How is an octave defined in terms of frequency?

An octave is defined as the interval between one frequency and another frequency that is double its original value. This means that if you start with a certain frequency and double it, you have moved up one octave. For instance, if you take a frequency of 440 Hz (the pitch of the note A above middle C), its octave would be 880 Hz. This relationship is fundamental in music theory and sound analysis, forming the basis for harmonic structures and scales.

The other options describe different relationships of frequency change but do not align with the precise definition of an octave. For example, decreasing a frequency by half refers to a different interval called a "descending octave" but does not serve to define an octave itself. Similarly, an increase of one-third of a frequency would not correspond to any specific or universally accepted musical interval. Lastly, when a frequency remains constant, it does not reflect any change or interval, thereby falling outside the definition of octave entirely.