Xenharmonic Wiki

Septischismic family: Difference between revisions

← Older editNewer edit →
VisualWikitext
Tag: Manual revert
m Units & misc. cleanup
Line 10: Line 10:


{{Mapping|legend=1| 1 0 0 25 | 0 1 0 -14 | 0 0 1 0 }}
{{Mapping|legend=1| 1 0 0 25 | 0 1 0 -14 | 0 0 1 0 }}
: mapping generators: ~2, ~3, ~5
: mapping generators: ~2, ~3, ~5


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~3/2 = 702.2224, ~5/4 = 386.3137
* [[CTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.2224{{c}}, ~5/4 = 386.3137{{c}}
* [[CWE]]: ~2 = 1\1, ~3/2 = 702.2124, ~5/4 = 386.4496
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.2124{{c}}, ~5/4 = 386.4496{{c}}


{{Optimal ET sequence|legend=1| 12, 29, 41, 53, 94, 164, 176, 217, 229, 270, 593, 863, 1133, 1996d, 2037, 2307, 2900bd, 3170bd, 4303bcd }}
{{Optimal ET sequence|legend=1| 12, 29, 41, 53, 94, 164, 176, 217, 229, 270, 593, 863, 1133, 1996d, 2037, 2307, 2900bd, 3170bd, 4303bcd }}


[[Badness]]: 1.31 × 10<sup>-3</sup>
[[Badness]] (Smith): 1.31 × 10<sup>-3</sup>


== Cassaschismic ==
== Cassaschismic ==
Line 29: Line 28:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~3/2 = 702.2280, ~5/4 = 386.3137
* [[CTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.2280{{c}}, ~5/4 = 386.3137{{c}}
* [[CWE]]: ~2 = 1\1, ~3/2 = 702.2290, ~5/4 = 386.3819
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.2290{{c}}, ~5/4 = 386.3819{{c}}


{{Optimal ET sequence|legend=1| 41, 53, 94, 176, 217, 270, 581, 851, 1121 }}
{{Optimal ET sequence|legend=1| 41, 53, 94, 176, 217, 270, 581, 851, 1121 }}


[[Badness]]: 1.41 × 10<sup>-3</sup>
[[Badness]] (Smith): 1.41 × 10<sup>-3</sup>


=== 13-limit ===
=== 13-limit ===
Line 44: Line 43:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 702.2289, ~5/4 = 386.2869
* CTE: ~2 = 1200.0000{{c}}, ~3/2 = 702.2289{{c}}, ~5/4 = 386.2869{{c}}
* CWE: ~2 = 1\1, ~3/2 = 702.2303, ~5/4 = 386.3031
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.2303{{c}}, ~5/4 = 386.3031{{c}}


{{Optimal ET sequence|legend=1| 41, 53, 94, 176, 217, 270, 581, 851, 2283b }}
{{Optimal ET sequence|legend=0| 41, 53, 94, 176, 217, 270, 581, 851, 2283b }}


Badness: 0.872 × 10<sup>-3</sup>
Badness (Smith): 0.872 × 10<sup>-3</sup>


=== 2.3.5.7.11.13.19 subgroup ===
=== 2.3.5.7.11.13.19 subgroup ===
Line 56: Line 55:
Comma list: 1216/1215, 1540/1539, 1729/1728, 2080/2079
Comma list: 1216/1215, 1540/1539, 1729/1728, 2080/2079


Sval mapping: {{mapping| 1 0 0 25 -33 -13 -6 | 0 1 0 -14 23 12 5 | 0 0 1 0 0 -1 1 }}
Subgroup-val mapping: {{mapping| 1 0 0 25 -33 -13 -6 | 0 1 0 -14 23 12 5 | 0 0 1 0 0 -1 1 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.2293, ~5/4 = 386.3021
Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~3/2 = 702.2293{{c}}, ~5/4 = 386.3021{{c}}


{{Optimal ET sequence|legend=1| 41, 53, 94, 176, 217, 270, 581, 851 }}
{{Optimal ET sequence|legend=0| 41, 53, 94, 176, 217, 270, 581, 851 }}


Badness: 0.496 × 10<sup>-3</sup>
Badness (Smith): 0.496 × 10<sup>-3</sup>


== Androschismic ==
== Androschismic ==
[[Subgroup]]: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 151263/151250, [[Reef comma|200704/200475]]
[[Comma list]]: 151263/151250, 200704/200475


{{Mapping|legend=1| 1 0 0 25 62 | 0 1 0 -14 -34 | 0 0 1 0 -2 }}
{{Mapping|legend=1| 1 0 0 25 62 | 0 1 0 -14 -34 | 0 0 1 0 -2 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* CTE: ~2 = 1\1, ~3/2 = 702.2308, ~5/4 = 386.3806
* [[CTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.2308{{c}}, ~5/4 = 386.3806{{c}}
* CWE: ~2 = 1\1, ~3/2 = 702.2178, ~5/4 = 386.5048
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.2178{{c}}, ~5/4 = 386.5048{{c}}


{{Optimal ET sequence|legend=1| 12, 29, 41, …, 229, 270, 581, 822, 851, 863e, 1133, 1403, 3117bce, 3387bce, 4520bcdee, 4790bbcdee, 5923bbccddeee }}
{{Optimal ET sequence|legend=1| 12, 29, 41, …, 229, 270, 581, 822, 851, 863e, 1133, 1403, 3117bce, 3387bce, 4520bcdee, 4790bbcdee, 5923bbccddeee }}


[[Badness]]: 1.64 × 10<sup>-3</sup>
[[Badness]] (Smith): 1.64 × 10<sup>-3</sup>


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 2080/2079, [[Punctisma|43904/43875]], 154880/154791
Comma list: 2080/2079, 43904/43875, 154880/154791


Mapping: {{mapping| 1 0 0 25 62 82 | 0 1 0 -14 -34 -43 | 0 0 1 0 -2 -3 }}
Mapping: {{mapping| 1 0 0 25 62 82 | 0 1 0 -14 -34 -43 | 0 0 1 0 -2 -3 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 702.2305, ~5/4 = 386.3748
* CTE: ~2 = 1200.0000{{c}}, ~3/2 = 702.2305{{c}}, ~5/4 = 386.3748{{c}}
* CWE: ~2 = 1\1, ~3/2 = 702.2174, ~5/4 = 386.4968
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.2174{{c}}, ~5/4 = 386.4968{{c}}


Optimal ET sequence: {{Optimal ET sequence| 12f, 29, 41, …, 229, 241, 270, 552, 581, 822, 851, 863ef, 1133, 1403, 2536bcdef, 3117bcef, 4250bcdeeff, 4520bcdeeff, 5653bbccddeeeff }}
{{Optimal ET sequence|legend=0| 12f, 29, 41, …, 229, 241, 270, 552, 581, 822, 851, 863ef, 1133, 1403, 2536bcdef, 3117bcef, 4250bcdeeff, 4520bcdeeff, 5653bbccddeeeff }}


Badness: 1.01 × 10<sup>-3</sup>
Badness (Smith): 1.01 × 10<sup>-3</sup>


[[Category:Temperament families]]
[[Category:Temperament families]]
Retrieved from "https://en.xen.wiki/w/Septischismic_family"