User:BudjarnLambeth/12edo as a 2.3.5.17.19 tuning: Difference between revisions
| Line 43: | Line 43: | ||
## If it is not, then add the smallest multiple of 3, 60 or lower, it approximates within 15 cents (if any) | ## If it is not, then add the smallest multiple of 3, 60 or lower, it approximates within 15 cents (if any) | ||
## Optionally, add the second-smallest multiple of 3, 60 or lower, it approximates within 15 cents, which is not a multiple of the previous one (if any) | ## Optionally, add the second-smallest multiple of 3, 60 or lower, it approximates within 15 cents, which is not a multiple of the previous one (if any) | ||
## If 3 and all its multiples up to 60 are not approximated, then add the smallest 13-limit taxicab-2 interval containing 3 (if any) | |||
# 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 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 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 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 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: | ||
## If this is the same as a number already added, just keep that one | ## 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 this is the same as a fraction already added, just keep that one | |||
# If any composite basis elements now in the subgroup share no common factors with any other element in the subgroup, remove them | # If any composite basis elements now in the subgroup share no common factors with any other element 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) | ||