Calculate metric modulation tempo changes from note equivalence, subdivision ratios, or time-signature pivots between BPM and BPS.

The selected old note and new note have equal real duration. Tempo uses quarter-note beats.

Metric Modulation Formula

The following formula is used to calculate the Metric Modulation. 

MM = OT × PNO / PNN

Variables:

  • MM is the new bar rate (bars per minute)
  • OT is the old bar rate (bars per minute) 
  • PNN is the number of pivot note values in the new measure 
  • PNO is the number of pivot note values in the old measure 

With an equal-duration pivot pulse, new bar rate = old bar rate × old pivot count / new pivot count. For quarter-note BPM, new tempo = old tempo × new pivot-note fraction / old pivot-note fraction. A time-signature change alone does not change quarter-note BPM.

How to Calculate Metric Modulation?

The following steps outline how to calculate the Metric Modulation.

  1. First, determine the old bar rate. If using quarter-note BPM, divide it by the number of quarter notes in the old bar.
  2. Next, determine the number of pivot note values in the new measure. 
  3. Next, determine the number of pivot note values in the old measure. 
  4. Next, gather the formula from above = MM = OT * PNO / PNN.
  5. Finally, calculate the Metric Modulation.
  6. After inserting the variables and calculating the result, check your answer with the calculator above. 

Example Problem:

Use the following variables as an example problem to test your knowledge.

old bar rate = 84 bars per minute; the pivot pulse stays constant

number of pivot note values in the new measure = 3

number of pivot note values in the old measure = 2

MM = 84 × 2 / 3 = 56 bars per minute. Quarter-note BPM also depends on the notated pivot values, so this bar-rate example is not a quarter-note tempo by itself.