Tempo Modulation Calculator
Every BPM ratio from a single source tempo.
What is tempo modulation?
Tempo modulation — sometimes called metric modulation — is the technique of shifting tempo by reinterpreting a sub-division. If an eighth-note triplet in the old tempo becomes the new quarter note, the tempo changes exactly by a 3:2 ratio; a dotted quarter becoming the new quarter gives you 2:3. Every practical modulation is a rational ratio between two note values, and those ratios compose.
What the calculator does
Enter a source BPM and the calculator builds the full matrix of resulting tempos you can reach in a single pivot. Rows are the target note value (what the new quarter note becomes); columns are the source note value (what that pulse used to be). Each cell shows the resulting BPM, flags integer matches within tolerance, and marks tempos that fall outside practical range.
Inputs
- Source BPM — the starting tempo, referenced to the quarter note.
- Tuplet complexity — include triplets, quintuplets, septuplets up to whatever limit is musically useful for the piece.
- Dotted and double-dotted — toggle compound note values independently.
- Integer tolerance — how close to a round BPM a cell has to land before it gets flagged as "clean."
- Target BPM — highlight every cell that modulates to a specific tempo, within tolerance.
- Custom ratios — add your own pivot fractions (e.g., 5:4, 8:7) alongside the standard note values.
Reading the matrix
Every cell answers a single question: "If the old [column] becomes the new [row], what is the new quarter-note BPM?" The math is exact — Calcophony uses true fractional arithmetic, so there is no rounding drift. Cells that land on an integer BPM within your tolerance are highlighted; cells that fall outside the 10–300 BPM range are dimmed as impractical.
When to use it
Composing a passage where the pulse needs to shift from 120 to 144? The matrix shows which pivot gets you there in one step (dotted quarter = quarter, as it happens) and which ratios don't quite land. For multi-step paths between distant tempos, use Metric Modulation instead — that module searches ordered chains of pivots and reports cumulative deviation. For nested-tuplet durations and click-track subdivisions, use Rhythm & Subdivision.