3 Notes: The Second-simplest in the Music Theory of Scales

Next, add a tone derived from the next simplest ratio of frequencies, 3:2. (The simplest possible frequency ratio that can identify a relationship between two tones is 2:1.) For reasons that will become clear in a little while, you can label the 3:2 tone G.
Notice that when you add G to the scale, the relationship between G and the C above Middle C also happens to be a simple ratio of frequencies, 4:3.
Now you’ve got a scale of three notes. It sounds good, too. The organizing principle looks promising (Figure 6).

FIGURE 6: C - G - C, a Scale of 3 Notes

Notice the big gap between Middle C and G. Fortunately, a tone derived from the simple frequency ratio 5:4 fits beautifully, right between Middle C and G. Call it E.