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What is the difference in the execution of these 3 rhythmic notations? A crotchet with staccato, a quaver note followed by a quaver rest, and a quaver note with staccato followed by a quaver rest

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Sometimes it is said that a staccato dot is equivalent to reducing the note's duration to half of its nominal value and adding a rest to account for the balance of the time. Under this definition, the first two examples are the same.

In practice, however, the staccato dot isn't necessarily so precise. The execution of a staccato dot could be to sound the note for as short a time as possible, or it could be to insert as short a break as possible between the staccato note and the following note. It is a matter of taste. It depends on the tempo, on the period and style of music, on the instrument for which the piece is written, on the notational context (such as the presence of other articulatory marks in the piece), on the composer's notational practice, and so on.

Of course, one also need not play a quaver followed by a quaver rest completely strictly, either, but there is probably less room for flexibility than there is with the staccato crotchet.

The only thing that's objectively certain is that a staccato quaver is shorter than both a staccato crotchet and a non-staccato quaver. But even there, the objective comparison only holds within the same piece, since the length of an unmarked note is largely a matter of the performer's discretion.

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Any rest is the same concept as any note: a quaver rest will last equally as long as a quaver note.

Staccato markings reduce the duration of notes. Often roughly by half, but the idea is that if the composer wants sound and silence in exact proportions, he'll write out notes and rests. If he wants to give some leeway for interpretation, he'll write staccato notes, giving the performer some licence.

So, generally, there's no exact comparison between what you use as examples. That's the point of staccato markings - or not.

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