3.1 Introduction


3.1.1 The chord-scale technique

Through the years a large number of educational methods on how to improvise in jazz have been published (for instance Oliver Nelson 1966; Jerry Coker, Jimmy Casale, Gary Campbell and Jerry Greene 1970; Bunky Green 1985; David Baker 1988; Hal Crook 1991; Jamey Aebershold 2010).  The instructions and examples in these publications are basically meant to develop the musician’s skills in chord-scale improvisation, which is generally considered as the basis of linear improvisation in functional and modal harmonies. In section 1.4.1, I have already discussed my endeavors to broaden my potential to play “outside” the stated chord changes, as one of the ingredients that would lead to a personal sound. Although few of the authors mentioned above have discussed comprehensive techniques of creating “alternative” jazz languages beyond functional harmony, countless jazz artists have developed their individual theories and strategies of “playing outside”, as an alternative to or an extension of their conventional linear improvisational languages. Although in the present study the melodic patterns often sound “pretty far out”, I agree with David Liebman’s thinking pointed out in section 3.2.1, that improvised lines are generally related to existing or imaginary underlying chords. Unsurprisingly, throughout this study the chord-scale technique as a potential way to address melodic improvisation will occasionally emerge.  


3.1.2 Playing outside the changes

With the notions “outside the changes”, “playing outside”, “outside sound” or “outside” in this study, I mean that an improviser intentionally plays phrases that do not correspond to the scales that match the underlying chords. Separated from each other, the melodic line and the harmony both sound right, but put together they create a surprising dissonance, a bitonal sound that is different from what the listener might expect.  Whether such an outside phrase sounds "right" depends both on the authority with which the performer phrases his line and on the competence and the empathy of the listener. 


    The difference between inside and outside can be illustrated by a phrase that starts inside, goes outside and ends inside again. For instance in the next example of a solo by alto saxophonist Eric Marienthal in Chick Corea’s composition “Got A Match” (2003). The notes he plays in bars 1-8 of this fragment match correctly with the original chords that are written above the staff. But in bars 10–14 he goes outside the stated chords by playing lines that evoke the alternative chords that are indicated by the brackets under the staff. From the second half of bar 14, his notes match the original chords again. 

Once again it should be emphasized that the effect of this desired dissonance depends on the listener’s ability to explicitly or intuitively recognize the relation between the melodic line of the improviser and the harmonies played by the rhythm section. Even if the pianist plays sparsely (such as in this example), or even stops accompanying temporarily, and even when the bass player obscures the original chords by superimposing a stationary bass pedal, the listener should be able to keep imagining the form and the original changes of the tune, in order to appreciate the improviser’s performance. 


    In the following chapters, the theories, techniques and practical applications published by jazz saxophonists and educators David Liebman, Jerry Bergonzi, George Garzone, Walt Weiskopf and John O’Gallagher will be evaluated. Which techniques do they apply when playing outside the chords and – led by my intended operations with the Tone Clock and Messiaen’s modes in the remainder of this study – what are their connections to serial compositional techniques? 


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Got a Match” – fragment of alto saxophone solo by Eric Marienthal

In the next example of a fragment of Liebman’s solo it is easy to recognize the intervallic structure of the melody lines, as he plays ten intervals of a major seventh and two intervals of a minor ninth. Because he intends to follow the pianist’s “chords for melody 1”, he emphasizes the tonal anchors that these harmonies evoke, rather than taking the twelve-tone rows of melody 1 and 2 above into account.  Examples of tonal anchors are Dmaj7 (bars 1–2), Ammaj7 and Amaj7#11 (bar 3), Bmaj79/C (bars 3–4), Dmaj7/B and Dmmaj7 (bars 8–9). From bar 8 on, the two intervals are interwoven in diatonic scale patterns (bar 10) and sequences (bar 11) with an increasing dense texture (bar 13).


New York Straight Ahead”fragment of tenor saxophone solo

My operations in this solo, meant to play intentionally outside the original chord changes of this tune represent a number of the superimposition techniques that I had developed by trial and error. The analysis confirmed my assumption that according to Liebman’s theory I mainly applied tonal, rather than non-tonal superimpositions.


“Invocation” (David Liebman) – melody lines]


“Invocation” (David Liebman) – harmonies

3.2.4 Evaluation

At the time of finding the first edition of Liebman’s book in 1991, I had already applied a number of his techniques intuitively. Since then his terminology such as “tritone”, “alternate ii-V”, “scale quality”, “modal”, and “pedal point” and the step-by-step stratification of terms and practices served as a useful theoretical framework to articulate my endeavors of extending my playing beyond conventional linear improvisation. 


    Liebman’s applications of twelve-tone operations are obvious in the examples above, but his interpretation of the twelve-tone theory in section 3.2.3 is quite global. By only mentioning the name Schoenberg he does not define his own position to the current state of affairs in twelve-tone music. In the following paragraphs I will summarize composer and theorist Charles Wuorinen’s discussion of the theory and development of twelve-tone music (Wuorinen 1994) to clarify its relations with the applications by Liebman and the other authors to be discussed in the remainder of this study. 


