Canopic clan: Difference between revisions

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The '''~~mirkwai~~ clan''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[~~mirkwai~~ comma]] ({{monzo|legend=1| 0 3 4 -5 }}, [[ratio]]: 16875/16807), a no-twos comma.

The '''canopic clan''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[canopic comma]] ({{monzo|legend=1| 0 3 4 -5 }}, [[ratio]]: 16875/16807), a no-twos comma.

== Canopus ==

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[[Comma list]]: 16875/16807

: mapping generators: ~3, ~15/7

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=== Overview to extensions ===

The full 7-limit extensions' relation to canopus is clearer if the mapping is normalized in terms of 3.5.7.2. In fact, the strong extensions are nusecond and octoid. These temperaments are distributed into different temperament collection pages.

The full 7-limit extensions' relation to canopus is clearer if the mapping is normalized in terms of 3.5.7.2. In fact, the strong extensions are nusecond and octoid. These temperaments are distributed into different temperament clan and collection pages.

* ''[[Nusecond]]'' (+126/125) → [[Starling temperaments #Nusecond|Starling temperaments]]

* ''[[Octoid]]'' (+4375/4374) → [[~~Ragismic microtemperaments~~ #Octoid|~~Ragismic microtemperaments~~]]

* [[Octoid]] (+4375/4374) → [[Stearnsmic clan #Octoid|Stearnsmic clan]]

The others are weak extensions. Mirkat tempers out [[19683/19600]], splitting the generator in two with a semitwelfth period. Sqrtphi tempers out [[15625/15552]], splitting the period in six. Semisept tempers out [[1728/1715]] and [[3136/3125]], splitting the generator in six. Miracle tempers out [[225/224]]. Pluto tempers out [[4000/3969]]. These split the generator in five. Kwai tempers out [[5120/5103]], splitting the generator in ten. Quanharuk tempers out [[32805/32768]], splitting the generator in three with a 1/5-twelfth period. Grendel tempers out [[6144/6125]], splitting the generator in eleven. Finally, eris tempers out [[65625/65536]], splitting the generator in sixteen.

Members of the clan discussed elsewhere are:

* ''[[Kwai]]'' (+5120/5103) → [[~~Hemifamity~~ temperaments #Kwai|~~Hemifamity~~ temperaments]]

* ''[[Kwai]]'' (+5120/5103) → [[Aberschismic temperaments #Kwai|Aberschismic temperaments]]

* ''[[Octokaidecal]]'' (+28/27 or 50/49) → [[Trienstonic clan #Octokaidecal|Trienstonic clan]]

* ''[[Meantritone]]'' (+81/80) → [[Meantone family #Meantritone|Meantone family]]

Line 44:

* [[Sqrtphi]] (+15625/15552) → [[Kleismic family #Sqrtphi|Kleismic family]]

* ''[[Rainwell]]'' (+2100875/2097152) → [[Semicomma family #Rainwell|Semicomma family]]

* ''[[Browser]]'' (+78732/78125) → [[Sensipent family #Browser|Sensipent family]]

* ''[[Quintiquart]]'' (+390625000/387420489) → [[Quartonic family #Quintiquart|Quartonic family]]

For ''no-~~twos~~'' extensions, see [[No-twos subgroup temperaments #Canopus]].

For ''no-2's'' extensions, see [[No-twos subgroup temperaments #Canopus]].

Considered below are mirkat, eris, subsemifourth, septendesemi, gaster, hemiseptisix~~, browser~~, and grazer, in the order of increasing [[badness]].

Considered below are mirkat, eris, subsemifourth, septendesemi, gaster, hemiseptisix, and grazer, in the order of increasing [[badness]].

== Mirkat ==

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Comma list: 540/539, 1375/1372, 8019/8000

~~Mapping:~~ {{~~mapping~~| 3 2 1 2 9 | 0 6 13 14 3 }}

Optimal tunings:

Line 90:

Line 91:

Comma list: 351/350, 540/539, 676/675, 1375/1372

~~Mapping:~~ {{~~mapping~~| 3 2 1 2 9 1 | 0 6 13 14 3 22 }}

Optimal tunings:

Line 105:

Line 106:

Comma list: 351/350, 442/441, 540/539, 561/560, 715/714

~~Mapping:~~ {{~~mapping~~| 3 2 1 2 9 1 4 | 0 6 13 14 3 22 18 }}

Optimal tunings:

Line 140:

Line 141:

Comma list: 540/539, 1375/1372, 65625/65536

~~Mapping:~~ {{~~mapping~~| 1 -19 8 -5 -37 | 0 29 -8 11 57 }}

Optimal tunings:

Line 155:

Line 156:

Comma list: 540/539, 625/624, 1375/1372, 4096/4095

~~Mapping:~~ {{~~mapping~~| 1 -19 8 -5 -37 47 | 0 29 -8 11 57 -61 }}

Optimal tuning:

Line 188:

Line 189:

Comma list: 540/539, 1375/1372, 234375/234256

~~Mapping:~~ {{~~mapping~~| 1 -8 -4 -8 -10 | 0 47 31 53 66 }}

Optimal tunings:

Line 203:

Line 204:

Comma list: 540/539, 847/845, 1375/1372, 1575/1573

~~Mapping:~~ {{~~mapping~~| 1 -8 -4 -8 -10 -12 | 0 0 47 31 53 66 77 }}

Optimal tunings:

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== Septendesemi ==

~~The name ''septendesemi'' means a septendecimal semitone ([[17/16]]). The septendesemi temperament (80 & 103)~~ tempers out the mirkwai comma and 1959552/1953125 (parkleiness comma) in the 7-limit. [[183edo]] provides an excellent tuning for 7-, 11-, 13-, and 17-limit septendesemi.

