How is an 'octave' defined in music theory?

An octave in music theory is defined as the distance between two notes where one note has a frequency that is double the frequency of the other. When you move an octave higher, you reach a note that sounds similar in quality, but it is one full step higher in frequency. For example, if the note A has a frequency of 440 Hz, the note A one octave higher will have a frequency of 880 Hz. This interval is perceived as highly consonant, meaning that notes an octave apart harmonically blend well together in music.

The other options do not accurately define the concept of an octave. The first note of a scale refers to the tonic and is specific to any given scale rather than the general idea of an octave. A repeated musical idea may refer to a motif or a phrase but does not pertain to the definition of an octave in terms of frequency. Finally, a collection of chords indicates a harmonic structure and does not relate to the specific interval measured by an octave.