Metric Modulation Calculator
Plan multi-step tempo paths and compare them at a glance.
Why multiple steps?
A single-pivot tempo modulation can only land on ratios that exist between two note values. Getting from 120 to 100 BPM in one clean step would need a 5:6 pivot, which is only playable if the parts can notate quintuplets against sextuplets. Split the move into two steps and you can often reach the same target with simpler pivots: 120 → 108 (via a 9:10 approximation or a dotted-quarter pivot), then 108 → 100 through another manageable ratio. The cost is more steps to perform; the payoff is cleaner rhythms at each transition.
What the calculator does
Enter a start BPM, a target BPM, and the maximum number of steps you are 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 final deviation from the target, tuplet complexity, and the wall-clock duration needed to execute it, so you can choose between simpler rhythms spread over more steps or fewer steps with 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 candidate tempos to a practical BPM window.
- Prefer clean: bias the scoring toward simple pivot ratios such as 2:3 and 3:4.
Outputs per path
- Ordered steps: each with the pivot note values (from/to) and the BPM after the step.
- Final 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
Reach for Metric Modulation when a single-pivot leap between two tempos feels too abrupt, or when you are writing in a tradition where every tempo change must be a notated pivot rather than a hidden click-track edit. It is equally useful in teaching: a student can rehearse a modulation step by step, hearing each pivot land before moving on. When you are still exploring where to land from a fixed source BPM, start with Tempo Modulation instead; the ratio matrix shows every single-step destination at once.