    Wuorinen’s publication Simple Composition (1994) provides a basic outline of the twelve-tone system of composition accompanied by assignments for composition students. The author defines the difference between the tonal and the twelve-tone systems as “the tonal system is based upon interval content, the twelve-tone system upon interval order” (Wuorinen 1994:5). In tonal music the content of pitches and intervals can be identified by their positions in the diatonic scale and its implied triads and tetrachords. This content is fixed, and independent of where the notes appear in the melody, or in the chord. In twelve-tone music, all twelve pitches of the chromatic scale are equally important, in other words: there are no notes dominating the others. The twelve pitches are arranged in a row in which the fundamental structure principle is determined by the order of the pitches and their connecting intervals. 


    As to the state of affairs of twelve-tone music, at the time of publication 75 years after its introduction by Schoenberg, Wuorinen expresses observations that are important in the context of this study. He states that, now twelve-ness and the non-repetition of pitches before all twelve have been exposed is no longer compulsory, the principle of ordered interval succession is the main organizing factor of twelve-tone music. He considers the ongoing merging of content-based principles of pitch organization with the basically order-determined music as a next step “to demonstrate our assertion that the tonal and twelve-tone systems are not really separate musical entities” (Wuorinen 1994:9). 


    Now, if Liebman’s chromatic concept of non-tonal superimposition can be considered as an example of Wuorinen’s “highly chromatic music of the present day” resulting from this “reconciliation of the two principles of pitch organization, content and order (Wuorinen 1994:9)”, his treatise can be regarded a stratification of operations that demonstrate this process within jazz music. Wuorinen’s concept of reconciliation also sheds light on Liebman’s observation quoted in subchapter 3.2.1 that non-tonal improvisation is a very relative term because any configuration of notes can be identified by root oriented chord symbols.  This relativeness results from the combination of the vertically stacking of horizontally ordered pitches, and the orientation on a root note in a principally keyless situation. These mixed operations again witness the merging of tonal and twelve-tone techniques. 


    Today's almost intuitively blending of (elements from) tonal and twelve-tone techniques explains the paradox throughout Liebman’s book between his definition of non-tonal chromaticism referring to “melodic lines and harmonies that have no discernable key or root orientation [and can be considered to result from] linear counterpoint” (Liebman 2013: 34) and his positioning of chromaticism in “specifically […] a situation in which there is an intentional relationship between melody and harmony. [Because] for jazz, it is the harmonic accompaniment which frames the melody” (Liebman 2013:13).


    Although the way Liebman designs and analyzes his complex chords and related scales is clear and useful, the complexity and quantity of his suggested twelve-tone operations might hinder the spontaneous creative process on stage. Simpler applications of twelve-tone techniques would be more attractive to help improvisers “inventing melodies which are fresh, alive and full of meaningful emotional and thoughtful content” (Liebman 1993: 13). As a demonstration of these simpler applications I will come back to “Invocation” in subchapter 4.6, discussing trichord analysis as a potential alternative to Liebman’s derivation of scales from the complex chords in the fourth part of this composition.  


    One last comment on Liebman’s line compendium. His adding of instructions and examples of line analysis and line variations, are an improvement compared to earlier editions of his book. As a kind of thesaurus it may indeed inspire the interested reader to adapt (fragments of) these examples to his personal needs and taste. However by the absence of musical context it still misses the instructional quality to help the improviser creating melodic lines alike. An example of the combination of a compendium with an explicit model to generate melodic lines beyond functional harmony, as an alternative to a mere thesaurus, will be discussed in the next subchapter.


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3.2 David Liebman (2013). A Chromatic Approach to Jazz Harmony and Melody. Rottenburg: Advance Music. 


3.2.1 Theory

Liebman’s publication can serve as a theoretical framework and a treatise on how to step forward from conventional linear jazz improvisation by applying the concepts of tonal and non-tonal superimposition. The author defines his chromatic approach as “the construction of melodies and harmonies which can coexist with, or replace given key centers. It implies setting up contrary tonalities, thus creating a heightened degree of tension and release in order to expand one’s expressive palette” (Liebman 2013:9). The term chromaticism is meant “specifically for a situation in which there is an intentional relationship between melody and harmony. [Because] for jazz, it is the harmonic accompaniment which frames the melody” (Liebman 2013:13). 

    Liebman discerns three categories of melodies in relation to the diatonic system, to define his concepts of tonal and non-tonal superimposition. In the first category are melodies that stay for the most part within the given harmonic background. If any chromatic tones appear, they are quickly resolved. In the second category are melodies that hold chromatic tones for longer periods. This can be called tonal chromatism. The third category hosts melodies that are not related to any specific overall tonal center, though they may temporarily resolve. This is called non-tonal chromatism.

    Tonal chromaticism is achieved by applying techniques of harmonic superimposition, for example, in Liebman’s terms,  “tri-tone”, “alternate ii-V”, “scale quality”, “modal”, and “pedal point” substitutions.  Although the resulting melodic lines may sound far outside the basic harmonic structures, Liebman still considers these techniques as extensions of the improviser’s conventional chord-scale skills, and uses the familiar chord terminology to identify the notes. 


