Jubilismic clan: Difference between revisions

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[[Comma list]]: 50/49

: mapping generators: ~7/5, ~5

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Lemba finds the perfect fifth three steps away by tempering out [[1029/1024]]. Astrology, five steps away by tempering out [[3125/3072]]. Decimal, two steps away by tempering out [[25/24]] and [[49/48]]. Walid merges ~5/4 and ~4/3 by tempering out [[16/15]].

Diminished adds 36/35 and splits the ~7/5 period in a further two. Pajara adds 64/63 and slices the ~7/4 in two, with antikythera being every other step thereof. Dubbla adds 78125/73728 and slices the ~5/4 in two. Injera adds 81/80 and slices the ~5/1 in four. Octokaidecal adds 28/27. Bipelog adds 135/128. Those splits the generator into three in various ways. Hexe adds 128/125 and slices the period in three. Hedgehog adds 250/243. Elvis adds 8505/8192. Those slice the generator in five. Comic adds 2240/2187. Crepuscular adds 4375/4374. Those slice the generator in seven. Byhearted adds 19683/19208. Bipyth adds 20480/19683. Those slice the generator in nine.

Diminished adds 36/35 and splits the ~7/5 period in a further two. Pajara adds 64/63 and slices the ~7/4 in two, with antikythera being every other step thereof. Dubbla adds 78125/73728 and slices the ~5/4 in two. Injera adds 81/80 and slices the ~5/1 in four. Octokaidecal adds 28/27. Bipelog adds 135/128. Vishy adds 110592/109375. Those splits the generator into three in various ways. Hexe adds 128/125 and slices the period in three. Hedgehog adds 250/243. Elvis adds 8505/8192. Those slice the generator in five. Comic adds 2240/2187. Crepuscular adds 4375/4374. Those slice the generator in seven. Byhearted adds 19683/19208. Bipyth adds 20480/19683. Those slice the generator in nine.

Temperaments discussed elsewhere are:

* ''[[Antitonic]]'' (+9/8) → [[Very low accuracy temperaments #Antitonic|Very low accuracy temperaments]]

* ''[[Charon]]'' (+10/9) → [[Very low accuracy temperaments #Charon|Very low accuracy temperaments]]

* ''[[Codex (temperament)|Codex]]'' (+27/25) → [[Very low accuracy temperaments #Codex|Very low accuracy temperaments]]

* [[Decimal]] (+25/24) → [[Dicot family #Decimal|Dicot family]]

* [[Diminished (temperament)|Diminished]] (+36/35) → [[Diminished family #Septimal diminished|Diminished family]]

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

* ''[[Bipelog]]'' (+135/128) → [[Mavila #Bipelog|Mavila family]]

* ''[[Vishy]]'' (+110592/109375) → [[Vishnu family #Vishy|Vishnu family]]

* ''[[Hexe]]'' (+128/125) → [[Augmented family #Hexe|Augmented family]]

* ''[[Hedgehog]]'' (+~~250~~/243) → [[~~Porcupine family~~ #Hedgehog|~~Porcupine family~~]]

* ''[[Hedgehog]]'' (+245/243) → [[Stearnsmic clan #Hedgehog|Stearnsmic clan]]

* ''[[Crepuscular]]'' (+4375/4374) → [[Fifive family #Crepuscular|Fifive family]]

* ''[[Weasel]]'' (+19683/19208) → [[Tetracot family #Byhearted|Tetracot family]]

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Comma list: 45/44, 50/49, 385/384

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

Optimal tunings:

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Comma list: 45/44, 50/49, 65/64, 78/77

~~Mapping:~~ {{~~mapping~~| 2 2 5 6 5 7 | 0 3 -1 -1 5 1 }}

Optimal tunings:

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== Astrology ==

[[:de:Magische_Temperaturen#Astrology|Deutsch]]

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Comma list: 50/49, 121/120, 176/175

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

Optimal tunings:

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Comma list: 50/49, 65/64, 78/77, 121/120

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

Optimal tunings:

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Comma list: 50/49, 66/65, 105/104, 121/120

~~Mapping:~~ {{~~mapping~~| 2 0 4 5 5 3 | 0 5 1 1 3 7 }}

Optimal tunings:

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Comma list: 16/15, 22/21, 50/49

~~Mapping:~~ {{~~mapping~~| 2 0 8 9 7 | 0 1 -1 -1 0 }}

Optimal tunings:

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== Doublewide ==

: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Doublewide ~~(5-limit)~~]].''

