Harmonic minor

The borrowed leading tone

The natural minor scale has no leading tone. The article The leading tone explains it with A minor: between G and A lies a whole tone, the dominant would then be E–G–B, a minor triad, and that does not pull. That is why composers artificially raise the seventh degree in minor: G becomes G♯, Em becomes E major. This scale is called harmonic minor.

The home page sums it up like this: the seventh degree is raised so that the dominant pulls more strongly to the tonic. The exercise page on scale ear training shows the blueprint: natural minor follows the pattern whole, half, whole, whole, half, whole, whole. Harmonic minor raises the seventh degree by a semitone.

The price: the augmented second

The raised seventh degree has a side effect. Between F and G♯ in A minor a distance of a tone and a half arises, an augmented second. The article calls the step characteristic, awkward and hard to sing. It gives harmonic minor its exotic, eastern-sounding flavour.

Because this leap can be disturbing in a melody, there is a third variant, melodic minor: ascending, the sixth and seventh degrees are raised, descending the scale returns to the natural form.

Em or E? The difference in sound

The difference lies in only one note, but it changes the character of the ending. Compare both versions:

In the first example the middle chord is the minor triad Em. It closes softly and without pull. In the second example the middle chord is E major with the leading tone G♯, and the ending in A minor sounds decisive. The page Diatonic chords describes the same contrast: in natural minor the fifth degree is a minor chord that lacks the leading tone. For an effective ending you raise the seventh degree.

What changes in the chords

When the seventh degree is raised, three chords of the key change. The other four stay the same. The table shows the changes in A minor:

The Cadences page records that in minor the dominant is raised from v (minor) to V (major) for an effective ending, that is, to harmonic minor. See also Full close (authentic cadence).

The article The diminished seventh shows a consequence: if in A minor you build a four-note chord from thirds on the seventh degree G♯, you get G♯–B–D–F, a diminished seventh chord. It is a by-product of the borrowed leading tone, a degree that does not exist at all in natural minor.

Harmonic minor in sheet music

In real pieces the raised seventh degree often occurs as a single accidental. Two examples from the archive:

Piano

• Für Elise Ludwig van Beethoven, WoO 59 · piano · 3 pages

  In 3/8, “Poco moto” above the first system. In bar 3 the right hand has E–G♯–B, the left E and G♯: the E major triad with the leading tone G♯. In bar 4 the left hand follows with A–E–A, the ending in A minor.

• Menuett g-Moll BWV Anh. 115, from the Notebook for Anna Magdalena Bach · piano · 1 page

  Two flats in the key signature, 3/4, G minor. In bar 7 the left hand has A–F♯–G, in bars 27, 29 and 31 F♯ occurs in the course of the music, although the key signature contains only B♭ and E♭. Shortly before the end, in bar 31, F♯ leads to G. The PDF notes that the piece is attributed to Christian Petzold.

Common mistakes

• Writing the raise into the key signature: The G♯ always appears as an accidental within the bar, never at the start of the line. It applies until the barline.
• Reading the augmented second as a “third leap”: Between F and G♯ lie a tone and a half; on the piano that sounds like a minor third. It is nevertheless written as a second.
• Confusing harmonic and melodic minor: Harmonic minor raises only the seventh degree and applies in both directions. Melodic raises the sixth and seventh degrees ascending.