Frequency is the rate anything vibrates for a set period of time.
A vibration is one complete period of a sinusoidal waveform.
Frequency in music is measured per second; 440 refers to 440 vibrations per second.
Pitch is the "music note" name we apply to vibrations.
When something vibrates 440 times per second, it is said to be the note A.
A natural framework of frequency based on mathematical ratios. We will learn more about this in Lesson 6 Intervals.
The octave is the first and complete building block of the Harmonic Series.
The octave marks the repetition of the seven note pattern and thus defines the boundaries of music. All of western music is built upon the octave and it's ratio of 2:1.
Music is based on a repeating pattern of seven notes A-B-C-D-E-F-G. The pattern repeats on the eighth note and it is called an Octave; from the Latin word Octavus, which means "8th".
The octave has a ratio of 2:1, meaning the vibration of any octave is half or double the original note's frequency.
If the original note is A=440, the octave above vibrates 880 (440x2) times per second, and below 220 (440/2).
An octave remains in the same pitch class. If you double the frequency of A=440, you get A=880. Both are the note A, but obviously in different octaves which we hear as higher (faster) or lower (slower) vibrations.
Notice in the Human Vocal Range chart there are more than one A: A=110, A=220, A=440 and A= 880.