> with(numtheory):

Warning, the protected name order has been redefined and unprotected

Pure fifth is 3/2

> w7:=evalf(2^(7/12));

> (3/2-w7)/(3/2);

> cfrac(w7,4);

Pure fourth is 4/3

> w5:=evalf(2^(5/12));

> (w5-4/3)/(4/3);

> cfrac(w5,4);

Pure major third is 5/4

> w4:=evalf(2^(4/12));

> (w4-5/4)/(5/4);

> cfrac(w4,4);

Pure minor third is 6/5

> w3:=evalf(2^(3/12));

> (6/5-w3)/(6/5);

> cfrac(w3,4);