Stacking perfect fifths yields the octave, fifth, and fourth intervals.

Evidence

We begin with a note and add the notes one, two, and so on octaves above. We next add a perfect fifth above the low note, obeying the ratio 3:2, introducing a new note between the octaves. Counting the octave, we now already have three intervals: the octave, the perfect fifth, and a perfect fourth—that is, the jump from the fifth to the octave above. — Eric J. Heller, Why You Hear What You Hear- An…, 2360

Categorization

• XREF: connects to: The major and minor sixth ratios derive by complementing thirds within an octave — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 806