    Non-tonal chromatism refers to melodic lines and harmonies in which, in Liebman’s words, no key centers are given priority, but “shape, ambiguous tonality and overall color (resulting from factors of phrasing) are the important aspects” (Liebman 2013: 55). However, although these melodic lines are structured by interval connections, it is still possible to identify their pull towards to temporary tonal centers. Liebman defines these as tonal anchors, which means that in these sort of melodic lines “tonality is flexible and in continuous flux as a line evolves. Within the progress of the line itself, temporary points of tonality may be established as anchors. This is a form of linear tonality and may result from several musical developments: the emphasis of one pitch or pitch cluster, leading tone activity (half or whole tone step pull), rhythmical stress on a pitch, or how the intervallic shape seems to lead to a tonal center” (Liebman 2013: 55). 


    Liebman argues that in jazz harmony, non-tonal improvisation is a very relative term because any configuration of notes can be identified by using similar chord terminology, the numbered system figured from the root, as in functional harmony, or by constructing complex chords of stacked triads on the root. 


    How Liebman’s theoretical concepts are put into practice depends on individual aesthetic choices and on the musical relationships in a group of musicians. One group may choose to facilitate musical communication by using names of chords or scales, to create a familiar point of reference. Another, without the need of such a safety net, will be challenged to communicate more instinctively and create fresh reference points. “Harmonically speaking, the spontaneous reference point may turn out to be diatonic or non-tonal; this has to do with the situation, style and particular musicians involved. Achieving a sense of no pervading harmonic center implies the absence of direct superimposition and means that the music is purely intervallic” (Liebman 2013: 30). In this type of playing the improvisers will have to use intervallic recognition as an important tool to react and play by ear instead of by knowledge of chords and scales. According to Liebman, this spontaneous playing in response to the direct musical context, without thinking of tonal references and harmonic relationships, can be truly called free music.

According to Liebman, hearing intervallically is the highest goal in chromatic playing. To facilitate intervallic recognition he maps the intervals in three categories. The first contains major and minor seconds, thirds and sixths. These are considered smooth and relatively consonant (Liebman 2013:71). Second are the fifth and the perfect and augmented fourth intervals. The fifth and perfect fourth can be associated with the dominant and sub-dominant functions in diatonic harmony, while the tritone stands out because of its striking color (Liebman 2013:72). The third category hosts the major and minor sevenths and ninths. By using these intervals, one creates an angular shape in chromatic lines. Liebman argues that, “together with the half step, these intervals are the most characteristic of twentieth century contemporary music” (Liebman 2013:73).


    Liebman’s advice to practice intervallic construction by applying only one class of intervals moved me to conceive “New York Straight Ahead” (1994). The 12-bar melody of this tune consists of a limited number of notes (basically five notes in the first ten bars with four extra notes mainly in the second voice) using Liebman’s first category intervals only: mostly minor and major seconds and minor thirds, and two major thirds. Only because I added a second voice from the end of bar 10, four intervals of augmented fourths occur in the two-voice harmonies. The bass ostinato and the frequent appearance of the note b tend to imply the tonal color of G minor, but by the meandering character due to the many chromatic notes the tune lacks a specific harmonic color. In Liebman’s terms it could be called “G-keyish.”

In this recording I wanted to challenge my group to shine a different light on both a well-known jazz standard and on the beaten tracks of our improvisation practices. Before we took off, I asked the rhythm section to strive for a maximum degree of harmonic vagueness, by giving priority to the pedal points and avoiding the original chords as much as possible. As expected, it appeared to be impossible to totally neglect the original changes of the jazz standard that were so upfront in our collective memory. Yet in this act of explicitly trying to avoid the expected harmonic structure of this tune, the chromatic techniques proved their worth to a maximum. The next fragment shows a number of examples in my first three solo choruses.


    In bars 9–12 the Abmaj7 chord and the incomplete Gb triad sound like temporary tonal centers, obscuring the original changes Am75 - D79 – Gm.  In bars 13–14 an altered cadence Ebm11 – Abm is played instead of the original Dm75 – G79 – Cmaj7 chords. The A minor chord can be considered the upper structure of the G7 altered chord. 


   Likewise in bars 21–24, where an alternate cadence blurs the original changes Em7 – A7 – Dm7 – G7, and the Am6 chord in bar 24 can be considered the upper structure of G7 altered again.


“Tilt” tenor saxophone solo first fragment: temporary tonal centers and altered cadences

3.2.3 Twelve-tone techniques


Encouraged by my acquaintance with the serial elements of the Tone Clock as discussed in chapter 1 and hereafter in chapter 4, I was attracted by Liebman’s assertion that in his concept of non-tonal chromaticism the same principles are observed as in Arnold Schoenberg’s concepts of the tone row. Liebman summarizes his interpretation of twelve-tone techniques as avoiding the harmonic dominance of any of the twelve tones, and the application of certain row variations.  In this music, tension and release is effected by density of texture, speed and grouping of ideas, range, dynamics and form, rather than by the cadential resolution to fixed key centers in functional harmony. The row variations (retrograde, inversion and retrograde inversion) and compositional operations such as octave displacement, various serial techniques, and rhythmic permutations are applied to add variety and relative points of tension to the melodic lines (Liebman 2013:34).


