Categories
Books Chords Composition Tools Inversions Permutations & Combinations Quartal Harmony Tetrachords Uncategorized

Two New Books!

Three & Four-Note Chord Compendiums: Permutation-Based Harmony Workbooks for Guitarists

I’m excited to announce the publication of two new books, both available worldwide on Amazon.com!

Three & Four-Note Chord Compendiums: Permutation-Based Harmony Workbooks for Guitarists

The Four-Note Chord Compendium is the first mathematically-complete book on four-part guitar harmony ever published. 

Nearly 400 pages in length, it contains 5,535 unique chord forms for analysis and exploration: every possible combination of four notes on the instrument.

Also included: suggestions for fingerings, practice approach, and harmonic analysis.

An all-encompassing encyclopedic text, and an essential part of every guitarist’s reference library, this permutation-based workbook will enable you to:

  • Explore all of the possibilities for four-part harmony on the guitar
  • Develop a personal harmonic language through the discovery of unique chord voicings and harmonies
  • Improve analytical skills
  • Expand your harmonic palette exponentially
  • Reinforce your current knowledge base by the comprehensive review of four-note chords and arpeggios

Price: $29.99

Available exclusively from Amazon.com. Please click here to view samples and purchase on Amazon.com


The Three-Note Chord Compendium is the first mathematically-complete book on three-part guitar harmony ever published. 

Over 150 pages in length, it contains 1,820 unique chord forms for analysis and exploration: every possible combination of three notes on the instrument.

Also included: suggestions for fingerings, practice approach, and harmonic analysis.

An all-encompassing encyclopedic text, and an essential part of every guitarist’s reference library, this permutation-based workbook will enable you to:

  • Explore all of the possibilities for three-part harmony on the guitar
  • Develop a personal harmonic language through the discovery of unique chord voicings and harmonies
  • Improve analytical skills
  • Expand your harmonic palette exponentially
  • Reinforce your current knowledge base by the comprehensive review of three-note chords and arpeggios

Price: $19.99

Available exclusively from Amazon.com. Please click here to view samples and purchase on Amazon.com

Categories
Chord Cycles Chord Progressions Chords Harmonic Motion Harmonized Scales Intervals Inversions Suspensions Tetrachords Triads

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.

Categories
Arpeggios Chords Intervals Inversions Symmetrical Scales Triads

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”: