Metric Modulation Calculator
Multi-step tempo paths, ordered and scored.
Why multiple steps?
Single-pivot tempo modulations can only land on ratios that exist between two note values. To get from 120 to 100 BPM in one clean step, you'd need a 5:6 pivot — playable, but only if you can notate quintuplets against sixtuplets. Split the move into two steps and you can often reach the same target using simpler pivots: 120 → 108 (via a 9:10 approximation or a dotted-quarter pivot) then 108 → 100 by another manageable ratio. The cost is more pivots to perform; the payoff is simpler rhythms at each transition.
What the calculator does
Enter a start BPM, a target BPM, and the maximum number of steps you're willing to take. Calcophony performs a breadth-first search over pivot combinations and returns every ordered chain that lands within tolerance of the target. Each path is annotated with its cumulative deviation, tuplet complexity, and the wall-clock duration needed to execute it. You choose between simpler rhythms with more steps or fewer steps at the cost of harder pivots.
Inputs
- Start and target BPM — the tempos you want to bridge.
- Max steps — how deep to search (more steps = more candidate paths).
- Max tuplet — the largest tuplet division to consider at each pivot.
- BPM tolerance — how close to the target a final BPM has to land.
- Search range — clamp intermediate tempos to a practical BPM window.
- Prefer clean — bias the scoring toward integer-BPM intermediates.
Outputs per path
- Ordered steps — each with the pivot note values (from/to) and the BPM after the step.
- Cumulative deviation — drift from target in BPM at each intermediate stage.
- Total deviation — absolute distance from target at the end of the path.
- Complexity score — sum of tuplet complexities across the path; lower is easier to perform.
- Transition duration — wall-clock time to execute the modulation at the given tempos.
When to use it
Composing a transition from a slow section to a fast one and the 1.6× leap is too abrupt. Writing in a tradition where every tempo change has to be a notated pivot (Carter, Ferneyhough, much of post-war modernism). Teaching a student to perform a modulation that would otherwise require a click track to sell. For single-pivot exploration from a fixed source BPM, use Tempo Modulation instead — that's the right tool when you're not yet sure where you want to land.