1.3 Musical Intervals
The interval between notes: the basis of harmony and melody
Key Concepts
- Interval: The distance between two notes, measured in degrees and semitones
- Melodic vs Harmonic: Notes played in sequence or simultaneously
- Number: Unison (1), Second (2), Third (3)... up to the Octave (8)
- Quality: Correct, Greater, Lesser, Increased, Decreased
- Inversion: Interval sum + inversion = 9
- Consonance/Dissonance: Stable sounds versus sounds that require resolution
What is an interval?
Definition
An interval is the distance between two musical notes. This distance is measured by counting the scale degrees from the lowest note to the highest, including both notes. Intervals are the fundamental building blocks of musical harmony: every chord is built by stacking intervals, and every melody moves through a sequence of intervals.
Major third interval: from C to E (counting C-D-E = 3 degrees, a distance of 4 semitones)
Why Are They Important?
Harmony
Chords are constructed by stacking thirds. A major chord = a major third + a minor third.
Melody
The melodies move in leaps or by consecutive steps. Recognising intervals improves sight-reading.
Ear Training
Being able to recognise intervals by ear is essential for transcribing music and playing by ear.
Historical Background
The ancient Greeks (Pythagoras, 6th century BC) were the first to study intervals mathematically, discovering that simple ratios (2:1 for the octave, 3:2 for the fifth) produce consonant sounds. In the Middle Ages, the Church classified intervals as ‘perfectus’ (fourth, fifth, octave) and ‘imperfectus’ (third, sixth), regarding the third as dissonant right up until the Renaissance!
Melodic and Harmonic Intervals
Intervals can be played in two different ways, each with a specific musical function.
Melodic Interval
The two notes are played in succession (one after the other). They form melodies and musical phrases.
Example: The opening of ‘Somewhere Over the Rainbow’ (ascending octave)
Harmonic Interval
The two notes sound simultaneously (together). They form chords and harmonies.
Example: Two notes of a chord played on the piano
Auditory Perception
Melodic intervals are easier for beginners to recognise by ear, because the notes are separated in time. Harmonic intervals require more practice because you need to perceive the ‘quality’ of the combined sound (consonant or dissonant).
Classification by Number
How Do You Count an Interval?
The number of an interval is determined by counting the scale degrees from the starting note to the ending note, including both. For example, from C to E: C (1), D (2), E (3) = a third.
| Number | Name (ITA) | English | Example from Do | Spacing between letters |
|---|---|---|---|---|
| 1 | Unison | Unison / Prime | C - C | 0 letters (same note) |
| 2 | Second | Second | C - D | 1 letter (C → D) |
| 3 | Third | Third | C - E | 2 letters (C → D → E) |
| 4 | Fourth | Fourth | C - F | 3 letters (C → D → E → F) |
| 5 | Fifth | Fifth | C - G | 4 letters |
| 6 | Sixth | Sixth | C - A | 5 letters |
| 7 | Seventh | Seventh | C - B | 6 letters |
| 8 | Octave | Octave | C – C (8th) | 7 letters (full cycle) |
Warning!
The interval is always measured in degrees, not in semitones! C–E♭ and C–E are both thirds (because they span three degrees: C–D–E), but they have different qualities (minor vs major) due to the number of semitones.
Quality of the Intervals
What is quality?
The quality of an interval specifies the exact distance in semitones between the two notes. Two intervals with the same number may have different types. The types are: Perfect, Major, Minor, Augmented and Diminished.
✓ Perfect intervals (Perfect)
The unison, fourth, fifth and octave are called ‘just’ because they have a stable, harmonious sound. In the physics of sound, they have simple frequency ratios (2:1, 3:2, etc.).
- Perfect Unison (P1): 0 semitones (C – C)
- Perfect fourth (P4): 5 semitones (C – F)
- Perfect fifth (P5): 7 semitones (C – G)
- Perfect octave (P8): 12 semitones (C – C)
± Major/Minor Intervals
The second, third, sixth and seventh intervals may be major or minor, differing by a semitone.
- Minor Second (m2): 1 semitone (C – D♭)
- Second Major (M2): 2 semitones (C – D)
- Minor third (m3): 3 semitones (C – E♭)
- Major Third (M3): 4 semitones (C – E)
- Minor sixth (m6): 8 semitones (C – A♭)
- Major Sixth (M6): 9 semitones (C – A)
- Minor seventh (m7): 10 semitones (C – B♭)
- Major Seventh (M7): 11 semitones (C – B)
↑ Augmented Intervals (Aug)
An augmented interval is a semitone wider than the corresponding major or perfect interval.
