An octave effect unit is an audio signal processor that blends the original signal with its pitch-shifted copy, transposed by an octave up or down. As the natural frequencies of perfect octaves are pictured in a 2:1 ratio, the derived signal is obtained by doubling or halving the initial frequency of the input signal. Octave effects are usually found in forms of stomp boxes and 19" rackmount units, or in different portable multi-effect units. They are used both in studio and live sound environments. In most cases, they are associated with electric guitars and basses but can be used in many creative ways with other instruments. They are used mainly as monophonic effects.
Probably the most notable early use of an octave effect would be by Jimi Hendrix, who combined its powers with a fuzz circuit  in a guitar pedal called as the Octavia.  Some say that the first octave effect unit was Conn's Multi-vider.
Octave effects can be divided into octave-up, octave-down and multi-octave units. Analog octave effects aren't necessarily used to color the tone of the input signal, but to enhance the sound by adding more depth or extending the range of an instrument. It can be used in subtle notion  , or to totally distort the original signal for a more profound effect. They are generally used for one or two note playing, as chordal playing might make unintended and rather unpleasant harmonic distortion and mismatch. This leads to the biggest problem with octave pedals – tracking. It had always been an imperative for octave effect clients for their units to "track well," as the effects themselves didn't replicate the transposed material accurate enough and without sonic artifacts or note aliasing.  Sub octave effects usually don't playback the original input signal, rather than signal triggers an internal synth generator to reproduce a sound with a certain frequency. 
MusicRadar Basics: octave and pitch guitar effects explained
Octave pedals controls
Octave pedals commonly have a mix (dry/blend/direct) knob, while multi-octave stomp boxes also have separate level knobs for each octave. If an octave effect is able to transpose the pitch of the blended signal for more than one octave, the given setting is usually chosen with a dedicated switch. Some octave pedals even have a drive knob that controls the saturation amount of the blended signal as well as a tone knob that alters the character of it.
EFFECTS 101: Octaver. Example of controls of Boss Octave Pedal.
Jimi Hendrix famously utilized the octave effect along with some fuzz in songs such as "Purple Haze" and "Tax Free."
Rory Gallagher was also a notable user of the effect, with live works such as "Bad Penny" at the '85 Montreux Festival.
Speaking of bass, there are some notable examples of the use of bass octave pedal:
Paul Young - I'm Gonna Tear Your Playhouse Down
Michael Jackson - Earth Song
Peter Gabriel - Sledgehammer
- ↑ Guitar World "The Secrets of Jimi Hendrix's Guitar Setup: Interview with Roger Mayer"
- ↑ www.roger-mayer.co.uk "Octavia"
- ↑ Sweetwater.com "Effects Tip: Use an Octave Effect to Thicken Your Sound"
- ↑ Tonereport.com "Who Needs Digital 8 Awesome Analog Octave Boxes"
- ↑ SeymourDuncan.com "Finger on the Trigger: Using Octave Effects"
- ↑ ilovefuzz.com "Octave up effects"
- ↑ DIYStompboxes.com "Simple Octave Up schematic"