Father–3 equivalence continuum: Difference between revisions

Rework into a more typical definition of n. The old n is now k.
Review data
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== 3 & 33c ==
== 3 & 33c ==
This low-accuracy high-complexity temperament corresponds to ''n'' = 9/4 and ''m'' = 9/5.


Comma list: {{monzo| 16 3 -9 }}
[[Subgroup]]: 2.3.5


POTE generator: 34.0971 cents
[[Comma list]]: 1953125/1769472


Mapping: [{{val| 3 5 7 }}, {{val| 0 -3 -1 }}]
{{Mapping|legend=1| 3 2 6 | 0 3 1 }}


{{Optimal ET sequence|legend=1| 3, 6, 9b, 33c }}
: mapping generators: ~125/96, ~5/4


[http://x31eq.com/cgi-bin/rt.cgi?ets=3_33c&limit=5 The temperament finder - 5-limit 3 & 33c]
[[Optimal tuning]]s:  
* [[CTE]]: ~125/96 = 1\3, ~5/4 = 368.2534 (~25/24 = 31.7466)
* [[CWE]]: ~125/96 = 1\3, ~5/4 = 366.8103 (~25/24 = 33.1897)
 
{{Optimal ET sequence|legend=1| 3, …, 33c, 36c, 69cc }}
 
[[Badness]]: 0.682


== Isnes ==
== Isnes ==
Isnes is so called because the generator is half of a [[8/5]] minor sixth, in a similar way that [[sensi]] has a generator of half a [[5/3]]. This corresponds to ''n'' = 19/7 and ''m'' = 19/12.
[[Subgroup]]: 2.3.5


So called because the generator is half of a [[8/5]] minor sixth, in a similar way that [[sensi]] has a generator of half a [[5/3]].
[[Comma list]]: {{monzo| 41 2 -19 }}


Comma list: {{Monzo|41 2 -19}}
{{Mapping|legend=1| 1 8 3 | 0 -19 -2 }}


POTE generator: 12582912/9765625 ~ 1953125/1572864 = 405.1047 cents
: mapping generators: ~2, ~1953125/1572864


Mapping: [{{val| 1 8 3 }}, {{val| 0 -19 -2 }}]
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~1953125/1572864 = 405.1689
* [[CWE]]: ~2 = 1\1, ~1953125/1572864 = 405.1272


{{Optimal ET sequence|legend=1| 3, 74, 77, 80, 83, 154, 157, 160 }}
{{Optimal ET sequence|legend=1| 3, 71b, 74, 77, 157, 548ccc }}


[http://x31eq.com/cgi-bin/rt.cgi?ets=3_77&limit=5 The temperament finder - 5-limit 3 & 77]
[[Badness]]: 1.30


[[Category:3edo]]
[[Category:3edo]]
[[Category:Equivalence continua]]
[[Category:Equivalence continua]]