The Continuum of Dissonance: A Rational Guide for the Modern Arranger

Harmonic Dissonance

For the young arranger, the temptation to be “hip” might seem like the path to recognition and success. Fresh out of school and armed with a vocabulary of altered extensions and polytonal clusters, there is an urge to throw the “kitchen sink” at every commission. However, professional arrangingThe process of adapting a piece of music for a different ensemble, style, or performance context. is as much about psychoacoustic diplomacy as it is about music theory.

To create a successful arrangementrefers to the structure and order of musical elements in a composition, such as melody, harmony, rhythm, and instrumentation., one must understand that dissonance is not a binary state, but a continuum of “opposition” to a natural foundation. By understanding the physics of the overtone seriesSub-components of a musical tone arrayed in a series of ratios, theoretically to infinity, we can make rational choices that honor the client’s “rudeness tolerance” while still pushing creative boundaries.

The Foundation: Tonal Gravity and the Overtone Series

The “Inside” begins with the overtone series—a collapsing array of ratios that forms our natural sense of harmonic stability, and the basis for the 12-tone chromatic system. This series acts as a “tonal gravity.” The closer a notea symbol used to represent a specific pitch and duration is to the fundamentalLowest, most predominant perceived pitch of a musical tone in the overtone series, the more “kind” or “natural” it sounds to the ear.

As the ratios become more complex and move further away from the fundamental, the “beating” between frequencies increases. This is the source of “rudeness.”

• The “Inside” (Ratios 2:1, 3:2): The octaveA range of eight notes, starting with a particular note and ending with the next instance of that same note, either higher or lower in pitch. and fifth. These are the “simple and dumb” structures that satisfy even the most conservative ear.
• The “Flavorful” (Ratios 7:4, 11:8): The natural seventh and the sharp eleventh. These exist in the series but begin to lean away from the equal-tempered foundation.
• The “Outside”: Notes that have no immediate relationship to the local overtone series, creating maximum friction.

Mapping the Spectrum of Rudeness

To navigate a client’s expectations, consider this “Dissonance Dial.” It allows you to quantify your choices based on academic theory and jazz vernacular.

Strategy 1: Identifying the Tolerance Threshold

Before putting pen to paper (or mouse to notationA system of symbols used to write down music. app), you might want to audit your client.

1. Reference Checks: Ask for three recordings or artist names they love to get a sense of their comfort level
2. The “Sacred” MelodyA sequence of single pitches perceived as a unit, usually the main theme or tune in a piece of music.: Deliver the “safe” version first, with an action plan in mind to increase the sonic variety, if required or permitted
3. The Context of the Venue: Is the audience looking for something close to the source? or is this a more artistic opportunity for exploration?

Strategy 2: Letting Knowledge Guide the Process

Once you know the threshold, use the Continuum of Dissonance to justify your deviations.

• Start Simple: Build the “dumb” version first. Establish the tonal gravity so the listener knows where “home” is.
• Introduce “Kind” Opposition: If the client is conservative, introduce tensionTemporary music dissonance or increased density through the higher partials of the overtone series. It feels “grounded” because it’s physically present in the harmonic seriesArray of notes contained within a pitch with a mathematical (rationic) relationship to the "fundamental," which is the container note for all the rationic subcomponents. Also see "Overtone Series" of the root.
• Rationalize the “Outside”: When you do go “outside,” do it with a sense of distance. Jazz musicians describe “outside” playing as a departure from the environment’s foundation. If you choose a “rude” voicingThe distribution of musical notes between different parts in an ensemble; the intervallic structure of a harmonic array, ensure the surrounding environment provides enough Tier 1 stability to make the opposition feel intentional, not accidental.

Melodic Dissonance – The Continuum of Propinquity

While the Continuum of Dissonance manages the vertical “stack” of a chordTwo or more notes played simultaneously; a group of three or more notes played or sung at the same time to create harmony., the arranger must also navigate the Continuum of Propinquity—the physical distance between notes in a melodic gesture. If vertical dissonance is the “flavor” of the sound, propinquity is the “effort” the listener must expend to follow the line.

The “Kindest” Rudeness: Chromatic Neighbors

In the realm of high propinquity (small distances), we find the diatonic and  chromatic neighbors. Even though a b2 or #4 might be a non-harmonic tone that “opposes” the foundation, its proximity to a chord tone makes it the “kindest kind of rude”. Because the “gap” is so small, the listener’s brain perceives the tension and its resolutionRelease of musical tension almost simultaneously.

The Gap-Fill Principle

When an arranger chooses to move from high propinquity (steps) to low propinquity (large skips), they invoke what Leonard Meyer calls the Gap-Fill Principle.

