An appoggiatura is a small grace note written to suspend the resolution of a chord. It takes half of the actual note's value, usually. So, why write that when it could be written out with ordinary notes with their correct values? Would there be any difference in the way each ought to be played?
I arrived at two reasons immediately:
As part of ornamentation it is a clear indication, that a beginnner may skip the appogiatura without losing essential parts of the piece; informative in fast movements. (Ornamentation often being added later by the score editor is somewhat more arbitrary in any case.)
It is also a statement (unfortunately depending on the epoch of the piece), how the emphasis should be distributed between appogiatura and the following main note.
An appoggiatura in Baroque music often represents a note held over from a previous chord, a dissonance that clouds the chord and then is resolved. Writing each note as equals would imply that they should take the same amount of time. An appoggiatura typically puts emphasis on the first note, and the two may not be the same length.
See, for example, La Sylva (on pg. 37 of this document). The piece is slow and regretful, with nothing lining up precisely on the beat. The appoggiaturas emphasize the regretful and slightly chaotic nature of the music. Perhaps Sylva was a lovely lady who got away, or a good friend who died.
If you are ever concerned that ornamentation was added later by an editor . . . get a better edition. While ornamentation should typically be left out when first learning a piece, in Baroque music is it essential to the overall artistic nature of the piece and should not be left out in performance. See, for example, the way these folks decorated their churches:
There's lots of physical ornamentation. Chipping St. Teresa and her stone columns and arch out of this alcove would leave a perfectly functional church, but it wouldn't be very Baroque. Likewise, removing ornamentation would alter the style of the music.
Finally, Baroque music has a strong tradition of improvisation, as exemplified in continuo playing and improvisational patterns like La Follia. Writing the two notes as an appoggiatura leaves room for the performer to vary the length of each of the two notes depending on the audience, the performing space, and the individual tastes of the performer.
For new music, IMO there is no point in writing appoggiaturas, unless the intention is to mimic a historical style of notation. Since the general style of ornaments changed from being notes played on the beat to before the beat (roughly around 1800) they are at best ambiguous and confusing.
But for music written when they were still contemporary notation, there are good arguments for retaining that notation - the most obvious one being that (whether or not you fully understand what it means) they are the notation that the original composer and contemporary performers were using.
Some other implications of the notation are:
- They indicate that the appoggiatura note is already an ornament. The contemporary performance practice involved adding a significant amount of un-notated ornamentation, but contemporary texts indicate that "ornamenting an ornamental note" was generally considered a mark of musical incompetence. If you destroy the original notation, there is no way for a modern performer to know when he/she is committing this solecism.
- There are instances where composers notated superficially "identical" rhythms and harmonic patterns in a phrase as a mixture of appoggiaturas and full-size notes. It is one thing to choose to ignore the distinction between those notations, but it's another thing entirely not to know that you that are ignoring something that was in the composer's original autograph.
- They often help to show the underlying harmony. Since contemporary performance practice often involved extemporizing an accompaniment to a solo part at sight, without the luxury of a "run-through," and without any form of chord notation, the more clues that were available to the performers, the better.
Also, it is an indication of whether the note in question is part of the chord or not. A grace note is inherently nonchordal. If the Appoggiatura is written out then it may be construed as for instance a seventh of a chord, if the grace note is used such then it is clear this is not part of the chord and any further confusion is prevented.
In drum music, the appoggiatura before another note indicates that the drum is to be played with a "flam" technique - the two notes should occur slightly separated. This represents an actual physical technique that the drummer must adopt, involving different positioning of the two sticks before the two notes are struck. If the two notes were to be written out with precise values, the drummer would not play using the "flam" technique (which gives a very well-known and recognisable effect) but rather would play the exact notes, resulting in the wrong sound being produced from the drum (usually, but not always, the snare drum).
I might observe that I have wondered for a long time whether, when playing a flam on the snare drum, the grace note should be on the precise beat of the bar and the primary note a fraction late... or the grace note should be just before the precise beat of the bar and the primary note exactly on time. Using my computer, my drum machine and several rainy afternoons, I have discovered that for the appoggiatura plus the primary note to produce the desired "flam" effect, the actual precise beat of the bar should be between the two notes! In other words, neither of the notes should occur on the precise beat of the bar; the grace note should be a short time before the beat and the primary note should be a short time after it. However, from the drummer's point of view this is largely intuitive - he or she would not contrive or calculate these timings. An appoggiatura followed by a primary note in drum music would simply instruct the drummer to play a "flam", and so on sight of those two notes the drummer would simply deploy that technique.
But as I said earlier, if the precise note values were written out instead, the drummer would not play the flam technique and instead would play the precise note values, resulting in the wrong sound and desired musical effect.
An appoggiatura takes at least its written value from the main note. The main note's onset itself is unaccented; basically the onset of the appoggiatura counts as it. Reverting to the main note is not necessarily synchronized with other notes. It is at the player's discretion where to exactly place it.
When executing on a piano, you can't really avoid another onset. When playing on a guitar, you'd usually not strike the string again but rather pull-off or hammer-on. On a violin, you'd continue the bow and stay on the same string. A singer would not change syllables or interrupt breath.
Conceptually, appoggiatura and main note are one note falling into place eventually.
You can write it out as a normal note but that will remove information regarding the purpose of the appoggiatura and a reasonable range of its conceivable interpretations.