Intervals: Naming the Distance
Two notes, one distance. Count the letters for the number, count the semitones for the quality — and learn the flip that turns a third into a sixth.
Builds on: 2.1 The Major Scale
Number: count the letters
An interval is the distance between two notes, and every one has a two-part name. The first part is a number, found by counting letter names from the lower note to the upper one, including both: C up to E is C, D, E — three letters, a third. C to G is a fifth; C to the next C an octave (eighth); C to itself a unison. Letters only: C to E♭ is still a third, because it still spans three letter names.
Quality: count the semitones
The number is coarse; two thirds can differ by a semitone. The second part of the name, the quality, fixes that. Unisons, fourths, fifths and octaves come in one natural size and are called perfect (5, 7 and 12 semitones); seconds, thirds, sixths and sevenths come in a larger major size and a smaller minor size one semitone below it. Shrink a minor or perfect interval by another semitone and it is diminished; stretch a major or perfect one and it is augmented. The augmented fourth and diminished fifth are the same six semitones — the tritone, which splits the octave exactly in half.
The major scale is the ruler: every interval from the tonic up to a scale degree is major or perfect. C to E is a major third (4 semitones); the minor third (C to E♭) is the one that makes minor keys minor.
Consonant and dissonant
Intervals with simple frequency ratios sound settled — consonant: the octave (2:1), the fifth (3:2), the fourth (4:3), and the thirds and sixths. The seconds and sevenths and the tritone sound tense — dissonant — and want to move. Music needs both: dissonance is not a mistake but the source of motion, resolving into consonance the way the leading tone resolves into the tonic.
Inversion: flip it over
Move the lower note up an octave and the interval turns upside down: C–E (a third) becomes E–C (a sixth). The rule is exact — the numbers add up to 9 (3 + 6, 2 + 7, 4 + 5), and the qualities swap: major becomes minor, minor major, augmented diminished; perfect stays perfect. A major third inverts to a minor sixth (4 + 8 = 12 semitones); a perfect fifth to a perfect fourth. Intervals larger than an octave are called compound (a ninth is a second plus an octave) and keep the quality of their simple form.
C–E♭ and C–D♯ are both three semitones, but the first is a minor third and the second an augmented second. Spelling follows the key: in C minor the note is E♭ and the interval a third. The ear cannot tell; the page can.
The lab lets you build any interval on any root, up or down, see it on the staff and the keys, and hear it both ways. The table above is also on the reference page, with a song for each entry — that is the next lesson.
🎼 Lab — Interval Builder
Choose a root, an interval and a direction. The two notes appear on the staff (melodic, then as a chord), light up on the piano, and play one after the other and together.
- Build a major third on C, then a minor third: one semitone less, a whole mood less.
- Build a perfect fifth up, then the same interval down — read the inversion readout.
- Try the tritone (6 semitones). Listen to how much it wants to move.
Work it by hand — 0 / 3
No multiple choice here: compute the value and type it. Suffixes like 2.5k or 20m are understood; answers within ±2% count.