Septendesemi tempers out the mirkwai comma and 1959552/1953125 (parkleiness comma) in the 7-limit, and may be described as the {{nowrap| 80 & 103 }} temperament. [[183edo]] provides an excellent tuning for 7-, 11-, 13-, and 17-limit septendesemi. Septendesemi was named by [[Xenllium]] in 2021; the name ''septendesemi'' refers to a septendecimal semitone ([[17/16]]).

[[Subgroup]]: 2.3.5.7

Line 238:

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Comma list: 540/539, 1375/1372, 43923/43750

~~Mapping:~~ {{~~mapping~~| 1 -2 -1 -2 -1 | 0 41 38 55 51 }}

Optimal tunings:

Line 253:

Line 254:

Comma list: 351/350, 540/539, 1375/1372, 4225/4224

~~Mapping:~~ {{~~mapping~~| 1 -2 -1 -2 -1 3 | 0 41 38 55 51 8 }}

Optimal tunings:

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Comma list: 351/350, 540/539, 561/560, 715/714, 4225/4224

~~Mapping:~~ {{~~mapping~~| 1 -2 -1 -2 -1 3 4 | 0 41 38 55 51 8 1 }}

Optimal tunings:

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~~The gaster temperament (111 & 113)~~ tempers out {{monzo| -70 72 -19 }} ~~(quadbila-negu)~~ in the 5-limit; mirkwai comma (16875/16807) and [[scheme comma]] (14348907/14336000) in the 7-limit. ~~The~~ word "[[Wiktionary: gaster|gaster]]" means [[Wiktionary: abdomen|abdomen]] or [[Wiktionary: stomach|stomach]], but also a restructuring of the words "gassormic tritone", which is a generator of this temperament. This temperament is sufficient to obtain high prime limit harmonics like a stomach, so that patent vals [[111edo|111]], [[113edo|113]] and [[224edo|224]] support it even in the 41-limit.

Gaster tempers out {{monzo| -70 72 -19 }} in the 5-limit, mirkwai comma (16875/16807) and [[scheme comma]] (14348907/14336000) in the 7-limit, and may be described as the {{nowrap| 111 & 113 }} temperament.

It was named by [[Xenllium]] in 2022; the word "[[Wiktionary: gaster|gaster]]" means [[Wiktionary: abdomen|abdomen]] or [[Wiktionary: stomach|stomach]], but also a restructuring of the words "gassormic tritone", which is a generator of this temperament. This temperament is sufficient to obtain high prime limit harmonics like a stomach, so that patent vals [[111edo|111]], [[113edo|113]] and [[224edo|224]] support it even in the 41-limit.

[[Subgroup]]: 2.3.5.7

Line 308:

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Comma list: 540/539, 1375/1372, 14348907/14336000

~~Mapping:~~ {{~~mapping~~| 1 -8 -34 -32 8 | 0 19 72 69 -9 }}

Optimal tunings:

Line 323:

Line 326:

Comma list: 540/539, 729/728, 1375/1372, 2200/2197

~~Mapping:~~ {{~~mapping~~| 1 -8 -34 -32 8 -19 | 0 19 72 69 -9 45 }}

Optimal tunings:

Line 338:

Line 341:

Comma list: 540/539, 715/714, 729/728, 936/935, 2200/2197

~~Mapping:~~ {{~~mapping~~| 1 -8 -34 -32 8 -19 -6 | 0 19 72 69 -9 45 20 }}

{{Mapping|legend=0| 1 -8 -34 -32 8 -19 -6 | 0 19 72 69 -9 45 20 }}

Optimal tunings:

Line 353:

Line 356:

Comma list: 324/323, 400/399, 495/494, 540/539, 715/714, 1445/1444

~~Mapping:~~ {{~~mapping~~| 1 -8 -34 -32 8 -19 -6 -24 | 0 19 72 69 -9 45 20 56 }}

{{Mapping|legend=0| 1 -8 -34 -32 8 -19 -6 -24 | 0 19 72 69 -9 45 20 56 }}

Optimal tunings:

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Comma list: 324/323, 400/399, 460/459, 495/494, 529/528, 540/539, 715/714

~~Mapping:~~ {{~~mapping~~| 1 -8 -34 -32 8 -19 -6 -24 2 | 0 19 72 69 -9 45 20 56 5 }}

{{Mapping|legend=0| 1 -8 -34 -32 8 -19 -6 -24 2 | 0 19 72 69 -9 45 20 56 5 }}

Optimal tunings:

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Comma list: 290/289, 324/323, 400/399, 460/459, 495/494, 529/528, 540/539, 715/714

~~Mapping:~~ {{~~mapping~~| 1 -8 -34 -32 8 -19 -6 -24 2 21 | 0 19 72 69 -9 45 20 56 5 -32 }}

{{Mapping|legend=0| 1 -8 -34 -32 8 -19 -6 -24 2 21 | 0 19 72 69 -9 45 20 56 5 -32 }}

Optimal tunings:

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Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 540/539, 715/714

~~Mapping:~~ {{~~mapping~~| 1 -8 -34 -32 8 -19 -6 -24 2 21 10 | 0 19 72 69 -9 45 20 56 5 -32 -10 }}

{{Mapping|legend=0| 1 -8 -34 -32 8 -19 -6 -24 2 21 10 | 0 19 72 69 -9 45 20 56 5 -32 -10 }}

Optimal tunings:

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Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 540/539, 667/666, 715/714

~~Mapping:~~ {{~~mapping~~| 1 -8 -34 -32 8 -19 -6 -24 2 21 10 38 | 0 19 72 69 -9 45 20 56 5 -32 -10 -65 }}

{{Mapping|legend=0| 1 -8 -34 -32 8 -19 -6 -24 2 21 10 38 | 0 19 72 69 -9 45 20 56 5 -32 -10 -65 }}

Optimal tunings:

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Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 533/532, 540/539, 575/574, 667/666

~~Mapping:~~ {{~~mapping~~| 1 -8 -34 -32 8 -19 -6 -24 2 21 10 38 -35 | 0 19 72 69 -9 45 20 56 5 -32 -10 -65 80 }}

{{Mapping|legend=0| 1 -8 -34 -32 8 -19 -6 -24 2 21 10 38 -35 | 0 19 72 69 -9 45 20 56 5 -32 -10 -65 80 }}

Optimal tunings:

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== Hemiseptisix ==

~~The name ''hemiseptisix'' means a half of septimal major sixth ([[12/7]]). The hemiseptisix temperament (103 & 121)~~ tempers out the mirkwai comma and 95703125/95551488 (pontiqak comma) in the 7-limit. [[224edo]] provides an excellent tuning for 7-, 11-, and 13-limit hemiseptisix.

Hemiseptisix tempers out the mirkwai comma and 95703125/95551488 (pontiqak comma) in the 7-limit, and may be described as the {{nowrap| 103 & 121 }} temperament. [[224edo]] provides an excellent tuning for 7-, 11-, and 13-limit hemiseptisix. Hemiseptisix was named by [[Xenllium]] in 2021; the name ''hemiseptisix'' refers to a half of septimal major sixth ([[12/7]]).

[[Subgroup]]: 2.3.5.7

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Comma list: 540/539, 1375/1372, 2734375/2725888

~~Mapping:~~ {{~~mapping~~| 1 -19 -7 -17 -28 | 0 53 24 51 81 }}

Optimal tunings:

Line 478:

Line 481:

Comma list: 540/539, 625/624, 1375/1372, 2200/2197

~~Mapping:~~ {{~~mapping~~| 1 -19 -7 -17 -28 -13 | 0 53 24 51 81 43 }}

Optimal tunings:

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Comma list: 375/374, 540/539, 625/624, 715/714, 2200/2197

~~Mapping:~~ {{~~mapping~~| 1 -19 -7 -17 -28 -13 -13 | 0 53 24 51 81 43 44 }}

{{Mapping|legend=0| 1 -19 -7 -17 -28 -13 -13 | 0 53 24 51 81 43 44 }}

Optimal tunings:

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Badness (Sintel): 0.948

== ~~Browser~~ ==

== Grazer ==

~~{{See also| Sensipent family }}~~

Named by [[Xenllium]] in 2022, grazer may be described as the {{nowrap| 113 & 121 }} temperament.

~~This can also be considered a~~ [[~~non-over-1 temperament~~]]~~, with considerable scope for harmony~~ in ~~the 2.5/3.7/3.11/3.13/3.17/3 subgroup with mos scales of 8~~, ~~15, 23, and 31 notes despite no harmonics from~~ the ~~root. It can be considered a detemperament of 8d-et, with a generator very slightly flat of 7\8~~.

