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This will be an oversimplified question for most of you so please pardon my ignorance in advance.

I practice 16th note exercises in which each rhythm, or 16 bars, is practices 20 times each and there are a total of 24 sections of 16 note rhythms. The metronome is set to 152 beats per minute. I was curious and decided to do the math.

Where is my math wrong below?

(16 x 20) = 320 beats per section (24 x 320) = 7,680 total beats in the 24 sections (7,680 / 152) = 50 <- This is how long the math is telling me it would take to finish all sections at 152 beats per minute.

I finish the exercise in around 24 minutes, not 50. I know the answer is simple and probably relates to my warped notion of beat per minute.

@152 beats per minute

1 [ !!!! !!!! !!!! !!!! ] 16 x 20 times
2 [ !!!! !!!! !!!! !!!! ] 16 x 20 times
3 [ !!!! !!!! !!!! !!!! ] 16 x 20 times
...
24[ !!!! !!!! !!!! !!!! ] 16 x 20 times
Ross Bush
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1 Answers1

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Trombonist here.

Assuming each bar is in $\frac{4}{4}$ time, we have $16 \cdot 4 = 64$ quarter note beats per phrase. Each phrase is repeated $20$ times, for a total of $64 \times 20 = 1280$ quarter notes. Now your metronome is set to $152$ BPM (i.e., quarter-note 152), so doing this exercise completely should take $\frac{1280}{152} \approx 8.42$ minutes.

Your mistake is treating each sixteenth note as a beat - unless, of course, your time signature is $\frac{k}{16}$. That requires a difference calculation.

Sean Roberson
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  • Doh! I see my error. Each sixteenth note is measured as a beat, not each beat of a sixteenth note? – Ross Bush Dec 22 '21 at 00:27
  • Correct. Note, however, that if you're playing in, say, $\frac{9}{16},$ each sixteenth note counts as a beat. This computation assumes the rhythms are in common time. – Sean Roberson Dec 22 '21 at 00:31
  • If I measure each 16th note as a beat in 4/4 time then I get 4x20=80 and 80x24=1920 and 1920 / 152 = 12, however, I finish in 24 minutes. It could be the difference in drum notes but weird. I have never considered the mathematical component to playing an instrument. – Ross Bush Dec 22 '21 at 00:34
  • First - "If I measure each 16th note as a beat in 4/4 time..." No. It's no longer 4/4 time if you use a 16th note as the basis of a beat. Second - I encourage you to try the computation with something simpler, say, 60 BPM, and convince yourself that the numbers are the way they should be. – Sean Roberson Dec 22 '21 at 00:35
  • Doh, you were right. I was incorrectly referring to 16th notes while in fact it was 4/4 bars of quarter notes. – Ross Bush Dec 24 '21 at 16:16