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A Note equivalent in Pitch to another note but with a different notation. e.g. G# and Ab.

This only works in modern equal tempering where many of the notes are changed in pitch to fit all keys.
It is worth noting that they would occur on different scales. In this example G# occurs on the scale for the key of A as the 7th Degree and Ab occurs as the 4th degree on the scale for the key of Eb. In modern tuning, the two notes have exactly the same pitch and are played in the same position on an Instrument.