~~[[Subgroup]]: 2.3.5.7~~

~~[[Comma list]]: 16875/16807, 78732/78125~~

~~{{Mapping|legend=1| 1 -29 -37 -47 | 0 35 45 57 }}~~

~~: mapping generators: ~2, ~90/49~~

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

* [[WE]]: ~2 = 1199.9313{{c}}, ~90/49 = 1048.5414{{c}}

~~: [[error map]]: {{val| -0.069 -1.013 +0.592 +1.264 }}~~

* [[CWE]]: ~2 = 1200.0000{{c}}, ~90/49 = 1048.5998{{c}}

~~: error map: {{val| 0.000 -0.962 +0.677 +1.362 }}~~

~~{{Optimal ET sequence|legend=1| 103, 111, 214 }}~~

~~[[Badness]] (Sintel): 4.57~~

~~=== 11-limit ===~~

~~Subgroup: 2.3.5.7.11~~

~~Comma list: 540/539, 1375/1372, 78732/78125~~

~~Mapping: {{mapping| 1 -29 -37 -47 -28 | 0 35 45 57 36 }}~~

~~Optimal tunings:~~

* WE: ~2 = 1200.1344{{c}}, ~11/6 = 1048.7124{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~11/6 = 1048.5981{{c}}

~~{{Optimal ET sequence|legend=0| 103, 214 }}~~

~~Badness (Sintel): 1.91~~

~~=== 13-limit ===~~

~~Subgroup: 2.3.5.7.11.13~~

~~Comma list: 351/350, 540/539, 847/845, 1375/1372~~

~~Mapping: {{mapping| 1 -29 -37 -47 -28 -33 | 0 35 45 57 36 42 }}~~

~~Optimal tunings:~~

* WE: ~2 = 1200.1344{{c}}, ~11/6 = 1048.7124{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~11/6 = 1048.5984{{c}}

~~{{Optimal ET sequence|legend=0| 103, 111, 214 }}~~

~~Badness (Sintel): 1.19~~

~~=== 17-limit ===~~

~~Subgroup: 2.3.5.7.11.13.17~~

~~Comma list: 351/350, 540/539, 561/560, 715/714, 847/845~~

~~Mapping: {{mapping| 1 -29 -37 -47 -28 -33 -23 | 0 35 45 57 36 42 31 }}~~

~~Optimal tunings:~~

* WE: ~2 = 1199.9191{{c}}, ~11/6 = 1048.5324{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~11/6 = 1048.6014{{c}}

~~{{Optimal ET sequence|legend=0| 103, 111, 214 }}~~

~~Badness (Sintel): 1.04~~

~~=== 19-limit ===~~

~~Subgroup: 2.3.5.7.11.13.17.19~~

~~Comma list: 324/323, 351/350, 456/455, 495/494, 540/539, 715/714~~

~~Mapping: {{mapping| 1 -29 -37 -47 -28 -33 -23 -91 | 0 35 45 57 36 42 31 109 }}~~

~~Optimal tunings:~~

* WE: ~2 = 1199.9145{{c}}, ~11/6 = 1048.5290{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~11/6 = 1048.6021{{c}}

~~{{Optimal ET sequence|legend=0| 103h, 111, 214 }}~~

~~Badness (Sintel): 1.07~~

~~== Grazer ==~~

[[Subgroup]]: 2.3.5.7

Line 608:

Line 531:

Comma list: 540/539, 1375/1372, 218750/216513

~~Mapping:~~ {{~~mapping~~| 1 -3 -4 -5 -1 | 0 37 51 63 36 }}

Optimal tunings:

Line 623:

Line 546:

Comma list: 325/324, 364/363, 540/539, 2200/2197

~~Mapping:~~ {{~~mapping~~| 1 -3 -4 -5 -1 -2 | 0 37 51 63 36 46 }}

Optimal tunings:

Line 638:

Line 561:

Comma list: 325/324, 364/363, 540/539, 595/594, 2000/1989

~~Mapping:~~ {{~~mapping~~| 1 -3 -4 -5 -1 -2 0 | 0 37 51 63 36 46 33 }}

Optimal tunings:

Line 653:

Line 576:

Comma list: 325/324, 364/363, 400/399, 540/539, 595/594, 665/663

~~Mapping:~~ {{~~mapping~~| 1 -3 -4 -5 -1 -2 0 4 | 0 37 51 63 36 46 33 2 }}

{{Mapping|legend=0| 1 -3 -4 -5 -1 -2 0 4 | 0 37 51 63 36 46 33 2 }}

Optimal tunings:

Line 663:

Line 586:

Badness (Sintel): 1.37

[[Category:Canopic clan| ]]

[[Category:Canopic| ]]

[[Category:Temperament clans]]

