The minor thirteenth is a compound interval that spans 20 semitones (or 10 whole steps) above the root note. It consists of a minor tenth (16 semitones) plus a minor third (3 semitones). In practical terms, it's equivalent to a minor seventh chord with added ninth, eleventh, and thirteenth.

Historical Context

This interval gained prominence during the late Romantic period and became a staple in jazz harmony during the 20th century. Composers like Debussy and Ravel began experimenting with these extended sonorities, while jazz musicians like Duke Ellington and Bill Evans fully incorporated them into their harmonic vocabulary.

Technical Construction

Interval Structure

• Root (1)
• Minor third (b3)
• Perfect fifth (5)
• Minor seventh (b7)
• Major ninth (9)
• Perfect eleventh (11)
• Minor thirteenth (b13)

Chord Formula

The complete minor thirteenth chord is expressed as: 1-b3-5-b7-9-11-b13

Practical Applications

Jazz Usage

In jazz, minor thirteenth chords often function as tonic minor chords (i in minor keys) or as predominant chords (ii in major keys). A classic progression would be: Dm13 - G7alt - Cmaj7

Contemporary Music

Modern R&B and neo-soul frequently use minor thirteenth voicings for rich harmonic textures. Try this progression: F#m13 - Bm11 - E13 - Amaj9

Ear Training Exercises

Level 1: Interval Recognition

Practice identifying the minor thirteenth by comparing it to an octave plus minor sixth. Play C to Ab across two octaves and internalize the sound.

Level 2: Chord Identification

Listen to various minor chord extensions (m7, m9, m11, m13) and train your ear to distinguish the characteristic color of the minor thirteenth.

Level 3: Improvisation

Over a Dm13 chord, improvise using D Dorian (D-E-F-G-A-B-C) with occasional chromatic approaches to the b13 (Bb).

Instrument-Specific Voicings

Piano

Left hand: Root + b7 | Right hand: 9-11-b13 (no fifth needed). For Cm13: LH (C-Bb) RH (D-F-Ab)

Guitar

Try this movable shape (x-5-3-5-4-5 for Am13). Omit the root for tighter voicings when playing with a bassist.

Classical Examples

Analyze how Ravel uses minor thirteenth sonorities in "Jeux d'eau" through arpeggiated figurations that imply the extended harmony without vertical stacking.

Common Variations

• Minor thirteenth (b13): The standard form
• Minor major thirteenth: With natural 13th (rare)
• Minor thirteenth flat nine: Adds extra tension

Composition Tips

When writing for ensembles, distribute the extensions across instruments rather than stacking everything in one part. The string section might take the basic minor seventh while woodwinds handle the upper extensions.