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<h1>Harmonic Minor Scale</h1>
<p>Harmonic minor is the natural minor scale with a raised seventh degree. The reason for the raising is harmonic: in a minor key, you want a major V7 chord (not a minor v7) to get the strong dominant pull toward the tonic. Raising the seventh creates that leading tone — the half-step pull from the seventh up to the root — while keeping all the other minor scale notes intact. Classical minor key cadences run on harmonic minor harmony. It also produces an exotic, slightly Middle Eastern quality from the augmented second between the sixth and seventh.</p>

<h2>Construction</h2>
<pre>
A natural minor:  A B C D E F G  A
A harmonic minor: A B C D E F G# A
                               ↑ raised 7th (leading tone)

Formula:      1  2  ♭3  4  5  ♭6  7
Step pattern: W  H  W   W  H  A2  H

A2 = augmented second (3 semitones) between ♭6 and raised 7th (F and G# in A).
This A2 is the characteristic interval — it sounds Middle Eastern or dramatic.
</pre>

<h2>Harmonic Minor in Common Keys</h2>

<table>
  <thead><tr><th>Key</th><th>Natural minor</th><th>Harmonic minor (raised 7th)</th><th>Leading tone</th></tr></thead>
  <tbody>
    <tr><td>A harmonic minor</td><td>A B C D E F G</td><td>A B C D E F G#</td><td>G#</td></tr>
    <tr><td>E harmonic minor</td><td>E F# G A B C D</td><td>E F# G A B C D#</td><td>D#</td></tr>
    <tr><td>D harmonic minor</td><td>D E F G A B♭ C</td><td>D E F G A B♭ C#</td><td>C#</td></tr>
    <tr><td>G harmonic minor</td><td>G A B♭ C D E♭ F</td><td>G A B♭ C D E♭ F#</td><td>F#</td></tr>
    <tr><td>B harmonic minor</td><td>B C# D E F# G A</td><td>B C# D E F# G A#</td><td>A#</td></tr>
    <tr><td>C harmonic minor</td><td>C D E♭ F G A♭ B♭</td><td>C D E♭ F G A♭ B</td><td>B</td></tr>
  </tbody>
</table>

<h2>Why It Exists: The V7 Chord in Minor</h2>
<pre>
In A natural minor, the V chord is Em7:
  E G B D  — minor 7th chord, no leading tone
  Em7 → Am: G → A is a whole step — weak pull

Raise the 7th (G → G#):
  V chord becomes E7: E G# B D — dominant 7th chord
  E7 → Am: G# → A is a half step — strong resolution (leading tone!)

This is why V7-i (E7→Am) is a strong cadence in minor key music.
Classical composers used this constantly — Bach, Mozart, Beethoven.
The harmonic minor scale is what makes that V7 chord available
while keeping the other natural minor notes intact.
</pre>

<h2>Diatonic Chords of A Harmonic Minor</h2>

<table>
  <thead><tr><th>Degree</th><th>Chord</th><th>Quality</th><th>Function</th></tr></thead>
  <tbody>
    <tr><td>i</td><td>Am(maj7)</td><td>Minor-major 7th</td><td>Tonic (exotic sound due to M7)</td></tr>
    <tr><td>ii°</td><td>Bm7♭5</td><td>Half-diminished</td><td>Pre-dominant</td></tr>
    <tr><td>♭III+</td><td>Cmaj7#5</td><td>Augmented major 7th</td><td>Tonic substitute (unstable)</td></tr>
    <tr><td>iv</td><td>Dm7</td><td>Minor 7th</td><td>Subdominant</td></tr>
    <tr><td>V7</td><td>E7</td><td>Dominant 7th</td><td>Dominant — strong pull to i</td></tr>
    <tr><td>♭VI</td><td>Fmaj7</td><td>Major 7th</td><td>Subtonic major</td></tr>
    <tr><td>vii°</td><td>G#dim7</td><td>Fully diminished</td><td>Dominant function (leading tone chord)</td></tr>
  </tbody>
</table>

<h2>The Augmented Second (A2)</h2>
<p>The interval between the ♭6 and the raised 7th (F and G# in A harmonic minor = 3 semitones = augmented second) is the scale's most distinctive feature. In Western classical music, composers sometimes considered this interval awkward in vocal lines — which is why melodic minor was developed (raises the 6th too, smoothing the jump). But in Middle Eastern, gypsy, and neoclassical guitar contexts, the augmented second is the point — it's the exotic, ornamental leap that defines the style.</p>
<pre>
A harmonic minor: ... E F . . G# A
                        ↑ aug. 2nd ↑
                   ♭6   skip    raised 7th

The "skip" of 3 semitones in the middle of the scale is the sound.
Gypsy jazz (Django Reinhardt), flamenco, klezmer, and neoclassical metal
all exploit this interval deliberately.
</pre>

<h2>Modes of Harmonic Minor</h2>

<table>
  <thead><tr><th>Mode</th><th>Common name</th><th>Use case</th></tr></thead>
  <tbody>
    <tr><td>1st</td><td>Harmonic minor</td><td>Over Im or Im(maj7) chords</td></tr>
    <tr><td>2nd</td><td>Locrian ♮6</td><td>Over m7♭5 in minor key (rare)</td></tr>
    <tr><td>3rd</td><td>Ionian #5 (Augmented major)</td><td>Over maj7#5 chords (uncommon)</td></tr>
    <tr><td>4th</td><td>Dorian #4 (Ukrainian Dorian)</td><td>Exotic folk sound</td></tr>
    <tr><td>5th</td><td>Phrygian dominant</td><td>Over V7 in minor key — flamenco, klezmer, jazz</td></tr>
    <tr><td>6th</td><td>Lydian #2</td><td>Exotic, rare</td></tr>
    <tr><td>7th</td><td>Diminished altered (Ultra Locrian)</td><td>Over dim7 or V7♭9♭5 chords</td></tr>
  </tbody>
</table>

<h2>References</h2>
<ul>
  <li>Levine — <em>The Jazz Theory Book</em></li>
  <li>Aldwell &amp; Schachter — <em>Harmony and Voice Leading</em></li>
  <li><a href="https://www.musictheory.net/lessons/24" target="_blank" rel="noopener">musictheory.net — Minor Scales ↗</a></li>
</ul>
