I. Core Theoretical Foundations of Pitch Class Set Improvisation

What is a Trichord? Beyond the Traditional Triad

For most musicians, the word “chord” immediately brings to mind tertian harmony—chords built by stacking thirds (Major, Minor, Augmented, or Diminished). While this system has served Western music for centuries, it is only one way to organize sound.

A Trichord is simply any collection of three distinct pitch classes. By moving beyond thirds, we open the door to “intervallic thinking.” Instead of thinking “Root, 3rd, 5th,” we begin to think in terms of intervals (half-steps, whole-steps, fourths, etc.). This shift is revolutionary for an improviser: it frees you from the gravity of “key centers” and allows you to navigate the chromatic scale with structural logic rather than just “playing outside.”

The 12 Essential Pitch Class Sets: A Master List

In the world of Pitch Class Set (PCS) theory, we use a concept called “Prime Form” to categorize sounds. Think of Prime Form as the “musical DNA” or the most condensed version of a chord. Because we treat all octaves as equal and ignore the order of the notes, there are mathematically only 12 unique three-note shapes (trichords) possible in our 12-tone system.

Whether you play a C Major triad (C-E-G), an F Major triad, or a G Major triad in second inversion, they all share the same Prime Form: [0,3,7]. By mastering these 12 basic “formulas,” you aren’t just learning 12 chords; you are learning the structural foundation for every possible three-note combination in existence. This radical simplification allows you to see the entire fretboard as a finite, manageable map of sonic possibilities.

Unordered vs. Ordered Sets: Understanding the Musical DNA

To truly master Pitch Class Set Improvisation using hexatonics and pitch class sets, one must understand the difference between Ordered and Unordered sets.

• Ordered Sets: This is what we typically think of as a melody or a specific voicing. The sequence of notes matters.
• Unordered Sets: This is the “cloud” of notes available to you. Much like a master chef looks at a basket of three ingredients and sees infinite ways to combine them, an improviser looks at an unordered pitch class set as a source of raw material.

The set remains the same regardless of inversions, registers, or octaves. This is why the system is so powerful for the guitar: a “set” isn’t a “grip” or a “fingering”—it is a harmonic identity. When you internalize the sound of an [0,1,3] set, you recognize it whether it’s played as a tight cluster in the low register or as a wide-interval skip across three octaves. You are no longer playing shapes; you are playing meaning.

Why Organize Sound with Pitch Class Set Improvisation Ideas?

The biggest advantage of Pitch Class Set Improvisation is efficiency. It drastically reduces the number of “shapes” you need to learn. In Pitch Class Set Improvisation, any combination or inversion of C, D, and G is simply an 027. By identifying these core identities, we discover there are only 12 possible three-note combinations (trichords) in total.

The 12 Foundational Trichords: The Building Blocks of Pitch Class Set Improvisation

In the world of Pitch Class Set theory, every possible three-note combination can be reduced to one of these 12 “Prime Forms.” Mastering these is the key to unlocking the hexatonic universe. Think of these as the primary colors from which all other harmonic shades are mixed.

Technical Spotlight: The (013) Trichord

The (013) pitch class set is perhaps the most versatile tool in the modern improviser’s kit. On the guitar, it is easily visualized as a half-step followed by a whole-step (for example: C, Db, Eb). Because it contains both a minor and major third relationship depending on the root, it acts as a harmonic chameleon.

In my 013 Hexatonic Études, I explore how 28 different hexatonic scales built from this single set can be applied to a Dominant 7th chord. It creates a shimmering, sophisticated effect that sounds “modern” without feeling mathematically cold.

Technical Spotlight: The (014) Trichord

The (014) set (a half-step and a major third, e.g., C, Db, F) is the gateway to the “Modernist” sound. It is dark, crunchy, and inherently dissonant. This set is a favorite of the Second Viennese School because it lacks a perfect fifth, immediately stripping away the “safety” of traditional tonal harmony.

For guitarists, (014) is highly ergonomic for sweep patterns and wide intervallic leaps. It is a “shortcut” to the sound of the early 20th-century avant-garde, providing immediate tension that sounds intentional rather than accidental.

