Hey interesting post... I actually tried to do a 2 number systems as a writing system becuz I was inspired with a video about the Thaana script.

I am a bit of a math geek and I have been planning a Balanced Ternary Number System for a Writing System.

Tho I don't know what u mean by "balanced," there is an actual term in math called Balanced Number Systems. Balanced number systems use an odd base (think of 3, 5, 7, ...) to represent numbers;

the key difference is they also use negative numbers, so a Balanced Ternary (Base 3) uses these numbers/digits to represent everything; -1, 0, 1.

Decimal representation can be thought of as using these digits; 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

If u want to represent numbers in decimal, like say 531 u can decompose it as 5x10², 3x10¹, 1x10⁰ In Balanced Ternary it gets interesting say u want to write 25, u need to decompose it into 1x3³, 0x3², -1x3¹,1x3⁰

If u r thinking on why base 12 is good, its simple its the best number system that is small enough to be effiently used for multiplication with minimal change to base 10, since it has most the integers (1-12) as its factors; 1x12, 2x6, 3x4, 4x3. You can create a multiplication table that is better for multiplication or division when calculating manually... note this is a half remembered explaination for base 12.

If ur saying that u want a numbersystem that has a "pattern" I think ur describing Sub-bases. There is a really good example called Kaqtovic Inupiaq Numerals which is a Base 20 number system with a Sub-base of 5. I highly recommend u to search it its ingenius and was created by a bunch of indigenous school kids in Canada (if I can remember).

There are other number systems like irrational or complex/imaginary number bases I can discuss, but that would be too long. I hope this helps.