Consistency: Difference between revisions

Inthar (talk | contribs)
m Consistency to distance d: var changed to d
Tags: Mobile edit Mobile web edit
Inthar (talk | contribs)
mNo edit summary
Tags: Mobile edit Mobile web edit
Line 39: Line 39:
# every instance of an interval in C is mapped to the same size in C', and
# every instance of an interval in C is mapped to the same size in C', and
# no interval within ''C' '' has [[relative error]] 1/(2(''d''+1)) or more.  
# no interval within ''C' '' has [[relative error]] 1/(2(''d''+1)) or more.  
(The 1/(2(''d''+1)) threshold is meant to allow stacking ''d'' dyads that occur in the chord without having the sum of the dyads have over 50% relative error.)
(The 1/(2(''d''+1)) threshold is meant to allow stacking ''d+1'' chords, including the original chord, that occur in the chord without having the sum of the dyads have over 50% relative error. That is, you can make a copy of a chord up to distance d away from the original chord without inconsistency.)


Since a consistent approximation must be unique, it suffices to find the consistent approximation and check the relative error of that one chord to check distance-''d'' consistency.
Since a consistent approximation must be unique, it suffices to find the consistent approximation and check the relative error of that one chord to check distance-''d'' consistency.