In brief
An interval is a relationship between two pitches. In Western staff-based terminology, its name combines a number, based on note letters, with a quality such as major, minor or perfect.
What you’ll learn
- Count interval numbers inclusively.
- Identify common interval qualities in twelve-tone equal temperament.
- Distinguish an interval's size from the musical roles of its notes.
Useful first: Pitch and frequency
Two notes, one relationship
Play or sing two notes in succession and you have a melodic interval; sound them together and you have a harmonic interval. Direction matters when describing a melody: an ascending third and a descending third have opposite contours. The same size can feel different when placed near a phrase ending, over a new bass note or in another register.
Before memorising names, practise saying same, higher or lower. Then distinguish a small step from a wider leap. These simple observations keep interval work connected to hearing. A numerical answer is not the only useful result: you may also notice that a leap is followed by a return, that a repeated note gains emphasis, or that two parts move in different directions.
References: [1]
Number and quality answer different questions
To find the number of a notated interval, count letter names inclusively. C to E spans C, D, E, so it is a third. C to F spans four letters, so it is a fourth. Accidentals do not change that letter count. C to E-flat remains a third, but its quality changes because its sounding size is smaller than C to E.
In the usual twelve-tone equal-tempered model, a major third spans four semitones and a minor third three. A perfect fourth spans five and a perfect fifth seven. Seconds, thirds, sixths and sevenths commonly have major or minor qualities; unisons, fourths, fifths and octaves belong to the perfect family. Augmented and diminished qualities extend both families. “Perfect” is a classification, not an instruction to prefer that interval.
References: [1]
Why spelling matters
C to D-sharp and C to E-flat can sound the same on an equal-tempered piano, but their written interval names differ. C to D-sharp is an augmented second because the letter span is two; C to E-flat is a minor third because it spans three. The notation can communicate how a note relates to a scale, chord or moving line.
Use both checks when naming an interval: letter span first, sounding distance second. Reversing the order often leads to a plausible sound label with the wrong spelling. In other tuning systems, enharmonically equivalent piano keys need not represent identical frequencies, so be explicit about your model. Staff-based interval names are a valuable vocabulary, but other traditions may organise pitch relationships through different concepts.
References: [2]
Move from isolated drills to phrases
Practising an isolated interval can build recognition, but a melody gives its notes roles. In a C-major setting, C to E moves from degree one to degree three; D to F moves from degree two to degree four and is a smaller third. Both are thirds, yet their relationships to the tonic differ. Train interval size and scale-degree hearing together rather than asking one skill to replace the other.
Invent a short phrase with one deliberate leap, then sing it in another comfortable register. Keep its contour and rhythm recognisable. Ask whether the leap functions as an opening, a high point or a return. If you use a familiar song as a memory aid, remember that its rhythm, harmony and timbre are also cues. Eventually you want to recognise the relationship beyond that one remembered setting.
References: [2]
A worked example
Three spellings to inspect
Use a keyboard or a drawing of one, and keep all examples ascending within an octave. The semitone counts below assume twelve-tone equal temperament.
- C to E: count C–D–E for a third; count four semitone steps for major quality. The result is a major third.
- C to E-flat: the same three-letter span now covers three semitones, giving a minor third.
- C to D-sharp: count C–D for a second; its three-semitone size makes it an augmented second.
- Play the last two examples. They share piano keys at the upper end, yet preserve different written information.
- Now place E-flat in C–E-flat–G and D-sharp in B–D-sharp–F-sharp. Consider how the spellings make the two chord structures easier to read.
Notice: Interval naming combines notation and sound. Counting semitones alone loses information that may help explain the musical context.
Try it / Listening experiment
Hear a relationship.
Two short, pure tones: a starting pitch followed by a higher pitch. This model uses twelve-tone equal temperament. It does not model a raga’s intonation or ornamentation.
Frequency ratio: 27/12 ≈ 1.4983
Choose an interval, then listen to the two tones.
Start with a comfortable device volume. Audio plays only when you press Listen.
Try it yourself
Name three intervals and explain your method.
- Identify D to F-sharp, E to F and G to D above.
- For each pair, write its inclusive letter count.
- Check the semitone count before assigning a quality.
Compare your thinking
D to F-sharp is a major third: three letters, four semitones. E to F is a minor second: two letters, one semitone. G to the D above is a perfect fifth: five letters, seven semitones. Count movement between adjacent keys, not the number of keys including both endpoints.
What to remember
- Interval number follows letter span; quality refines the size.
- Enharmonic spellings can have different interval names.
- Hear intervals in phrases as well as in isolation.
References & further study
Use these sources to check terminology and continue studying. The worked examples and exercises are written for this collection.
- Introduction to Intervals
Robert Hutchinson, University of Puget Sound
Supports the distinction between interval number and quality and standard interval categories.
- Intervals
Andre Mount, Fundamentals, Function, and Form
Develops interval spelling, quality and the relationship between notation and sounding distance.
Educational writing by Burnt Chapati. Send a correction or suggest a source.