Harmonic minor scale
The harmonic minor scale is a diatonic scale in Western music theory consisting of seven pitches, constructed by raising the seventh scale degree of the natural minor scale by a semitone, which introduces an augmented second interval between the sixth and seventh degrees.[1][2] Its interval pattern from the tonic is whole step, half step, whole step, whole step, half step, augmented second (three half steps), and half step, remaining identical in both ascending and descending forms.[1][2] For example, the A harmonic minor scale comprises the notes A, B, C, D, E, F, G♯, and A.[2] This scale serves primarily as a harmonic framework in classical music, providing a leading tone (the raised seventh degree) that resolves strongly to the tonic, enabling dominant-to-tonic progressions such as the major V chord, which enhances tonal closure absent in the natural minor.[1] Unlike the melodic minor, which alters both the sixth and seventh degrees ascendingly for smoother stepwise motion, the harmonic minor prioritizes chordal functionality over melodic flow, making it foundational for minor-key compositions from the Baroque era onward.[1] The harmonic minor, one of the scale variants of the minor mode that emerged around 1600 during the early transition from modal to tonal systems in Western music, became a standard form by the early 19th century, addressing instabilities in the minor mode by incorporating the leading tone while retaining the minor third from the tonic.[3] Theorists like Jean-Philippe Rameau initially favored the natural minor but acknowledged variants for harmony; by the early 19th century, the harmonic minor became standard, despite debates over its augmented triad (built on the third degree), which some, like Gottfried Weber, viewed as dissonant until rehabilitated by Carl Friedrich Weitzmann in 1853.[3] Today, it remains essential in tonal harmony, influencing genres beyond classical music, though always derived from the natural minor's key signature with an accidental on the seventh degree.[1]Definition and Construction
Scale Degrees and Intervals
The harmonic minor scale is a diatonic scale variant of the natural minor scale, distinguished by raising the seventh scale degree by a half step.[1] This modification preserves the minor tonality while introducing a leading tone that ascends to the tonic.[4] The scale degrees are designated as follows: 1 (tonic), 2 (supertonic), ♭3 (mediant), 4 (subdominant), 5 (dominant), ♭6 (submediant), and 7 (leading tone).[5] These degrees form an interval pattern of whole step (W), half step (H), whole step (W), whole step (W), half step (H), augmented second (W + H), and half step (H).[6] In terms of half steps from the tonic, the cumulative intervals are 0, 2, 3, 5, 7, 8, 11, and 12 (octave).[5] This scale derives from the natural minor by sharpening the seventh degree, which enables the construction of a major triad on the dominant (scale degree 5).[4] For example, in C harmonic minor, the notes are C (1), D (2), E♭ (♭3), F (4), G (5), A♭ (♭6), B (7), returning to C (8).[1] On a piano keyboard, these correspond to white keys for C, D, F, and G, and black keys for E♭ (between D and E), A♭ (between G and A), and B (between A and C in the upper octave).[6] In staff notation, the ascending scale appears as:with the augmented second interval notably spanning from A♭ to B.[6] This foundational structure supports stronger harmonic resolutions, as detailed in the harmonic properties section.[4]C D E♭ F G A♭ B CC D E♭ F G A♭ B C
Examples in Different Keys
The harmonic minor scale is constructed by starting on the tonic of any minor key and applying the fixed interval pattern, resulting in a raised seventh scale degree relative to the natural minor. This section provides concrete examples in the keys of C, A, and E, illustrating the notes, required accidentals, and notation considerations for practical use in composition and performance. In the key of C, the harmonic minor scale consists of the notes C, D, E♭, F, G, A♭, B, C. The key signature for C minor includes three flats (B♭, E♭, A♭), but the harmonic form requires raising the seventh degree from B♭ to B natural via an accidental, typically notated as a natural sign (♮) on B. In treble clef notation, the ascending (and descending, as the form is identical in both directions) scale appears as follows, with the accidental marked on the B:This construction maintains the characteristic augmented second between A♭ (sixth degree) and B (raised seventh).[7][8] For A harmonic minor, begin with the A natural minor notes A, B, C, D, E, F, G and raise the seventh degree G to G♯, yielding A, B, C, D, E, F, G♯, A. A minor has no key signature sharps or flats, so the only accidental is the sharp (♯) on G, placed in the score as needed. In treble clef, the scale is notated ascending and descending identically:Treble clef: C - D - E♭ - F - G - A♭ - B♮ - CTreble clef: C - D - E♭ - F - G - A♭ - B♮ - C
This key is commonly used in classical and folk music due to its lack of key signature, facilitating easier reading for beginners.[9][6] The E harmonic minor scale starts on E with the notes E, F♯, G, A, B, C, D♯, E. The E minor key signature features one sharp (F♯), and the harmonic variant raises the seventh degree D to D♯ with an additional sharp accidental. Treble clef notation for the bidirectional scale is:Treble clef: A - B - C - D - E - F - G♯ - ATreble clef: A - B - C - D - E - F - G♯ - A
Here, the raised D♯ creates the leading tone effect prominent in this key, often employed in violin and orchestral writing.[10][11] Enharmonic equivalents can arise in transpositions to more remote keys; for instance, the raised seventh G♯ in A harmonic minor is enharmonically A♭, though standard notation prefers G♯ to align with the key's conventions and avoid unnecessary flats. A common pitfall during transposition is inconsistently applying the raised seventh relative to the tonic, which may inadvertently revert the scale to natural minor and eliminate the leading tone resolution essential to its harmonic function.[6][12]Treble clef: E - F♯ - G - A - B - C - D♯ - ETreble clef: E - F♯ - G - A - B - C - D♯ - E
Comparison to Other Minor Scales
Versus Natural Minor
The natural minor scale, also known as the Aeolian mode, follows the interval pattern of whole, half, whole, whole, half, whole, whole steps, corresponding to the formula 1, 2, ♭3, 4, 5, ♭6, ♭7 relative to the tonic.[13] In contrast, the harmonic minor scale modifies this structure by raising the seventh scale degree from ♭7 to a natural 7, resulting in the pattern whole, half, whole, whole, half, augmented second, half step.[2] This alteration introduces a leading tone—a half step below the tonic—that strengthens the pull toward resolution, particularly in dominant-to-tonic progressions, which is absent in the natural minor's minor seventh interval (a whole step below the tonic) that creates a more ambiguous ending.[1] The primary structural difference lies in this raised seventh, which enables the construction of a major V chord (or diminished vii°) in the harmonic minor, facilitating the functional harmony central to Western tonal music, whereas the natural minor yields a minor v chord with weaker resolution.[14] Auditory effects further distinguish the two: the natural minor produces a smoother, more melancholic and stepwise flow, while the harmonic minor's augmented second between the ♭6 and 7 creates a distinctive tension and exotic flavor, often evoking a sense of urgency or drama.[13] Historically, the natural minor served as the foundation for diatonic modes in medieval and Renaissance music, reflecting the pure Aeolian mode without alterations.[14] The harmonic minor emerged during the Baroque era (circa 1600–1750) to address the need for stronger cadential resolutions in emerging tonal harmony, as exemplified in works by composers like Johann Sebastian Bach, who employed the raised seventh for melodic and harmonic clarity.[14] For illustration, consider the C minor key:| Scale Degree | Natural Minor | Harmonic Minor |
|---|---|---|
| 1 | C | C |
| 2 | D | D |
| ♭3 | E♭ | E♭ |
| 4 | F | F |
| 5 | G | G |
| ♭6 | A♭ | A♭ |
| ♭7 / 7 | B♭ | B |
Versus Melodic Minor
The melodic minor scale modifies the natural minor by raising both the sixth and seventh scale degrees in its ascending form, resulting in the pattern: 1, 2, ♭3, 4, 5, 6, 7 (intervals: whole, half, whole, whole, whole, whole, half). In contrast, the descending form typically reverts to the natural minor pattern: 1, 2, ♭3, 4, 5, ♭6, ♭7 (intervals: whole, half, whole, whole, half, whole, whole).[14] This bidirectional variability distinguishes it from the harmonic minor, which consistently raises only the seventh degree while keeping the sixth flattened, yielding the fixed pattern: 1, 2, ♭3, 4, 5, ♭6, 7 (intervals: whole, half, whole, whole, half, augmented second, half).[15] The primary structural difference arises from the harmonic minor's retention of the ♭6, which creates an augmented second interval between the sixth and seventh degrees—a feature absent in the ascending melodic minor. This adjustment in the melodic minor eliminates the "awkward" leap, promoting smoother stepwise motion in linear melodies, while the harmonic minor's configuration supports stronger vertical harmonic progressions, such as the major dominant chord (V). Auditory effects include the melodic minor's more fluid, diatonic-like ascent that enhances melodic directionality and resolution toward the tonic, whereas the harmonic minor's augmented second imparts a distinctive, tense character better suited to chordal contexts.[14] The practice of raising both the sixth and seventh scale degrees in the ascending melodic minor emerged during the Baroque era to avoid the augmented second for smoother melodies, as seen in works by composers like Johann Sebastian Bach. The convention of reverting to the natural minor in the descending form became a standard pedagogical tool during the 19th-century Romantic era, aligning with emphases on expressive melodic lines and chromatic flexibility while maintaining tonal coherence.[14] For example, in C minor, the ascending melodic minor proceeds as C–D–E♭–F–G–A–B–C, avoiding the harmonic minor's C–D–E♭–F–G–A♭–B–C leap between A♭ and B; the descending melodic form then follows the natural minor: C–B♭–A♭–G–F–E♭–D–C.[15] This context-dependent application underscores the melodic minor's role in balancing melodic elegance with harmonic functionality.[14]Harmonic Properties