[[Category:~~Mirkwai clan| ]] <!~~-~~- main article -->~~

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

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

@@ Line 1: / Line 1: @@
 {{Technical data page}}
-The '''mirkwai clan''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[mirkwai comma]] ({{monzo|legend=1| 0 3 4 -5 }}, [[ratio]]: 16875/16807), a no-twos comma.
+The '''canopic clan''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[canopic comma]] ({{monzo|legend=1| 0 3 4 -5 }}, [[ratio]]: 16875/16807), a no-twos comma.
 == Canopus ==
@@ Line 9: / Line 9: @@
 [[Comma list]]: 16875/16807
-{{Mapping|legend=2| 1 -2 -1 | 0 5 4 }}
+{{Mapping|legend=3| 1 -2 -1 | 0 5 4 }}
 : mapping generators: ~3, ~15/7
@@ Line 23: / Line 23: @@
 === Overview to extensions ===
-The full 7-limit extensions' relation to canopus is clearer if the mapping is normalized in terms of 3.5.7.2. In fact, the strong extensions are nusecond and octoid. These temperaments are distributed into different temperament collection pages.
+The full 7-limit extensions' relation to canopus is clearer if the mapping is normalized in terms of 3.5.7.2. In fact, the strong extensions are nusecond and octoid. These temperaments are distributed into different temperament clan and collection pages.
 * ''[[Nusecond]]'' (+126/125) → [[Starling temperaments #Nusecond|Starling temperaments]]
-* ''[[Octoid]]'' (+4375/4374) → [[Ragismic microtemperaments #Octoid|Ragismic microtemperaments]]
+* [[Octoid]] (+4375/4374) → [[Stearnsmic clan #Octoid|Stearnsmic clan]]
 The others are weak extensions. Mirkat tempers out [[19683/19600]], splitting the generator in two with a semitwelfth period. Sqrtphi tempers out [[15625/15552]], splitting the period in six. Semisept tempers out [[1728/1715]] and [[3136/3125]], splitting the generator in six. Miracle tempers out [[225/224]]. Pluto tempers out [[4000/3969]]. These split the generator in five. Kwai tempers out [[5120/5103]], splitting the generator in ten. Quanharuk tempers out [[32805/32768]], splitting the generator in three with a 1/5-twelfth period. Grendel tempers out [[6144/6125]], splitting the generator in eleven. Finally, eris tempers out [[65625/65536]], splitting the generator in sixteen.
 Members of the clan discussed elsewhere are:
-* ''[[Kwai]]'' (+5120/5103) → [[Hemifamity temperaments #Kwai|Hemifamity temperaments]]
+* ''[[Kwai]]'' (+5120/5103) → [[Aberschismic temperaments #Kwai|Aberschismic temperaments]]
 * ''[[Octokaidecal]]'' (+28/27 or 50/49) → [[Trienstonic clan #Octokaidecal|Trienstonic clan]]
 * ''[[Meantritone]]'' (+81/80) → [[Meantone family #Meantritone|Meantone family]]
@@ Line 44: / Line 44: @@
 * [[Sqrtphi]] (+15625/15552) → [[Kleismic family #Sqrtphi|Kleismic family]]
 * ''[[Rainwell]]'' (+2100875/2097152) → [[Semicomma family #Rainwell|Semicomma family]]
+* ''[[Browser]]'' (+78732/78125) → [[Sensipent family #Browser|Sensipent family]]
 * ''[[Quintiquart]]'' (+390625000/387420489) → [[Quartonic family #Quintiquart|Quartonic family]]
-For ''no-twos'' extensions, see [[No-twos subgroup temperaments #Canopus]].
+For ''no-2's'' extensions, see [[No-twos subgroup temperaments #Canopus]].
-Considered below are mirkat, eris, subsemifourth, septendesemi, gaster, hemiseptisix, browser, and grazer, in the order of increasing [[badness]].
+Considered below are mirkat, eris, subsemifourth, septendesemi, gaster, hemiseptisix, and grazer, in the order of increasing [[badness]].
 == Mirkat ==
@@ Line 75: / Line 76: @@
 Comma list: 540/539, 1375/1372, 8019/8000
-Mapping: {{mapping| 3 2 1 2 9 | 0 6 13 14 3 }}
+{{Mapping|legend=0| 3 2 1 2 9 | 0 6 13 14 3 }}
 Optimal tunings:
@@ Line 90: / Line 91: @@
 Comma list: 351/350, 540/539, 676/675, 1375/1372
-Mapping: {{mapping| 3 2 1 2 9 1 | 0 6 13 14 3 22 }}
+{{Mapping|legend=0| 3 2 1 2 9 1 | 0 6 13 14 3 22 }}
 Optimal tunings:
