Musical Interval Calculator

In short An interval is the distance between two notes, and in equal temperament it is simply a count of semitones: C to E is four, which is a major third. What that count hides is that equal temperament is a compromise, and this page shows the size of it. Tuning that is genuinely in tune uses small whole-number frequency ratios — a pure fifth is 3 to 2, a pure major third is 5 to 4 — because those ratios make the overtones of the two notes line up instead of beating against each other. Equal temperament deliberately misses them so that all twelve keys work equally well, and the misses are not all small. The fifth is 1.96 cents flat of pure, which nobody can hear. The major third is 13.69 cents SHARP of pure, which a trained ear hears immediately on a sustained chord. That single number explains a great deal: why an unaccompanied choir or a string quartet sounds sweeter than a piano on the same chord, why barbershop singers describe "locking" a chord, and why guitarists complain that their instrument is never quite in tune. Singers and string players bend toward the pure ratios instinctively; a keyboard or a fretted instrument physically cannot. The trade was made deliberately in the eighteenth century, because tuning any one key purely makes the distant keys unusable, and being equally slightly wrong everywhere is what lets music modulate freely.