- Second Augmented (A2): 3 semitones (C – D♯)
- Augmented Fourth (A4): 6 semitones (C – F♯) – ‘Tritone’
- Augmented Fifth (A5): 8 semitones (C – G♯)
↓ Diminished Intervals (Dim)
A diminished interval is a semitone smaller than the corresponding minor or perfect interval.
- Minor third (d3): 2 semitones (C – E♭♭)
- Diminished Fifth (d5): 6 semitones (C – G♭) – ‘Tritone’
- Diminished 7th (d7): 9 semitones (C – B♭♭)
Complete Table of Intervals
| Interval | Abbrev. | Semitones | From Do (C) | Character |
|---|---|---|---|---|
| In Unison, Right | P1 | 0 | C - C | Identity |
| Second Minor | m2 | 1 | C - D♭ | Very tense |
| Second Major | M2 | 2 | C - D | Sweet, melodic |
| Minor Third | m3 | 3 | C - E♭ | Sad, melancholic |
| Major Third | M3 | 4 | C - E | Cheerful, bright |
| Perfect fourth | P4 | 5 | C - F | Stable, open |
| Augmented Fourth (Tritone) | A4 | 6 | C - F♯ | Diabolical, unstable |
| Diminished Fifth (Tritone) | d5 | 6 | C - G♭ | Diabolical, unstable |
| Perfect fifth | P5 | 7 | C - G | Powerful, empty |
| Minor Sixth | m6 | 8 | C - A♭ | Bittersweet |
| Major Sixth | M6 | 9 | C - A | Bright, spacious |
| Minor Seventh | m7 | 10 | C - B♭ | Blues, tension |
| Major Seventh | M7 | 11 | C - B | Tense; requires resolution |
| Perfect octave | P8 | 12 | C - C | Full-bodied, resonant |
Il Tritono: ‘Diabolus in Musica’
The tritone (3 whole tones = 6 semitones) was known as the ‘diabolus in musica’ (the devil in music) in the Middle Ages and was banned from sacred music because of its extremely dissonant and unstable sound. Today, it is fundamental to blues, jazz and rock music. It is the only interval which, when inverted, remains a tritone (A4 ↔ D5).
Consonance and Dissonance
What Do They Mean?
Intervals can be classified according to their tonal stability: consonant intervals sound stable and relaxed, whilst dissonant intervals create tension and require resolution towards a consonant interval.
Perfect Harmonies
Extremely stable, hollow, ‘open’ sounds. Used for millennia across all musical cultures.
- Unison Giusto (P1)
- Perfect fourth (P4)
- Perfect fifth (P5)
- Perfect octave (P8)
Imperfect Harmonies
Sweet, pleasant sounds, but with more ‘colour’ than perfect intervals. Essential for chords.
- Minor Third (m3)
- Major Third (M3)
- Minor Sixth (m6)
- Major Sixth (M6)
Slight Dissonances
They create moderate tension. They are widely used in modern tonal music.
- Second Major (M2)
- Minor seventh (m7)
Sharp Dissonances
Very tense and unstable. They require immediate resolution in classical music, but are used freely in jazz and contemporary music.
- Second Minor (m2)
- Major Seventh (M7)
- Tritone (A4 / d5)
- All augmented/diminished intervals
Historical Development
What is considered consonant has changed over time! In the Middle Ages, only unison, the fourth, the fifth and the octave were considered consonant. Third and sixth intervals were regarded as dissonant until the Renaissance (15th century). In the 20th century, composers such as Debussy, Stravinsky and Schoenberg treated dissonances as stable sounds, no longer in need of resolution.
Reversal of Intervals
What is inversion?
To invert an interval means to raise the lower note by an octave (or lower the higher note by an octave). This creates a new interval with precise mathematical properties.
If you invert a major third (4 semitones), you get a minor sixth (8 semitones). Together: 4 + 8 = 12 (an octave).
