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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.

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    Your confusion probably comes from the redefinition of '=' in computer languages as an assignment operator. There the new value is on the left of the sign. In music the semantics are different.
    – PiedPiper
    Commented Oct 6, 2021 at 18:58

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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.

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    I just want to add that the same goes for the "eight note equals quarter note" marking - ♪=♩ ♪ equals ♩. I tried googling these terms and didn't find any solution. Later on I found this answer and it's exactly what I needed, so I hope google will index my answer so people like me will be able to find this :))
    – Aleksandar
    Commented Oct 26, 2023 at 8:03
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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).

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