    The following example shows Liebman’s operations with twelve-tone rows on a duo recording with pianist Richie Beirach of “Invocation” (2006). The six lines in the following example are played alternately by the soprano saxophonist (melody 1) and the pianist (melody 2) at the beginning of the first part. In bars 1–5 Liebman plays a twelve-tone row containing five major seventh intervals. In bars 11–16 the arrows mark his retrograde inversions of these intervals. Because in bar 16, he repeats the note e♭ in the lower octave instead of playing it as the note e, the row contains eleven notes instead of twelve. In bars 24–28, constructed with only eight different notes, he plays again five intervals of a major seventh. Beirach keeps more strictly to the twelve-tone rows than Liebman, whose line in bars 6–10 contains four intervals of a major seventh and three intervals of a minor ninth. In bars 17–23 he repeats two of these minor ninth intervals as retrograde inversions. His last line in bars 29–33 is roughly a repetition of the one in bars 6–10. 


“Invocation” (David Liebman) – soprano saxophone solo fragment

An application of intervallic analysis is shown in the next example. All four-note patterns begin and end with a major second interval. The initial interval of all first patterns of bars 1–3 is put in descending direction; the initial interval of all second patterns in ascending direction. These alternating directions are repeated in the four-note pattern in bar 4. Then, the second pattern of bar 1 has the shape of a retrograde inversion, although the intervals between the mid voices are not similar. The same appears in bar 3, where the second pattern represents only the shape of a retrograde of the first without observing the correct intervals.


line compendium #12 (Liebman 2013:192)

Bars 33–45 can be seen as an example of Liebman’s definition of non-tonal chromaticism. By putting the accent on the mere shape and the overall color of the melodic lines as done here, the original chords completely disappear to the background. The uninterrupted succession of quavers in bars 33-37, gives the line a high density. A number of triads and chords are identifiable, but the line as a whole doesn’t evoke an obvious tonal center. Bars 38–43 have a more open rhythmic structure and contain three- and four-note sequences. As a result of the A major triad in bar 38, the Amaj9 chord in bar 41, and the A7 chord in bars 42–43 a tonal anchor of A-keyish is perceived.


“Sailing” – fragment of tenor saxophone solo

The following example is an illustration of the application of linear tonality in the first line of my improvisation on “New York Straight Ahead”. It starts with Ebm7 that suggests the upper structure of a D7 altered chord to resolve to G. But by changing the note d into a d in bar 4, Em7 tends to sound as a temporary tonal center on its own. Next, as an example of diatonic lyricism, the notes f and c together with the G-pedal in the rhythm section evoke the sound of Gsus4. The C7 chord in bar 7 can be seen as the next temporary tonal center. It resolves from the three chromatically ascending chords Fsus4, F/C and G7 in bars 5-6. On the last eight note of bar 7, a C octatonic scale starts (with extra notes d and b added) that ends on the first note of bar 9. Bars 9 and 10 contain two similar descending patterns built upon the major thirds of A79 and E79, two dominant seventh chords at a tritone distance. Finally bars 11–12 contain a line over F79, sounding a minor second below the stated G-keyish tonality. Just like C7, F7  sounds convincingly like an independent temporary tonal center. But, together with the C7, A79 and E79 chords it can also be considered as the last of four chords whose root notes together would form a diminished tetrachord and as such would extend the tonal color of C7 octatonic in bar 8. 

As to Liebman’s techniques of superimpositions it is evident that most of these result in increasing harmonic tension. Different chords are added to existing ones, chains of chords are superimposed on single chords and scales and modes on given chords are substituted by other types of scales built on the same root. To his stratification of techniques I would add an intervention that first goes the opposite way, by simplifying an existing harmonic structure, for example by creating a bass ostinato that obscures a number of chords, and by consequently applying Liebman’s pedal point superimposition. 


    This operation relates to what Liebman calls the “slack theory” in which emphasizing on one element is compensated by proportionally de-emphasizing others. For instance in an improvisation on a complicated harmonic progression, an interesting effect can be created by playing a simple melodic line. And vice versa, on a basic rhythmic and harmonic fundament, one can superimpose a complex harmonic and melodic structure.


    The following example shows this in “Tilt”, my contrafact of the jazz standard “What Is This Thing Called Love” on the CD Sailing (1995). The original chord changes in the A-section are replaced by a single G pedal point, those in de B-part by three different pedal points, respectively G, A and again G. 


“Tilt” – theme

Bars 73–76 contain a series of ascending and descending triad sequences that start on Am and end on Gm, obscuring the original Gm75 – C79 changes. Gm replaces Fm as a temporary tonal center. 


    Also the end of this third solo chorus is well endowed with E and D triads. In bars 89–90 the combination of the  A and Gtriads replaces the Gm5 – C79 chords. This is a common tonal harmonic superimposition because all notes in these triads belong to the scale of the C7 altered chord that resolves to F minor.  Likewise the Eb and Db triads in bars 92 – 94 are superimposed on the Dm75 – G79 chords. Their notes together belong to the scale of the G7 altered chord that resolves to C minor. 

