Metric Modulation

The Fundamental Truth of Metric Modulation

What You Just Experienced

The pulse (orange circles, high clicks) stayed at exactly 0.5 seconds throughout.

In the old tempo, we notated this pulse as eighth notes (♪) and grouped every 2 pulses into a quarter note.

In the new tempo, we notated the same pulse as triplet eighths and grouped every 3 pulses into a quarter note.

Because the grouping changed (2 → 3), the beat (blue circles, low clicks) had to change speed. The BPM changed from 60 to 40.

Two Ways to Notate It

Here's the same music notated in two equivalent ways. Both sound identical:

Key insight: All three examples sound identical. The metric modulation notation (Bar 2, second version) makes the constant pulse and the changing beat explicit.

Elliott Carter: Metric Modulation in Action

Elliott Carter pioneered this technique. In "Canaries" from Eight Pieces for Timpani, listen for smooth tempo changes where one duration stays constant:

Carter's metric modulations create seamless transitions between different temporal worlds, allowing multiple "characters" to coexist with independent rhythmic identities.

Build Intuition: Duration and BPM

To calculate metric modulations, you need to understand the relationship between tempo (BPM) and duration (seconds).

Key Questions

If ♩ = 60, how long is ONE quarter note?
Answer: 1 second (60 seconds ÷ 60 beats = 1 second per beat)

If ♩ = 120, how long is ONE quarter note?
Answer: 0.5 seconds (60 seconds ÷ 120 beats = 0.5 seconds per beat)

If ♩ = 100, how long is ONE quarter note?
Answer: 0.6 seconds (60 seconds ÷ 100 beats = 0.6 seconds per beat)

The Method: Duration Stays Constant

Practice Problems

Putting It Together with Carter

Watch the Canaries score while the timpanist performs. Follow the metric modulations in real time and notice how Carter keeps the pulse constant as the notation pivots.