How is a note's absolute duration calculated?

The beat (the denominator note) lasts 60 ÷ BPM seconds. A whole note is that beat times the denominator, and every other value is a fraction of the whole note: a quarter is a whole note ÷ 4, an eighth ÷ 8, and so on.

What is a metric modulation?

A metric modulation re-labels the pulse so a note value in the old tempo becomes a different note value at a new tempo while a common subdivision stays constant. Composers like Elliott Carter used it to shift tempo smoothly.

How does the tool compute the new tempo?

It scales the BPM by the ratio of the new pulse note value to the old one. For example moving the felt pulse from a quarter to a triplet-eighth multiplies the tempo by the appropriate ratio so the printed beat changes but the music flows continuously.

Why does the denominator matter for note durations?

BPM counts the denominator note, so the denominator fixes which note value equals one beat. A whole note is always the beat value times the denominator, which keeps every other note value in correct proportion.

Can this help with polyrhythms?

Yes. Compute the duration of each layer's note value and find a common time grid. When two layers' durations share a least common multiple you know where the rhythms realign within the bar.

Time Signature Note Value Converter

A working tool for composers and arrangers who need the exact length of any note value, or who are planning a tempo change via metric modulation rather than a simple tempo marking.

How it works

Every note value has an absolute duration that depends only on the tempo and the note the tempo counts (the time-signature denominator):

beat duration  = 60 / BPM          (one denominator note)
whole note     = beat duration × denominator
note value     = whole note / (relative value)

At 120 BPM with a quarter-note beat (denominator 4): the beat is 0.5 s, the whole note is 0.5 × 4 = 2 s, a quarter is 2 / 4 = 0.5 s, and an eighth is 0.25 s. Triplets divide the whole note into 12 (triplet eighths) or 6 (triplet quarters), and dotted values multiply the base by 1.5.

Metric modulation

A metric modulation changes the tempo by re-interpreting the pulse. Suppose the music is in quarter notes at 90 BPM and you want the triplet-eighth to become the new quarter. The new tempo scales by the ratio of the two pulse note values:

BPM_new = BPM_old × (new pulse value / old pulse value)

The tool reports the old pulse duration, the new tempo, and the new pulse duration so you can write an exact ”♩ = ♪” equivalence in the score.

Tips and notes

Choose the denominator that matches how your conductor or DAW counts the beat — it determines which note equals one click.
Dotted and triplet values are included because they are where timing errors most often creep in; the table gives them to four decimal places.
For polyrhythms, look for note durations whose ratio is a simple fraction (3:2, 4:3) — those are the ones that lock cleanly within a bar.

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