The next example shows how Liebman constructed vertical harmonies by stacking and intertwining the characteristic major seventh and minor ninth intervals from the soprano saxophone lines (melody 1). The pitch collection is played five times. Only the first time, in bars 1–6, are all twelve pitches from the row played. Bars 7–9 contain an elven-tone row (the note f is missing), just as bars 9–10 (the note b is missing), and 14–15 (the note f is missing). Bars 12–13 contain a ten-tone row (the notes b and c are missing). 


line compendium #29 (Liebman 2013: 194)


line compendium #31 (Liebman 2013: 194)

3.2.2 Practical applications

With most of the discussed techniques of tonal chromaticism I had become familiar by analyzing musical examples, by the advice of my teachers and by experimenting with peers. Applying harmonic superimpositions such as tri-tone substitutions, alternate II-V substitutions and altered cadences had - by trial and error- become part of my musical language. This goes even more so for superimpositions of chord sequences such as cycles of fifths, chromatic ascending or descending ii-V patterns or whole tone sequences on a stationary chord or pedal note. The following example shows a number of these techniques in a recording of my improvisation over a C-pedal point in the A-part in “Sailing” (1995). 

    The first sixteen bars exhibit an overall whole-tone color. Firstly, by the fragmented descending Bb whole tone scale b, a, d, c, b, a) and its intervals of fourths (e– a; d – g; c – f; d – a) in bars 2–4.  Secondly, by the whole tone ascending augmented patterns in bars 5 and 6, and by the whole tone descending patterns in bars 9–13.


    Bars 24–40 feature a number of superimpositions. The B augmented chord in bars 24–25 is a tri-tone substation of F7 and resolves to Bb as a temporary tonal center. Bars 26–28 contain one chromatically ascending and one whole-tone descending ii-V pattern. Bars 31–37 show eight chromatically ascending patterns. The shapes of these patterns are different but in bars 31–34 the intervals of fourths suggest cycles of fifths. Finally an altered cadence starts on the second half of bar 38 and resolves to the tonality of C in bar 41.


“Tilt” tenor saxophone solo second fragment: non-tonal chromatism


“Tilt” tenor saxophone third fragment: superimposed triads

Twelve-tone techniques also appear in Liebman’s line compendium, which consists of 100 randomly presented melodic lines. Liebman advises the reader to apply chromatic line variations to these lines: rhythmic variations, such as diminution, augmentation and syncopation, and pitch variations, such as sequence change, neighboring tones, octave displacement and transpositions. He also advises to analyze his chromatic lines in order to identify tonal anchors, to apply intervallic analysis and to identify an implied tonality of the line in general. 


    The next example shows my analysis of one of Liebman’s examples to define implied tonalities. As a result of both octave displacement of the notes e and c, and of the augmentation of the notes e and a in bar 1, the keys of E and Ammaj7 can be identified as temporary tonal centers. Further line analysis reveals the tonal anchors F and B in bar 2.  Fm7 results from accentuating the note f, while B (with tension notes ♭9, ♭10, ♯11) results by both the accent on, and the augmentation of the note b. Because I hear these tension notes evoke the tonal color E, I have added this as the root in the last bar, according to Liebman’s observation that  “consonance is achieved through diatonic lyricism: the well timed use of a phrase which clearly outlines a tonal center” (Liebman 2013:15). 

Line analysis of the next example reveals a quite strict twelve-tone application. Analysis of this line reveals three phrases. The first and the third contain twelve-tone rows, the first with three and the third with two pitches repeated. The second phrase contains eleven notes, with six repetitions. Because the overall phrasing of the line, just as in the example above, is mainly done in eighth notes, it suggests a dense texture. Or, in Liebman’s terms (and depending on what tempo the line is played) it features a fast grouping of ideas. It doesn’t contain any apparent implied tonalities, although the last four notes to my ears sound like F#7 pulling to Bmaj. 



New York Straight Ahead” – theme

ex – four-interval melody /-2 /2/ -3/ 3/

The following example shows the manipulation of a four-interval combination with a minor second, a major second, a minor third and a major third, written /-2 /2/-3/ 3/ and manipulated by B1. With starting note c, Note Direction B (the first three intervals ascending and the fourth descending) and intervallic permutation 1 (in the order ABCD), the following four-interval melody occurs.

3.3.2 Practical applications

Before I discuss my experiences with Bergonzi’s model, I will explain shortly how it works. As I have already mentioned, Bergonzi’s choices of interval combinations are intuitive and based on concentrated listening. The sizes of these intervals range between a minor second and a major sixth. Major and perfect intervals are marked with numbers 2 (major second) until 6 (major sixth). Minor or diminished intervals are marked with a minus sign: -2 (minor second) until  -6 (minor sixth). Augmented intervals are not identified. The following example shows Bergonzi’s collection of “some three-interval combinations”.

ex – table of note directions of five-interval melodies (Bergonzi 2000:73)

and one hundred twenty permutations.

Bergonzi convincingly proposes educational applications of his model such as ear training and rhythmic development. However in the context of this study I am primarily interested in the generative application of his model for the composing improviser. Analysis of the thesaurus reveals three types of intervallic melodies.


