Metric Modulation Calculator

This free online metric modulation calculator is a specialized tool used in music theory and composition to help musicians and composers determine the precise tempo relationships between different rhythmic subdivisions.

This calculator is particularly useful when dealing with complex tempo changes or when trying to achieve smooth transitions between different meters or rhythmic patterns.

Metric modulation, also known as tempo modulation, is a technique where the pulse of the music shifts from one meter or tempo to another. This shift is often achieved by reinterpreting a rhythmic value from the original tempo as a new rhythmic value in the target tempo. A metric modulation converter simplifies this process by performing the necessary mathematical calculations, allowing musicians to focus on the creative aspects of their work.

Also See : – Note Frequency CalculatorMusic Transposition Calculator

Metric Modulation Calculator

Calculate the new tempo based on a change in the beat subdivision.

ScenarioOld Tempo (BPM)Old Note ValueNew Note ValueNew Tempo (BPM)Description
11201/4 (quarter note)1/3 (triplet quarter note)90Modulating from quarter notes to triplet quarter notes
2601/4 (quarter note)1/6 (triplet eighth note)90Modulating from quarter notes to triplet eighth notes
31001/8 (eighth note)1/5 (quintuplet eighth note)80Modulating from eighth notes to quintuplet eighth notes
4803/8 (dotted quarter note)1/4 (quarter note)120Modulating from dotted quarter notes to quarter notes
51401/4 (quarter note)3/16 (dotted eighth note)186.67Modulating from quarter notes to dotted eighth notes
6961/3 (triplet quarter note)1/4 (quarter note)72Modulating from triplet quarter notes to regular quarter notes
71601/16 (sixteenth note)1/12 (triplet sixteenth note)120Modulating from sixteenth notes to triplet sixteenth notes
8721/4 (quarter note)5/16 (5:4 polyrhythm)90Modulating from quarter notes to a 5:4 polyrhythm

Calculations for each scenario:

  1. New BPM = (120 × 1/4) / (1/3) = 90 BPM
  2. New BPM = (60 × 1/4) / (1/6) = 90 BPM
  3. New BPM = (100 × 1/8) / (1/5) = 80 BPM
  4. New BPM = (80 × 3/8) / (1/4) = 120 BPM
  5. New BPM = (140 × 1/4) / (3/16) ≈ 186.67 BPM
  6. New BPM = (96 × 1/3) / (1/4) = 72 BPM
  7. New BPM = (160 × 1/16) / (1/12) = 120 BPM
  8. New BPM = (72 × 1/4) / (5/16) = 90 BPM

Metric Modulation Calculation Formula

The formula for metric modulation is based on the principle of proportional relationships between note values and tempos.

The general formula can be expressed as:

New BPM = (Old BPM × Old Note Value) / New Note Value

Where:

  • BPM stands for Beats Per Minute
  • Note Value refers to the duration of a note, often expressed as a fraction (e.g., 1/4 for a quarter note, 1/8 for an eighth note)

How to convert dotted quarter note to bpm?

Converting a dotted quarter note to BPM is a common application of metric modulation. A dotted quarter note is equivalent to 1.5 times the duration of a regular quarter note.

To convert a dotted quarter note pulse to BPM, follow these steps:

  1. Determine the current tempo in BPM (let’s call this “Old BPM”).
  2. Identify the note value you’re starting with (in this case, a quarter note, which is 1/4).
  3. Calculate the new note value: A dotted quarter note is 1.5 times a quarter note, so the new note value is 3/8 (1/4 × 1.5 = 3/8).
  4. Apply the metric modulation formula: New BPM = (Old BPM × 1/4) / (3/8)

For example, if the original tempo is 120 BPM: New BPM = (120 × 1/4) / (3/8) = 80 BPM

This means that if you were to play dotted quarter notes at the new tempo of 80 BPM, it would sound equivalent to quarter notes at the original tempo of 120 BPM.

What is an example of metric modulation?

A classic example of metric modulation can be found in the works of composer Elliott Carter, who frequently used this technique.

Let’s consider a hypothetical example to illustrate the concept:

Imagine a piece of music with the following progression:

  1. The music begins at a tempo of 120 BPM, with the quarter note as the primary pulse.
  2. The composer introduces a triplet rhythm (three notes in the space of two) in the quarter note pulse.
  3. These triplet eighth notes gradually become more prominent.
  4. The composer then reinterprets these triplet eighth notes as the new primary pulse.
  5. The music transitions smoothly to a new tempo where these former triplet eighth notes are now perceived as regular eighth notes.

To calculate the new tempo:

  • Old BPM: 120
  • Old Note Value: 1/4 (quarter note)
  • New Note Value: 1/6 (triplet eighth note)

New BPM = (120 × 1/4) / (1/6) = 180 BPM

The music has now modulated from 120 BPM to 180 BPM, but the transition feels smooth because the triplet eighth notes from the original tempo are now perceived as regular eighth notes in the new tempo.

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