The ornament called the short appoggiatura has a long history. While notated simply as a small note (of small value, e.g. an eighth or sixteenth note) close to or slurred to a normal note (the main note or principal note) in the 18th century, it became common to denote it by a similar small note, but with a diagonal slash or stroke through its stem, circa 1830.
The small-note-with-a-slash was not common earlier. For example, my understanding is that Mozart and Beethoven never used it. Appearances of this slashed note in their music (as in the Grove's article available below) is not original; the slashes have been added by copyists or editors.
The short appoggiatura is usually performed in modern music as a very short note inserted before the time of the main note. But it was expected to be played in the time of the main note (on-beat) throughout the 19th century and into the 20th. It is often heard misinterpreted by performers of 19th century music.
Every rule in music has exceptions, but it does seem that on-beat performance of the small-note-with-a-slash WAS THE RULE. We find it given over and over again in 19th century sources. But often the language is not perfectly clear. A writer may say that the short appoggiatura takes "negligable time" or that is so quick that it seems to take no time from the principal note. Often the short appoggiatura is said to be unaccented—the stress is to be on the main note—and this makes some (erroneously) believe that pre-beat performance is expected.
We collect here a few 19th century sources where the instructions for performance of the short appoggiatura are not ambiguous, because the directions are accompanied by illustrations!
We remark that the small-note-with-a-slash was called, inaccurately, an acciaccatura by several 19th century authors. The true acciaccatura is a keyboard ornament. See the last page of the Grove article below.
There were exceptions to the on-beat rule (e.g. in Schumann). We give at the end of this page one source that gives the contradictory rule, but this is a minority opinion.
The article on the appoggiatura from the 1880 Grove's Dictionary is available in PDF format here (1.3 MB).
Part I of Rudolf Tillmetz's Melodic Etudes, Op.47, for two flutes is available in PDF format here (5 MB). Tillmetz indicates how all ornaments indicated by symbols or small notes are to be performed at the end of each etude.
