Harmonic relationships refer to the connections between different musical notes that create a pleasing sound when played together. These relationships are often based on mathematical ratios, which help define how notes interact. For example, the interval of an octave, where one note vibrates at double the frequency of another, is a fundamental harmonic relationship in music. In addition to music, harmonic relationships can also be found in nature and mathematics. For instance, the Fibonacci sequence and golden ratio illustrate how harmony can manifest in patterns and proportions. These concepts highlight the importance of balance and symmetry in both art and science.