Herbie Hancock’s funky anthem, “Watermelon Man,” from Head Hunters, was originally painted with lighter colors as a piano-driven jazz tune in 1962. While it opens with some rocking back and forth on two chords, at 0:15, the first two notes of the lead melody take us a minor seventh down.
It’s easy to make the rest of the notes in a C major scale just by combining our three existing intervals. Let’s start with D. If you know your music theory, you know that D has the same relationship to G that G has to C. Just like you can make a G by multiplying C’s frequency by 3/2, so too can you make your D by multiplying G’s frequency by 3/2. The interval between C and G, and between G and D, is called a perfect fifth. You can go up a perfect fifth from any note by multiplying its frequency by 3/2. So let’s go up a fifth from G at 3/2 Hz, multiplying it by 3/2 to get a D at 9/4 Hz. Then we can bring it down an octave by dividing its frequency in half, giving us a D at 9/8 Hz. So far, so good.