I have mathematically figured out how to map the chromatic scale onto the circle of fifths for even temperaments. The equation is to multiply each interval by
(n/2)+1 where n is the n TET.
For example, for 12 TET, we apply the function
(n/2)+1 and get 7 ((12/2)+1=7), from there I multiply each interval by 7:
0 semitones * 7 = 0 semitones (eg: C is mapped to C);
1 semitone * 7 = 7 semitones (eg: C# is mapped to G);
2 semitone * 7 = 14 semitones (eg: D is mapped to D);
3 semitone * 7 = 21 semitones (eg: D# is mapped to A)
This will give me 12 TET circle of fifths.
However, I've noticed this equation only works for even temperaments because for odd temperaments, we have to multiply by a number with a half, giving me quartertones.
Are there no odd temperament circle of fifths equivalent?
Any guidance would be appreciated