The fundamental intervals are the superparticular ratios 2/1 (the octave), 3/2 (the perfect fifth) and 5/4 (the major third).
That is, the notes of the major triad are in the ratio 1:5/4:3/2 or 4:5:6.
The intervals within the diatonic scale are shown in the table below.
(The Pythagorean minor second is found by adding 5 perfect fourths.)
The table below shows how these steps map to the first 31 scientific harmonics, transposed into a single octave.