Mathematical Rules of Inversion
1. Interval number:
Interval + Inversion = 9
- Unison (1) ↔ Octave (8) → 1 + 8 = 9
- Second (2) ↔ Seventh (7) → 2 + 7 = 9
- Third (3) ↔ Sixth (6) → 3 + 6 = 9
- Year 4 (4) ↔ Year 5 (5) → 4 + 5 = 9
2. Quality of the Interval:
- Major (M) ↔ Minor (m)
- Increased (A) ↔ Decreased (d)
- True (P) ↔ True (P)
Examples of Inversion
| Original Range | Semitones | ↔ | Reversed Interval | Semitones | Sum of Semitones |
|---|---|---|---|---|---|
| Second Minor (m2) | 1 | ↔ | Major Seventh (M7) | 11 | 12 |
| Second Major (M2) | 2 | ↔ | Minor seventh (m7) | 10 | 12 |
| Minor Third (m3) | 3 | ↔ | Major Sixth (M6) | 9 | 12 |
| Major Third (M3) | 4 | ↔ | Minor Sixth (m6) | 8 | 12 |
| Perfect fourth (P4) | 5 | ↔ | Perfect fifth (P5) | 7 | 12 |
| Tritone (A4 or d5) | 6 | ↔ | Tritone (D5 or A4) | 6 | 12 |
Practical Use
Inversion is useful for recognising difficult intervals: if you can’t identify a seventh, try mentally inverting it into a second (which is easier!). It is also essential in voice leading and four-part harmony, where intervals are often inverted to avoid problematic doublings.
Compound Intervals
Intervals Beyond the Octave
Compound intervals are intervals wider than an octave. They are formed by adding an octave (12 semitones) to a simple interval. They are very common in music for the piano, orchestra and jazz voicings.
| Simple Interval | Semitones | + | Octave | = | Compound Interval | Total Semitones |
|---|---|---|---|---|---|---|
| Second (2) | 1-2 | + | Octave (8) | = | Ninth (9) | 13-14 |
| Third (3) | 3-4 | + | Octave (8) | = | Tenth (10) | 15-16 |
| Fourth (4) | 5 | + | Octave (8) | = | Eleventh (11) | 17 |
| Fifth (5) | 7 | + | Octave (8) | = | Twelfth (12) | 19 |
| Sixth (6) | 8-9 | + | Octave (8) | = | Thirteenth (13) | 20-21 |
In Jazz and Modern Music
Jazz chords make extensive use of compound intervals: ninths (9), elevenths (11) and thirteenths (13) are common additions to seventh chords. A ‘C13’ contains: C–E–G–B♭–D–F–A (seven notes!).
At the Piano
Tenths (compound thirds) are widely used in classical and Romantic piano music because they create a rich, full sound. They require large hands or the use of the pedal.
Enharmonic Intervals
Same Sound, Different Name
Two intervals are enharmonic when they have the same number of semitones (and therefore sound identical on the piano) but are written and named differently. This is because the notes are written differently (e.g. F♯ vs G♭).
A Classic Example: The Triton
Augmented Fourth (A4): C – F♯ = 6 semitones
Diminished Fifth (d5): C – G♭ = 6 semitones
They sound identical but have different harmonic functions: A4 tends to expand towards the sixth, whilst d5 tends to contract towards the third.
Common Enharmonic Intervals
| Interval 1 | Example | = | Interval 2 | Example | Semitones |
|---|---|---|---|---|---|
| Augmented Second (A2) | C - D♯ | = | Minor Third (m3) | C - E♭ | 3 |
| Major Third (M3) | C - E | = | Diminished Fourth (d4) | C - F♭ | 4 |
| Augmented Fourth (A4) | C - F♯ | = | Diminished Fifth (d5) | C - G♭ | 6 |
| Augmented Fifth (A5) | C - G♯ | = | Minor Sixth (m6) | C - A♭ | 8 |
| Augmented Sixth (A6) | C - A♯ | = | Minor seventh (m7) | C - B♭ | 10 |
Context is Everything
In music theory, the choice of notation depends on the harmonic context. In the key of G major, F♯ is correct; in the key of A♭ major, it is written as G♭. Although they sound the same, writing intervals correctly helps musicians understand their harmonic function and makes sight-reading easier.
Recognition of Intervals
Why Learn to Recognise Intervals?
Being able to recognise intervals by ear is one of the most important skills for a musician. It enables you to transcribe melodies, learn songs by ear, improvise more effectively and understand music on a deeper level.
Association with Famous Songs
The most effective way to recognise intervals is to link them to the first two notes of well-known songs that you know well. Here is a complete list:
| Interval | Ascendant ↑ | Down ↓ |
|---|---|---|
| Second Minor (m2) | "Jaws Theme" (Jaws) / "Für Elise" (Beethoven) | "Joy to the World" (verse) |
| Second Major (M2) | "Happy Birthday" / "Silent Night" / "Frère Jacques" | "Yesterday" (The Beatles) / "Mary Had a Little Lamb" |
| Minor Third (m3) | "Greensleeves" / "O Sole Mio" / "Smoke on the Water" | "Hey Jude" (chorus) / "Frosty the Snowman" |
| Major Third (M3) | "Oh When the Saints" / "Kumbaya" / "Whilst the Shepherds Watched" | "Swing Low, Sweet Chariot" / "Hey Jude" (beginning) |
| Perfect fourth (P4) | "Here Comes the Bride" / "Amazing Grace" / "O Tannenbaum" | "O Come All Ye Faithful" / "Born Free" |
| Triton (A4/d5) | "The Simpsons Theme" / "Maria" (West Side Story) | "Blue Seven" (Sonny Rollins) |
| Perfect fifth (P5) | "Twinkle Twinkle Little Star" / "Star Wars Theme" | "The Flintstones" / "Feelings" |
| Minor Sixth (m6) | "The Entertainer" / "Black Orpheus" | "Love Story Theme" |
| Major Sixth (M6) | "My Bonnie Lies Over the Ocean" / "NBC Chime" | "Nobody Knows the Trouble I've Seen" |
| Minor seventh (m7) | "There's a Place for Us" (West Side Story) / "Watermelon Man" | "Watermelon Man" (bridge) |
| Major Seventh (M7) | "Take On Me" (A-ha) / "I Love You" (Cole Porter) | "I Love You" (bridge) |
| Octave (P8) | "Somewhere Over the Rainbow" / "Bali Ha'i" | "Willow Weep for Me" |
Recognition Techniques
Melodic Intervals
- Listen to the direction (upwards or downwards)
- Assess the distance (short, medium, long)
- Match it to a well-known song
- Check by counting the semitones (if necessary)
Harmonic Intervals
- Assess the consonance (stable or tense?)
- Identify the flavour (sweet, bland, sour?)
- Listen to the melody by singing the notes one by one
- Compare with known ranges
Recommended Apps and Tools
- Teoria.com – Free ear training exercises
- Perfect Ear – Comprehensive mobile app (Android/iOS)
- EarMaster – Professional software for PC/Mac
- Functional Ear Trainer – An approach based on tonal function
- musictheory.net - Free interactive online exercises
Study Tips
Recommended Exercises
- Practise ear training for 10–15 minutes a day using specialised apps
- Learn one song for each interval (ascending and descending)
- Play all the intervals from every note on your instrument
- Analyse simple melodies by identifying all the intervals
- Sing the intervals a cappella to get a feel for them
- Write intervals on the staff and check them on the piano
Common Mistakes to Avoid
- Confusing quantity and quality (e.g. ‘it’s a third’, but is it more or less?)
- Do not include the starting note in the count (C–E is a third, not a second!)
- Counting semitones rather than degrees to determine the number
- Forgetting that enharmonic intervals have different functions
- Only practise ascending intervals (practise descending ones as well!)
- Studying theory alone without training your ear
Recommended Course of Study
- Weeks 1–2: Learn the theory and terminology. Play all the intervals starting from C
- Weeks 3–4: Memorise songs for each interval. Practise ascending melodies
- Weeks 5–6: Add descending intervals. Practise from all the notes
- Weeks 7–8: Start on harmonic intervals. Focus on consonance and dissonance
- Week 9+: Compound intervals. Practical application in the analysis of musical pieces
Summary
Intervals form the foundation of all tonal music. We have seen that every interval has two components: the number (count of degrees) and the quality (exact distance in semitones). Intervals can be melodic or harmonic, consonant or dissonant, and have precise mathematical properties such as inversion (sum = 9).
Mastering intervals requires constant practice, both theoretical and aural. Make the most of associations with well-known songs, practise using ear-training apps, and, above all, apply the intervals to the actual music you play and listen to every day.
Next Steps
Now that you understand intervals, you’re ready to learn how they’re combined to form:
- Basic Scales (1.4) – Sequences of intervals that form major and minor scales
- Triad (1.5) – Three-note chords formed by stacking thirds
- Theory Index – Back to the full list of lessons
Remember: Intervals are used EVERYWHERE in music. Investing time in mastering them fully (theory and aural training) will pay dividends throughout your musical life!