80 & 130 & 270 }} temperament. It tempers out 9801/9800 and 391314/390625 in the 11-limit; 1001/1000, 4225/4224, and 4459/4455 in the 13-limit. The 1/10-octave period interval represents 15/14, three of which represents 16/13, and five of which represents both 99/70 and 140/99.
 [[Subgroup]]: 2.3.5.7.11
@@ Line 159: / Line 180: @@
 {{Mapping|legend=1| 10 0 0 -11 4 | 0 1 0 1 -1 | 0 0 1 1 2 }}
-[[Optimal tuning]] ([[CTE]]): ~15/14 = 1\10, ~3/2 = 702.0010, ~5/4 = 386.5927
+[[Optimal tuning]]s:
+* [[WE]]: ~15/14 = 119.9975{{c}}, ~3/2 = 702.0188{{c}}, ~5/4 = 386.6399{{c}}
+: [[error map]]: {{val| -0.025 +0.039 +0.276 -0.215 -0.143 }}
+* [[CWE]]: ~15/14 = 120.0000{{c}}, ~3/2 = 702.0181{{c}}, ~5/4 = 386.6218{{c}}
+: error map: {{val| 0.000 +0.063 +0.308 -0.186 -0.092 }}
 {{Optimal ET sequence|legend=1| 50, 60e, 80, 130, 190, 270, 670, 940, 1130, 1400, 1800c, 2070c, 2340c }}
-[[Badness]]: 1.12 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 1.34
 === 13-limit ===
@@ Line 172: / Line 197: @@
 Mapping: {{mapping| 10 0 0 -11 4 37 | 0 1 0 1 -1 0 | 0 0 1 1 2 0 }}
-Optimal tuning (CTE): ~15/14 = 1\10, ~3/2 = 702.0010, ~5/4 = 386.5928
+Optimal tunings:
+* WE: ~15/14 = 120.0054{{c}}, ~3/2 = 701.9625{{c}}, ~5/4 = 386.4910{{c}}
+* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 701.9533{{c}}, ~5/4 = 386.5119{{c}}
-Optimal ET sequence: {{Optimal ET sequence| 50, 60e, 80, 130, 190, 270, 590, 730, 860, 1130, 1590df, 1860def }}
+{{Optimal ET sequence|legend=0| 50, 60e, 80, 130, 190, 270, 590, 730, 860, 1130, 1590df, 1860def }}
-Badness: 0.771 × 10<sup>-3</sup>
+Badness (Sintel): 0.721
 [[Category:Temperament collections]]
 [[Category:Kalismic temperaments| ]] <!-- main article -->
-[[Category:Kalismic| ]] <!-- key article -->
 [[Category:Rank 3]]