Transposing tempos

If you have a track in one of the following common tempos, and want to pitch it up or down by a few semitones, changing its key and tempo proportionally, these tables will tell you its new tempo.

If you're adventurous, you can sidestep this whole issue by using what I like to call pitched tempos.

Tempo (BPM)	-2 semitones	-1 semitone	+1 semitone	+2 semitones
80	71.272	75.510	84.757	89.797
85	75.726	80.229	90.054	95.409
90	80.181	84.949	95.352	101.022
95	84.635	89.668	100.649	106.634
100	89.090	94.387	105.946	112.246
105	93.544	99.107	111.244	117.859
110	97.999	103.826	116.541	123.471
115	102.453	108.546	121.838	129.083
120	106.908	113.265	127.136	134.695
125	111.362	117.984	132.433	140.308
130	115.817	122.704	137.730	145.920
135	120.271	127.423	143.028	151.532
140	124.726	132.142	148.325	157.145

Source code

I tabulated these using a simple C program, transpose-bpm.c:

/* BPM transposer, for ANSI C, by Zoe Blade, 2024-04-04 */

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

void transposeBeatsPerMinute(int beatsPerMinute) {
    int semitones;

    /*
     * The new tempo = the old tempo * 2 ^ (the pitch change in semitones / 12)
     */

    for (semitones = -2; semitones < 3; semitones++) {
        printf("%3d\t%+3d\t%7.3f\n", beatsPerMinute, semitones, beatsPerMinute * pow(2, semitones / 12.0));
    }

    return;
}

int main(int argc, char *argv[]) {
    int beatsPerMinute;

    printf("BPM\tSts\tBPM\n");
    printf("===\t===\t=======\n\n");

    if (argc == 1) {
        for (beatsPerMinute = 80; beatsPerMinute < 145; beatsPerMinute += 5) {
            transposeBeatsPerMinute(beatsPerMinute);
        }
    } else {
        transposeBeatsPerMinute(atoi(argv[1]));
    }

    return 0;
}

C programs: BPM to milliseconds | Transposing tempos

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Transposing tempos

Source code