Acording to
here, dub is short for double anyway!
Quote:
dub3 (dŭb) pronunciation
tr.v., dubbed, dub·bing, dubs.
1.
1. To transfer (recorded material) onto a new recording medium.
2. To copy (a record or tape).
2. To insert a new soundtrack, often a synchronized translation of the original dialogue, into (a film).
3. To add (sound) into a film or tape: dub in strings behind the vocal.
n.
1. The new sounds added by dubbing.
2. A dubbed copy of a tape or record.
3. A mostly instrumental style of music originating in Jamaica, produced by remixing existing recordings to emphasize bass and drum rhythms and adding audio effects
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Anyway, in common use AFAIK its dubbing to copy one tape to another, and double to repeat a musical part (note that double is a musical description, whereas dub is a technical one).
Overdub is derived from dub, so it really means over doubling!
The name 'Double bass' could have come about because the double bass was originally used to double the cello part an octave lower.