Pepper ambiguity: Difference between revisions
added relative error as see also; within the text, the reference wasn't really precise (v is a measure - or equal to - abs(relative error)) |
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Given a finite set s of positive rational numbers, the maximum value of ambig(''N'', ''q'') for all ''q'' ∈ ''s'' is the '''Pepper ambiguity''' of ''N'' with respect to ''s''. If the set ''s'' is the ''L'' odd limit [[tonality diamond]], this is the ''L''-limit Pepper ambiguity of ''N''. Lists of ''N'' of decreasing Pepper ambiguity can be found on the [[On-Line Encyclopedia of Integer Sequences]]: | Given a finite set s of positive rational numbers, the maximum value of ambig(''N'', ''q'') for all ''q'' ∈ ''s'' is the '''Pepper ambiguity''' of ''N'' with respect to ''s''. If the set ''s'' is the ''L'' odd limit [[tonality diamond]], this is the ''L''-limit Pepper ambiguity of ''N''. Lists of ''N'' of decreasing Pepper ambiguity can be found on the [[On-Line Encyclopedia of Integer Sequences]]: | ||
* [[OEIS: A117554]] | * [[OEIS: A117554]] — 5-odd-limit | ||
* [[OEIS: A117555]] | * [[OEIS: A117555]] — 7-odd-limit | ||
* [[OEIS: A117556]] | * [[OEIS: A117556]] — 9-odd-limit | ||
* [[OEIS: A117557]] | * [[OEIS: A117557]] — 11-odd-limit | ||
* [[OEIS: A117558]] | * [[OEIS: A117558]] — 13-odd-limit | ||
* [[OEIS: A117559]] | * [[OEIS: A117559]] — 15-odd-limit | ||
We may also define the mean ambiguity for ''N'' with respect to ''s'' by taking the mean of ambig(''N'', ''q'') for all members ''q'' of ''s''. | We may also define the mean ambiguity for ''N'' with respect to ''s'' by taking the mean of ambig(''N'', ''q'') for all members ''q'' of ''s''. | ||