3/4 eigth notes to 4/4 triplets? How to calculate tempo?
So I have a piece that I'm writing that is mostly in 3/4 with a main melody purely in eighth notes.
I'm trying to implement a time signature change to 4/4, where what was an eighth note melody in 3/4 turns to triplet eighth notes in 4/4 while playing the melody at the same speed... but of course the tempo can't be the SAME.
How do I calculate which tempo I'm changing to?
The first ten seconds of this:
is kind of what I'm going for. Notice how the time signature changes.
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This is straightforward arithmetic, if you can remember what you learned about fractions in elementary school.
If the 3/4 tempo is X quarter notes per minute, you are playing 2X 8th-notes per minute.
If you group those notes in threes, there are 2X/3 groups per minute.
If you write the group as a triplet, that means the tempo is 2X/3 quarter notes per minute.
As an example, if the 3/4 tempo was quarter-note = 72, the 4/4 would be quarter-note = 72x2/3 = 48.
New Tempo:Old Tempo = New Pivot Value:Old Pivot Value
So what does this mean? The Pivot is the length of the note that you want to remain constant. In your case, you want the eighth notes of the old tempo to be equal to the quarter note triplets in the new tempo. Which means that the old pivot value is 1/2 (half a beat) and the new pivot value is 1/3 (third of a beat). 1/3:1/2 = 1/3*2/1 = 2/3. So if you want to move from the old tempo to the new tempo, you multiply the tempo by 2/3 (for example: old tempo=90, new tempo=60).
This is called a metric modulation (or tempo modulation, or proportional tempi).
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