: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Doublewide]].''

Doublewide is generated by a sharply tuned ~6/5 minor third, four of which and a semi-octave period give the 3rd harmonic~~. It may be described as the {{nowrap| 22 & 26 }} temperament;~~ its ploidacot is diploid alpha-tetracot. An 11-limit extension is immediately available by identifying two generator steps as ~16/11. [[48edo]] makes for an excellent tuning.

Doublewide tempers out not only the keema, [[875/864]], but the orwellisma, [[1728/1715]], and may be described as the {{nowrap| 22 & 26 }} temperament. It is the unique temperament that equates the classical chroma ([[25/24]]), the large septimal diesis ([[49/48]]), and the interval between the classical and septimal thirds ([[36/35]]). It is generated by a sharply tuned [[~]][[6/5]] minor third, four of which and a [[semi-octave]] period give the [[3/1|3rd]] [[harmonic]], so its [[ploidacot]] is diploid alpha-tetracot. An [[11-limit]] extension is immediately available by identifying two generator steps as ~[[16/11]]. [[48edo]] makes for an excellent tuning.

[[Subgroup]]: 2.3.5.7

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Comma list: 50/49, 99/98, 385/384

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

Optimal tunings:

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Comma list: 50/49, 55/54, 176/175

~~Mapping:~~ {{~~mapping~~| 2 1 3 4 2 | 0 4 3 3 9 }}

Optimal tunings:

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Comma list: 50/49, 55/54, 65/63, 176/175

~~Mapping:~~ {{~~mapping~~| 2 1 3 4 2 3 | 0 4 3 3 9 8 }}

Optimal tunings:

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Comma list: 45/44, 50/49, 875/864

~~Mapping:~~ {{~~mapping~~| 2 1 3 4 1 | 0 4 3 3 11 }}

Optimal tunings:

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Comma list: 45/44, 50/49, 78/77, 325/324

~~Mapping:~~ {{~~mapping~~| 2 1 3 4 1 2 | 0 4 3 3 11 10 }}

Optimal tunings:

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Comma list: 45/44, 50/49, 1344/1331

~~Mapping:~~ {{~~mapping~~| 2 1 10 11 8 | 0 2 -5 -5 -1 }}

Optimal tunings:

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Comma list: 45/44, 50/49, 78/77, 1053/1024

~~Mapping:~~ {{~~mapping~~| 2 1 10 11 8 16 | 0 2 -5 -5 -1 -8 }}

Optimal tunings:

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Comma list: 50/49, 99/98, 2662/2625

~~Mapping:~~ {{~~mapping~~| 2 1 -3 -2 -4 | 0 2 7 7 10 }}

Optimal tunings:

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Comma list: 50/49, 65/63, 99/98, 968/945

~~Mapping:~~ {{~~mapping~~| 2 1 -3 -2 -4 3 | 0 2 7 7 10 4 }}

Optimal tunings:

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Comma list: 50/49, 121/120, 896/891

~~Mapping:~~ {{~~mapping~~| 2 0 -24 -23 -9 | 0 1 9 9 5 }}

Optimal tunings:

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Comma list: 50/49, 385/384, 1331/1323

~~Mapping:~~ {{~~mapping~~| 16 0 37 45 30 | 0 1 0 0 1 }}

Optimal tunings:

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== Subgroup extensions ==

=== Antikythera (2.9.5.7) ===

~~Named~~ by [[~~Gene Ward Smith~~]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101481.html Yahoo! Tuning Group | ''Antikythera'']</ref>~~, antikythera is every other step of [[pajara]]~~.

Antikythera is every other step of [[pajara]]. It was allegedly named by [[Keenan Pepper]] in 2011 after the {{w|Antikythera mechanism}} for its association with [[astrology]] and [[machine]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101481.html Yahoo! Tuning Group | ''Antikythera'']</ref>.

[[Subgroup]]: 2.9.5.7

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[[Comma list]]: 50/49, 64/63

: mapping generators: ~7/5, ~9

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== References ==

[[Category:Jubilismic clan| ]]

[[Category:Temperament clans]]

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

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

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

@@ Line 9: / Line 9: @@
 [[Comma list]]: 50/49
-{{Mapping|legend=2| 2 0 1 | 0 1 1 }}
+{{Mapping|legend=3| 2 0 1 | 0 1 1 }}
-{{Mapping|legend=3| 2 0 0 1 | 0 0 1 1 }}
+{{Mapping|legend=5| 2 0 0 1 | 0 0 1 1 }}
 : mapping generators: ~7/5, ~5
@@ Line 28: / Line 28: @@
 Lemba finds the perfect fifth three steps away by tempering out [[1029/1024]]. Astrology, five steps away by tempering out [[3125/3072]]. Decimal, two steps away by tempering out [[25/24]] and [[49/48]]. Walid merges ~5/4 and ~4/3 by tempering out [[16/15]].
-Diminished adds 36/35 and splits the ~7/5 period in a further two. Pajara adds 64/63 and slices the ~7/4 in two, with antikythera being every other step thereof. Dubbla adds 78125/73728 and slices the ~5/4 in two. Injera adds 81/80 and slices the ~5/1 in four. Octokaidecal adds 28/27. Bipelog adds 135/128. Those splits the generator into three in various ways. Hexe adds 128/125 and slices the period in three. Hedgehog adds 250/243. Elvis adds 8505/8192. Those slice the generator in five. Comic adds 2240/2187. Crepuscular adds 4375/4374. Those slice the generator in seven. Byhearted adds 19683/19208. Bipyth adds 20480/19683. Those slice the generator in nine.
+Diminished adds 36/35 and splits the ~7/5 period in a further two. Pajara adds 64/63 and slices the ~7/4 in two, with antikythera being every other step thereof. Dubbla adds 78125/73728 and slices the ~5/4 in two. Injera adds 81/80 and slices the ~5/1 in four. Octokaidecal adds 28/27. Bipelog adds 135/128. Vishy adds 110592/109375. Those splits the generator into three in various ways. Hexe adds 128/125 and slices the period in three. Hedgehog adds 250/243. Elvis adds 8505/8192. Those slice the generator in five. Comic adds 2240/2187. Crepuscular adds 4375/4374. Those slice the generator in seven. Byhearted adds 19683/19208. Bipyth adds 20480/19683. Those slice the generator in nine.
 Temperaments discussed elsewhere are:
+* ''[[Antitonic]]'' (+9/8) → [[Very low accuracy temperaments #Antitonic|Very low accuracy temperaments]]
+* ''[[Charon]]'' (+10/9) → [[Very low accuracy temperaments #Charon|Very low accuracy temperaments]]
+* ''[[Codex (temperament)|Codex]]'' (+27/25) → [[Very low accuracy temperaments #Codex|Very low accuracy temperaments]]
 * [[Decimal]] (+25/24) → [[Dicot family #Decimal|Dicot family]]
 * [[Diminished (temperament)|Diminished]] (+36/35) → [[Diminished family #Septimal diminished|Diminished family]]
@@ Line 38: / Line 41: @@
 * ''[[Octokaidecal]]'' (+28/27) → [[Trienstonic clan #Octokaidecal|Trienstonic clan]]
 * ''[[Bipelog]]'' (+135/128) → [[Mavila #Bipelog|Mavila family]]
+* ''[[Vishy]]'' (+110592/109375) → [[Vishnu family #Vishy|Vishnu family]]
 * ''[[Hexe]]'' (+128/125) → [[Augmented family #Hexe|Augmented family]]
-* ''[[Hedgehog]]'' (+250/243) → [[Porcupine family #Hedgehog|Porcupine family]]
+* ''[[Hedgehog]]'' (+245/243) → [[Stearnsmic clan #Hedgehog|Stearnsmic clan]]
 * ''[[Crepuscular]]'' (+4375/4374) → [[Fifive family #Crepuscular|Fifive family]]
 * ''[[Weasel]]'' (+19683/19208) → [[Tetracot family #Byhearted|Tetracot family]]
@@ Line 74: / Line 78: @@
 Comma list: 45/44, 50/49, 385/384
-Mapping: {{mapping| 2 2 5 6 5 | 0 3 -1 -1 5 }}
+{{Mapping|legend=0| 2 2 5 6 5 | 0 3 -1 -1 5 }}
 Optimal tunings:
@@ Line 89: / Line 93: @@
 Comma list: 45/44, 50/49, 65/64, 78/77
-Mapping: {{mapping| 2 2 5 6 5 7 | 0 3 -1 -1 5 1 }}
+{{Mapping|legend=0| 2 2 5 6 5 7 | 0 3 -1 -1 5 1 }}
 Optimal tunings:
@@ Line 100: / Line 104: @@
 == Astrology ==
+[[:de:Magische_Temperaturen#Astrology|Deutsch]]
 {{see also| Magic family }}
@@ Line 127: / Line 133: @@
 Comma list: 50/49, 121/120, 176/175
-Mapping: {{mapping| 2 0 4 5 5 | 0 5 1 1 3 }}
+{{Mapping|legend=0| 2 0 4 5 5 | 0 5 1 1 3 }}
 Optimal tunings:
@@ Line 142: / Line 148: @@
 Comma list: 50/49, 65/64, 78/77, 121/120
-Mapping: {{mapping| 2 0 4 5 5 8 | 0 5 1 1 3 -1 }}
+{{Mapping|legend=0| 2 0 4 5 5 8 | 0 5 1 1 3 -1 }}
 Optimal tunings:
@@ Line 160: / Line 166: @@
 Comma list: 50/49, 66/65, 105/104, 121/120
-Mapping: {{mapping| 2 0 4 5 5 3 | 0 5 1 1 3 7 }}
+{{Mapping|legend=0| 2 0 4 5 5 3 | 0 5 1 1 3 7 }}
 Optimal tunings:
@@ Line 196: / Line 202: @@
 Comma list: 16/15, 22/21, 50/49
-Mapping: {{mapping| 2 0 8 9 7 | 0 1 -1 -1 0 }}
+{{Mapping|legend=0| 2 0 8 9 7 | 0 1 -1 -1 0 }}
 Optimal tunings:
@@ Line 207: / Line 213: @@
 == Doublewide ==
-: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Doublewide (5-limit)]].''
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Doublewide]].''
-Doublewide is generated by a sharply tuned ~6/5 minor third, four of which and a semi-octave period give the 3rd harmonic. It may be described as the {{nowrap| 22 & 26 }} temperament; its ploidacot is diploid alpha-tetracot. An 11-limit extension is immediately available by identifying two generator steps as ~16/11. [[48edo]] makes for an excellent tuning.
+Doublewide tempers out not only the keema, [[875/864]], but the orwellisma, [[1728/1715]], and may be described as the {{nowrap| 22 & 26 }} temperament. It is the unique temperament that equates the classical chroma ([[25/24]]), the large septimal diesis ([[49/48]]), and the interval between the classical and septimal thirds ([[36/35]]). It is generated by a sharply tuned [[~]][[6/5]] minor third, four of which and a [[semi-octave]] period give the [[3/1|3rd]] [[harmonic]], so its [[ploidacot]] is diploid alpha-tetracot. An [[11-limit]] extension is immediately available by identifying two generator steps as ~[[16/11]]. [[48edo]] makes for an excellent tuning.
 [[Subgroup]]: 2.3.5.7
@@ Line 234: / Line 240: @@
 Comma list: 50/49, 99/98, 385/384
-Mapping: {{mapping| 2 1 3 4 8 | 0 4 3 3 -2 }}
+{{Mapping|legend=0| 2 1 3 4 8 | 0 4 3 3 -2 }}
 Optimal tunings:
@@ Line 249: / Line 255: @@
 Comma list: 50/49, 55/54, 176/175
-Mapping: {{mapping| 2 1 3 4 2 | 0 4 3 3 9 }}
+{{Mapping|legend=0| 2 1 3 4 2 | 0 4 3 3 9 }}
 Optimal tunings:
@@ Line 264: / Line 270: @@
 Comma list: 50/49, 55/54, 65/63, 176/175
-Mapping: {{mapping| 2 1 3 4 2 3 | 0 4 3 3 9 8 }}
+{{Mapping|legend=0| 2 1 3 4 2 3 | 0 4 3 3 9 8 }}
 Optimal tunings:
@@ Line 279: / Line 285: @@
 Comma list: 45/44, 50/49, 875/864
-Mapping: {{mapping| 2 1 3 4 1 | 0 4 3 3 11 }}
+{{Mapping|legend=0| 2 1 3 4 1 | 0 4 3 3 11 }}
 Optimal tunings:
@@ Line 294: / Line 300: @@
 Comma list: 45/44, 50/49, 78/77, 325/324
-Mapping: {{mapping| 2 1 3 4 1 2 | 0 4 3 3 11 10 }}
+{{Mapping|legend=0| 2 1 3 4 1 2 | 0 4 3 3 11 10 }}
 Optimal tunings:
@@ Line 332: / Line 338: @@
 Comma list: 45/44, 50/49, 1344/1331
-Mapping: {{mapping| 2 1 10 11 8 | 0 2 -5 -5 -1 }}
+{{Mapping|legend=0| 2 1 10 11 8 | 0 2 -5 -5 -1 }}
 Optimal tunings:
@@ Line 347: / Line 353: @@
 Comma list: 45/44, 50/49, 78/77, 1053/1024
-Mapping: {{mapping| 2 1 10 11 8 16 | 0 2 -5 -5 -1 -8 }}
+{{Mapping|legend=0| 2 1 10 11 8 16 | 0 2 -5 -5 -1 -8 }}
 Optimal tunings:
@@ Line 385: / Line 391: @@
 Comma list: 50/49, 99/98, 2662/2625
-Mapping: {{mapping| 2 1 -3 -2 -4 | 0 2 7 7 10 }}
+{{Mapping|legend=0| 2 1 -3 -2 -4 | 0 2 7 7 10 }}
 Optimal tunings:
@@ Line 400: / Line 406: @@
 Comma list: 50/49, 65/63, 99/98, 968/945
-Mapping: {{mapping| 2 1 -3 -2 -4 3 | 0 2 7 7 10 4 }}
+{{Mapping|legend=0| 2 1 -3 -2 -4 3 | 0 2 7 7 10 4 }}
 Optimal tunings:
@@ Line 436: / Line 442: @@
 Comma list: 50/49, 121/120, 896/891
-Mapping: {{mapping| 2 0 -24 -23 -9 | 0 1 9 9 5 }}
+{{Mapping|legend=0| 2 0 -24 -23 -9 | 0 1 9 9 5 }}
 Optimal tunings:
@@ Line 470: / Line 476: @@
 Comma list: 50/49, 385/384, 1331/1323
-Mapping: {{mapping| 16 0 37 45 30 | 0 1 0 0 1 }}
+{{Mapping|legend=0| 16 0 37 45 30 | 0 1 0 0 1 }}
 Optimal tunings:
@@ Line 482: / Line 488: @@
 == Subgroup extensions ==
 === Antikythera (2.9.5.7) ===
-Named by [[Gene Ward Smith]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101481.html Yahoo! Tuning Group | ''Antikythera'']</ref>, antikythera is every other step of [[pajara]].
+Antikythera is every other step of [[pajara]]. It was allegedly named by [[Keenan Pepper]] in 2011 after the {{w|Antikythera mechanism}} for its association with [[astrology]] and [[machine]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101481.html Yahoo! Tuning Group | ''Antikythera'']</ref>.
 [[Subgroup]]: 2.9.5.7
@@ Line 488: / Line 494: @@
 [[Comma list]]: 50/49, 64/63
-{{Mapping|legend=2| 2 0 11 12 | 0 1 -1 -1 }}
+{{Mapping|legend=3| 2 0 11 12 | 0 1 -1 -1 }}
-{{Mapping|legend=3| 2 0 11 12 | 0 1/2 -1 -1 }}
+{{Mapping|legend=5| 2 0 11 12 | 0 1/2 -1 -1 }}
 : mapping generators: ~7/5, ~9
@@ Line 506: / Line 512: @@
 == References ==
+[[Category:Jubilismic clan| ]] <!-- main article -->
 [[Category:Temperament clans]]
-[[Category:Jubilismic clan| ]] <!-- main article -->
+[[Category:Catalogs of rank-2 temperaments]]
-[[Category:Rank 2]]

Jubilismic clan: Difference between revisions

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