User:BudjarnLambeth/12edo as a 2.3.5.17.19 tuning: Difference between revisions

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 # Add prime 2 to the subgroup
 # If 3 is approximated within 15 cents, add 3 to the subgroup
-## If it is not, then add the smallest 1- or 2-digit multiple of 3 it approximates within 15 cents
+## If it is not, then add the smallest multiple of 3, 60 or lower, it approximates within 15 cents (if any)
-## If no such multiple exists, move on to the next step
+## Then 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 5 is approximated within 15 cents, add 5 to the subgroup
-## If it is not, then add the smallest multiple of 5, 80 or lower, which it approximates within 15 cents
+## If it is not, then add the smallest multiple of 5, 60 or lower, which it approximates within 15 cents (if any)
-## If no such multiple exists, move on to the next step
+## If this is the same as a multiple of already added, keep that one
 # If 7 is approximated within 15 cents, add 7 to the subgroup
-## If it is not, then add the smallest multiple of 7, 77 or lower, which it approximates within 15 cents
+## If it is not, then add the smallest multiple of 7, 56 or lower, which it approximates within 15 cents (if any)
-## If no such multiple exists, move on to the next step
+## If this is the same as a multiple of already added, keep that one
 # 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, then add the smallest multiple of 11, 77 or lower, approximated within 15 cents to the subgroup, if any
+# If there are still spots free, then 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 multiple of already added, keep that one
 # 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
 === EDOs with 13 to 27 tones/octave ===
-# The subgroup should have 6 basis elements
+# The subgroup should have 5 basis elements
 # Add prime 2 to the subgroup
 # If 3 is approximated within 15 cents, add 3 to the subgroup
-## If it is not, then add the smallest 1- or 2-digit multiple of 3 it approximates within 15 cents
+## If it is not, then add the smallest multiple of 3, 60 or lower, it approximates within 15 cents (if any)
-## If no such multiple exists, move on to the next step
+## Then 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 5 is approximated within 15 cents, add 5 to the subgroup
-## If it is not, then add the smallest multiple of 5, 80 or lower, which it approximates within 15 cents
+## If it is not, then add the smallest multiple of 5, 60 or lower, which it approximates within 15 cents (if any)
-## If no such multiple exists, move on to the next step
+## If this is the same as a multiple of already added, keep that one
 # If 7 is approximated within 15 cents, add 7 to the subgroup
-## If it is not, then add the smallest multiple of 7, 77 or lower, which it approximates within 15 cents
+## If it is not, then add the smallest multiple of 7, 56 or lower, which it approximates within 15 cents (if any)
-## If no such multiple exists, move on to the next step
+## If this is the same as a multiple of already added, keep that one
 # 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, then add the smallest multiple of 11, 77 or lower, approximated within 15 cents to the subgroup, if any
+# If there are still spots free, then 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 multiple of already added, keep that one
 # 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