Suspensions are prepared, dissonant non-chord notes which resolve downwards by step. They fall on a strong beat, but are not normally accented in themselves, because they are usually tied backwards to the previous beat, to their preparation note.
In this example, the soprano F in chord IV can be “suspended”, or “held over” into chord I. It is held with a tie, and then moves downwards to the chord note E, a moment later than the rest of the chord sounds.
Suspensions are described by number, which refers to the interval of the suspended note above the bass note, then the interval of the resolution note. The above is an example of a 4-3 suspension (4th above the bass note, resolving to a 3rd above the bass note).
In root position chords, the two most-used suspensions are the 4-3 and the 9-8. Here is an example of a 9-8 suspension. The note D is held over. D is a 9th above C, and its resolution note C is an octave higher (8th).
In first inversion chords, the most common suspension is the 7-6. The 7th above the bass note resolves to the 6th.
Suspensions should be dissonant notes. The interval between the bass and the suspended note can be a 4th, 7th or 9th.
If a non-chord note is used which is not dissonant, such as a 6th, the effect is not the same. In this example, the D has been held over into a chord of F major. D is a 6th above the bass note F. The effect is that of a first inversion D minor chord, rather than the intended F major chord with a suspension. This type of figure is best avoided.
Take care not to double the resolution note in any of the upper three parts. Here, the resolution note C is already sounding in the tenor part, so this is a doubled resolution note and should be avoided.
Doubling the resolution note in the bass part is fine however:
Retardations are a type of suspension. In a normal suspension, the resolution is by a downwards step. In a retardation, the resolution is by an upwards step.
Here the A is a non-chord note within chord V. It resolves upwards to B, which is a chord note.