@@ Line 105: / Line 106: @@
 Comma list: 351/350, 442/441, 540/539, 561/560, 715/714
-Mapping: {{mapping| 3 2 1 2 9 1 4 | 0 6 13 14 3 22 18 }}
+{{Mapping|legend=0| 3 2 1 2 9 1 4 | 0 6 13 14 3 22 18 }}
 Optimal tunings:
@@ Line 140: / Line 141: @@
 Comma list: 540/539, 1375/1372, 65625/65536
-Mapping: {{mapping| 1 -19 8 -5 -37 | 0 29 -8 11 57 }}
+{{Mapping|legend=0| 1 -19 8 -5 -37 | 0 29 -8 11 57 }}
 Optimal tunings:
@@ Line 155: / Line 156: @@
 Comma list: 540/539, 625/624, 1375/1372, 4096/4095
-Mapping: {{mapping| 1 -19 8 -5 -37 47 | 0 29 -8 11 57 -61 }}
+{{Mapping|legend=0| 1 -19 8 -5 -37 47 | 0 29 -8 11 57 -61 }}
 Optimal tuning:
@@ Line 188: / Line 189: @@
 Comma list: 540/539, 1375/1372, 234375/234256
-Mapping: {{mapping| 1 -8 -4 -8 -10 | 0 47 31 53 66 }}
+{{Mapping|legend=0| 1 -8 -4 -8 -10 | 0 47 31 53 66 }}
 Optimal tunings:
@@ Line 203: / Line 204: @@
 Comma list: 540/539, 847/845, 1375/1372, 1575/1573
-Mapping: {{mapping| 1 -8 -4 -8 -10 -12 | 0 0 47 31 53 66 77 }}
+{{Mapping|legend=0| 1 -8 -4 -8 -10 -12 | 0 0 47 31 53 66 77 }}
 Optimal tunings:
@@ Line 214: / Line 215: @@
 == Septendesemi ==
-The name ''septendesemi'' means a septendecimal semitone ([[17/16]]). The septendesemi temperament (80 & 103) tempers out the mirkwai comma and 1959552/1953125 (parkleiness comma) in the 7-limit. [[183edo]] provides an excellent tuning for 7-, 11-, 13-, and 17-limit septendesemi.
+Septendesemi tempers out the mirkwai comma and 1959552/1953125 (parkleiness comma) in the 7-limit, and may be described as the {{nowrap| 80 & 103 }} temperament. [[183edo]] provides an excellent tuning for 7-, 11-, 13-, and 17-limit septendesemi. Septendesemi was named by [[Xenllium]] in 2021; the name ''septendesemi'' refers to a septendecimal semitone ([[17/16]]).
 [[Subgroup]]: 2.3.5.7
@@ Line 238: / Line 239: @@
 Comma list: 540/539, 1375/1372, 43923/43750
-Mapping: {{mapping| 1 -2 -1 -2 -1 | 0 41 38 55 51 }}
+{{Mapping|legend=0| 1 -2 -1 -2 -1 | 0 41 38 55 51 }}
 Optimal tunings:
@@ Line 253: / Line 254: @@
 Comma list: 351/350, 540/539, 1375/1372, 4225/4224
-Mapping: {{mapping| 1 -2 -1 -2 -1 3 | 0 41 38 55 51 8 }}
+{{Mapping|legend=0| 1 -2 -1 -2 -1 3 | 0 41 38 55 51 8 }}
 Optimal tunings:
@@ Line 268: / Line 269: @@
 Comma list: 351/350, 540/539, 561/560, 715/714, 4225/4224
-Mapping: {{mapping| 1 -2 -1 -2 -1 3 4 | 0 41 38 55 51 8 1 }}
+{{Mapping|legend=0| 1 -2 -1 -2 -1 3 4 | 0 41 38 55 51 8 1 }}
 Optimal tunings:
@@ Line 284: / Line 285: @@
 {{Main| Gaster temperament }}
-The gaster temperament (111 & 113) tempers out {{monzo| -70 72 -19 }} (quadbila-negu) in the 5-limit; mirkwai comma (16875/16807) and [[scheme comma]] (14348907/14336000) in the 7-limit. The word "[[Wiktionary: gaster|gaster]]" means [[Wiktionary: abdomen|abdomen]] or [[Wiktionary: stomach|stomach]], but also a restructuring of the words "gassormic tritone", which is a generator of this temperament. This temperament is sufficient to obtain high prime limit harmonics like a stomach, so that patent vals [[111edo|111]], [[113edo|113]] and [[224edo|224]] support it even in the 41-limit.
+Gaster tempers out {{monzo| -70 72 -19 }} in the 5-limit, mirkwai comma (16875/16807) and [[scheme comma]] (14348907/14336000) in the 7-limit, and may be described as the {{nowrap| 111 & 113 }} temperament.
+It was named by [[Xenllium]] in 2022; the word "[[Wiktionary: gaster|gaster]]" means [[Wiktionary: abdomen|abdomen]] or [[Wiktionary: stomach|stomach]], but also a restructuring of the words "gassormic tritone", which is a generator of this temperament. This temperament is sufficient to obtain high prime limit harmonics like a stomach, so that patent vals [[111edo|111]], [[113edo|113]] and [[224edo|224]] support it even in the 41-limit.
 [[Subgroup]]: 2.3.5.7
@@ Line 308: / Line 311: @@
 Comma list: 540/539, 1375/1372, 14348907/14336000
-Mapping: {{mapping| 1 -8 -34 -32 8 | 0 19 72 69 -9 }}
