Metric modulation

Definition

Metric modulation is a tempo change in which a duration of the old tempo becomes, by equivalence, a different duration of the new tempo. It is written as an equation above the staff, for example "eighth-note triplet = eighth note": the triplets that previously fit in a quarter note are now ordinary eighths, so the new quarter note is faster. The term is associated above all with Elliott Carter (Sonata for Cello and Piano, 1948; String Quartet No. 1, 1951), but the principle has existed for centuries in the proportions of the Renaissance (tempus perfectum/imperfectum) and in "double movement" passages.

The formula

New BPM = old BPM × (number of units per quarter note in the old tempo) ÷ (number of units per quarter note in the new tempo).

• At 120 BPM, "eighth-note triplet = eighth note": in the old tempo there are 3 triplets per quarter note, in the new 2 eighths per quarter note → 120 × 3 ÷ 2 = 180 BPM.
• At 120 BPM, "sixteenth note = eighth-note triplet": 120 × 4 ÷ 3 = 160 BPM.
• In 12/8 at 90 BPM measured on the quarter note, "dotted quarter = quarter": the dotted quarter is worth 1.5 quarters → 90 ÷ 1.5 = 60 BPM for the new quarter note of the 4/4. The perceived pulse doesn't change (60 beats per minute before and after), only the subdivision changes from ternary to binary: it is the way to go from 12/8 to 4/4 without jolts.
• At 140 BPM, "eighth = quarter": the new tempo is 280... or, read the other way around, the section sounds in half-time at 70.

Why it works

The modulation exploits a subdivision that is already audible before the change: if the listener already has the triplets in their head, when they become the new pulse the change seems inevitable. It is the rhythmic equivalent of a pivot chord in harmonic modulation.

Useful types for a producer

• Triplet → eighth (3/2 acceleration): sudden energy, typical of progressive metal and modern jazz.
• Eighth → triplet (2/3 slowdown): a section that "sits down."
• Dotted quarter → quarter: swing/12/8 ↔ straight passage, or from Afro 6/8 to 4/4.
• Half-time and double-time are metric modulations with ratios of 1:2 and 2:1, the simplest.
• Implied: the drums stay in tempo but the groove sounds in triplets (or in groups of 5 sixteenths) as if the tempo had changed; it is also called metric illusion or implied metric modulation and is frequent in Meshuggah, Animals As Leaders, in the jazz of Tigran Hamasyan.

Example in A minor

Verse at 120 BPM in 4/4: Am – F – C – G, hi-hat in eighth-note triplets in the last bar of the verse. Chorus: the triplet becomes the eighth → 180 BPM, same progression Am – F – C – G but with one chord every two bars (so the harmonic rhythm in seconds stays nearly the same: 2 s per chord before, 2.67 s after). The listener perceives an explosion of energy without losing the reference.

In FL Studio

• Create a tempo automation (right-click on the tempo display → Create automation clip) and set a sharp jump (step) exactly at the start of the bar.
• Before the jump, write the triplets in the Piano Roll with "1/3 beat" snap: after the jump, the same notes written as eighths (1/2 beat) must have the same duration in milliseconds. At 120 BPM an eighth-note triplet lasts 166.7 ms; at 180 BPM an eighth lasts 166.7 ms: check it in the note tooltip or with a tempo-synced delay.
• Synced delays and LFOs follow the new tempo: make sure the tails don't "jump" at the change point.

Practical exercise

1. Program 4 bars at 100 BPM with a shaker in eighth-note triplets, then a "triplet = eighth" modulation to 150 BPM. Confirm with the metronome that the shaker doesn't change speed in the transition.
2. Do the opposite: from 150 to 100 with "eighth = triplet."
3. Listen to a track with a half-time change and note the phrase that "prepares" the change.

Related entries

"Meter, subdivision, half-time and double-time," "Advanced half-time and double-time," "Tempo map, rubato and tempo changes," "Triplets and irregular groupings," "Polyrhythm, hemiola and polymeter." Texts: Kostka-Payne (chapter on rhythm in the 20th century), Elliott Carter, writings on time (collection "Collected Essays and Lectures").