Abstract This article examines four jazz compositions by Wayne Shorter, “El Toro,” “Iris,” “Pinocchio,” and “Face of the Deep,” to determine the applicability of analysis based on harmonic prolongation, voice leading, and the derivation of structural levels to works whose tonality is ambiguous. The works, in the order listed, become progressively more ambiguous harmonically, and, accordingly, the application of such Schenker-based techniques becomes progressively less convincing. In the final piece, “Face of the Deep,” the inference of harmonic prolongation becomes untenable. The author also proposes a series of style factors that can be rated from 0 to 10 to help determine the applicability of prolongational analysis to works in the jazz improvisational repertory. Wayne Shorter (b. 1933) has been a major presence in the jazz world since the late 1950s, rising to prominence as a composer and saxophonist, first in the Art Blakey band, which he joined in 1959, and then in the Miles Davis “second quintet,” which he joined in 1964. During this period, Shorter contributed significant repertory to both groups with pieces that were challenging and influential while also making his first recordings as a leader. Moreover, he expanded the resources of jazz composition by regularly incorporating the techniques of modal jazz into a harmonic palette that weaved functional and nonfunctional progressions against a formal backdrop whose overall tonality might be unclear or lacking entirely. Adding further interest was his occasional use of irregular forms, which obfuscated the four-, eight-, sixteen-, and thirty-two-measure hypermetrical structures typical of jazz tunes before 1960. In this article, I examine four of Shorter’s compositions from the 1960s by applying analytical techniques based on voice leading, prolongation, and structural levels, which have proven fruitful in previous study of the jazz repertory.1 Furthermore, in focusing on voice leading and prolongation, my article builds on prior publications2 that make use of these methods to explore both the tonal jazz repertory and John Coltrane’s middle-period compositions. Broze and Shanahan, in a corpus study of jazz harmony over a period of decades, found that during the 1950s, and in particular 1956, there was a significant transformation of tonal norms.3 The four compositions of Shorter that I discuss illustrate elements of this transformation, in which analysis by voice leading and prolongation becomes progressively less convincing as various tonal norms are less in evidence. The “jazz repertory” can be thought of as comprising two main divisions: small-scale works written or selected for improvisation, and larger-scale works, such as Duke Ellington’s Black, Brown, and Beige. While this dichotomy is deserving of fuller explication and study, my immediate concern is with four of Shorter’s smaller-scale works, which are all “tunes” or “heads” composed for improvisation.4 A difficult problem in discussing a work from this more informal side of the jazz repertory is deciding what “is” the work in question. These works often exist in multiple forms, arrangements, and performances because jazz musicians and performers in popular formats readily change and adapt the works to specific circumstances. Parts may be revised on the fly, and, although original manuscripts (when available) are surely pertinent, they may vary significantly from actual performances.5 (We shall encounter such a case below in the discussion of Shorter’s “Iris.”) Rather than considering this issue at length, as its scrutiny deserves full consideration and would sidetrack us from the main theme of this essay, I adopt Strunk’s view that the most authoritative version of a piece is its recording.6 In a given recording, the tune or head being improvised on, however, is often referred to casually as the “piece,” particularly when the following desiderata are present: the recording is an early one (if not the first) of the piece in question, it is well known, and the composer participates in and ideally directs the recording. The Shorter pieces studied in this article satisfy these criteria (although Shorter was music director only on “Face of the Deep”), so I rely principally on transcriptions of the premiere recordings. Prolongational techniques, which underlie Schenkerian analysis, are sometimes thought to be tangential to the practical concerns of jazz musicians, but they are, in fact, tools that jazz musicians use frequently. For example, the basic harmonic structure of the blues amounts to a higher-level outline that can be seen to motivate a more complex chordal surface, as in, for example, Charlie Parker’s “Blues for Alice” or the superimposed harmonies of a Coltrane improvisation. George Russell implies a similar level distinction in his comparison of Coleman Hawkins to Lester Young, with the former catching all the chords and the latter functioning as an “express steamer” that stops at only the more significant harmonic landmarks.7 Thus, musicians implicitly use prolongational concepts when they compose or reharmonize tunes and either simplify the changes or superimpose new harmonies via improvisation. Analysis through voice leading and prolongation provides a comprehensive way to examine pieces in the repertory, enabling more convenient comparisons among performers, revealing stylistic evolution, and clarifying issues in tonality and form. It may also help uncover fascinating internal subtleties of the compositions themselves. In particular, such analysis enables us to observe the clear tonalities of virtually all pre-1950s jazz evolve into a practice that by the 1960s no longer presumes the presence of a key.8 Because this article builds on previous work, let me begin with a brief summary. Martin (2011) analyzes classic jazz and popular standards, that is, tunes mostly written before 1950. These pieces are all clearly tonal, but in dealing with them via voice leading and prolongation, modifications to Schenkerian theory were suggested that seem to accord more closely with their stylistic vocabulary. A summary of primary lines in this repertory appears in Example 1. The controversial point here is an expansion of the three Schenkerian Ursätze to accommodate the tunes’ stylistic tendencies.9Martin (2012–13) explores the compositions of John Coltrane’s middle period in the late 1950s and early 1960s, in which harmonic progressions are not always functional and often feature thirds progressions. Some of the results of that study correlate well with the Shorter tunes examined here, and, hence, I reserve reference to this work until the latter part of this article.10 EXAMPLE 1. View largeDownload slide Background forms in the standard jazz repertory (Martin 2011, 16–17) EXAMPLE 1. View largeDownload slide Background forms in the standard jazz repertory (Martin 2011, 16–17) Prolongation by arrival, or PBA, is a technique first proposed in Martin (1980) that has proven useful in analyzing jazz tunes.11 The four- and eight-measure formal segments that are among the most salient features of tunes intended for improvisation generate the conditions for PBA. The basic idea is that we hear the harmonies set up at the end of four- and eight-measure segments as prolonged backward through the segment. This is because we learn to expect the arrival of those harmonies on the basis of the metrical regularity of the four- and eight-measure units and, often, by the predictable flow of the chord progression. The initial chord of a given four- or eight-measure unit, which receives hypermetrical emphasis from its placement in the form, may also be prolonged at a higher level, depending on the circumstances of the progression. Harmonic arrivals (cadences or tonicizations, for example) at mm. 3 or 4 of a four-measure unit, mm. 7 or 8 of an eight-measure group, and mm. 15 or 16 of a sixteen-measure group often prove significant. Because the pieces I discuss below were created for improvisation, they are usually repeated cyclically in the course of the performance. The periodic return of the regular four- and eight-measure units reinforces the effect of PBA and the harmonies are thus prolonged at various structural levels. Although PBA is generally created by harmonic flow and formal regularity, immediate voice-leading and tonal circumstances may influence how it is applied to a specific work. Prolongation by arrival helps to expand the possibilities of what are considered to be prolonging progressions. Example 2 shows how prolongation by arrival can be created by the harmonic and formal regularity of an eight-measure period. Staff d has the chord changes of the popular standard “Autumn Leaves.”12 At staff c, the II7–V7–I progressions of the bottom staff reduce to V7–I progressions. At level b, we see the tonicized G-major and E-minor chords, and at staff a, we see the overall key of E minor, a chord that is prolonged by the chord changes, but heard only when tonicized at m. 7 of the eight-measure period. We hear E minor as the key of the piece because of its position relative to the tonicized G major as completing the eight-measure period: G major is first heard as I, but then is understood as III at the period’s completion when E minor emerges as i. The G-major III is a standard substitute for i, and hence, at level a, we retrospectively hear an E-minor tonic prolonged throughout the eight-measure span. The tonicization of E minor at m. 7 takes precedence at the eight-measure level over the tonicization of G major at m. 3. As the harmonies repeat during improvisations, the E-minor tonic of this section is confirmed.13 In Example 2, I have aligned the prolonged chords with hypermetrical downbeats and will largely continue to do so, although in specific analyses that depict voice leading, it may be preferable to align prolonged chords at the points of arrival (such as the E-minor tonic over m. 7, as it appears at levels d and c). That is, the placement of the prolonged chords on deeper structural levels is flexible, depending on voice leading and the import of the argument. Here, for example, showing E minor over m. 1 at level a supports the idea of the entire section giving rise to E minor. EXAMPLE 2. View largeDownload slide Prolongation by arrival in “Autumn Leaves” EXAMPLE 2. View largeDownload slide Prolongation by arrival in “Autumn Leaves” Example 3, another instance of how PBA can be applied, shows the eight-measure unit that begins the refrain of the jazz standard “Sweet Georgia Brown,”14 which begins chromatically with a V7/ii chord (D7), then proceeds through the circle of fifths to the tonic F major at the end of the span, again in m. 7 of the eight-measure unit. The pattern of cycling dominant sevenths, which is quite common in American popular music, suggests that intermediate levels of prolongation may not be relevant, so level a shows the entire eight-measure span as prolonging F major.15 Again, I place the prolonged F major over m. 1 of level a to show its effect through the eight-measure span; however, an analyst may prefer to emphasize the arrival point at m. 7. EXAMPLE 3. View largeDownload slide Prolongation by arrival in “Sweet Georgia Brown” EXAMPLE 3. View largeDownload slide Prolongation by arrival in “Sweet Georgia Brown” Example 4, an excerpt from Shorter’s “El Toro,” shows how PBA can be expanded to include chord patterns that are not based on the circle of fifths but are, arguably, still prolongational. The piece is a sixteen-measure composition that divides into two eight-measure units. In the example, level d begins at m. 7, in which D♭ major has just been tonicized. Measure 8 has a Bm7–E7 progression that is a pickup to A major at the downbeat of the hyperbar at m. 9. This Bm7–E7–A progression continues a series of ii7–V7–I progressions with tonics linked by major third: A major, F major, D♭ major, and A major again at m. 15.16 Within the second eight-measure span (mm. 9–16), the arrival of A major at m. 15 would seem to be a point of emphasis, analogous with the tonicizations seen at m. 7 of “Autumn Leaves” and “Sweet Georgia Brown.” Hence, the pattern of major-third progressions at level b, isolated from the first eight measures, can be seen as prolonging A major at level c through the entire eight-measure unit of mm. 9–16. And yet, as I will argue when the work as a whole is analyzed below, other factors suggest it may be preferable to hear this section in D♭ major rather than in A major. EXAMPLE 4. View largeDownload slide Prolongation by arrival in “El Toro” EXAMPLE 4. View largeDownload slide Prolongation by arrival in “El Toro” Application of PBA becomes less convincing as works depart from the regularities observed in these three examples. While the analysis of the first tune examined, “El Toro,” does use PBA, the remaining discussions of the Shorter pieces in this article rely on it less conspicuously. The inference of a series of structural levels via PBA depends on the clarity of the four- and eight-measure hypermetrical units in which the chord progressions follow predictable or at least comprehensible patterns. As noted, the tonal and melodic factors that vary from piece to piece will affect how PBA may be understood and applied. Still, the basic idea of PBA may be grasped from analysis of the harmonic voice leading implied by the chord progressions alone, as summarized in Example 5. EXAMPLE 5. View largeDownload slide Composing-out harmonies in PBA EXAMPLE 5. View largeDownload slide Composing-out harmonies in PBA In Example 5(a), the first eight measures of “Autumn Leaves” show the initially tonicized G as a prefix to the tonic E minor; E minor, as a result, would be advanced to the next level. The chord changes, based on the diatonic circle of fifths, not only culminate in E minor, but the hypermetrical placement of this tonic in relation to G major also strengthens the inference. In Example 5(b), the first eight measures of “Sweet Georgia Brown,” the converging cycle of dominant sevenths prolongs F major, the tonic that would be advanced to the next level. Here the circle-of-fifths progression is chromatic. Example 5(c), “El Toro,” shows a cycle of third-related harmonies as prolonging AM7, which would be advanced to the next level. Although the FM7 and D♭M7 chords do not exhibit traditional tonal function in relation to A major, the sequential pattern of tonicized downbeats that can be connected by smooth voice leading within the eight-measure span (mm. 9–15) allows the inference of prolongation. If the progressions and time spans are sufficiently unpredictable or if the chords themselves are non-standard, then the harmonies will not exhibit prolongational interrelationships amenable to analysis via PBA. If other prolongational strategies, with or without PBA, also seem ineffective, then salience might be the only basis for any potential positing of structural levels.17 This is evident in the last analysis, “Face of the Deep,” but the slippery slope leading to this situation will be observable as the analyses proceed.18 EL TORO Example 6 shows an analysis of the first of the four tunes that we’ll consider, “El Toro.”19 This work was likely influenced by Coltrane’s “Giant Steps,” since much of it is based on tonicizations related by major third.20 The tune and its chord changes appear at level g. What is unclear about the tune tonally is that it begins in D minor but ends ambiguously. The tune’s clear rhythm, harmonic patterns, and four-measure phrase structure make it a good candidate for analysis by PBA. EXAMPLE 6. View largeDownload slide “El Toro” (The Freedom Rider, Blue Note BLP4156, 1961) EXAMPLE 6. View largeDownload slide “El Toro” (The Freedom Rider, Blue Note BLP4156, 1961) Although the first four measures of “El Toro” are in D minor, its second four measures tonicize D♭ major. At the second half of the tune (beginning at m. 9), the relationship to “Giant Steps” becomes clear, with tonicizations every two measures related by major thirds; that is, A major at m. 9, F major at m. 11, D♭ major at m. 13, and A major at m. 15. The melodic sequence is abandoned in m. 12 at the II–V of D♭ major, but the harmonic sequence continues to A major at m. 15 to complete the cycle (as observed previously in Exx. 4 and 5[c]).21 The A major at either end of the cycle in the tune’s second half could be seen as a weak dominant of D minor, thus motivating the D minor at the tune’s beginning upon repeat. Although the AM7 chords are not dominant-seventh chord types, one of Strunk’s insights into Shorter’s harmony in general is that standard root motion for chord progressions may be maintained but with the chordal type associated with the progressions altered (Strunk 2005, 305). Ultimately, however, the A major that connects m. 9 to m. 15 is undercut by the priority given to D♭ major in the tune.22 This is clearest at level e of Example 6, which shows the tune’s harmonic outline. There, we see the opening D-minor move to its dominant V7 at m. 4 before D♭ major is tonicized in m. 7. Hence, the first half of the tune, mm. 1–8, proceeds from D minor to a tonicization of D♭ major before the second half begins at m. 9. The harmony then proceeds from D♭ at m. 7 via tonicized major thirds, that is, A major over m. 9, F major over m. 11, and the culmination of the cycle at D♭ major over m. 13. Measure 13 may also be considered the cadential end of the tune, with the four-measure unit in mm. 13–16 (which includes the harmonic cycle’s completion to A major) acting as a turnaround to the tune’s beginning. Not only does the tune come to rest on A♭4 (mm. 13–15), but its approach is also emphasized through change of melodic sequence: in place of descending fourths in pairs of measures (A5–E5 in mm. 8–9 and F5–C5 in mm. 10–11), we hear B♭4–A♭4 (mm. 12–13; in place of D♭4–A♭4). Further emphasis is given to the A♭4 through the change in syncopation (E5 and C5 are on the “and” of beat 2, whereas A♭4 is on the “and” of beat 4). Level d shows the opening D minor connecting to D♭ major over m. 7 and revoices the major-thirds section in the second half to clarify the prolongation of the high A♭. At level c, we see the large-scale thrust of the tune as D minor to D♭ major and the final tonicization of A major (over m. 15) as connecting back to D minor at the top. Note that D minor appears only in the first four measures of the tune, whereas the rest of the tune supports D♭ major. Level b presents the tune as based on a progressive (or “directional”) tonality that moves from D minor to D♭ major, with D minor as prefix. On repeated choruses, the tune alternates these tonalities at level b. At level a, PBA shows the tune proceeding from D♭ major, which then generates the progressive tonality of the b level. At level f, we see all the chords of the piece, and, at this more foreground level, the turnaround in mm. 13–16 is interesting. After the tonic D♭, the tonicization of A major is followed by an Fm7–B♭7 progression in m. 16. This II–V progression is common in jazz, but here it is not the II–V of D minor, the tonality of the tune’s opening. Rather, this B♭7 chord can be seen as a “cadential augmented-sixth chord” in D minor that proceeds directly to the tonic at the beginning of the tune. This progression is intriguing and worth pausing over to view in further detail. The cadential augmented-sixth chord, a harmony theorized by Reese,23 occurs at the end of “El Toro” and in other Shorter compositions as well. Example 7(a) shows a standard augmented-sixth chord as a predominant, designated as PD + 6. In Example 7(b), the dominant chord is omitted from the progression. Instead, the augmented sixth proceeds directly to the tonic, and this is the usage that Reese has called the cadential augmented-sixth chord. The augmented sixth here loses its usual dominant-preparation function by substituting for the dominant. Found also in Romantic and Impressionist music, this chord has also been called a common-tone augmented sixth, but Reese’s analysis emphasizes the weakened functionality of the progression when it occurs at cadences. In Example 7(c), we see a substitute II–V–I progression commonly found in jazz. The E♭9(♯11) chord is a tritone substitute of the dominant seventh, or A7. The B♭7 can be read as a V7 of the E♭7 chord, that is, V7/subV. However, it can also be understood as a predominant augmented sixth that would normally resolve to A7. In Example 7(d), the dominant is omitted, so that the B♭7 becomes a cadential augmented sixth—the progression seen in m. 16 of “El Toro.” (In Ex. 7(e), the same progression is shown in E♭ minor—a progression that we will later see in Shorter’s “Pinocchio.”) By substituting for the dominant, the cadential augmented-sixth chord weakens arrival at and establishment of the tonic. EXAMPLE 7. View largeDownload slide Cadential augmented-sixth chords (a. and b. from Reese 2013, 6) EXAMPLE 7. View largeDownload slide Cadential augmented-sixth chords (a. and b. from Reese 2013, 6) Returning to the issue of prolongation in “El Toro,” I note that Julien in her discussion of the tune asserts that a monotonal understanding is not justified, but rather that the work’s four keys are D minor, A major, F major, and D♭ major, an interpretation that can be seen at level d of Example 6.24 Waters, on the other hand, in his discussion of “El Toro” (2010, 142–46) arrives at two tonal centers: D minor and D♭ major, an interpretation that appears at level b of Example 6. Waters does not read D♭ major in relation to the opening D minor, but rather conceives of them as “. . . those two primary keys… .” (2010, 146). The tonal viewpoints of Julien and Waters on levels d and b are certainly possible, yet I think level a is also defensible, i.e., that D♭ major can be understood as generating the piece from a monotonal perspective. Example 8 shows a hypothetical reconstruction of the tune. The first four measures are transposed a half step down to D♭ minor, a change that clarifies the underlying D♭ tonality that I am arguing for.25 My reconstruction of “El Toro” in Example 8 is aesthetically questionable, since the primary line seems stuck on A♭. Hence, Shorter’s composition, with the first four measures in D minor, is preferable to a consistent but humdrum D♭ major. Nonetheless, the reconstruction does show how the piece can be generated from D♭ major: the brief, rhythmic, and strophic nature of the work and a reading via PBA allow us to posit D♭ major at the background from which the more foreground harmonies of the piece develop. EXAMPLE 8. View largeDownload slide “El Toro” normalized EXAMPLE 8. View largeDownload slide “El Toro” normalized Whether level a, b, or d of Example 6 best captures the tonal landscape of the piece depends on how strongly the force of PBA is understood to generate harmonic prolongation at the middleground. Given the expectations in this literature, I find it more reasonable to hear a single background tonality because this norm underlies a short, regular, rhythmic, four-measure-based form, and because the higher levels can be generated from level a so readily. Further, as the work cycles, the D-minor-to-D♭-major shift “settles in,” allowing one more easily to hear the D minor as a prolongational prefix. The tonal issue of “El Toro” is distinct from the phenomenon, frequently encountered in jazz and popular music, of beginning a song in one key, then moving to other keys as part of the arrangement. The initial key may be changed for one that better accommodates a vocalist, or to provide a “lift,” more variety, or more excitement as the arrangement proceeds. In ragtime, we encounter a related procedure, as the Trio is usually in the key of the subdominant relative to the original key, which is typically abandoned. And, of course, ragtime adopted this form from the march and other popular multi-strain forms of the nineteenth century, such as the concert waltz. These forms were very popular with the public, showing that various strategies for achieving coherence can function in place of large-scale monotonality. One can even think of such pieces as a series of tunes—a medley—whose keys have no large-scale relationship. The ear readily accepts each key in turn, and tonal comprehension takes place at the level of the individual tune or strain. In such cases as rags, marches, or multi-key arrangements of songs, it is also reasonable to claim that there is no overall tonic. Alternatively, one could argue that the final key functions as such, i.e., that PBA is operative at the level of the form. Under this model, the earlier key would be considered a prefix to the final tonic rather than the final tonic a suffix to the earlier key. In ragtime, for example, it would mean that the early strains function like a large-scale dominant to the tonic of the Trio. I think such a view may be defensible, as I have frequently listened to marches or rags and found myself looking forward to the tonality settling into the final key, which does feel to me like a tonic arrival. But what I claim for PBA within a jazz tune depends more on prolongational relationships, meter, and small-scale form rather than precedence given to a key simply from its placement alone. The nested levels—perhaps culminating in a single key—that can be inferred from a brief, rhythmic, and strophic piece based on four- and eight-measure phrase groupings seem more convincing than a diffuse medley of different tunes or strains. Such regularity is surely present in “El Toro”: it is rhythmic, with four four-measure phrases that are readily audible and, upon repetition, become predictable. Hence, its sixteen-measure strophic form allows us to internalize and develop expectations in which we can claim for it to be in four keys at level d and two keys at level b, but generated from a single key at level a. IRIS While PBA works well with a tune such as “El Toro,” let us now consider pieces in which it is less applicable, but still helpful. Example 9 presents an analysis of Shorter’s “Iris.”26 Level f of Example 9, the tune’s lead sheet, shows a sixteen-measure form that readily divides into four four-measure phrases as a double period. Each phrase ends with a long note, as seen in mm. 4, 8, 12, and 16. The especially long E4 in mm. 7–8 divides the piece in half before the long E♭4 in mm. 9–10 initiates the piece’s second half. Level d shows a melodic and harmonic outline of the piece. EXAMPLE 9. View largeDownload slide “Iris” (E.S.P., Columbia CL2350, 1965; transcription, Waters 2011, 85) EXAMPLE 9. View largeDownload slide “Iris” (E.S.P., Columbia CL2350, 1965; transcription, Waters 2011, 85) The tonality of “Iris” is unclear. As compared with “El Toro,” the tune features a slower tempo, no harmonic or melodic sequences, and melodic phrases that float within the four-measure units. Hence PBA is less applicable than in “El Toro,” although arrival points are significant at mm. 7 and 15 as well as the hypermetrical emphases of mm. 1, 5, 9, and 13. For large-scale prolongation in “Iris,” level b shows the tune’s principal harmonies most clearly. The Fm11 chord at the beginning supports G4 as the primary tone. The G4 proceeds to F4 over m. 4, as supported by the E♭m7 at the end of the first four-measure unit. (This E♭m11, a more conventional chord in the progression, appears at the deeper levels and is substituted by G♭M7 at the foreground.) The F4 proceeds to E4, supported by A♭M7(add♯5) in mm. 7–8. (I will explain the diagonal line between these two chords shortly.) Thus, the first half of the piece features a G–F–E descent. The second eight measures, as seen again at level b, are harmonically simpler than the first eight. The Cm11 at the beginning of m. 9 supports E♭4, which follows smoothly from the E4 of mm. 7–8. The C minor then proceeds to the D♭7(♯11) first supporting E♭4, then moving through D♭4 to B♭3, the thirteenth of the chord. Thus, we can follow a melodic descent through the piece supported by harmonies that emerge at hypermetrically important moments in the form. The concluding harmony of “Iris” (D♭7(♯11), prolonged in mm. 13–16) establishes a point of arrival, but it can also be heard as connecting to the opening chord of the piece (Fm11) as a cadential augmented sixth to a tonic, and, indeed, Strunk has suggested F minor as an overall tonic.27 C minor, however, may better capture the tonality of “Iris” than F minor. With a C-minor reading, the D♭7 harmonies prolonged in mm. 13–16 are tritone substitutes of G, the dominant of C minor. At the end of m. 16, D♭7(♯11) proceeds to the opening Fm11, a iv chord, deceptively. Level a of Example 9, to which I’ve added Roman numerals, clarifies a C-minor reading: this key, implied in the piece’s first half, sets up its explicit appearance in the second half. Over m. 7, I provide an implied dominant in parentheses, a chord that does not appear in the tune. I view it as motivated by an elision of the chords connected by the diagonal line at level b, where the F4 atop the E♭m7 chord is taken over by the A♭ harmony to provide, at level a, the A♭M7(add13) as a VI chord. This VI chord, then, is viewed as a standard slide chord into an implied G7. With the implied dominant over m. 7 at level a seen as supporting 4^ melodically, the piece’s primary line emerges as 5^– 4^–♭ 3^ of C minor. The piece never proceeds to 1^, thus providing the tune with a degree of circularity.28 The D♭7 chords in the piece’s second half strengthen a C-minor reading and hence the piece’s circularity, as the return to the beginning via a deceptive cadence propels the piece forward again to its more stable second half. The harmonies and form used for the solos can also be seen as supporting C minor. A C-minor reading for “Iris” supplies a raison d’être for the foreground chords in the first period (level f), as they can be read as a destabilization or “de-functionalization” of the more conventional background hypothesized at level a. For example, the melody at level f shows at m. 4 an extended G♭M7 chord. This chord can be thought of as a substitute for E♭m7 (hypothesized at the deeper levels), thus providing the opening Fm11–EM7–G♭M7 move a more conventional source.29 Another unusual progression appears in the second phrase of the first half of the tune, mm. 5–8 at level f. Here we find B♭7alt–D♭7–A♭M7(add♯5). In parallel with the first half of the period (mm. 1–4 at level f), we can see this nonfunctional progression as based on the more functional progression shown over these measures at level d. There, we find that B♭7 is a form of II chord in a II–V–I progression, with tritone substitution of the V to become A7, which then proceeds to A♭M7 at m. 7. In place of the A7, however, we find the foreground harmony replaced by D♭7. Some of the voice-leading motions to the A♭M7 chord are preserved by this transformation, but function is weakened because of the irregular root movements. The D♭7 also serves to anticipate the C-minor tonality of the piece’s second half. Additional support for “Iris” being in C minor is provided by Shorter’s original lead sheet, as seen in Example 10.30 The melody appears at level f of the example and is from the copyright deposit in the Library of Congress. Here, we find a mixed tonality of C major and C minor.31 As opposed to the standard (i.e., recorded) version of the piece, the draft differs insofar as it is in 44 time with two five-measure phrases. Under revision, each measure of the 44 draft is transformed into two measures of the 43 final, with the exceptions of the odd mm. 5 and 10, which are omitted. The final 43 version also omits the cadence to the tonic in mm. 9–10 by prolonging the dominant there as a tritone substitution, followed by the return to the top as a deceptive cadence. EXAMPLE 10. View largeDownload slide “Iris” reconstructed lead sheet from copyright deposit at The Library of Congress (Waters 2011, 85) EXAMPLE 10. View largeDownload slide “Iris” reconstructed lead sheet from copyright deposit at The Library of Congress (Waters 2011, 85) Level f of Example 10 shows that most of the harmonies are conventional functions in C major and C minor, although unusual progressions also appear. In the first phrase, the opening Fm9 can be seen as ultimately leading to the D♭7 at beat 3 of m. 3 (level a); this D♭7 is a tritone substitute for the dominant leading to the cadence on CM7 at mm. 4–5. The EM7 and G♭M7 chords in mm. 2–3 are more unconventional, but can be seen as suffix neighbors to the opening Fm9, as is clarified at levels c and b. In the second phrase, the chords are all functional in C minor except the AM9 chord in m. 8. This AM9 balances the chromatic EM7 and G♭M7 chords of the opening phrase and can be understood as a prefix neighbor to the dominant G9(♯5) at m. 9 (level c). The concluding C9(♭5) chord is both a tonic and a V7/iv that leads back to the opening Fm9. Shorter’s draft of “Iris” in Example 10 features a descent of a clear primary line from 5^ to 1^, with 1^ supported by a tonic C chord. The primary line is chromatic at level b, but, at level a, the piece conforms remarkably to a Schenkerian 5^– 4^– 3^– 2^– 1^ prototype supported by standard tonal functions (albeit, with jazz chords). I suspect that the Miles Davis group may have felt that the piece was too straightforward tonally and, hence, revised it into the recorded version with its tonal ambiguity and implied circularity. Moreover, because the draft is so clearly tonal and avoids an initial tonic, it would be possible to analyze it via the Schenkerian auxiliary cadence. The draft’s chromatic primary line, 5^– 4^– 3^–♭ 3^– 2^–♭ 2^– 1^ (level b of Ex. 10), introduces an EM7 over m. 3, an unusual chord that is here read as a neighbor prefix to the opening Fm7. Also at level b, the CM7 that cadences the first phrase in mm. 4–5 is transformed to C minor to open the second phrase at m. 6, as the primary line advances to E♭ and then to D. The cadence of the second phrase features a tritone substitution of the dominant (D♭7(♭5)) leading to the V chord, and then to C7(♭5). Comparison of levels b and c of the example reveals an elegant diminution. First, over level b we see a G–G♭–F voice-leading line extending from m. 1 to m. 3. At level c, this same line appears over the first two measures with a pause on F supported by G♭M7. In comparing both levels to the foreground at level f, we find Shorter retracing the basic melodic motion of the phrase. The unusual EM7 chord, moreover, occurs at both levels c and b. At level c (over m. 2), it leads to the G♭M7; then at level b (over m. 3), it proceeds through D♭7 to the cadence in C major. The unusual emphasis on the EM7 chord in the first phrase adds chromatic complexity to the C-major key, a complexity echoed by the AM7 chord in the second phrase (level c, over m. 8). Levels d and e embellish the basic outline found on the deeper levels. Level d adds pickup notes to significant tones found at level c. We also see the neighboring motion of the D♭7 chord (over m. 7), which serves to prolong C minor. At level d, all the chords in the piece are accounted for. At level e, the remaining melodic notes are viewed as embellishments to the principal notes appearing at level d. The clear C tonality of the draft of “Iris” prefigures the more ambiguous C tonality of the version as recorded.32 The recorded version improves the original while keeping many of its structures intact. PINOCCHIO My discussion of “Iris” proposes a structural-level analysis that, although less clear-cut than the analysis of “El Toro,” is straightforward. Example 11 presents an analysis of “Pinocchio,”33 a composition even more tonally ambiguous than “Iris.” In place of the sixteen-measure regularity of the double period seen in “El Toro” and “Iris,” here we find an eighteen-measure asymmetrical double period, where the second period is extended from eight to ten measures. This alteration, however, is a readily perceivable departure from the 8 + 8 convention.34 Level g provides a lead sheet; it shows how the first period, mm. 1–8, functions in a manner similar to a sentence with a one-measure melodic motive and two extensions of that motive that proceed to a cadence in mm. 7–8. EXAMPLE 11. View largeDownload slide “Pinocchio” (Nefertiti, Columbia CS9594, 1967; transcription Waters 2011, 229) EXAMPLE 11. View largeDownload slide “Pinocchio” (Nefertiti, Columbia CS9594, 1967; transcription Waters 2011, 229) The second period, mm. 9–18, begins with a contour inversion of the melodic motive seen in m. 1. The second phrase of the second period begins at m. 13, and it is this phrase that is expanded to six measures. In our previous two examples, the primary cadence occurred at m. 15 of the two-period sixteen-measure form, but here, the expanded second phrase puts the cadence at m. 17. There, the extended B13(♯11) chord may be read as a tonic, which, at the same time, is a cadencing augmented-sixth chord resolving back to the E♭m 96 of the beginning, a move seen in “El Toro.”35 Level b of the example shows the prolonged harmonies created by PBA at the main formal divisions of the tune. The E♭m 96 harmony at the beginning supports B♭4, and this chord proceeds to Gm9(♯7) over mm. 7–8 at the end of the first period, a harmony that supports A4. Over m. 9, the A4 continues melodically, now supported by a C13 chord. At this point, we note (from level g) the C7alt chord that cadences to the final B chord. This C7alt, a tritone substitute of the dominant F♯7, functions as a structural dominant. Hence at level b, I view this chord in its original F♯7 form as continuing the dominant function of the C13 over m. 9 and thereby tonicizing the final B13(♯11) that ends the tune. With the B chord that ends the tune understood as a tonic, the E♭-minor chord that begins the piece can be read as a iii chord, a standard substitute for tonic harmony.36 At level a over m. 1, this tonic substitute appears as an extended BM7 chord. Thus, level a posits an overall tonic-dominant-tonic structure spanning the tune, with these chords appearing over mm. 1, 9, and 17, the most significant measures of the form. This three-part harmonic structure supports a descending primary line of 7^–♭ 7^– 6^ in B major. At level b, the cadential Gm9(♯7) over mm. 7–8 sets up the C13 at m. 9. As already pointed out, this extended dominant seventh on C is viewed as prolonged to the F♯ extended dominant seventh over m. 16 that tonicizes the final B chord. At level c, the B tonality receives further support. Over m. 5, we find a B chord. Over m. 13, an extended F♯sus chord combines with the C13 over m. 9 to enhance the dominant motion to B for the cadence at the end of the tune.37 Although this concluding B13(♯11) chord includes a major third and therefore suggests B major, the other appearances of B chords in the tune are with a minor third. Hence, the piece can be viewed as in a mixed B-major and -minor tonality. As we proceed to the foreground, the tune takes on harmonies that gain coherence through their relationship to the overall B tonality, often as passing or neighbor chords and sometimes as substitutions that “de-functionalize” the principal tonality. For example, at level e, an Am9 chord over m. 2 supports the neighbor motion B♭–B♮–B♭. This is an instance of what may be called the “II-for-V” substitution, i.e., without the intervening D7 that would lead normally to D♭. The II-for-V substitution was first described by Waters,38 although he does not name it as such. Example 12 shows that its behavior is analogous to the cadential augmented-sixth chord in its weakening of tonic arrival. Example 12(a) shows a conventional II–V–I progression with the II–V as a tritone substitute. In Example 12(b), functionality is weakened: by omitting the dominant, the ii chord moves directly to the tonic. In effect, the ii of ♭II substitutes for the V chord. The lack of a dominant imparts a cadencing function to the Am7 because of its position. The II-for-V substitution parallels the function of the cadential augmented-sixth chord, as both proceed directly to the tonic and forego a dominant. Examples 12(c) and 12(d) show the same