Intervals

Why This Matters

Intervals are the DNA of music—every melody you hum, every chord that moves you, and every harmonic progression you analyze breaks down into these fundamental pitch relationships. You're being tested on your ability to identify intervals by ear and on paper, understand their role in building chords and scales, and recognize how composers use consonance and dissonance to create tension and resolution. This isn't just abstract theory; intervals determine whether a piece sounds happy or sad, stable or restless, resolved or yearning for more.

The key to mastering intervals is understanding that they fall into distinct categories based on their acoustic quality and harmonic function. Perfect intervals provide stability, thirds and sixths give music its emotional color, and seconds and sevenths create the tension that makes resolution satisfying. Don't just memorize the half-step counts—know what each interval does in a musical context and how it sounds compared to others.

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Perfect Intervals: The Stable Foundation

Perfect intervals—the unison, fourth, fifth, and octave—are called "perfect" because they maintain their quality in both major and minor contexts. These intervals have the simplest frequency ratios, which is why they sound so stable and foundational to the human ear.

Perfect Unison

• Zero half steps between pitches—two voices or instruments playing the exact same note
• Maximum consonance creates a reinforcing effect, strengthening melodic lines in orchestration
• Foundational in unison passages where composers want power without harmonic complexity

Perfect Fourth

• Five half steps (e.g., C to F)—the inversion of the perfect fifth
• Context-dependent consonance—stable in most situations, but creates tension when the lower note is the bass (this is why fourths resolve in suspensions)
• Melodic staple appearing in countless melodies and as the interval between many adjacent guitar strings

Perfect Fifth

• Seven half steps (e.g., C to G)—the most consonant interval after the unison and octave
• Foundational to Western harmony—defines key centers, root motion in chord progressions, and the structure of the overtone series
• Power chords in rock music use only roots and fifths, demonstrating the interval's raw stability

Perfect Octave

• Twelve half steps—the same pitch class at a different register
• Perceived as equivalent pitches due to the 2:1 frequency ratio, the simplest ratio after unison
• Defines the boundaries of scales and allows melodies to be doubled at the octave for richness

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Thirds and Sixths: The Color Intervals

These intervals determine the emotional quality of chords and melodies. Thirds and sixths are considered imperfect consonances—pleasant and stable, but with more character than perfect intervals.

Minor Third

• Three half steps (e.g., C to E♭)—the defining interval of minor chords
• Melancholic, introspective quality that gives minor keys their characteristic sadness
• Stacked minor thirds create diminished chords; combined with a major third, they form minor triads

Major Third

• Four half steps (e.g., C to E)—the defining interval of major chords
• Bright, happy quality that establishes major tonality and optimistic musical character
• Critical for chord identification—the third determines whether a triad is major or minor

Minor Sixth

• Eight half steps (e.g., C to A♭)—the inversion of the major third
• Bittersweet, longing quality frequently used in jazz voicings and romantic melodies
• Enharmonically complex—can function differently depending on harmonic context

Major Sixth

• Nine half steps (e.g., C to A)—the inversion of the minor third
• Warm, consonant sound often used in "added sixth" chords and as a melodic interval
• Common in folk and pop melodies—think of the opening interval of "My Bonnie Lies Over the Ocean"

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Seconds and Sevenths: The Tension Builders

These intervals create dissonance that demands resolution, driving harmonic motion forward. Seconds and sevenths are inversions of each other—a second inverted becomes a seventh, and vice versa.

Minor Second

• One half step (e.g., C to D♭)—the smallest interval in Western music
• Maximum melodic dissonance creates tension, suspense, and the "crunchy" sound of clusters
• Essential for chromatic motion and voice leading, where smooth half-step resolution is prized

Major Second

• Two half steps (e.g., C to D)—the whole step that defines major and minor scales
• Mild dissonance that sounds natural in melodies but creates tension in sustained harmony
• Building block of scales—the pattern of whole and half steps determines scale quality

Minor Seventh

• Ten half steps (e.g., C to B♭)—found in dominant seventh and minor seventh chords
• Bluesy, unresolved quality that creates forward momentum in jazz and blues progressions
• Defines dominant function—the minor seventh above the root in V7 chords creates the pull toward resolution

Major Seventh

• Eleven half steps (e.g., C to B)—just one half step short of the octave
• Lush, sophisticated dissonance prized in jazz for its dreamy, floating quality
• Characteristic of major seventh chords—the "jazz sound" that adds color without strong resolution tendency

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The Tritone: The Interval of Maximum Tension

The tritone occupies a unique position—exactly halfway through the octave. Its 1:√2 frequency ratio is the most complex of any interval, explaining its inherent instability.

Tritone (Augmented Fourth/Diminished Fifth)

• Six half steps (e.g., C to F♯ or C to G♭)—divides the octave exactly in half
• Maximum harmonic instability historically called "diabolus in musica" (the devil in music) due to its tension
• Essential to dominant function—the tritone between the 3rd and 7th of a dominant seventh chord creates the need to resolve

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Quick Reference Table

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Self-Check Questions

1. Which two intervals are inversions of each other and both considered "perfect," yet one can sound dissonant depending on its position in a chord?

2. A chord sounds sad and introspective rather than bright and happy. Which interval is most responsible for this quality, and how many half steps does it contain?

3. Compare and contrast the minor seventh and major seventh: How do they differ in half steps, sound quality, and harmonic function?

4. If you're asked to identify the interval that creates the strongest pull toward resolution in a dominant seventh chord, which interval should you name and why?

5. You hear two intervals that are only one half step apart in size, but one sounds completely stable while the other sounds extremely tense. What are these two intervals, and what principle does this illustrate about consonance and dissonance?