    In the first type all interval combinations are different. This results in capricious melodic lines that tend to serve the composer’s use. For the improviser they are quite complicated and therefore hard to memorize and to quickly transpose, especially when there is no obvious tonal center implied. See for instance the next two examples. Because the first example evokes Bb as a tonal anchor it might linger in the ear more easily than the second one, which sounds purely intervallic. Therefore for improvisers the first line would be easier to remember and manipulate than the second.

ex – sounds purely intervallic (Bergonzi 2000:78)

ex – table of permutations of four-interval melodies

(Bergonzi 2000:11)

ex – a semi sequential line (Bergonzi 2000:68)



In the third type of intervallic melodies all interval combinations have the same structure. The resulting “full-sequential lines” sound extremely methodical and predictable by which they are easy to manipulate by the improviser.

ex – whole tone scale as implied tonal color (Bergonzi 2000:25)

In the following example, with the note benharmonically altered to a, the intervals between the initial notes of the four-note groupings are major thirds. In combination with their internal structures, containing a flatted five and a major third this helps to evoke the tonal color of a D augcmented triad.

ex  table of permutations of three-interval melodies (Bergonzi 2000:55)

ex – alternative four-interval combination /-2 /2/ -3/ 3/

ex – D augmented triad implied (Bergonzi 2000:25)



Although it is not Bergonzi’s basic aim, some of his groupings of four-note patterns irresistibly evoke tonal references. For instance by combining A/-2, B/2, C/3 and D/4 the following line could refer to a D pedal point,

ex  implied tonalities (Bergonzi 2000:66)

ex – some three-interval combinations (Bergonzi 2000: 56)

ex – table of note directions of three-interval melodies (Bergonzi 2000:55)

In another example, the manipulation called F11, with note direction F (two intervals ascending, the third descending and the fourth again ascending) and intervallic permutation 11 (BCAD) would result in the following four-interval combination.

ex  – C pedal point as a target (Bergonzi 2000:28)

Five-interval melodies can take thirty-two note directions

ex  D pedal point implied (Bergonzi 2000:51)



while in the Interval Melody A/-2, B/3, C/5 and D/-6 the line could target a C pedal point.

ex  – “Night And Day” re-composed with Three-Interval Combinations

My next step was to obscure the existing chords changes and to intuitively apply rhythmic variations and form interventions. Finally, I put back what to my ears remained the most characteristic chord changes (the four chromatically descending chords in bars 26–29) and adapted them to the new melodic and rhythmic structures. The result was my composition “Bird Buzz” (2015) as shown in the next examples. The tune is played in a rhythmic feeling of straight eights, with the drummer copying the rhythm of the bass ostinato. In bars 26–41 the harmonic movement refers to the original Night And Day but both changes and form here are thoroughly modified. At bar 42 the rhythm is interrupted and a collective solo in free rhythm is started, with all four musicians improvising. On cue at bar 43 the tenor sax and drums lay out and the guitar and bass continue their improvisations. At the end of this, the drummer leaps in and plays a cue to section B.

ex “Bird Buzz” – sections B and C

As to the improvisations I asked the musicians to confine themselves as much as possible to the selected intervals. The next example shows the transcription of the first part of the collective improvisation at the end of section A, where guitarist Federico Castelli, bassist Stefan Lievestro and I improvise with the intervals  /2, /3, and /4 (a major second, a major third, and a perfect fourth). Apart from the idea to facilitate a close relation between composition and improvisation, I intended to avoid automatized diatonic scale patterns by leaving /-2 and /-3 (a minor second and a minor third) out.

    In the interaction between the players, the saxophone and the bass are taking the lead. Guitar and drums are sparsely adding their accentuated fragments in between the lines of the leaders. As to the interval instruction, although quantitative analysis of the total number of the intervals played, shows a considerable number of mistakes, several lines to my ears convincingly create the desired result to sound1. The bass for instance plays exemplary lines in bars 6–10  (with a minor third between the first two notes of bar 7 as the only mistake) and in bars 14–16. My opening line on the tenor saxophone reflects the intro before section A, by the mistaken fifths at the transition of bar 1 to bar 2. The second and third fragments of this line both contain a minor second as a leading note, and in bar 5 the interval of a major second is displaced one octave, into a major ninth. However to my ears, due to the overall phrasing and the presence of all preferred intervals during the final fragments in bars 4–5, I consider this line to be convincing. The same goes for the guitarist where he plays four fragments in bars 4–10 that all end with a chromatic leading note. Apart from his playing of a mistaken fifth at the beginning of bar 8 (sounding, just as the first fragment of the tenor sax in bar 1–2, as a response to the intro before the A-section), all intervals are correct, as is the fragment in bar 13–14 that concludes his well-phrased melodic line that started at the end of bar 3.

Next to the choice of the interval combinations, the essential parameters are the permutations (the order in which the intervals appear) and the note directions (either ascending or descending) of the chosen intervals. These tools to manipulate the interval combinations are listed in two separate tables. The note directions are marked in Arabic numerals, the intervallic permutations are marked in capitals.


    According to the numbers of intervals used, the thesaurus contains three types of melodies. In order of appearance, the first is constructed with four intervals, the second with three and the third with five. For each type Bergonzi has constructed separate tables. For all three types, the numbers of possible note directions and permutations are different. 


    As the next examples illustrate, four-interval melodies can take sixteen different note directions:

Three-interval melodies can take eight different note directions

ex – Bb as a tonal anchor (Bergonzi 2000:17)

In the second type of intervallic melodies two or more interval combinations have the same structure. Hereby these “semi-sequential lines” sound more methodical than those of the first type. This makes them more predictable and therefore probably less interesting for composers unless they are for instance looking for accompanying riffs as vehicles for improvisations. However for improvisers this type of line is easier to memorize and to quickly transpose.

    Bergonzi considers his model as a way to get outside the chord changes of a tune. His basic aim is not to imply any tonal references. Just as Liebman, he argues that the shape and sound of the melodic lines are the intended purpose and that it is up to the reader to decide to either ignore or opt for tonal references. However he admits that for skilled composers and improvisers, tonal references should be obvious. For instance in the next example, he combines the intervals of a minor third, a major third and a perfect fifth. This melodic line can be analyzed as four groups of four notes, with the implied Amaj, Fm, Bm and Emaj triads, or in two groups of eight notes with the implied Fm7 and E7 chords. 

ex – table of note directions of four-interval melodies (Bergonzi 2000: 11)

and twenty-four permutations:

ex – table of permutations of five-interval melodies (Bergonzi 2000:74)

and twenty-seven permutations. Six of these are true permutations starting with ABC and ending with CBA while the other twenty-one contain repetitions of one of the intervals by which they have in fact been changed into a two-interval combination.

ex  refers to a F# octatonic jazz pattern (Bergonzi 2000:21)]


Just like his three- and four-interval melodies Bergonzi continues phrasing his five-Interval Melodies in four-note groupings instead of ordering them more logically in four groups of five notes in a 5/4 or 5/8 meter. The rhythmic displacement that results makes it harder to distinguish the individual patterns and to identify the melodic line as a whole. Is this the reason why Bergonzi seems to prefer sequential melodies above type-1 and type-2 lines? Of the 180 examples with five-Interval Combinations no less than 135 examples are full-sequential type-3 lines.

    The following example is an illustration of such a line. By transposing the five-note patterns down by major seconds a feeling of resolving to the tonal color of Fmaj is suggested.

For a personal application of Bergonzi’s model, I was inspired by his ear training instruction on how to sing intervallic melodies over major triads and other chord types. I transmitted this suggested application of his model to the construction of a contrafact of the jazz standard “Night And Day”.

    First I took the three-interval combination A/2 B/3 C/4 to create a melody in quarter notes on top of the chords of the A1 and A2 sections of the tune, and the three-interval combination A/2 B/3 C/5 to do the same on the B and A3 sections. I limited myself to these three-interval combinations because of the option, in Bergonzi’s table of permutations, to apply similar intervals repeatedly. I assumed that this would facilitate spontaneity in the improvisations. My choice of the size of the intervals was based on intuition, as were my decisions about the directions and the permutations of the interval combinations, although I tried to avoid obvious clashes with the original chords. Only after I had finished this first part of my re-composition did I use Bergonzi’s tables of Note Directions and Intervallic Permutations to identify the Interval Melodies.

    The next example shows the result of this first intervention. The new melody in quarter notes is written in the upper staff, the original melody and chords in the lower.

3.3 Jerry Bergonzi (2000). Thesaurus of Intervallic Melodies. Rottenburg: Advance Music.


3.3.1 Theory

In this publication Bergonzi discusses a model to create melodic lines that are purely intervallic. The major part of it consists of a thesaurus of 1704 intervallic melodies that result from his applications of this model. (In fact the collection contains 852 melodies, because from 853 on the first 852 are repeated, transposed up a minor second, and put in retrograde). Like  Liebman, Bergonzi provides the reader with instructions to apply rhythmic and melodic variations to the lines in his thesaurus. However, the intervallic melodies in his book are presented consistently in four-note groupings of eight notes, without any rhythmic variations.


    With a limited amount of possible operations Bergonzi’s system should be able to generate an infinite amount of “original lines and melodies.” By calling his examples “some interval combinations” he wants to express that his selections are subjective, or in his words “motivated by intuition and based on the ear”.  Bergonzi’s book requires the reader to use his intuition “while at the same time it helps to develop that faculty” (Bergonzi 2000: 7). 


    With these quotes, Bergonzi seems to express a somewhat outdated idea about intuition per se. In addition to his somewhat cryptic notions regarding the relationship between knowledge and intuition in the praxes of (composing) improvisers, I would rather use the term “informed intuition”. Just like processing knowledge seems impossible without a certain degree of intuition, acting on intuition depends on a body of conscious or unconscious knowledge. I will use the term “informed intuition” to address the type of intuition allowing (composing) improvisers to (instantly) generate musical content in response to a variety of musical situations, depending on their knowledge acquired by formal education, professional experience, and taste.

ex – a full sequential line (Bergonzi 2000:51)



Memorizing a line is made even made easier by full-sequential lines in which the first notes of the four-note patterns are connected by similar intervals of major seconds (such as in the example above: f, e, d, and b), minor thirds, major thirds or perfect fourths.

    These connecting intervals can also help to facilitate the sounding of implied tonal colors such as in the next example. The four-interval combination A/-2, B/3, C/4 and D/-5, a minor second, a major third, a perfect fourth and a diminished fifth, with the directions O (first interval descending, second and third ascending and the fourth descending) and permutation BDAC, results in the interval melody below. As a result of the major second intervals between the initial notes of the four-note patterns, in combination with their similar internal structure with three notes from the same whole-tone-scale, this line creates the sound of the D whole-tone scale.