Leading Tone and Resolution
In the harmonic minor scale, the raised seventh scale degree functions as the leading tone, forming a semitone interval with the tonic and creating a powerful tendency to resolve upward to it, thereby enhancing the overall sense of tonality compared to the natural minor scale.[14] This leading tone strengthens the dominant-to-tonic cadence (V-i), a cornerstone of common practice harmony, by introducing a half-step pull that mimics the resolution pattern of the major scale.[16] The presence of the leading tone allows for the construction of a major V chord in minor keys, such as G major (with notes G, B, D) in C harmonic minor, rather than the minor v chord (G minor: G, B♭, D) derived from the natural minor.[14] This major quality in the V chord arises from the raised third (the leading tone itself), which provides greater harmonic tension and a more decisive resolution to the tonic than the weaker pull of the minor v.[16] Rooted in common practice tonality, this alteration ensures the dominant chord's major third avoids the reduced instability of a minor triad on the fifth scale degree, promoting smoother and more conclusive progressions.[14] In typical resolutions, such as the i-V-i or iv-V-i progressions, the leading tone in the V chord moves upward by semitone to the tonic, delivering a sense of closure absent in natural minor cadences.[16] For example, in C harmonic minor, the progression from C minor (C, E♭, G) to G major (G, B, D) and back to C minor highlights the B natural resolving to C, with the full V chord amplifying this motion through its inherent tendency tones.[14] This mechanism underscores the harmonic minor's role in achieving authentic cadential strength within tonal music.[16]Characteristic Augmented Second
The characteristic augmented second interval in the harmonic minor scale appears between the lowered sixth scale degree (♭6) and the raised seventh scale degree (7), encompassing three semitones or an interval of 1.5 whole steps.[17] For instance, in the key of C harmonic minor, this interval spans from A♭ to B.[18] This interval produces a tense, "exotic" sonic quality that contrasts with the smoother stepwise motion typical in Western tonal melodies, often evoking a sense of drama or unease.[19] In melodic contexts, it can approximate the sound of a minor third when voiced closely, contributing to its perceived awkwardness in horizontal lines.[20] Historically, Western composers viewed the augmented second as dissonant and foreign to diatonic frameworks, resulting in its infrequent use in melodic writing compared to the even intervals of the major scale.[17] This perception stemmed from its non-conformance to the hexachordal system of medieval and Renaissance music theory, where such leaps disrupted modal purity.[21] To circumvent the melodic challenges posed by this interval, composers commonly revert to the natural minor scale for descending passages or adopt the melodic minor scale, which raises the sixth degree to form a major second instead.[21] This augmented second arises as a necessary trade-off for the leading tone's strong harmonic resolution, balancing melodic tension against structural benefits.[20] In practice, the interval rarely appears as an explicit melodic leap; for example, in J.S. Bach's chorales, it is typically implied harmonically through the leading tone in V7 chords but avoided in the soprano line to maintain vocal smoothness.[17]Modes of the Harmonic Minor Scale
Mode Formulas and Names
The modes of the harmonic minor scale are obtained through cyclic permutation, or rotation, of its scale degrees (1, 2, ♭3, 4, 5, ♭6, 7), beginning each mode on a successive degree of the parent scale while preserving the pitch collection.[22] This process yields seven distinct modes, each with unique interval structures relative to its own root. By convention, the modes are identified by their starting note relative to the harmonic minor root; for example, in C harmonic minor (C–D–E♭–F–G–A♭–B), the fifth mode begins on G.[22] The following table summarizes the seven modes, including their standard names and scale degree formulas:| Mode | Name | Formula |
|---|---|---|
| 1st | Harmonic minor | 1, 2, ♭3, 4, 5, ♭6, 7 |
| 2nd | Locrian ♮6 | 1, ♭2, ♭3, 4, ♭5, 6, ♭7 |
| 3rd | Ionian ♯5 | 1, 2, 3, 4, ♯5, 6, 7 |
| 4th | Dorian ♯4 | 1, 2, ♭3, ♯4, 5, 6, ♭7 |
| 5th | Phrygian dominant | 1, ♭2, 3, 4, 5, ♭6, ♭7 |
| 6th | Lydian ♯2 | 1, ♯2, 3, ♯4, 5, 6, 7 |
| 7th | Superlocrian ♭♭7 | 1, ♭2, ♭3, ♭4, ♭5, ♭6, ♭♭7 |