Musical Intervals: Semitone Counts & Names

The distances between notes, pinned to the exact semitone counts and the simple ratios that name them.

Short answer: a musical interval is the distance between two pitches, and musicians describe it two ways that agree closely but not perfectly. One way counts semitones (a perfect fifth is 7, a major third is 4, a minor third is 3). The other uses the frequency ratio between the notes (an octave is exactly 2:1, a perfect fifth is close to 3:2). Names like perfect, major, minor, augmented, and diminished describe how many semitones an interval spans; the simple ratios explain why some of those intervals sound so stable.

Counting in semitones

The semitone, one step of the twelve that fill an octave, is the ruler for every interval. To name an interval you count the half steps between its two notes. Because an interval is a distance, it is the same size ascending or descending: a perfect fifth is seven semitones whether you climb up to it or drop down to it. That fixed count is what lets a musician label an interval reliably, by ear or on paper, and it is the first thing most ear-training courses drill. Once the number is secure, everything else about the interval, its spelling, its function in a key, its mood, hangs off it.

Perfect versus major and minor

Interval names fall into two families. The unison, fourth, fifth, and octave are called perfect, historically the most stable and consonant intervals. The second, third, sixth, and seventh come in major and minor versions a semitone apart. The clearest example is the third: a major third is 4 semitones and a minor third is 3. That single-semitone gap is a large part of why major harmony sounds bright and minor harmony sounds darker, even though the two thirds differ by the smallest step the system allows.

Augmented and diminished

Any interval can be stretched or squeezed by a half step. Augmented means one semitone wider than usual; diminished means one semitone narrower. Take the fifth: the perfect fifth is 7 semitones, the diminished fifth is 6, and the augmented fifth is 8. The same logic runs across the whole set: add a half step to augment, remove one to diminish. This is also why two intervals can cover the same keyboard distance yet carry different names, depending on how the notes are spelled.

The ratios behind the names

Long before anyone counted semitones, intervals were understood as ratios of string lengths or frequencies, and the most consonant ones turn out to be the simplest ratios. In just intonation the octave is exactly 2:1, the perfect fifth is 3:2, the perfect fourth is 4:3, and the major third is 5:4. The smaller the numbers, the more the harmonics of the two tones line up, and the smoother the blend the ear reports. That is the physical reason the perfect intervals earned their name: their ratios are the simplest of all, so their partials reinforce rather than beat against each other.

Just intonation versus equal temperament

Here is a subtlety worth knowing. The tidy semitone counts assume equal temperament (12-TET), the tuning almost every piano and digital instrument uses, in which the octave is split into twelve exactly equal steps of 100 cents each. That system is a deliberate compromise. It keeps the octave pure at 2:1 but bends every other interval slightly away from its just ratio, so that a keyboard can play in any key without retuning. The equal-tempered fifth is about two cents narrower than the pure 3:2, a gap small enough that most listeners never hear it. The equal-tempered major third is the larger compromise, sitting roughly 14 cents wide of the pure 5:4, which is why a sustained third on a piano sounds a touch more restless than the same third tuned justly. Neither tuning is wrong; they answer different questions, one about pure blend, the other about playing freely across all twelve keys.

Why the counts matter

Once the semitone count is fixed, the sound is broadly fixed too. Play any two notes seven semitones apart and you get the open, stable ring of a perfect fifth; four semitones give the bright major third; three give the plaintive minor third. Learning to attach a number, and behind it a ratio, to a sound is exactly the bridge between theory and ear. It is what turns that sounds nice into that is a perfect fifth, and here is why it rings. The names are not arbitrary labels; they are a compact record of both distance and blend.

Common misconceptions

A few ideas trip up beginners. First, an interval's name is not the same as the notes' letter names: C to E and C to F♭ cover the same four keyboard semitones but are spelled as a major third and a diminished fourth. Second, perfect does not mean in tune; it is a category inherited from medieval theory, not a claim about tuning accuracy. Third, the simple ratios describe just intonation, not the equal temperament your keyboard actually plays, so the two systems agree on the octave and diverge slightly on everything else. Keeping those three points straight prevents most of the confusion that surrounds interval names.

Put a name to what you hear

Related reading

• Interval ear-training guide: a step-by-step way to learn these intervals by ear.
• What is an octave?: the twelve semitones that every interval is built from.
• What are cents in music?: the fine unit used to compare just and tempered intervals.

Sources: Wikipedia, Interval (music) and Perfect fifth; Diana Deutsch (ed.), The Psychology of Music (Academic Press); Brian C. J. Moore, An Introduction to the Psychology of Hearing (Brill).