• The Emotional Gap: A large melodic leap (a 6th, 7th, or octave) creates a psychological “gap” that the listener subconsciously demands be filled by a stepwise motion in the opposite directionInstructions for an arranger or composer indicating style, instrumentation, mood, and purpose.
• The Shock of the Leap: Skipping to a non-harmonic tone is a high-risk arranging choice. It triggers what David Huron calls a “prediction error”—a biological surprise that can be perceived as profound or merely “rude” depending on the client’s tolerance.

Mapping Melodic Choice

Voicing and the Continuum of Sonority

While the previous continuums provide a rational basis for what notes to play, the Continuum of Sonority governs how to stack them. In arranging, this is core work. You might have the right ingredients (the notes), but the way you combine them—their density, vertical distribution, and internal friction—determines the effect.

Subjective Textures

Voicing is often considered subjective, yet specific structures carry predictable psychological weights. Just as a chef knows how a specific spice will react with a base, an arranger should become familiar with the sonic flavor of various voicing configurations to have a good idea what they sound like before going into the scoreA written representation of a piece of music, including the notation for all parts of an ensemble..

• Vincent Persichetti: The Tension ScaleA sequence of pitches organized in ascending or descending order from which a harmonic series can be derived. In Twentieth-Century Harmony1. The result of notes sounding together to create a sense of musical logic or agreement 2. Supporting musical material 3. A sense of musical environment, Persichetti provides a “flavor profile” for intervals. He distinguishes between “Soft” dissonances (Major 2nds) and “Sharp” dissonances (minor 2nds), noting that the sonority of a voicing is determined by the “intervallic friction” between its members.
• Bill Dobbins: The Architecture of the Stack. Dobbins codifies the specific “recipes” jazz arrangers use—quartal (4th) stacks, clusters, and “Upper Structure Triads.” He demonstrates how shifting a single note at the bottom of a voicing can change a texture from “open and neutral” to “dense and aggressive.”
• Ludmila Ulehla: Density vs. Clarity. In Contemporary Harmony, Ulehla explores the trade-off between power and detail. Doubling an octave in a voicing provides “power” (Tier 1 safety), while a close-position voicing with internal minor seconds provides “density” (Tier 4 rudeness).

Mapping the Sonority Continuum

Conclusion: The Arranger as Negotiator

To bring it all home, the art of arranging is ultimately the management of expectations. By looking at your score through these three lenses—the vertical foundation of the overtone series, the horizontal effort of melodic distance, and the textural density of your voicings—you gain a rational framework for making subjective choices. Instead of guessing how “hip” an arrangement should be, you can dial in the exact level of opposition your client can handle. Use the overtone series to ground your harmony, keep your melodies physically accessible through close proximity, and choose your voicing textures like a chef selects spices—to complement the core ingredients rather than mask them. When you align these three areas, you move beyond mere “spitballing” and into the realm of professional craftsmanship, ensuring that even your “rudest” choices feel intentional, balanced, and perfectly suited to the room.

Annotated Bibliography & References

The Vertical Axis: Dissonance & The Overtone Series

• Hindemith, P. (1937). The Craft of Musical Composition. (Establishes a hierarchy of intervals based on physical harmonic properties).
• Russell, G. (2001). Lydian Chromatic Concept of Tonal Organization. (Explores “Tonal Gravity” and the relationship between the overtone series and scales).
• Tenney, J. (1988). A History of ‘Consonance’ and ‘Dissonance’. (Traces the shifting cultural definitions of “rudeness” in music).
• Partch, H. (1949). Genesis of a Music. (A radical look at frequencya measurement of the number of oscillations per second of a sound wave, which determines its pitch. ratios and just intonation).

The Horizontal Axis: Propinquity & Melodic Distance

• Meyer, L. B. (1956). Emotion and Meaning in Music. (Introduces the “Gap-Fill Principle” and how the brain reacts to melodic skips).
• Huron, D. (2006). Sweet Anticipation: Music and the Psychology of Expectation. (Explains the biological “surprise” response to large intervalic leaps).

The Textural Axis: Voicing & Sonority

• Persichetti, V. (1961). Twentieth-Century Harmony: Creative Aspects and Practice. (A “cookbook” for the psychological tension inherent in different intervalic stacks).
• Dobbins, B. (1984). A Creative Approach to Jazz Piano Harmony. (Categorizes specific big band and jazz voicing structures by their “flavor”).
• Ulehla, L. (1966). Contemporary Harmony: Romanticism Through the Twelve-Tone Row. (Balances the need for vertical density with horizontal clarity).