What is the interval of an octave?

The interval of an octave is defined as the distance from one note to another note that bears the same letter name. This means that, for example, if you take the note C, the note that is one octave higher is also C, but it resonates at a frequency that is double that of the lower C. The octave represents a complete cycle of the musical alphabet, reaffirming the relationship of pitches. This concept is foundational in music theory and is vital for understanding scales, melodies, and harmonies.

In this context, the other options do not accurately define an octave. The distance between two adjacent notes refers to a whole step or half step, and does not account for the doubling of pitch that occurs in an octave. A half step in pitch specifically refers to the smallest interval used in Western music (like the distance between C and C#), while a full step is made up of two half steps (for example, from C to D). Thus, these definitions do not capture the broader and more comprehensive nature of an octave.