Intervals: The Building Blocks of Harmony

An interval is simply the distance between two pitches — but naming that distance precisely requires two separate pieces of information, and one of the two real interval categories traces directly back to the overtone series from Chapter 1.

Naming an Interval: Number and Quality

Every interval has a number (2nd, 3rd, 4th, 5th, 6th, 7th, octave — counted by letter names, inclusive of both notes) and a quality (perfect, major, or minor, among others). C to E is a third by number (C, D, E — three letter names); its quality (major, in this case) depends on the exact number of semitones between the two notes.

Perfect Intervals: A Real Physical Reason for the Name

Only four interval numbers ever take the quality "perfect": the unison, the fourth, the fifth, and the octave. This isn't an arbitrary label — it's a direct real consequence of Chapter 1's own overtone series. Each of these intervals corresponds to a genuinely simple, low-integer frequency ratio: unison is 1:1, the octave is 2:1, the perfect fifth is 3:2, and the perfect fourth is 4:3. Those simple ratios made these four intervals sound so stable and consonant, historically, that they were treated as a separate category entirely — "perfect" in the sense of already complete, needing no further classification into major or minor at all.

Major and Minor Intervals

Every other interval number — the 2nd, 3rd, 6th, and 7th — takes either a major or minor quality instead, corresponding to real, less simple frequency ratios and, historically, less immediate consonance than the perfect intervals.

Interval Inversion

Flip an interval upside-down — move the lower note up an octave instead — and you get its inversion, governed by a real, fixed rule: the original interval's number and its inversion's number always add up to 9. A quality rule accompanies it: major inverts to minor (and minor to major), while perfect always inverts to perfect.

Hands-On Exercises