16808edo: Difference between revisions

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== Theory ==

16808edo is distinctly [[consistent]] and highly accurate through the [[35-odd-limit]], being [[consistency #Generalization|consistent to distance 2]]~~. Its step size can be used as an [[interval size unit]] (the jinn) for most intervals which occur in practice~~. It is a very, very strong [[31-limit]] ~~division~~, and a [[zeta peak edo|zeta peak]], [[zeta peak integer edo|zeta peak integer]] and [[zeta integral edo]]. In the [[23-limit|23-]], [[29-limit|29-]] and 31-limit it has the lowest [[Tenney–Euclidean temperament measures #TE simple badness|relative error]] up until [[148418edo|148418]]; in the 17- and 19-limit up until [[20203edo|20203]]; though in the 13-limit it is beaten out by smaller edos {{EDOs| 5585, 6079, 8269, 8539, 13112 and 14618 }}.

16808edo is distinctly [[consistent]] and highly accurate through the [[35-odd-limit]], being [[consistency #Generalization|consistent to distance 2]]. It is a very, very strong [[31-limit]] system, and a [[zeta peak edo|zeta peak]], [[zeta peak integer edo|zeta peak integer]] and [[zeta integral edo]]. In the [[23-limit|23-]], [[29-limit|29-]] and 31-limit it has the lowest [[Tenney–Euclidean temperament measures #TE simple badness|relative error]] up until [[148418edo|148418]]; in the 17- and 19-limit up until [[20203edo|20203]]; though in the 13-limit it is beaten out by smaller edos {{EDOs| 5585, 6079, 8269, 8539, 13112 and 14618 }}. As such, its step size can be used as an [[interval size unit]] (the jinn) for most intervals which occur in practice.

Its [[3/2|perfect fifth]] ultimately comes from [[2101edo]].

Among the enormous list of 31-limit commas it tempers out, the simplest are 43681/43680, 49011/49010, 52326/52325 and 53361/53360. In the 13-limit it tempers out [[123201/123200]] and 1990656/1990625; in the 17-limit [[194481/194480]] and [[336141/336140]]; in the 19-limit 43681/43680, 89376/89375 and 104976/104975. Since 43681/43680 is both the simplest comma it tempers out and the limit is as low (in this context) as 19, it may be regarded as rather characteristic of 16808.

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 == Theory ==
-edo is distinctly [[consistent]] and highly accurate through the [[35-odd-limit]], being [[consistency #Generalization|consistent to distance 2]]. Its step size can be used as an [[interval size unit]] (the jinn) for most intervals which occur in practice. It is a very, very strong [[31-limit]] division, and a [[zeta peak edo|zeta peak]], [[zeta peak integer edo|zeta peak integer]] and [[zeta integral edo]]. In the [[23-limit|23-]], [[29-limit|29-]] and 31-limit it has the lowest [[Tenney–Euclidean temperament measures #TE simple badness|relative error]] up until [[148418edo|148418]]; in the 17- and 19-limit up until [[20203edo|20203]]; though in the 13-limit it is beaten out by smaller edos {{EDOs| 5585, 6079, 8269, 8539, 13112 and 14618 }}.
+edo is distinctly [[consistent]] and highly accurate through the [[35-odd-limit]], being [[consistency #Generalization|consistent to distance 2]]. It is a very, very strong [[31-limit]] system, and a [[zeta peak edo|zeta peak]], [[zeta peak integer edo|zeta peak integer]] and [[zeta integral edo]]. In the [[23-limit|23-]], [[29-limit|29-]] and 31-limit it has the lowest [[Tenney–Euclidean temperament measures #TE simple badness|relative error]] up until [[148418edo|148418]]; in the 17- and 19-limit up until [[20203edo|20203]]; though in the 13-limit it is beaten out by smaller edos {{EDOs| 5585, 6079, 8269, 8539, 13112 and 14618 }}. As such, its step size can be used as an [[interval size unit]] (the jinn) for most intervals which occur in practice.
+Its [[3/2|perfect fifth]] ultimately comes from [[2101edo]].
 Among the enormous list of 31-limit commas it tempers out, the simplest are 43681/43680, 49011/49010, 52326/52325 and 53361/53360. In the 13-limit it tempers out [[123201/123200]] and 1990656/1990625; in the 17-limit [[194481/194480]] and [[336141/336140]]; in the 19-limit 43681/43680, 89376/89375 and 104976/104975. Since 43681/43680 is both the simplest comma it tempers out and the limit is as low (in this context) as 19, it may be regarded as rather characteristic of 16808.