III. Advanced Improvisation Techniques: Hexatonic Construction

The transition from a three-note trichord to a six-note hexatonic scale is where the true power of Pitch Class Set Improvisation theory is unleashed. By combining two trichords, we create a specialized six-note “vocabulary” that provides more melodic movement than a simple chord, but more structural focus than a standard seven-note scale.

Building the ‘Magic’ Hexachords

A “Magic Hexachord” occurs when you combine two non-overlapping trichords to form a unique six-note set. The beauty of this approach is that it allows you to superimpose complex sounds over simple harmonies. For example, by combining an (027) trichord (C, D, G) with another (027) trichord starting a whole-step higher (D, E, A), you create a highly modern, open sound that floats beautifully over a C Major 7 or D Minor 7 chord.

This method moves you away from the “all-you-can-eat” buffet of the chromatic scale and gives you a specific “palette” of six notes. This limitation is actually a creative catalyst—it forces you to find new melodic shapes within a defined harmonic container.

Superimposition: One Set, Many Colors

One of the most efficient ways to use these sets is through < strong>Superimposition. A single hexatonic set can take on completely different “colors” depending on the bass note or underlying chord. Consider the (013) trichord pair:

• Over a Dominant 7th chord: It creates a sophisticated “altered” sound that highlights the b9 and #9.
• Over a Minor 7th chord: It creates a dark, “Phrygian” or “Dorian” hybrid texture.
• Over a Major 7th chord: It introduces Lydian-style tensions that push the harmony toward the avant-garde.

In my Sonic Resource Guide, I map out every possible hexatonic pair, providing a master roadmap for how these sets interact with standard jazz and rock harmonies. This allows the improviser to stay “inside” the logic of the set while being “outside” the traditional key signature.

The ‘Atomic Scales’ Method: Technical Mastery

How do you actually play this on a guitar at 200 BPM? You use what I call Atomic Scales. These are short, condensed fingerings designed to fit the specific architecture of the guitar’s fret board. Instead of thinking of long, linear scales, we think of these hexatonics as “clusters” of information that can be moved vertically and horizontally. See: Harmonic and Melodic Equivalence Courses for examples of Atomic Scales.

By breaking the 12-tone aggregate into these six-note “atoms,” the fret board stops being a mystery. You begin to see the geometry of music. You aren’t memorizing scales; you are internalizing the physical relationship between intervals. This is the key to the effortless, high-speed intervallic playing found in modern jazz and tech-metal.

IV. Practical Application and Resources for Pitch Class Set Improvisation

Theory remains an academic exercise until it is applied to the music you play every day. Whether you are a jazz guitarist re-imaging a standard, a metal player looking for a more “sinister” harmonic palette, or a composer seeking new textures, the following methods provide the bridge to mastery.

Reharmonization: Replacing Traditional Chords

One of the most immediate ways to modernize your sound is to replace traditional tertial chords (Major, Minor, Dominant) with pitch class set voicings. In my Applying Pitch Class Sets to Improvisation series, I show students how to swap out standard “stock” chords for modern trichords like (015), (016), or (027).

This isn’t about complexity for complexity’s sake—it’s about harmonic character. A standard G7 chord has a very specific “pull” toward C. However, if you replace that G7 with an (013) trichord pair, you retain the function of the dominant chord while introducing a sophisticated, shimmering tension that traditional chords simply cannot provide. This allows you to play “inside” the progression while sounding “outside” the clichés.

The Ear Training Key: Hearing the ‘Color’ of the Set

To improvise effectively with these sets, you must be able to hear them in real-time. My method of ear training—famously used at NYU and Princeton—moves away from interval-counting and toward Key Center Recognition.

Using tools like the Ear Training One Note Complete, students learn to identify the unique “sound” or “color” of each pitch class set against a static key center. If you can’t hear the tension of an (014) set against a key center, you won’t be able to use it authentically in a solo. True mastery comes when you can hear a complex hexatonic scale as a single, unified “sound” rather than six individual notes. This is the difference between “math” and “music.”

Also using tools like the MetroDrone®, students learn to “Feel Time not Count Time. I should also mention the “Long Line Rhythm®” course which teaches you the method in further detail. The MetroDrone® can also be used as a drone so everything you are practicing you can hear in a key center which has you doing ear training with everything you practice. Again, if you can’t hear the tension of an (014) set against a key center, you won’t be able to use it authentically in a solo.