+{{Mapping|legend=0| 1 -8 -34 -32 8 | 0 19 72 69 -9 }}
 Optimal tunings:
@@ Line 323: / Line 326: @@
 Comma list: 540/539, 729/728, 1375/1372, 2200/2197
-Mapping: {{mapping| 1 -8 -34 -32 8 -19 | 0 19 72 69 -9 45 }}
+{{Mapping|legend=0| 1 -8 -34 -32 8 -19 | 0 19 72 69 -9 45 }}
 Optimal tunings:
@@ Line 338: / Line 341: @@
 Comma list: 540/539, 715/714, 729/728, 936/935, 2200/2197
-Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 | 0 19 72 69 -9 45 20 }}
+{{Mapping|legend=0| 1 -8 -34 -32 8 -19 -6 | 0 19 72 69 -9 45 20 }}
 Optimal tunings:
@@ Line 353: / Line 356: @@
 Comma list: 324/323, 400/399, 495/494, 540/539, 715/714, 1445/1444
-Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 -24 | 0 19 72 69 -9 45 20 56 }}
+{{Mapping|legend=0| 1 -8 -34 -32 8 -19 -6 -24 | 0 19 72 69 -9 45 20 56 }}
 Optimal tunings:
@@ Line 368: / Line 371: @@
 Comma list: 324/323, 400/399, 460/459, 495/494, 529/528, 540/539, 715/714
-Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 -24 2 | 0 19 72 69 -9 45 20 56 5 }}
+{{Mapping|legend=0| 1 -8 -34 -32 8 -19 -6 -24 2 | 0 19 72 69 -9 45 20 56 5 }}
 Optimal tunings:
@@ Line 383: / Line 386: @@
 Comma list: 290/289, 324/323, 400/399, 460/459, 495/494, 529/528, 540/539, 715/714
-Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 -24 2 21 | 0 19 72 69 -9 45 20 56 5 -32 }}
+{{Mapping|legend=0| 1 -8 -34 -32 8 -19 -6 -24 2 21 | 0 19 72 69 -9 45 20 56 5 -32 }}
 Optimal tunings:
@@ Line 398: / Line 401: @@
 Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 540/539, 715/714
-Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 -24 2 21 10 | 0 19 72 69 -9 45 20 56 5 -32 -10 }}
+{{Mapping|legend=0| 1 -8 -34 -32 8 -19 -6 -24 2 21 10 | 0 19 72 69 -9 45 20 56 5 -32 -10 }}
 Optimal tunings:
@@ Line 413: / Line 416: @@
 Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 540/539, 667/666, 715/714
-Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 -24 2 21 10 38 | 0 19 72 69 -9 45 20 56 5 -32 -10 -65 }}
+{{Mapping|legend=0| 1 -8 -34 -32 8 -19 -6 -24 2 21 10 38 | 0 19 72 69 -9 45 20 56 5 -32 -10 -65 }}
 Optimal tunings:
@@ Line 428: / Line 431: @@
 Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 533/532, 540/539, 575/574, 667/666
-Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 -24 2 21 10 38 -35 | 0 19 72 69 -9 45 20 56 5 -32 -10 -65 80 }}
+{{Mapping|legend=0| 1 -8 -34 -32 8 -19 -6 -24 2 21 10 38 -35 | 0 19 72 69 -9 45 20 56 5 -32 -10 -65 80 }}
 Optimal tunings:
@@ Line 439: / Line 442: @@
 == Hemiseptisix ==
-The name ''hemiseptisix'' means a half of septimal major sixth ([[12/7]]). The hemiseptisix temperament (103 & 121) tempers out the mirkwai comma and 95703125/95551488 (pontiqak comma) in the 7-limit. [[224edo]] provides an excellent tuning for 7-, 11-, and 13-limit hemiseptisix.
+Hemiseptisix tempers out the mirkwai comma and 95703125/95551488 (pontiqak comma) in the 7-limit, and may be described as the {{nowrap| 103 & 121 }} temperament. [[224edo]] provides an excellent tuning for 7-, 11-, and 13-limit hemiseptisix. Hemiseptisix was named by [[Xenllium]] in 2021; the name ''hemiseptisix'' refers to a half of septimal major sixth ([[12/7]]).
 [[Subgroup]]: 2.3.5.7
@@ Line 463: / Line 466: @@
 Comma list: 540/539, 1375/1372, 2734375/2725888
-Mapping: {{mapping| 1 -19 -7 -17 -28 | 0 53 24 51 81 }}
+{{Mapping|legend=0| 1 -19 -7 -17 -28 | 0 53 24 51 81 }}
 Optimal tunings:
@@ Line 478: / Line 481: @@
 Comma list: 540/539, 625/624, 1375/1372, 2200/2197
-Mapping: {{mapping| 1 -19 -7 -17 -28 -13 | 0 53 24 51 81 43 }}
+{{Mapping|legend=0| 1 -19 -7 -17 -28 -13 | 0 53 24 51 81 43 }}
 Optimal tunings:
@@ Line 493: / Line 496: @@
 Comma list: 375/374, 540/539, 625/624, 715/714, 2200/2197
-Mapping: {{mapping| 1 -19 -7 -17 -28 -13 -13 | 0 53 24 51 81 43 44 }}
+{{Mapping|legend=0| 1 -19 -7 -17 -28 -13 -13 | 0 53 24 51 81 43 44 }}
 Optimal tunings:
@@ Line 503: / Line 506: @@
 Badness (Sintel): 0.948
-== Browser ==
+== Grazer ==
-{{See also| Sensipent family }}
+Named by [[Xenllium]] in 2022, grazer may be described as the {{nowrap| 113 & 121 }} temperament.
-This can also be considered a [[non-over-1 temperament]], with considerable scope for harmony in the 2.5/3.7/3.11/3.13/3.17/3 subgroup with mos scales of 8, 15, 23, and 31 notes despite no harmonics from the root. It can be considered a detemperament of 8d-et, with a generator very slightly flat of 7\8.
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 16875/16807, 78732/78125
-{{Mapping|legend=1| 1 -29 -37 -47 | 0 35 45 57 }}
-: mapping generators: ~2, ~90/49
-[[Optimal tuning]]s:
-* [[WE]]: ~2 = 1199.9313{{c}}, ~90/49 = 1048.5414{{c}}
-: [[error map]]: {{val| -0.069 -1.013 +0.592 +1.264 }}
-* [[CWE]]: ~2 = 1200.0000{{c}}, ~90/49 = 1048.5998{{c}}
-: error map: {{val| 0.000 -0.962 +0.677 +1.362 }}
-{{Optimal ET sequence|legend=1| 103, 111, 214 }}
-[[Badness]] (Sintel): 4.57
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 540/539, 1375/1372, 78732/78125
-Mapping: {{mapping| 1 -29 -37 -47 -28 | 0 35 45 57 36 }}
-Optimal tunings:
-* WE: ~2 = 1200.1344{{c}}, ~11/6 = 1048.7124{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~11/6 = 1048.5981{{c}}
-{{Optimal ET sequence|legend=0| 103, 214 }}
-Badness (Sintel): 1.91
-=== 13-limit ===
-Subgroup: 2.3.5.7.11.13
-Comma list: 351/350, 540/539, 847/845, 1375/1372
-Mapping: {{mapping| 1 -29 -37 -47 -28 -33 | 0 35 45 57 36 42 }}
-Optimal tunings:
-* WE: ~2 = 1200.1344{{c}}, ~11/6 = 1048.7124{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~11/6 = 1048.5984{{c}}
-{{Optimal ET sequence|legend=0| 103, 111, 214 }}
-Badness (Sintel): 1.19
-=== 17-limit ===
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 351/350, 540/539, 561/560, 715/714, 847/845
-Mapping: {{mapping| 1 -29 -37 -47 -28 -33 -23 | 0 35 45 57 36 42 31 }}
-Optimal tunings:
-* WE: ~2 = 1199.9191{{c}}, ~11/6 = 1048.5324{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~11/6 = 1048.6014{{c}}
-{{Optimal ET sequence|legend=0| 103, 111, 214 }}
-Badness (Sintel): 1.04
-=== 19-limit ===
-Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 324/323, 351/350, 456/455, 495/494, 540/539, 715/714
-Mapping: {{mapping| 1 -29 -37 -47 -28 -33 -23 -91 | 0 35 45 57 36 42 31 109 }}
-Optimal tunings:
-* WE: ~2 = 1199.9145{{c}}, ~11/6 = 1048.5290{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~11/6 = 1048.6021{{c}}
-{{Optimal ET sequence|legend=0| 103h, 111, 214 }}
-Badness (Sintel): 1.07
-== Grazer ==
 [[Subgroup]]: 2.3.5.7
@@ Line 608: / Line 531: @@
 Comma list: 540/539, 1375/1372, 218750/216513
-Mapping: {{mapping| 1 -3 -4 -5 -1 | 0 37 51 63 36 }}
+{{Mapping|legend=0| 1 -3 -4 -5 -1 | 0 37 51 63 36 }}
 Optimal tunings:
@@ Line 623: / Line 546: @@
 Comma list: 325/324, 364/363, 540/539, 2200/2197
-Mapping: {{mapping| 1 -3 -4 -5 -1 -2 | 0 37 51 63 36 46 }}
+{{Mapping|legend=0| 1 -3 -4 -5 -1 -2 | 0 37 51 63 36 46 }}
 Optimal tunings:
@@ Line 638: / Line 561: @@
 Comma list: 325/324, 364/363, 540/539, 595/594, 2000/1989
-Mapping: {{mapping| 1 -3 -4 -5 -1 -2 0 | 0 37 51 63 36 46 33 }}
+{{Mapping|legend=0| 1 -3 -4 -5 -1 -2 0 | 0 37 51 63 36 46 33 }}
 Optimal tunings:
@@ Line 653: / Line 576: @@
 Comma list: 325/324, 364/363, 400/399, 540/539, 595/594, 665/663
-Mapping: {{mapping| 1 -3 -4 -5 -1 -2 0 4 | 0 37 51 63 36 46 33 2 }}
+{{Mapping|legend=0| 1 -3 -4 -5 -1 -2 0 4 | 0 37 51 63 36 46 33 2 }}
 Optimal tunings:
@@ Line 663: / Line 586: @@
 Badness (Sintel): 1.37
+[[Category:Canopic clan| ]] <!-- main article -->
+[[Category:Canopic| ]] <!-- key article -->
 [[Category:Temperament clans]]
-[[Category:Mirkwai clan| ]] <!-- main article -->
+[[Category:Catalogs of rank-2 temperaments]]
-[[Category:Rank 2]]

Canopic clan: Difference between revisions

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