User:BudjarnLambeth/12edo as a 2.3.5.17.19 tuning: Difference between revisions
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# If any primes 13, 17, 19 or 23 are approximated within 15 cents, include as many of those as there are basis element spots free (giving preference to harmonics with closer approximations first) | # If any primes 13, 17, 19 or 23 are approximated within 15 cents, include as many of those as there are basis element spots free (giving preference to harmonics with closer approximations first) | ||
# If there are aren't enough of those to fill all spots, fill the remaining spots with taxicab-2 intervals the edo approximates within 15 cents, giving preference to intervals with small primes | # If there are aren't enough of those to fill all spots, fill the remaining spots with taxicab-2 intervals the edo approximates within 15 cents, giving preference to intervals with small primes | ||
# Optionally, replace any one basis element with any composite harmonic 60 or smaller, that shares factors in common with at least 2 other basis elements, is approximated within 15 cents, and has not yet been added | # Optionally, replace any one basis element with any composite harmonic 60 or smaller, that shares factors in common with at least 2 other basis elements in the subgroup, is approximated within 15 cents, and has not yet been added | ||
=== EDOs with 13 to 27 tones/octave === | === EDOs with 13 to 27 tones/octave === | ||
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# If any primes 13, 17, 19 or 23 are approximated within 15 cents, include as many of those as there are basis element spots free (giving preference to harmonics with closer approximations first) | # If any primes 13, 17, 19 or 23 are approximated within 15 cents, include as many of those as there are basis element spots free (giving preference to harmonics with closer approximations first) | ||
# If there are aren't enough of those to fill all spots, fill the remaining spots with taxicab-2 intervals the edo approximates within 15 cents, giving preference to intervals with small primes | # If there are aren't enough of those to fill all spots, fill the remaining spots with taxicab-2 intervals the edo approximates within 15 cents, giving preference to intervals with small primes | ||
# Optionally, replace any one basis element with any composite harmonic 60 or smaller, that shares factors in common with at least 2 other basis elements, is approximated within 15 cents, and has not yet been added | # Optionally, replace any one basis element with any composite harmonic 60 or smaller, that shares factors in common with at least 2 other basis elements in the subgroup, is approximated within 15 cents, and has not yet been added | ||
=== EDOs with 28 to 52 tones/octave === | === EDOs with 28 to 52 tones/octave === | ||