Intervals: the distances your ear actually hears

Here is a strange fact hiding in plain sight: your ear barely cares which notes you play. Drag a whole melody up five semitones in Live and every single note changes, yet it is obviously the same melody. What survived the move is the set of distances between the notes. Those distances are called intervals, and they, not the notes themselves, are what your ear actually listens to.

Taste them

Each button below is one interval: a fixed distance between two tones. Press Hear it and work through them slowly. Don't try to name the feelings yet, just notice that each distance has one:

Now move the base slider while an interval plays. The notes change, the flavor doesn't. A major third is bright and a semitone rubs no matter where you put them, which is the lead paragraph's claim made audible: the flavor lives in the distance, not in the notes.

Counting the distance

On the-piano-roll, an interval is simply a row count. One row is a semitone, the smallest step, and every interval is some number of them: the minor third is three rows, the major third four, the perfect fifth seven, the octave twelve. The traditional names (third, fifth) come from counting steps along a scale, which is its own article; for now the numbers in the demo's buttons are the honest measure, and they are what the piano roll shows you directly. Count rows between any two notes and you have named the interval's size, wherever it sits.

Why they have flavors

The flavors are not taste or tradition; they are physics your ear performs for free. Two notes a perfect fifth apart vibrate in a 3:2 relationship: their waves realign constantly, the sum settles, and you hear it as open and stable, what musicians call consonance. The major third is 5:4, a slightly longer pattern, sweet rather than hollow. The semitone and the tritone have no tidy small-number ratio at all, so the waves never settle and you hear the churn: dissonance, the rub the demo made obvious. Watch the sum line in the canvas flip between calm and boiling as you switch buttons; that line is the physics. The full arithmetic lives in The math behind music. (One honest footnote: the piano roll's intervals are nudged a hair away from these pure ratios so that all twelve keys can share one tuning. Why, and what it costs, is the temperament story, coming later in the math trail.)

Helmholtz worked out the physical basis of consonance in the 1860s, and Plomp and Levelt pinned down the modern version experimentally a century later: roughness is what your ear reports when two tones crowd the same critical band. The references below are the deep end.

In your music

Intervals are the working unit of nearly everything this site teaches. Chords are intervals stacked: a major chord is a major third with a perfect fifth around it, which is why the demo's 5:4 button sounds like the inside of happiness. Basslines against leads are intervals in motion, which is the whole subject of counterpoint. And when the Theory Aide extension names a chord in your Live set, it is doing exactly what you did above: measuring the distances between simultaneous notes and recognizing the flavor. Your ear has been fluent in intervals all along; now you know what it was tasting.