dividing a note (or multiplying) with another interval you has found intervalic formula for all the s factor numbers (aproximate, maybe you have to round the number) for example : dividing this number is the way you multiply or divide octave above or below,
a: 440 by g#: 415,30 you found 1.059475 to reach the 2b interval or the 7m interval, depending if the root with this number, and if you want to find th as you know, after multiply or divide by 2
obtain interval aprox -1 multiply root by >
+1 1.059475
<
divide root by
-2 multiply root by >
+2 1.1224489 <
divide root by
-3 multiply root by >
+3 1.1892213 <
divide root by
-4 multiply root by >
+4 1.2599146 <
divide root by
-5 multiply root by >
+5 1.3348299 <
divide root by
-6 multiply root by >
+6 1.4141998 <
divide root by
-7 multiply root by >
+7 1.4983314 <
divide root by
-8 multiply root by >
+8 1.5874161 <
divide root by
-9 multiply root by >
+9 1.6817643 <
divide root by
-10 multiply root by >
+10 1.7818093 <
divide root by
-11 multiply root by >
+11 1.8877638 <
divide root by
-12 multiply root by >
2
+12 <
divide root by
maybe you know that i've discovered but it helps me a lot, calculator on hand always je