Elf: Difference between revisions
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# For each interval of the temperament, keep only the least complex (in terms of [[Benedetti height]]) JI interpretation of that interval. | # For each interval of the temperament, keep only the least complex (in terms of [[Benedetti height]]) JI interpretation of that interval. | ||
# Construct a detempering of ''n''-edo as follows: For each integer value {{nowrap|1 ≤ ''i'' ≤ ''n''}}, set the ''i''th degree of the scale to be (a) the least temperamentally-complex interval (with ties broken by Benedetti height) among the intervals that remain after step 2 (b) which is in the preimage of ''i''\''n'' under ''V''. | # Construct a detempering of ''n''-edo as follows: For each integer value {{nowrap|1 ≤ ''i'' ≤ ''n''}}, set the ''i''th degree of the scale to be (a) the least temperamentally-complex interval (with ties broken by Benedetti height) among the intervals that remain after step 2 (b) which is in the preimage of ''i''\''n'' under ''V''. | ||
# Temper this detempering of ''n''-edo using a [[tuning map]] for the temperament. The result is an elf. | # Temper this detempering of ''n''-edo using a [[tuning map]] for the temperament. This step is done so that it becomes a scale of the given temperament. The result is an elf. | ||
== Rank two examples == | == Rank two examples == | ||