User:BudjarnLambeth/12edo as a 2.3.5.17.19 tuning: Difference between revisions
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=== EDOs with 28 to 52 tones/octave === | === EDOs with 28 to 52 tones/octave === | ||
# The subgroup should have 7 basis elements | # The subgroup should have 7 basis elements | ||
# Primes 3, 5, 7 and 11 must be added to the subgroup | # Primes 2, 3, 5, 7 and 11 must be added to the subgroup | ||
# If any primes 3, 5, 7 or 11 have more than 40% relative error, then they should be made a dual prime | # If any primes 3, 5, 7 or 11 have more than 40% relative error, then they should be made a dual prime | ||
# If there are more than 2 dual-primes, then only the two lowest dual-primes should be kept dual, and the rest made single again | # If there are more than 2 dual-primes, then only the two lowest dual-primes should be kept dual, and the rest made single again | ||
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=== EDOs with 53 to 71 tones/octave === | === EDOs with 53 to 71 tones/octave === | ||
# The subgroup should have 8 basis elements | # The subgroup should have 8 basis elements | ||
# Primes 3, 5, 7 and 11 must be added to the subgroup | # Primes 2, 3, 5, 7 and 11 must be added to the subgroup | ||
# If any primes 3, 5, 7 or 11 have more than 40% relative error, then they should be made a dual prime | # If any primes 3, 5, 7 or 11 have more than 40% relative error, then they should be made a dual prime | ||
# If there are more than 3 dual-primes, then only the three lowest dual-primes should be kept dual, and the rest made single again | # If there are more than 3 dual-primes, then only the three lowest dual-primes should be kept dual, and the rest made single again | ||
# If there are still spots left open, then they should be filled by every prime 13 and up which the EDO approximates with less than 35% relative error, preferencing the lowest primes first, until all spots are filled | # If there are still spots left open, then they should be filled by every prime 13 and up which the EDO approximates with less than 35% relative error, preferencing the lowest primes first, until all spots are filled | ||
=== EDOs with 72 | === EDOs with 72 to 117 tones/octave === | ||
# The subgroup should have 9 basis elements | # The subgroup should have 9 basis elements | ||
# Primes 3, 5, 7, 11 and 13 must be added to the subgroup | # Primes 2, 3, 5, 7, 11 and 13 must be added to the subgroup | ||
# If any primes 3, 5, 7, | # If any primes 3, 5, 7, 11 or 13 have more than 40% relative error, then they should be made a dual prime | ||
# If there are more than 4 dual-primes, then only the four lowest dual-primes should be kept dual, and the rest made single again | # If there are more than 4 dual-primes, then only the four lowest dual-primes should be kept dual, and the rest made single again | ||
# If there are still spots left open, then they should be filled by every prime 17 and up which the EDO approximates with less than 35% relative error, preferencing the lowest primes first, until all spots are filled | # If there are still spots left open, then they should be filled by every prime 17 and up which the EDO approximates with less than 35% relative error, preferencing the lowest primes first, until all spots are filled | ||
=== EDOs with 118 or more tones/octave === | |||
# The subgroup should have 11 basis elements | |||
# Primes 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 and 31 are initially added to the subgroup | |||
# If any primes 31 or lower have more than 40% relative error, then they should be made a dual prime | |||
# If there are now more than 11 basis elements, then the highest primes should be removed one by one until there are 11 basis elements left (31 removed first, then 29, so on) | |||
# If a dual-prime is the last one to be removed, and this causes there to be only 10 basis elements left, then add back the smallest non-dual prime that was removed | |||
== List of subgroups by EDO == | == List of subgroups by EDO == | ||