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Which notation system is similar to neumatic notation?

The notation system most similar to neumatic notation is early forms of staff notation. While neumatic notation uses only a limited set of symbols to indicate melodic contour and relative pitch, early staff notation (like that found in some 10th and 11th-century manuscripts) built upon this by adding more precise indications of pitch using lines and spaces, but still retained a somewhat fluid and flexible approach to rhythm that reflects the character of neumatic notation. The transition was gradual, not a sudden shift.
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