Complete Tetrachord Combinations: Major, Melodic Minor, Harmonic Minor, & Harmonic Major Scale Harmony

This post explores all of the possible tetrachords (four-note combinations) in Major, Melodic Minor, Harmonic Minor, & Harmonic Major Harmony.

(Download the accompanying PDF at the bottom of the post.)

These exhaustive lists may appear too information-packed to be useful. (There are 840 combinations per scale.)

I suggest dipping into them occasionally to more deeply explore the vertical (chords) and horizontal (melody) aspects of their all-important parent scales.

You’ll find every standard approach to chord voicing contained herein, as well as many uncommon sonorities.

Some structures may be impossible to play as chords unless one or more of the tones are raised an octave.

Experiment with the lists, and you’ll discover many new things about these commonly-used harmonic palettes (scales).

Below are a few examples of how the lists can be used to create chords and arpeggios (taking some liberties with octave placement and contour):

Bebop Scales & Harmonization

This post explores voice-leading major & minor 6th & 7th chords, dominant♭5, dominant♭9 & fully-diminished 7th chords, and more, through Bebop Major, Bebop Minor, Bebop Dominant, & Bebop Dominant♭5 scales, along with one & two octave scale fingerings, chord alterations & substitutions.

Triads with Doublings and Suspended 4ths (Harmonized Scale: “D” Harmonic Minor)

The following examples show various four-note triadic constructions with doublings and suspensions moved through a “D” Harmonic Minor scale.

The first chord is a commonly played triad with a duplicated root. The intervals, stacked vertically, are as follows: 5th, 4th, & 3rd. The intervallic construction is maintained and moved through the harmonized scale:

Next, the 3d is suspended (replaced with a diatonic fourth) and the resulting 5th, 4th & 4th construction is moved through the scale:

The second voicing type is a triad with a duplicated 3rd. The intervals, stacked vertically, are as follows: 3rd, 4th, & 3rd. The intervallic structure is maintained and moved through the harmonized scale:

Next, the upper 3d is suspended (replaced with a diatonic fourth) and the resulting 3rd, 4th & 4th construction is moved through the scale:

The third construction is a triad with a duplicated 5th. The intervals, stacked vertically, are as follows: 4th, 3rd, & 3rd. The intervallic structure is maintained and moved through the harmonized scale:

Next, the 3d is suspended (replaced with a diatonic fourth) and the resulting 4th, 4th & 2nd construction is moved through the scale:

Try finding additional four-note triads with duplicate notes or “doublings.” Here are two other possible starting chords:

Also, try transferring these voicings onto other string sets. Here is one of the previous chords transposed down an octave and placed on string set 5432:

Finally, experiment with various scales. Harmonic Minor is particularly useful, however, as it contains Major, Minor, Diminished, and Augmented triads.

Tetrachords (Triads with added 2nd’s)

These four-note combinations (tetrachords) consist of triads (major, minor, diminished, and augmented) with major 2nd’s (or 9th’s) added above the root.

Tetrachords are a convenient method for creating unassailably harmonically-correct lines.

I find that improvising with these patterns (rather than intricate arpeggios, chord-scales, and modes, etc.) frees up brain processing power to think more about rhythm, phrasing, and line direction.

Try improvising lines through chord changes using these patterns.

Emphasize half-step resolutions between changing harmonies.

Anchor the patterns in your memory by focusing on the triad forms embedded in these diagrams.

I have written the patterns on the root “C,” but they are easily transposable by shifting the shapes to new root locations.

Major Tetrachord:

Minor Tetrachord:

Diminished Tetrachord:

Augmented Tetrachord:

The Augmented Scale

The augmented scale is a symmetrical hexatonic scale.

It appears in music by composers as varied as Franz Liszt, Alberto Ginastera, Béla Bartók, Milton Babbitt, Arnold Schoenberg, John Coltrane, Oliver Nelson, and Michael Brecker.

There are various ways to derive the augmented scale:

  • start with an augmented triad and add a 1/2 below each tone
  • alternate minor thirds with 1/2 steps
  • combine two augmented triads an augmented second (or minor third) apart: C E G♯ and E♭ G B

Below are fretboard diagrams for the augmented scale, starting on the root C, then moving through the cycle of fourths through all 12 keys.

Try improvising melodic lines, diads, and triads, exploring the symmetries that this unique scale creates.

Root “C”:

Root “F”:

Root “B♭” or “A#”:

Root “E♭” or “D#”:

Root “A♭” or “G#”:

Root “D♭” or “C#”:

Root “G♭” or “F#”:

Root “B”:

Root “E”:

Root “A”:

Root “D”:

Root “G”: