"Piano" is the shortened form of what word?

Pianoforte - meaning soft loud, because the instrument is capable of producing both types of sounds.

http://www.thefreedictionary.com/pianoforte

The word piano is a shortened form of the word pianoforte, which is seldom used except in formal language and derived from the original Italian name for the instrument, clavicembalo [or gravicembalo] col piano e forte (literally harpsichord with soft and loud).

https://en.wikipedia.org/wiki/Piano

More accurately, the translation of "gravicembalo col piano e forte" is the "great harpsichord with soft and strong [capabilities]".

The word 'pianoforte' or 'piano', describes an instrument invented in about 1726 by Bartolomeo Cristofori. The origins of the word is an abbreviation of piano et forte (literally 'soft and loud'). The significance of 'soft and loud' as the name of a keyboard instrument derives from the fact that the harpsichord, a common household keyboard instrument of the day, could not vary the volume of playing, at least not note by note. The piano's unique "escapement" action makes this possible. The clavichord can produce subtle changes in volume, but the sound is so delicate and soft over-all that it can hardly be compared with the piano.

The piano first known as the pianoforte developed from the harpsichord around 1720, by Bartolomeo Cristofori of Padua, Italy. Francesco Mannucci noted in his diary (February 1711) that in 1698 Cristofori began work on the "arcicembal che fa il piano e il forte" (harpsichord with soft and loud) The inventory of Medici instruments for 1700 establishes that at least one had been completed by that date. From 1690 until his death Bartolomeo Cristofori (1655-1731) went to work at the court of Prince Ferdinand de' Medici in Florence as a designer and custodian of keyboard Instruments. He Is noted for various innovations in harpsichord construction and especially for the invention of the piano.

http://inventors.about.com/library/inventors/blpiano.htm

Cristofori's invention did not become the most popular instrument immediately. In fact, his pianos were not without their drawbacks and their dynamic capabilities were more of a theory than practice. There was only a little difference between "piano" and "forte". It wasn't until the German Silberman piano makers that the piano began to become popular - they had a much wider dynamic range. King Frederick the Great had a collection of Silbermann pianos, which was the brand introduced to J.S. Bach. Silbermann's pianos were also Mozart's instrument of choice. (Though Haydn and Beethoven prefered the English Broadwood pianos.) Besides the dynamic range, which only got to its relatively modern capabilities around the 1820s, the pitch range of the piano has only been the standard 88 keys for about the last eight decades. (There are even today some old pianos - Russian ones mostly - which have just 85 keys rather than 88.) Mozart's instrument had a range of five octaves, from FF to f3.