What term describes the doubling of the rhythmic value of each note in a musical context?

The term that describes the doubling of the rhythmic value of each note in a musical context is called augmentation. In musical composition, augmentation typically refers to a technique where the original notes are transformed into longer note values, effectively slowing down the rhythm while maintaining the same melodic contour. This is often used to create variation or to dramatize a musical idea by allowing more time for each note to resonate.

The other terms listed refer to different concepts in music. Diminuendo indicates a decrease in loudness rather than a change in rhythmic values. Ritardando is a gradual slowing down of tempo, but it does not specifically refer to the elongation of note values themselves. Syncopation involves placing emphasis on beats or parts of beats that are typically unaccented, creating a sense of unpredictability in the rhythm but not altering the note values to longer durations. Therefore, augmentation is the most accurate term for the process of doubling note values.