This blog contains material that I have created for my private students and for my own exploration of music theory, composition, fretboard harmony, and technique.

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Thank you! – Dan Cosley

# 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.

# 360 Double-Stroke Right-Hand Combinations

Practicing even a “handful” of the 360 possible double-stroke right-hand combinations will rapidly improve right-hand independence and flexibility.

The example below shows the first four combinations, realized on string group 6321:

String groups with an unused string (or two) between “m” and “a” are particularly important for developing strength and flexibility in the weaker (“m & a”) side of the right hand.

Here are the same four combinations on string set 6431:

Experiment with different degrees of separation between right-hand fingers, and also different rhythms, accents, and dynamics.

For reference, here are the 15 possible four-string groups:

Download the PDF below for a list of all 360 combinations:

# Pat Martino’s Linear Expressions – Phase I in all 12 keys, Cycle of Fourths

One of the most important books ever written on melodic improvisation for guitar, *Linear Expressions* by Pat Martino, was originally published in 1989.

I have created this video to show the “solution” to the “problem” Pat suggests in the first part of the book.

The video is very helpful for “drilling” the lines.

Minor 7 and Minor 6 Drop voicings are included for context and comping. These will come in very handy later when practicing chord substitutions.

Learn this first, then take the next step to recontextualize the lines using Pat’s “minor conversion” theory.

Linear Expressions is an absolutely essential book for every guitarist’s library.

# 7th Chord Arpeggio Permutations, Contours, & Chord Cycles

*“The poet only asks to get his head into the heavens. It is the logician who seeks to get the heavens into his head. And it is his head that splits.”* – G.K. Chesterton, Orthodoxy

Below are 24 possible orderings of a 7th chord arpeggio.

I have organized the combinations across a six-day practice cycle for digestibility:

Though notated as C Major 7 arpeggios, these permutations can represent other harmonies. I highly recommend playing the permutations through harmonized scale “cycle” progressions, “tweaking” the intervals to suit the chord qualities involved in a given progression:

Various contours are possible, depending on the octave chosen for each of the tones. Here are four different contours for the same combination (1357):

Here are the same four contours, transposed up an octave:

Now through the harmonized Melodic Minor scale, Cycle 2:

The same four contours, transposed up an octave:

Now through the harmonized Harmonic Minor scale, Cycle 2:

The same four contours, transposed up an octave:

As you can see, the possibilities are endless.

Try practicing a few permutations per day through either Major, Melodic Minor, or Harmonic Minor harmonized scales.

Remember to explore the various “Cycle” progressions, listed above.

It’s not reasonable to practice every pattern, but you’ll discover some exciting things if you occasionally dip into this well of possibility.

# 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”: