Jubilismic clan: Difference between revisions

The '''jubilismic clan''' tempers out the jubilisma, [[50/49]], which means [[7/5]] and [[10/7]] are both equated to the 600-cent tritone and the [[octave]] is divided in two.  

The head of this clan, jubilic, is generated by [[~]][[5/4]]. That and a semioctave give ~[[7/4]]. As such, a reasonable tuning would tune the 5/4 flat and 7/4 sharp.

[[Subgroup]]: 2.5.7

[[Comma list]]: 50/49

{{Mapping|legend=2| 2 0 1 | 0 1 1 }}

: sval mapping generators: ~7/5, ~5

{{Mapping|legend=3| 2 0 0 1 | 0 0 1 1 }}

[[Optimal tuning]]s:

: [[error map]]: {{val| -0.665 -7.016 +10.139 }}

* [[CWE]]: ~7/5 = 600.0000{{c}}, ~5/4 = 380.0086{{c}} (~8/7 = 219.9914{{c}})

: error map: {{val| 0.000 -6.305 +11.183 }}

{{Optimal ET sequence|legend=1| 2, 4, 6, 16, 22, 60d }}

[[Badness]] (Sintel): 0.140

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.  

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

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

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

Considered below are lemba, astrology, walid, antikythera, doublewide, elvis, comic, and bipyth.

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

Lemba tempers out 1029/1024, the gamelisma, and a stack of three ~8/7 generators gives an approximate perfect fifth. It may be described as the {{nowrap| 10 & 16 }} temperament; its [[ploidacot]] is diploid tricot.

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 50/49, 525/512

 

{{Mapping|legend=1| 2 2 5 6 | 0 3 -1 -1 }}

 

: mapping generators: ~7/5, ~8/7

 

[[Optimal tuning]]s:  

* [[WE]]: ~7/5 = 601.4623{{c}}, ~8/7 = 232.6544{{c}}

: [[error map]]: {{val| +2.925 -1.067 -11.656 +7.294 }}

* [[CWE]]: ~7/5 = 600.0000{{c}}, ~8/7 = 232.2655{{c}}

: error map: {{val| 0.000 -5.158 -18.579 -1.091 }}

 

{{Optimal ET sequence|legend=1| 10, 16, 26, 36c, 62c }}

 

 

 

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

 

 

* WE: ~7/5 = 601.1769{{c}}, ~8/7 = 231.4273{{c}}

* CWE: ~7/5 = 600.0000{{c}}, ~8/7 = 231.1781{{c}}

 

{{Optimal ET sequence|legend=0| 10, 16, 26 }}

 

Badness (Sintel): 1.37

 

Subgroup: 2.3.5.7.11.13

 

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

 

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

 

* WE: ~7/5 = 601.1939{{c}}, ~8/7 = 231.4261{{c}}

* CWE: ~7/5 = 600.0000{{c}}, ~8/7 = 231.1617{{c}}

 

{{Optimal ET sequence|legend=0| 10, 16, 26 }}

 

 

== Astrology ==

Astrology tempers out 3125/3072, the magic comma, and a stack of five ~5/4 generators gives an approximate harmonic 3. It may be described as the {{nowrap| 16 & 22 }} temperament; its ploidacot is diploid pentacot.

 

[[Subgroup]]: 2.3.5.7

 

 

{{Mapping|legend=1| 2 0 4 5 | 0 5 1 1 }}

 

: mapping geenerators: ~7/5, ~5/4

 

[[Optimal tuning]]s:  

* [[WE]]: ~7/5 = 599.6999{{c}}, ~5/4 = 380.3881{{c}} (~8/7 = 219.3119{{c}})

: [[error map]]: {{val| -0.600 -0.015 -7.126 +10.062 }}

* [[CWE]]: ~7/5 = 600.0000{{c}}, ~5/4 = 380.5123{{c}} (~8/7 = 219.4877{{c}})

: error map: {{val| 0.000 +0.606 -5.801 +11.686 }}

 

{{Optimal ET sequence|legend=1| 6, 16, 22, 60d }}

 

 

=== 11-limit ===

Subgroup: 2.3.5.7.11

 

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

 

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

 

Optimal tunings:  

* WE: ~7/5 = 600.0538{{c}}, ~5/4 = 380.5640{{c}} (~8/7 = 219.4897{{c}})

* CWE: ~7/5 = 600.0000{{c}}, ~5/4 = 380.5419{{c}} (~8/7 = 219.4581{{c}})

 

 

 

==== 13-limit ====

Subgroup: 2.3.5.7.11.13

 

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

 

 

* WE: ~7/5 = 600.7886{{c}}, ~5/4 = 380.2857{{c}} (~8/7 = 220.5028{{c}})

* CWE: ~7/5 = 600.0000{{c}}, ~5/4 = 379.9119{{c}} (~8/7 = 220.0881{{c}})

 

{{Optimal ET sequence|legend=0| 6, 16, 22, 38f }}

 

 

; Music

* [https://soundcloud.com/joelgranttaylor/astrology-percussion-quintet ''Astrology Percussion Quintet No 1'']{{dead link}} [http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/AstrologyPercQuintet1_c.mp3 play]{{dead link}} by [[Joel Taylor]]

 

Subgroup: 2.3.5.7.11.13

 

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

 

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

 

* WE: ~7/5 = 599.8927{{c}}, ~5/4 = 379.7688{{c}} (~8/7 = 220.1239{{c}})

* CWE: ~7/5 = 600.0000{{c}}, ~5/4 = 379.8117{{c}} (~8/7 = 220.1883{{c}})

 

{{Optimal ET sequence|legend=0| 6f, 16, 22f, 38 }}

 

Badness (Sintel): 1.46

 

This low-accuracy extension tempers out 16/15, so the perfect fifth stands in for ~8/5 as in [[father]]. Its ploidacot is diploid monocot.

 

[[Subgroup]]: 2.3.5.7

 

 

{{Mapping|legend=1| 2 0 8 9 | 0 1 -1 -1 }}

 

: mapping generators: ~7/5, ~3

 

* [[WE]]: ~7/5 = 589.0384{{c}}, ~3/2 = 735.7242{{c}} (~15/14 = 146.6857{{c}})

* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 750.4026{{c}} (~15/14 = 150.4026{{c}})

: error map: {{val| 0.000 +48.448 +63.284 +80.771 }}

 

{{Optimal ET sequence|legend=1| 2, 6, 8d }}

 

[[Badness]] (Sintel): 1.24

 

 

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

 

 

 

 

 

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]].