The next examples are rhythmic variations I added to the five-interval patterns in the example above, without changing their order of appearance. I applied two ways of re-arranging this interval melody as a means to clarify the obscured five-interval patterns. In the first example each 4/4 bar hosts one five-interval pattern.

The next semi-sequential intervallic melody demonstrates an interesting quality of Bergonzi’s system. Using A/2, B/-3, C/3 and D/-5, interval directions K and L, and permutation 10 (B D C A), the result is an intervallic sequence that clearly refers to the sound of F713/b9, as a line variation of the F octatonic scale. Thus, an original improvisational pattern that might not intuitively pop-up easily, is created to serve as an original addition to the jazz improviser’s vast collection of “familiar licks” to embellish the octatonic scale.

ex Bird Buzz” – section A

Section B is played in a reggae rhythm, with the saxophone improvising inside the modified chord changes of the B-section of “Night And Day”. Also this section turns into a collective and free form improvisation, again in a rubato rhythm, at bar 86. At the end of this the drummer plays a cue to section C in bar 87. This section is a transposed reprise of the theme in section A and played in the same tempo and rhythmic feeling.

ex  five-interval patterns in 4/4 bars

In the second example the same 5-interval patterns are re-arranged in six 5/8 bars.

ex “Bird Buzz” – collective solo section A


3.3.3 Twelve-tone techniques

In fact Bergonzi launches a personal approach to creating tone rows with intervals arranged in an ordered succession, but without using this term or expressing any twelve-tone related theoretical context to it. His aim is to create original melodies; his means are a three-stage generative model and a thesaurus. However, the way he combines his sets of intervals, permutations and note directions can be considered an intuitive application of twelve-tone techniques. Likewise, the basic twelve-tone row variations, transposition, retrograde, inversion and retrograde inversion, are not theoretically addressed, but practically implied. They simply result from the manipulation of interval combinations by his tables of note directions and permutations.

    Essential rhythmic variations are encouraged and discussed in his introduction, but how to apply these on the interval melodies in his thesaurus is left to the intuition of the reader. Likewise, compositional characteristics such as texture, range, dynamics and form are not within the scope of Bergonzi's method.

    In principle Bergonzi wants to avoid tonal references but he admits that the saturated composer-improviser cannot exclude these. This observation points back to Wuorinen’s (1994) notion of the reconciliation of the distinct principles of content (tonal music) and order (twelve-tone music) in section 3.2.4. Earlier in this chapter I discussed this phenomenon in relation to the performance of “Tilt” and again about the collective improvisation in “Bird Buzz”. Just like myself, most of my peers have learned the music they play in a context of functional harmony. In order to learn this or any other new musical language that is in any way related to techniques of twelve-tone music, it seems a good strategy to focus exclusively on this new idiom.  By doing so, one should try to reduce the analysis of each melodic line’s possible harmonic reference to a minimum. But, unwantedly, by an almost automatic pull to one’s musical “mother tongue”, the harmonic reference cannot be avoided popping up automatically as well. Although principally unwanted, this merging of new and existing idioms serves the part of the final goal of this operation: to connect these “new” idioms with the existing ones, or at least to use them alongside. “Tilt” serves as an example of how difficult this process of incubation can be in a group situation. At the relevant recording session I had to repeatedly convince my peers to let go or to “look beyond” their traditional approach of the original chord changes of  “What is this Thing Called Love”.  Next, in the collective improvisations in “Bird Buzz” the intuitively adding of filler patterns in between the requested limited number of intervals witnessed the automatic reflexes of the musicians to complete their musical lines as conventionally meaningful “sentences”.

3.3.4 Evaluation

Considered from an aesthetic standpoint Bergonzi’s intervallic approach facilitates the creation of melodic lines that one could find challenging to the ear. Therefore, it is well suited as a tool to create original melodic lines.  For instance picking a random or conscious collection of intervals and manipulating them freely with Bergonzi’s method can be a fruitful start of a composer's writing process. I used the process of creating “Bird Buzz” as an insightful illustration. Bergonzi's model served well to generate meaningful melodic lines, both in the composed and in the improvised parts.

    Composing improvisers in jazz, as well as professional composers who work principally by the ear and by musical intuition, may consider Bergonzi’s system as a detour. Concerning the jazz artists this has to do with their obligation of composing tunes that leave enough space for improvisation by themselves and their groups members, to be marked as true “vehicles for improvisation”. I would even dare to say that a good jazz tune is partly unfinished, because it must be completed by its performance on stage, every time in a slightly different way. To classical composers, experienced in working on intuition, the system by Bergonzi might recall the strict rules of serial composition in the second quarter of the twentieth century. All of them however should realize that Bergonzi’s aim is to present the reader with a system that can be used according to his taste, technical possibilities and musical needs, in any application that appeals to his informed intuition.

    As an analytic model, improvisers can use Bergonzi’s system to analyze complex melodic sequences in order to memorize, modify or quickly transpose them. In my creation of “Bird Buzz” the codification of the intervallic patterns with the two tables rather served as an analytic tool afterwards than as a generative device. On the other hand, the restriction to the three intervals in the improvisations inspired all group members to play meaningful lines.


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ex – the same melodic line re-arranged in 5/8 meter

ex – pull to F (Bergonzi 2000:76)