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PitchInterval NumberSemitone and Whole ToneMajor and Minor IntervalsPerfect IntervalsInterval InversionConsonance and DissonanceEnharmonicScale

An interval is the distance between two notes. That sounds like a throwaway line, but it hides the step everyone skips: a distance is not one thing, it is two — how many letter names you pass, and how many semitones you pass.

Miss this, and everything downstream — chords, scales, keys — stays fuzzy.

Degree and semitones

Two questions, both of which must be answered:

• Degree: counting from the lower note up, how many letter names are included. C to E is

C, D, E — three names — so it is a third.

• Semitones: how many half steps lie between them. From C to E: C–C♯–D–D♯–E, four semitones.

Degree reads letter names only. Semitones read positions on the keyboard only. Two rulers, each measuring something different — and neither is optional. Because a "third" can be C–E (four semitones) or D–F (three semitones). They cannot possibly be the same kind of third.

That is where major and minor intervals come from: a third of four semitones is a major third; a third of three semitones is a minor third. Semitones decide the quality; the degree decides the name.

Diagram: same degree, two semitone counts

Listen: a major third

Hear each note alone, then hear them sound together. That combined ring is the most direct impression of a major third.

Why "perfect" intervals are perfect

Unisons, fourths, fifths and octaves are not called major or minor — they are called perfect. That is not habit, it is history: their frequency ratios are the simplest. An octave is 2:1, a fifth 3:2, a fourth 4:3. In the harmonic series they appear among the earliest partials, which is why they sound the emptiest and least coloured.

Hence the rule: perfect intervals have no major or minor form, only augmented or diminished. Widen a perfect fifth by a semitone and it becomes an augmented fifth; narrow it and it becomes diminished. See Perfect Intervals.

Inversion: what happens when you flip it

Move the upper note down an octave (or the lower one up) and the interval inverts. One rule covers all of it:

The degrees add up to 9. The quality flips (major ↔ minor, augmented ↔ diminished). Perfect intervals stay perfect.

• Major third (3) + minor sixth (6) = 9 ✓
• Perfect fifth (5) + perfect fourth (4) = 9 ✓

Inversion halves what you have to memorise: learn up to the fifth, derive everything above it. Details in Interval Inversion.

Consonance and dissonance

To the ear, intervals fall into consonant and dissonant — but the line is not absolute. It is a gradient:

Western harmony's whole "tension → resolution" engine is built on this gradient — see Consonance and Dissonance. For a concrete case, listen to a cadence; Cadence has examples.

Common misconceptions

• "A third is three semitones." No. A third is a degree (three letter names); semitones are

a separate count. C–E is four semitones and D–F is three, and both are thirds.

• "An augmented fourth and a diminished fifth are the same interval." They sound alike (six

semitones each) but are written and function differently. C–F♯ expands outward; C–G♭ contracts inward. This is the enharmonic phenomenon.

• "Perfect means in tune." It does not. "Perfect" here refers to the **simplest frequency

ratio**, nothing to do with intonation.

• "Bigger intervals are harder to hear." Not so. The octave is the widest of all and one of the

easiest to identify — because the two notes sound like "the same note".

• "Just count keys on the piano." That gives you semitones only. Degrees must be counted on the

staff, where key signatures and accidentals do apply. The gap between the two counts is exactly where enharmonics and double sharps come from.

Next

Intervals are the building blocks of scales and the smallest parts of chords. To train your ear on them, see interval ear training, or use the interval trainer on the main site. :::

Sources

• 音程的度数与音数定义属乐理通则，各版教科书表述一致，本文为原创表述
• 《欢乐颂》《致爱丽丝》主题音高走向依通行乐谱（公有领域）

Used for fact-checking only; all prose is original.