User:BudjarnLambeth/12edo as a 2.3.5.17.19 tuning: Difference between revisions
| Line 31: | Line 31: | ||
# Add prime 2 to the subgroup | # Add prime 2 to the subgroup | ||
# If 3 is approximated within 15 cents, add 3 to the subgroup | # If 3 is approximated within 15 cents, add 3 to the subgroup | ||
## If it is not, then add the smallest multiple of 3 | ## If it is not, then add the smallest 1- or 2-digit multiple of 3 it approximates within 15 cents | ||
## If no such multiple exists, move on to the next step | ## If no such multiple exists, move on to the next step | ||
# 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 | ## If it is not, then add the smallest 2-digit multiple of 5 it approximates within 15 cents | ||
## If no such multiple exists, move on to the next step | ## If no such multiple exists, move on to the next step | ||
# 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 | ## If it is not, then add the smallest 2-digit multiple of 7 it approximates within 15 cents | ||
## If no such multiple exists, move on to the next step | ## If no such multiple exists, move on to the next step | ||
# 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, then add the smallest multiple of 11 | # If there are still spots free, then add the smallest 2-digit multiple of 11 approximated within 15 cents to the subgroup, if any | ||
# 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 | ||
| Line 49: | Line 49: | ||
# Add prime 2 to the subgroup | # Add prime 2 to the subgroup | ||
# If 3 is approximated within 15 cents, add 3 to the subgroup | # If 3 is approximated within 15 cents, add 3 to the subgroup | ||
## If it is not, then add the smallest multiple of 3 | ## If it is not, then add the smallest 1- or 2-digit multiple of 3 it approximates within 15 cents | ||
## If no such multiple exists, move on to the next step | ## If no such multiple exists, move on to the next step | ||
# 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 | ## If it is not, then add the smallest 2-digit multiple of 5 it approximates within 15 cents | ||
## If no such multiple exists, move on to the next step | ## If no such multiple exists, move on to the next step | ||
# 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 | ## If it is not, then add the smallest 2-digit multiple of 7 it approximates within 15 cents | ||
## If no such multiple exists, move on to the next step | ## If no such multiple exists, move on to the next step | ||
# 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, then add the smallest multiple of 11 | # If there are still spots free, then add the smallest 2-digit multiple of 11 approximated within 15 cents to the subgroup, if any | ||
# 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 | ||