Example of Written Intervals Increased: Understanding Augmented Intervals in Music Theory
When musicians talk about “written intervals increased,” they are referring to augmented intervals—the musical distance between two pitches that has been enlarged by one chromatic semitone (a half step) beyond its perfect or major form. This concept is essential for composers, arrangers, and performers who need to notate tension‑filled harmonies, modulate to distant keys, or create distinctive melodic colors. In this article we will explore what augmented intervals are, how they are written on the staff, and provide concrete examples that illustrate their sound and function. By the end, you’ll be able to identify, write, and use augmented intervals confidently in any musical context.
What Is an Augmented (Increased) Interval?
An interval is the pitch distance between two notes. In Western music theory, intervals are classified by their quality (perfect, major, minor, diminished, augmented) and their size (unison, second, third, etc.). An augmented interval occurs when a perfect or major interval is raised by one half step, making it larger than its standard counterpart Small thing, real impact..
- Perfect intervals (unison, fourth, fifth, octave) become augmented when increased by a semitone.
- Example: A perfect fifth (C–G) → augmented fifth (C–G♯).
- Major intervals (second, third, sixth, seventh) become augmented when increased by a semitone.
- Example: A major third (C–E) → augmented third (C–E♯).
Note: Augmented intervals are enharmonically equivalent to certain diminished intervals (e.g., an augmented fourth sounds the same as a diminished fifth), but their written spelling matters for harmonic analysis and voice‑leading.
How to Write Augmented Intervals on the Staff
Writing an augmented interval correctly involves two steps:
- Determine the interval size (the number of staff positions between the notes, counting both lines and spaces).
- Adjust the accidentals so that the interval is exactly one half step larger than its perfect or major form.
Step‑by‑Step Procedure
| Step | Action | Example (C to ?Think about it: | | 4 | Verify that the interval now spans the correct number of half steps (use a chromatic scale if needed). ) | |------|--------|-------------------| | 1 | Identify the generic interval (e.| | 2 | Write the perfect or major version of that interval using no accidentals (or the key signature). , fifth = 5 staff positions). Also, | | 3 | Add a sharp (♯) to the upper note or a flat (♭) to the lower note to increase the distance by one semitone. | C to G is a fifth. | Perfect fifth: C–G (no accidentals). Worth adding: g. Which means | Augmented fifth: C–G♯ (sharp on G) or C♭–G (flat on C). | C to G♯ = 8 half steps (perfect fifth = 7, +1 = 8) Worth keeping that in mind. That's the whole idea..
When the lower note already carries an accidental, you may need to add a double sharp (𝄪) or double flat (𝄫) to achieve the required increase Small thing, real impact..
Common Augmented Intervals and Their Written Forms
Below is a table that shows the most frequently encountered augmented intervals, their generic size, the number of half steps they contain, and two typical ways to notate them starting from C. Feel free to transpose these patterns to any root note No workaround needed..
Worth pausing on this one.
| Interval | Generic Size | Half‑Steps | Notation from C (Upper‑note sharp) | Notation from C (Lower‑note flat) |
|---|---|---|---|---|
| Augmented unison (aug1) | 1 | 1 | C–C♯ | C♭–C |
| Augmented second (aug2) | 2 | 3 | C–D♯ | C♭–D |
| Augmented third (aug3) | 3 | 5 | C–E♯ | C♭–E |
| Augmented fourth (aug4) | 4 | 6 | C–F♯ | C♭–F |
| Augmented fifth (aug5) | 5 | 8 | C–G♯ | C♭–G |
| Augmented sixth (aug6) | 6 | 10 | C–A♯ | C♭–A |
| Augmented seventh (aug7) | 7 | 12 | C–B♯ | C♭–B |
| Augmented octave (aug8) | 8 | 15 | C–C♯ (next octave) | C♭–C (next octave) |
Key observations:
- The augmented fourth (also called the tritone) and augmented fifth are the most harmonically tense intervals, often resolving inward or outward by half‑step motion.
