The note relationships in a chromatic scale are based on the 12th root of 2.
An octave has a ratio of 2. An octave is divided into 12 equal steps.
For example, to find the ratio of one semi-tone (half step), on a scientific calculator, use this button:
Here’s the result where x = 2 and y = 12
This Max patch shows the relationships between any two notes and how to calculate the pitch of a note based on the semi-tone interval. You might use it as a starting point to design your own scales. For example, a 13 note chromatic scale. Or relationships based on randomness.