Consistency: Difference between revisions
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If ''m'' ≥ 1, a chord ''C'' is '''consistent to distance''' ''m'' in ''N''-edo if there exists an approximation ''C' '' of ''C'' in ''N''-edo such that: | If ''m'' ≥ 1, a chord ''C'' is '''consistent to distance''' ''m'' in ''N''-edo if there exists an approximation ''C' '' of ''C'' in ''N''-edo such that: | ||
# 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\ | # no interval within ''C' '' has [[relative error]] 1\2''m'' or more. | ||
(The 1\2m threshold is meant to allow stacking ''m'' dyads that occur in the chord without having the sum of the dyads have over 50% relative error. Since "consistent to distance m" conveys the idea that a small part of the JI lattice is mapped nicely, an approximation consistent to distance m would play more nicely in a regular temperament-style [[subgroup]] context.) | (The 1\2m threshold is meant to allow stacking ''m'' dyads that occur in the chord without having the sum of the dyads have over 50% relative error. Since "consistent to distance m" conveys the idea that a small part of the JI lattice is mapped nicely, an approximation consistent to distance m would play more nicely in a regular temperament-style [[subgroup]] context.) | ||