- The augmented unison and augmented octave are rarely used in melodic writing but appear in certain contemporary or avant‑garde contexts where a pitch is deliberately “bent” upward.
- Enharmonic equivalents (e.g., C–E♯ = C–F) exist, but the spelling changes the harmonic function: an augmented third implies a leading‑tone relationship to the note a half step below the upper note, whereas a major third does not.
Practical Examples in Musical Contexts
1. Augmented Fourth (Tritone) in Dominant Seventh Chords
A dominant seventh chord (V⁷) contains a major triad plus a minor seventh. On top of that, when the fifth of that chord is raised, you get a V⁷♯5 (also notated V⁷⁺5). The interval between the root and the raised fifth is an augmented fifth.
- C⁷♯5: C–E–G♯–B♭
- Written intervals: C–E (major third), E–G♯ (minor third), G♯–B♭ (minor third), C–G♯ (augmented fifth).
- The augmented fifth creates a strong pull toward the tonic (F major) because G♯ wants to resolve up to A, and B♭ wants to resolve down to A.
2. Augmented Second in Harmonic Minor Scales
In the harmonic minor scale,
2. Augmented Second in Harmonic Minor Scales
In a natural minor scale the interval between the sixth and seventh degrees is a whole step (e.g.Because of that, , in A minor: F–G). Raising the seventh degree to create the leading tone (A B C D E F G♯) turns the interval between the sixth and seventh into an augmented second (F–G♯).
| Scale degree | Example (A harmonic minor) | Interval | Half‑steps |
|---|---|---|---|
| ♭6 → ♮7 | F → G♯ | Augmented second (aug2) | 3 |
| ♭7 → 1 | G♯ → A | Augmented unison (aug1) | 1 (if spelled as G♯–A) |
The augmented second is a hallmark of the harmonic minor’s “exotic” color. Composers often treat it as a chromatic mediants—a stepwise motion that resolves outward: the raised seventh (G♯) typically resolves up to the tonic (A), while the preceding whole step (F–G♯) can resolve down to E or up to G♯‑A, depending on voice‑leading choices Worth keeping that in mind. Less friction, more output..
Voice‑leading tip: Because the augmented second spans three half‑steps, it can be approached by step from either direction without creating a dissonance that demands immediate resolution. Even so, when the upper note is the leading tone (G♯), it strongly pulls toward the tonic (A), making the interval a powerful vehicle for tension‑release patterns That's the part that actually makes a difference..
3. Augmented Third in Jazz and Chromatic Harmony
The augmented third (five half‑steps) is a common chromatic interval in jazz, especially in altered dominant chords and minor‑key progressions Simple as that..
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C⁺⁷ (C–E–G♯–B♭) contains an augmented third between C and G♯ (C–E is a major third, E–G♯ is an augmented second, G♯–B♭ is a minor third). The augmented third creates a “bluey” tension that resolves outward to a perfect fourth (C–F) or inward to a major sixth (E–F♯).
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In minor‑key ii‑V‑i progressions, the ii° chord often carries an augmented third (e.g., in A minor: B–D–F♯). The interval B–F♯ is an augmented fourth (tritone), but the B–D is a major third and D–F♯ is an augmented second, collectively contributing to the chord’s dissonant character It's one of those things that adds up. Nothing fancy..
Practical tip: When writing voice‑leading for augmented thirds, treat the outer notes as a chromatic neighbor pair. Resolve the upper note by step (up or down) while allowing the lower note to move stepwise in the opposite direction, preserving the interval’s shape.
4. Augmented Sixth in Minor‑Key Contexts
The augmented sixth (ten half‑steps) is a striking interval that appears in the Italian sixth (It⁶) and German sixth (Ge⁶) chords. In a minor key, the interval between the lowered sixth degree (♭6) and the raised fourth degree (♯4) is an augmented sixth.
It sounds simple, but the gap is usually here.
