I came across a marking in music where it says that the quarter note = half note and then says double time. I don't understand why the notation implies double time. Can someone explain how saying the quarter note equals the half note means the tempo quickens.
It means the quarter note of the previous tempo is equal to the half note of the new tempo. Since the quarter note nominally is half of a half note, the new tempo is twice as fast.
For example, if the previous tempo had 80 quarter notes a minute, the new tempo will have 80 half notes a minute. Because that means 160 quarter notes a minute, it's nominally twice as fast.
Did this marking also come at a change of time signature? The "=" language often helps performers figure out how the change in meter affects the tempo (or doesn't). In this case, if perhaps it came at a change from 4/4 to 2/2, it would mean the new half notes take up the same bpm length as the old quarter notes.
But without a change in time signature, both "Double time" and the "=" notation could be saying the same thing redundantly: If your quarter note beat was previously 100 bpm, now it's 200 (and, presumably, quarters are still the beat).