An ornament is a small note or symbol which imposes an embellishment on a note or chord.
An appoggiatura is a species of grace note. Placed before a given note, it leans in and takes a certain amount of time.
Placed before an regular note, it usually takes half the time value:
Figure 1: An appoggiatura before a regular note.
Placed before a dotted note, it usually takes two-thirds of the time value:
Figure 2: An appoggiatura before a dotted note.
Placed before two tied notes, it usually takes the whole value of the first note:
Figure 3: An appoggiatura before two tied notes.
If an appoggiatura leans upon a chord, only one note is affected:
Figure 4: An appoggiatura before a chord.
An acciaccatura is a species of grace note, written with a line through its stem.
Placed before a given note, it indicates to be crushed as quickly as possible, leaving the principal note with almost all time value.
Figure 5: Two acciaccaturas.
An acciaccatura before a chord indicates to spread the chord:
Figure 6: An acciaccatura before a chord.
A trill is a line placed above the staff which indicates the rapid alteration between a given note, and the diatonic note above. The alternating notes are slurred together and played legato.
Figure 7: One bar of trill.
A mordent is a symbol which indicates to crush two notes in before a given note to produce a short trill effect.
There are two types of mordent: upper mordent and lower mordent.
An upper mordent has the middle note higher than the principal note:
Figure 8: An upper mordent.
A lower mordent has the middle note lower than the principal note:
Figure 9: A lower mordent.
The middle note of a mordent may be altered in pitch by adding an accidental above the symbol:
Figure 10: An upper mordent with a sharp.
A gruppetto (or turn) is a symbol which implements a four-note figure after or before a given note depending on whether the sign is placed after or over it:
Figure 11: A gruppetto after the principal note.
Figure 12: A gruppetto over the principal note.
The pivot note of a gruppetto may be altered in pitch by adding an accidental above or below the symbol:
Figure 13: A gruppetto with a flat.
Figure 14: A gruppetto with a sharp.
Figure 15: A gruppetto with a natural.
Also see Tremolos | Noteheads.