- In C harmonic minor (C–D–E♭–F–G–A–B), the interval between A♭ (♭6) and F♯ (♯4) is an augmented sixth (A♭–F♯). This interval resolves outward to a perfect fifth (A♭–E) and inward to a minor third (C–E♭), depending on the voice‑leading scheme.
Voice‑leading rule: The augmented sixth resolves outward to a perfect fifth (or inward to a minor third) because the interval contains a built‑in tendency to “split” into two half‑step motions that move in opposite directions.
5. Augmented Octave (Double Unison) – Rare but Expressive
The augmented octave (fifteen half‑steps) is essentially a perfect octave plus a semitone. It is rarely used melodically but appears in contemporary music to create a sense of pitch inflation or to point out a harmonic shift.
- Example: In a spectral composition, a line may ascend from C₄ to C♯₅, spanning an augmented octave. The extra semitone adds a subtle “stretch” that can be exploited for timbral effects.
Synthesis: Why Augmented Intervals Matter
Augmented intervals are the **chromatic
6. Augmented Fourth (Tritone) – The Ultimate Tension Generator
The augmented fourth (six half-steps), also known as the tritone, is perhaps the most notorious augmented interval in Western music. Its symmetrical nature and dissonant quality make it a central player in both harmonic and melodic contexts.
- In equal temperament, the tritone divides the octave symmetrically, creating ambiguity between major and minor tonal centers. This duality is exploited in jazz to construct tritone substitutions, where a dominant seventh chord is replaced by another dominant seventh chord a tritone away (e.g., G⁷ ↔ D♭⁷), resulting in smooth voice leading and rich harmonic color.
- Melodically, the tritone often appears in bebop lines, where it functions as an expressive leap that propels the phrase forward. Composers like Bartók and Stravinsky also used the tritone to destabilize tonal expectations, embedding it within modal scales and polytonal constructs.
Compositional strategy: To harness the tritone’s power without overwhelming the listener, resolve each side of the interval by contrary motion—one voice moves up by step, the other down—restoring stability while preserving the harmonic journey Which is the point..
7. Augmented Second – Exotic Flavor and Modal Ambiguity
The augmented second (three half-steps) introduces a distinctive brightness that evokes Middle Eastern maqams and Spanish modalities.
- In harmonic minor scales, the interval between the flatted second and natural sixth degrees creates this augmented second (e.g., in A harmonic minor: B♭–F♯). This interval contributes to the scale’s characteristic “exotic” sound, frequently employed in flamenco guitar and film scoring to evoke mystery or longing.
- Composers such as Mozart and Beethoven occasionally used the augmented second to add chromatic spice to otherwise diatonic passages, particularly in developmental sections where tonal ambiguity heightens dramatic tension.
Performance note: Due to its wide span, the augmented second can challenge singers and wind players. Care should be taken to balance the interval dynamically, ensuring clarity rather than harshness in execution.
8. Contextual Function vs. Fixed Identity
While augmented intervals possess inherent dissonance, their emotional impact depends heavily on contextual usage. The same augmented fourth may signal resolution in a cadential dominant (resolving to a perfect fifth) or suggest modal mixture when embedded within a Dorian or Mixolydian framework. Similarly, an augmented sixth might herald a dramatic modulation in Romantic literature or serve as a fleeting chromatic embellishment in impressionist harmony.
Understanding these nuances allows composers and performers to wield augmented intervals not merely as technical devices, but as expressive tools capable of shaping narrative arc, defining genre identity, and guiding listener perception through complex harmonic landscapes Most people skip this — try not to..
Conclusion
Augmented intervals—from the familiar tritone to the rarefied augmented octave—are far more than mathematical curiosities. In real terms, they function as vital agents of tension, color, and directional motion across diverse musical styles. By recognizing their unique properties and applying thoughtful voice-leading principles, musicians can reach new dimensions of creativity, transforming potential dissonance into compelling musical storytelling. Whether navigating the blue notes of jazz, the modal inflections of world music, or the chromatic explorations of contemporary classical composition, the augmented family remains an indispensable resource for any serious student or practitioner of music theory and composition.