progression proceeding to E♭ minor—the latter progression being the one just observed in “Pinocchio.” EXAMPLE 12. View largeDownload slide The II-for-V Substitution (from Waters 2011, 232) EXAMPLE 12. View largeDownload slide The II-for-V Substitution (from Waters 2011, 232) Returning to the Pinocchio analysis (Ex. 11), we see that at level f an Am chord reappears over m. 4. Waters points out that its resolution to Bm in m. 5 can be understood by viewing this Am as a substitute for CM7,39 which is shown at level e. The II-for-V move occurs yet again at level e, with the Bm chord in m. 10 as a ii chord with missing E7 in moving to E♭m over m. 11. Finally, at level e, we view the dominant of B over m. 16 as being introduced by the Em9 in m. 14 and F13(♯11) in m. 15. The smooth passing motion of these chords to the F♯7 in m. 16 is then subverted at level f, as C7alt in m. 16 substitutes for the F♯7. In “Pinocchio,” we can often interpret seemingly nonfunctional foreground chords by seeing them in relationship to the principally prolonged chords occurring at the deeper levels. These more foreground chords are then interpreted according to their voice leading, participation in standard harmonic substitutions, and position within the phrase. Also, PBA helps determine the hierarchy of the harmonic prolongations according to corresponding levels of hyperbars and cadential arrivals within the double-period form.40 As “Pinocchio” recycles, the irregularity of its eighteen-measure form and lack of a strong cadence to any key help emphasize the vagueness of its tonality. I have tried to build a case for “Pinocchio” as being in B with a 7^–♭ 7^– 6^ primary line, but I emphasize that more significant than determining a final key is the voice leading of the chords and melody through metrical placement and prolongational relationships in the expanded double-period form. Whether the piece is in B or not, Shorter has ably organized the tune via the primary line supported by B-related harmonies, diminutions of the primary line, and the harmonic interrelationship of the chords as supported by the form’s metrical hierarchy. FACE OF THE DEEP For our final analysis, let us consider “Face of the Deep,”41 which appears in Example 13. The piece is not tonal, but continues to project the four-measure segments in 44 time found in most jazz tunes. Is it possible to understand harmonic prolongation, perhaps assisted by PBA, as viable despite the lack of tonal functionality? The score at level d is taken from the copyright deposit in the Library of Congress; I’ve recopied it as it appears there with the exception of the “and” of beat 4 in m. 6, where I changed the E♯ shown in the soprano to the D♯ that Freddie Hubbard actually plays.42 The example also omits an out-of-tempo introduction and, as a whole, is performed freely. EXAMPLE 13. View largeDownload slide “Face of the Deep,” The All-Seeing Eye, Blue Note BLP4219, 1965; from Shorter’s score as copyright deposit at The Library of Congress EXAMPLE 13. View largeDownload slide “Face of the Deep,” The All-Seeing Eye, Blue Note BLP4219, 1965; from Shorter’s score as copyright deposit at The Library of Congress “Face of the Deep” doesn’t look like a jazz-tune lead sheet; rather, the score appears as a four- or five-part chorale without supporting chord symbols. Many of the harmonies appear to be jazz chords, but not all of them, and they are not linked by functional progressions. Nat Hentoff, who wrote the album’s liner notes, quotes Shorter as thinking of the piece “in minor” while avoiding “traditional cadences”43—an interesting remark, but note that Shorter prefers to think of a general “minor” quality as pervading the piece in place of a specific tonality.44 The upper staff of level d shows the melody in the soprano. The main motive appears in mm. 1 and 2. In mm. 2–4, we see an expansion of this motive, leading to a long F in m. 4 to complete the phrase. Measure 5 implies a parallel four-measure phrase, since the melody begins as it did m. 1. A deviation begins in m. 6, but the four-measure unit is again completed at m. 8 over the long BM7 chord. The last segment, mm. 9–13, is five measures long, in which m. 13 repeats m. 12; hence, this is a four-measure phrase extended to five measures. The relative structural weight of the events depicted at layer c of the analysis emerges from the foreground emphasis on chords that support melodic resting points. Obvious melodic embellishing tones are also omitted at this level. Level b further simplifies level c, showing more clearly the harmonies that support the key melodic moments of the piece. Salience is the criterion from which levels b and c were derived. It would be difficult to argue that the more foreground events at level c harmonically prolong the events advanced to level b; rather, the deeper level emerges directly from the basic melodic motion and durational emphases. We proceed to level a by simplifying level b in just the same way, and thus arrive at the piece’s most significant harmonies. Here I’ve added lead-sheet chord symbols to emphasize their lack of harmonic function. Does the rationale of the analysis, creating structural levels from the relative weight of foreground events, result in a nested prolongational structure? The lack of functional relationships between the harmonies at level a would seem to render traditional conceptions of prolongation as inappropriate. Moreover, asserting prolongation via PBA would also not be convincing, because the lack of rhythmic articulation in the performance obscures hyperbars and, as a result, negates metrical emphases. That is, although the score visually clarifies the beginnings and ends of two-, four-, and eight-measure units, any implied formal hierarchy is undermined by the lack of rhythmic articulation. Ultimately, the analysis as presented merely assumes that the chords supporting melodic resting points and phrase beginnings take on more significance than intervening harmonies. While such a procedure is reasonable, it does not demonstrate prolongation in the traditional sense of composing out larger-scale harmonies. Another approach would be necessary to claim that level a generates the lower structural levels or that level a is itself a product of some deeper background.45 Despite the lack of prolongation in the analysis, significant compositional points emerge from viewing the relative weight of foreground events. For example, the melodic motive A♭–G–F in m. 1 (level d) reappears in mm. 2–4. At level a, this motive stretches over mm. 1–4, so its more foreground occurrences can be heard as diminutions. As seen in the score at level d, the A♭–G–F motive returns in mm. 9 and 10; at