Consistency limits of small EDOs: Difference between revisions

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An [[EDO]] N is [[consistent]] with respect to a set of rational numbers s if the [[direct approximation]] of every element of s is the closest N-EDO approximation. It is [[distinctly consistent]] if every element of s is mapped to a distinct value. If the set s is the q [[odd limit]], we say N is q-limit consistent and q-limit distinctly consistent, respectively. Below is a table of every EDO up to 99. "Consistent" gives its "consistency limit", i.e. the highest odd limit to which the EDO is consistent, and "Distinct" gives the "distinct consistency limit" i.e. the highest odd limit to which the EDO is distinctly consistent. The remaining columns give the [[Consistent#Consistency to distance ''d''|"Consistency distance"]] (also called "consistency level"<ref>This term was coined by [[Paul Hahn]] in 1996: https://yahootuninggroupsultimatebackup.github.io/mills-tuning-list/topicId_884.html</ref>) for every odd limit from 3 to 23.

An [[EDO]] N is [[consistent]] with respect to a set of rational numbers s if the [[direct approximation]] of every element of s is the closest N-EDO approximation. It is [[distinctly consistent]] if every element of s is mapped to a distinct value. If the set s is the q [[odd limit]], we say N is q-limit consistent and q-limit distinctly consistent, respectively. Below is a table of every EDO up to 99. "Consistent" gives its "consistency limit", i.e. the highest odd limit to which the EDO is consistent, and "Distinct" gives the "distinct consistency limit" i.e. the highest odd limit to which the EDO is distinctly consistent. The remaining columns give the [[Consistent#Consistency to distance d|"Consistency distance"]] (also called "consistency level"<ref>This term was coined by [[Paul Hahn]] in 1996: https://yahootuninggroupsultimatebackup.github.io/mills-tuning-list/topicId_884.html</ref>) for every odd limit from 3 to 23.

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Revision as of 16:14, 29 July 2022 view source Cmloegcmluin (talk \| contribs) autopatrolled, emailconfirmed 5,170 edits add historical information about "consistency level" terminology; add subtle highlighting to table to help illuminate relationship between limit and level ← Older edit		Revision as of 20:12, 29 July 2022 view source Cmloegcmluin (talk \| contribs) autopatrolled, emailconfirmed 5,170 edits fix link Newer edit →
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	An [[EDO]] N is [[consistent]] with respect to a set of rational numbers s if the [[direct approximation]] of every element of s is the closest N-EDO approximation. It is [[distinctly consistent]] if every element of s is mapped to a distinct value. If the set s is the q [[odd limit]], we say N is q-limit consistent and q-limit distinctly consistent, respectively. Below is a table of every EDO up to 99. "Consistent" gives its "consistency limit", i.e. the highest odd limit to which the EDO is consistent, and "Distinct" gives the "distinct consistency limit" i.e. the highest odd limit to which the EDO is distinctly consistent. The remaining columns give the [[Consistent#Consistency to distance ''d''\|"Consistency distance"]] (also called "consistency level"<ref>This term was coined by [[Paul Hahn]] in 1996: https://yahootuninggroupsultimatebackup.github.io/mills-tuning-list/topicId_884.html</ref>) for every odd limit from 3 to 23.		An [[EDO]] N is [[consistent]] with respect to a set of rational numbers s if the [[direct approximation]] of every element of s is the closest N-EDO approximation. It is [[distinctly consistent]] if every element of s is mapped to a distinct value. If the set s is the q [[odd limit]], we say N is q-limit consistent and q-limit distinctly consistent, respectively. Below is a table of every EDO up to 99. "Consistent" gives its "consistency limit", i.e. the highest odd limit to which the EDO is consistent, and "Distinct" gives the "distinct consistency limit" i.e. the highest odd limit to which the EDO is distinctly consistent. The remaining columns give the [[Consistent#Consistency to distance d\|"Consistency distance"]] (also called "consistency level"<ref>This term was coined by [[Paul Hahn]] in 1996: https://yahootuninggroupsultimatebackup.github.io/mills-tuning-list/topicId_884.html</ref>) for every odd limit from 3 to 23.

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