The short octave was a method of assigning notes to keys in early keyboard instruments (harpsichord, clavichord, organ), for the purpose of giving the instrument an extended range in the bass range. 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 closely related system, the broken octave, added more notes by using split keys: the front part and the back part of the (visible) key controlled separate levers and hence separate notes.
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:
the player would hear the musical scale of C major in the bass:
The actual note assignments can be seen in the following diagram, which shows the lowest eight keys of an early keyboard: