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How does a fermata change the written length of a note or rest?

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In musical notation, a fermata (also known as a hold) indicates that a note, chord, or rest should be prolonged beyond its standard written time value.12

Rather than following a strict mathematical extension, the duration of the hold is left to the discretion of the performer or the conductor. This allows for expressive flexibility, enabling the musician to extend the sound or silence as they see fit within the context of the performance.12