Tempo Modulation Calculator
Find every tempo you can reach from a single pivot.
What is tempo modulation?
Tempo modulation, sometimes called metric modulation, shifts the tempo by reinterpreting a subdivision of the pulse. Turn a quarter-note triplet into the new quarter note and the tempo changes by exactly 3:2; let a dotted quarter become the new quarter and you get 2:3. Every practical modulation is a rational ratio between two note values, and those ratios can be combined.
What the calculator does
Enter a starting tempo, and Calcophony builds the complete matrix of tempos you can reach in a single pivot. Rows show the target note value (what the new beat becomes); columns show the source note value (what that pulse used to be). Each cell reports the resulting BPM, flags close integer matches, and dims tempos that fall outside a practical performing range.
Inputs
- Source BPM and beat unit: the starting tempo and reference pulse for the matrix.
- Tuplet complexity: include triplets, quintuplets, septuplets, and higher if the music calls for them.
- Dotted and double-dotted: toggle compound note values on or off.
- Tolerance: how close a cell must be to a target BPM or round BPM before it is highlighted.
- Target BPM: highlight every cell that modulates to a specific tempo within tolerance.
- Custom ratios: add your own pivot fractions, such as 5:4 or 8:7, alongside the standard note values.
Reading the matrix
Each cell answers one question: if the old [column] becomes the new [row], what is the new 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 chosen tolerance are highlighted, and cells that fall outside your configured practical BPM range are dimmed as impractical.
When to use it
Say you are writing a passage where the pulse needs to shift from 120 to 144 BPM. The matrix shows which pivot gets you there in a single step (in this case, a dotted quarter becoming the new quarter), and which ratios miss by a hair. For multi-step paths between more distant tempos, reach for Metric Modulation, which searches ordered chains of pivots and compares each candidate by final deviation and transition duration. For nested-tuplet durations and click-track subdivisions, see Rhythm & Subdivision.