In one variant of the short octave system, the lowest note on the keyboard was nominally E, but the pitch to which it was tuned was actually C. Nominal F# was tuned to D, and nominal G# was tuned to E. Thus, in playing the keys
E F# G# F G A B C
the player would hear the musical scale of C major in the bass:
C D E F G A B C
The rationale behind this system was that the low notes F# and G# are seldom needed in early music. Deep bass notes typically form the root of the chord, and F# and G# chords were seldom used at this time. In contrast, low C and D, both roots of very common chords, are sorely missed if a harpsichord with lowest key E is tuned to match the keyboard layout.
A second type of short octave used the following keys:
B C# D# C D E F# G
to play the G major scale
G A B C D E F# G
Here, the "exotic" bass notes C# and D# are sacrificed to obtain the more essential G and A.
In stringed instruments like the harpsichord, the short octave system created a defect: the strings which were tuned to mismatch their keyboard notes were in general too short to sound the reassigned note with good tone quality. To reach the lower pitch, the strings had to be tuned too slack. During the 17th and 18th centuries, harpsichord builders gradually increased the size and bass range of their instruments, to the point where every bass note could be properly played with its own key.
Short octaves were also sometimes used in the organ. Here, the practice would not have yielded poor tone quality (since the associated pipes would have to be built with the correct length in any event); nevertheless, because of the loss of musical flexibility they entailed, short octaves ultimately came to be abandoned in organs as well.
Source:
Three Centuries of Harpsichord Making by Frank Hubbard (1967, Cambridge, MA: Harvard University Press; ISBN 0674888456)