User:BudjarnLambeth/12edo as a 2.3.5.17.19 tuning: Difference between revisions
| Line 46: | Line 46: | ||
# If 5 is approximated within 15 cents, add 5 to the subgroup | # If 5 is approximated within 15 cents, add 5 to the subgroup | ||
## If it is not, then add the smallest multiple of 5, 60 or lower, which it approximates within 15 cents (if any) | ## If it is not, then add the smallest multiple of 5, 60 or lower, which it approximates within 15 cents (if any) | ||
## | ## (''If this is the same as a number already added, just keep that one'') | ||
## If 5 and all its multiples up to 60 are not approximated, then add the smallest 13-limit taxicab-2 interval containing 5 (if any) | ## If 5 and all its multiples up to 60 are not approximated, then add the smallest 13-limit taxicab-2 interval containing 5 (if any) | ||
## | ## (''If this is the same as a fraction already added, just keep that one'') | ||
# If 7 is approximated within 15 cents, add 7 to the subgroup | # If 7 is approximated within 15 cents, add 7 to the subgroup | ||
## If it is not, then add the smallest multiple of 7, 56 or lower, which it approximates within 15 cents (if any) | ## If it is not, then add the smallest multiple of 7, 56 or lower, which it approximates within 15 cents (if any) | ||
## | ## (''If this is the same as a number already added, just keep that one'') | ||
## If 7 and all its multiples up to 56 are not approximated, then add the smallest 13-limit taxicab-2 interval containing 7 (if any) | ## If 7 and all its multiples up to 56 are not approximated, then add the smallest 13-limit taxicab-2 interval containing 7 (if any) | ||
## | ## (''If this is the same as a fraction already added, just keep that one'') | ||
# If 11 is approximated within 15 cents, add 11 to the subgroup | # If 11 is approximated within 15 cents, add 11 to the subgroup | ||
# If there are still spots free, and 13 is approximated within 7 cents, add 13 to the subgroup | # If there are still spots free, and 13 is approximated within 7 cents, add 13 to the subgroup | ||
# If there are still spots free, and 11 is not in the subgroup: | # If there are still spots free, and 11 is not in the subgroup: | ||
## Add the smallest multiple of 11, 77 or lower, approximated within 15 cents to the subgroup (if any) | ## Add the smallest multiple of 11, 77 or lower, approximated within 15 cents to the subgroup (if any) | ||
## | ## (''If this is the same as a number already added, just keep that one'') | ||
## If 11 and all its multiples up to 77 are not approximated, then add the smallest 13-limit taxicab-2 interval containing 11 (if any) | ## If 11 and all its multiples up to 77 are not approximated, then add the smallest 13-limit taxicab-2 interval containing 11 (if any) | ||
### If this is the same as a fraction already added, just keep that one | ### (''If this is the same as a fraction already added, just keep that one'') | ||
# If any composite basis elements now in the subgroup share | # If any composite basis elements now in the subgroup share zero common factors with anything else in the subgroup, remove them | ||
# 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 which haven’t been added yet, 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 in the subgroup, is approximated within 15 cents, and has not yet been added (''do not replace pure 2, 3, 5, 7 or 11'') | # 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 (''do not replace pure 2, 3, 5, 7 or 11'') | ||