The ancient Greeks figured out that if you have a bunch of strings, it sounds really good if you tune them according to the frequency ratios you get from the natural overtone series. In such tuning systems, you get all your notes by picking a starting frequency, and then multiplying or dividing it by whole numbers. The good-sounding (to Western people) note combinations are the ones derived from the lowest harmonics — the ones that have you multiplying or dividing by the smallest prime factors: two, three, and five.
Modes and Key Signatures have a variety of different characteristics and are great for outside-the-box songwriting. Here’s a cheat sheet to remember them!