The Sonic Resource Guide: Your 800-Page Roadmap

For those ready to truly master this language, the Sonic Resource Guide is the ultimate reference. It reduces the infinite combinations of the 12-tone system into 220 “Prime Forms.” This book maps out every possible chord, scale, and trichord pair, allowing you to look up any group of notes and instantly see its harmonic potential.

Think of it as a dictionary for the modern improviser. It bridges the gap between high-level mathematics and the practical needs of a working musician, providing the structural DNA for a lifetime of musical exploration.

The Path to Pitch Class Sets: A Personal and Musical Evolution

For over thirty years, my musical life has been defined by a single, obsessive pursuit: the integration of 20th-century compositional systems into the visceral world of improvisation. This wasn’t a choice made in a vacuum, but rather a slow-motion collision between high-level jazz pedagogy and the radical structures of the European avant-garde.

1. The Banacos Foundation: Double Mambos and Hexatonic Seeds

My deep dive into this world began around 1990, after spending five formative years studying with the legendary Charlie Banacos. Charlie had a unique way of codifying complex sounds into actionable exercises. He assigned me concepts he called “Double Mambos” and “Non-Tertial Double Mambos.”

In the Banacos system, a “Double Mambo” is essentially a pair of triads or structures that form a larger six-note set—a Hexatonic. While many jazz players use triad pairs (like Eb and F over an F7 chord), Charlie pushed me toward the non-tertial variety. These weren’t just chords; they were pitch class sets that broke the traditional “stack of thirds” logic. They forced me to hear intervals as independent cells rather than just “extensions” of a root. I questioned Charlie a lot on how he knew so much about music. He made many book recommendations. If you are interested check out the Charlie Banacos recommended reading list.

2. The Second Viennese Influence: Schoenberg, Berg, and Webern

As I practiced these hexatonic structures, I started noticing their architectural shadows in the music of the Second Viennese School. The works of Arnold Schoenberg, Alban Berg, and particularly Anton Webern became my primary listening. I realized that Webern’s highly distilled style was almost entirely built on the interaction of small trichords—the same three-note building blocks that make up a hexatonic set.

Webern’s influence was the “Rosetta Stone” for my playing. His music demonstrated that you could achieve incredible emotional depth and structural integrity without relying on traditional functional harmony. I saw a direct line from his 12-tone rows to the improvisational “cells” I was developing on the guitar. This led me to the concept of Pitch Class Set Improvisation.

3. Spooky Actions: Improvising with the Modernists

To put these theories into practice, I co-founded the ensemble Spooky Actions with woodwind specialist John Gunther. Our goal was audacious: we didn’t want to just “play jazz” over classical themes; we wanted to learn to improvise within the specific set structures used by the composers. On our debut recordings of Webern, we used the exact trichords found in his scores to inform our solos.

This forced me to abandon “pattern playing.” If a piece was built on a [0, 1, 4] trichord, my improvisation had to honor that interval set. This realization shifted my focus from what scales to play to how melodic ideas must reference the music being played, ensuring the improvisation is an organic extension of the composition rather than a collection of generic licks.

4. A Unified Theory: Melodic and Harmonic Synthesis

This journey eventually led me to a radical conclusion: if my melodies were organized by trichords and hexatonics, my chords had to reflect that same organization. Traditional jazz voicings often felt “out of place” against these modern melodic lines. I began using trichords to replace standard chords entirely, creating a unified harmonic language where every voicing and every melody line shared the same DNA.

Mastering this has been my central mission since 1990. It is a “whole new world” that requires a complete re-mapping of the fret board, moving away from scale-shapes and toward a deep, intervallic understanding of the 12-tone aggregate.

5. Proving the Living Language: From Metal to Early Music

Since those early days, I’ve spent my career proving that Pitch Class Set Theory is a living language applicable to any genre. I’ve used these hexatonic constructs in everything from Heavy Metal and Rock to Avant-Garde Jazz and even Early Music. Whether I’m performing with the Boston Symphony Orchestra or playing a distorted guitar solo, these sets provide a structural rigour that allows for total creative freedom.