Kalismic temperaments: Difference between revisions

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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~~

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

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

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.

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

~~[[Optimal tuning]]s:~~

* [[WE]]: ~55/49 = 200.0008{{c}}, ~3/2 = 701.9318{{c}}, ~5/4 = 386.3342{{c}}

~~: [[error map]]: {{val| +0.005 -0.018 +0.031 -0.004 -0.018 }}~~

* [[CWE]]: ~55/49 = 200.0000{{c}}, ~3/2 = 701.9320{{c}}, ~5/4 = 386.3393{{c}}

~~: error map: {{val| 0.000 -0.023 +0.026 -0.011 -0.028 }}~~

~~{{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]] (Sintel): 0.140~~

~~== Lycoris ==~~

[[Subgroup]]: 2.3.5.7.11

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== 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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== 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

@@ Line 15: / 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
-[[Comma list]]: 9801/9800, 151263/151250
-{{Mapping|legend=1| 6 0 0 8 17 | 0 1 0 -2 -4 | 0 0 1 2 3 }}
+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.
-: mapping generators: ~55/49, ~3, ~5
-[[Optimal tuning]]s:
-* [[WE]]: ~55/49 = 200.0008{{c}}, ~3/2 = 701.9318{{c}}, ~5/4 = 386.3342{{c}}
-: [[error map]]: {{val| +0.005 -0.018 +0.031 -0.004 -0.018 }}
-* [[CWE]]: ~55/49 = 200.0000{{c}}, ~3/2 = 701.9320{{c}}, ~5/4 = 386.3393{{c}}
-: error map: {{val| 0.000 -0.023 +0.026 -0.011 -0.028 }}
-{{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]] (Sintel): 0.140
-== Lycoris ==
 [[Subgroup]]: 2.3.5.7.11
@@ Line 93: / Line 79: @@
 == 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 145: / Line 133: @@
 == 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