Consistency: Difference between revisions
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Non-technically, a chord ''C'' is '''consistent to distance''' ''m'' if a small piece of the JI lattice surrounding the chord (namely, all intervals up to distance ''m'' from notes that occur in the chord) is mapped consistently. So an approximation consistent to distance ''m'' would play more nicely in a regular temperament-style [[subgroup]] context. | Non-technically, a chord ''C'' is '''consistent to distance''' ''m'' if a small piece of the JI lattice surrounding the chord (namely, all intervals up to distance ''m'' from notes that occur in the chord) is mapped consistently. So an approximation consistent to distance ''m'' would play more nicely in a regular temperament-style [[subgroup]] context. | ||
Formally, if ''m'' ≥ 0, 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/(2(''m''+1)) or more. | # no interval within ''C' '' has [[relative error]] 1/(2(''m''+1)) or more. | ||