Originally Posted by: icebreaker1588Is there a way to measure the octave as being a certain distance from your original melody?[/quote]
An octave is always the specific interval of an 8th. To play a harmony of an octave means to double the melody 8 scale degrees higher or lower than the original notes of the melody.

For example, if you are in the key of C major, you start on the note C, you want to play an octave lower, then you'd count 8 scales down the scale from your starting note.

Starting note C.

E ||---|---|---|---|---|---|---|---|---|
B ||---|---|---|---|---|---|---|---|---|
G ||---|---|---|---|-c-|---|---|---|---|
D ||---|---|---|---|---|---|---|---|---|
A ||---|---|---|---|---|---|---|---|---|
E ||---|---|---|---|---|---|---|---|---|

Count down an octave.

c-b-a-g-f-e-d-c
1-2-3-4-5-6-7-8

These C's are an octave apart. The lower one is an octave lower than the starting one.

E ||---|---|---|---|---|---|---|---|---|
B ||---|---|---|---|---|---|---|---|---|
G ||---|---|---|---|-c-|---|---|---|---|
D ||---|---|---|---|---|---|---|---|---|
A ||---|---|-c-|---|---|---|---|---|---|
E ||---|---|---|---|---|---|---|---|---|

Or if you want to go up an octave, then count 8 scale degrees up.

c-d-e-f-g-a-b-c
1-2-3-4-5-6-7-8

E ||---|---|---|---|---|---|---|-c-|---|
B ||---|---|---|---|---|---|---|---|---|
G ||---|---|---|---|-c-|---|---|---|---|
D ||---|---|---|---|---|---|---|---|---|
A ||---|---|---|---|---|---|---|---|---|
E ||---|---|---|---|---|---|---|---|---|

As opposed to an interval of a 3rd. Here's a 3rd lower than C, which is an A. To get from C to A you count 3 scale degrees down.

c-b-a
1-2-3

E ||---|---|---|---|---|---|---|---|---|
B ||---|---|---|---|---|---|---|---|---|
G ||---|-a-|---|---|-c-|---|---|---|---|
D ||---|---|---|---|---|---|---|---|---|
A ||---|---|---|---|---|---|---|---|---|
E ||---|---|---|---|---|---|---|---|---|

To harmonize a 3rd higher than C, count 3 scale degrees up from C to E.

c-d-e
1-2-3

E ||---|---|---|---|---|---|---|---|---|
B ||---|---|---|---|-e-|---|---|---|---|
G ||---|---|---|---|-c-|---|---|---|---|
D ||---|---|---|---|---|---|---|---|---|
A ||---|---|---|---|---|---|---|---|---|
E ||---|---|---|---|---|---|---|---|---|

[QUOTE=icebreaker1588] Or is it always referred to as being an octave lower or higher than the melody?

I'm not entirely sure what you are asking here. A harmony note can be any interval higher or lower than the original starting melody note. An octave is simply one possible interval to use. But the harmony note can be a 2nd, 3rd, 4th, 5th, 6th, 7th, or 8th (octave) or any chromatic interval in between those.

Does that make sense?