level a, we can see the A♭–F minor third of this motive extended a further minor third downward to D, the last note of the melody. Level a also shows a melodic succession akin to a primary line, which builds to C over m. 6 before descending to the final D. The important notes in this primary line are closely associated via register, although a purely stepwise pattern is lacking. CONCLUDING REMARKS AND “INSIDE-OUTSIDE” METRICS Throughout this article, I have been concerned with determining if a piece can be understood as being in a certain key. If nested prolongational levels can be shown to exist, then the deepest level of that prolongation would be some form of the work’s tonic, i.e., the key of the piece, itself a “level” abstracted from the harmonies of the primary line. (In the case of directional tonality, then the deepest level would show the progression from one key to the next.) A tonal piece’s key signature not only provides notational convenience, but also designates (or at least suggests) the piece’s overall tonic.46 Thus, determining a piece’s key helps provide an understanding of its tonal norms, how its harmonies may be hierarchized, and—if hierarchization occurs—how structural levels may be inferred. Whether a single key for a work exists depends on how deeply the sequence of prolongational levels is found to be convincing. Moreover, our ability to infer a convincing sequence of structural levels depends on style factors that can be compared among works in the repertory. The works by Wayne Shorter examined in this article feature progressively more challenging prolongational relationships, as a result of the accumulation and intensification of nonfunctional harmony allied to less clearly articulated form. We can see how the syntaxes of these pieces vary by comparing them to a chart developed in Martin (2012–13, 216), which specifies a range of significant style factors in jazz tunes. This Jazz Repertory Style Factors chart appears as Example 14. EXAMPLE 14. View largeDownload slide Jazz Repertory Style Factors (Martin 2012–13, 216) EXAMPLE 14. View largeDownload slide Jazz Repertory Style Factors (Martin 2012–13, 216) The Jazz Repertory Style Factors chart categories jazz tunes according to four criteria: form, foreground harmony, primary cadence, and secondary cadence; a proper mix of these four categories may result in a series of structural levels, given as a fifth category, and a primary line, given as the sixth category. Under each of the first five categories a series of stylistic factors appears as A, B, C, and so forth. As one progresses through these factors, the tunes featuring them move from regular and “inside” to irregular and “outside.” For example, the classic tunes of pre-1950s jazz all take the A, B, or C possibility for form, the first stylistic category; and, for categories II through V, possibility A.47 The inside or outside quality of a tune can then be approximated numerically, as seen in Example 14. For example, category A under each factor shows a metric of . Thus, a classic jazz tune might show an AABA form, which equates to ; its foreground harmonies will be functional, hence a ; it is likely to end with a perfect authentic cadence, hence a ; its secondary cadence is likely to be a half cadence, hence a ; and the inference of structural levels is likely to be convincing, hence a . The total stylistic metric for such a jazz standard will equate to , since all five categories will be . Tunes written after 1950 are more likely to feature a wider stylistic range and, hence, a descriptive metric less than . In colloquial jazz parlance, metrics that are lower correspond to more “outside” tunes, and those that are higher correspond to more “inside” tunes. While I emphasize that the results are merely suggestive, this chart helps provide a sense of a work’s amenability to analysis based on prolongation. Let us consider each piece in turn. Both Julien and Waters agree that tonal centers exist in “El Toro”; however, Julien argues for four irreducible tonics, Waters for two, and this article for one. Julien understands the tonics as only local phenomena, arguing that standard harmonic function does not link the tonicizations of F major, A major, and D♭ major, thus ruling out prolongation at higher levels. This is a consequence of the transformation rules she develops from the Strunk model, in which bebop-oriented functional changes underlie harmonic prolongation. Further, Julien reads the form as an irregular 7 + 9, which further complicates the inference of prolongation. Waters seems to agree that prolongation is possible when a tonicization pattern occurs through major-third relationships, as in the second half of “El Toro.” Although he points out that A major can be seen as prolonged through the second half (and hence motivating the D minor at the top), he ultimately settles on D♭ major as the key of the second half. While I agree that the question of key(s) cannot be resolved definitely, I think that, within a sixteen-measure regular form with standard bebop progressions resolving to tonics linked by major third, a D♭-major tonality is prolonged through the piece’s second half. The D minor in the first four measures is also clear, although this key is never tonicized, even upon cyclic return from m. 16, where the augmented-sixth substitution is used. Because D minor in mm. 1–4 is succeeded by D♭ major in mm. 5–16, are there then two keys (Waters’s argument) or can we think of D minor as a prefix to D♭ major in a prolongational relationship? A summary of the overall tonal model of “El Toro” appears in Example 15. The D-minor tonality opening the piece, as a prefix to the tonicization of D♭ that is completed in m. 7, functions rather like a large-scale appoggiatura. This prolongation of D♭ major equates to how we understand prolongation arising diatonically, but extended here to the half-step voice leading of D minor to D♭ major. Afterward, D♭ major is prolonged through the major-thirds tonicizations of the piece’s second half. The large-scale ♭II7–I7 can be viewed as a subv7–I7 in D♭ with the subV7 appearing as a Dm7 chord rather than a form of dominant seventh (D7 as subV7). This relationship expands our understanding of how prolongation may occur by a major-third-to-minor-third alteration in the standard jazz substitute dominant and ultimately permits the inference of a large-scale D♭ major over the course of the tune. EXAMPLE 15. View largeDownload slide Large-scale prolongations in “El Toro” EXAMPLE 15. View largeDownload slide Large-scale prolongations in “El Toro” The Library of Congress deposit of “Iris,” which I am calling a draft, is also fairly regular in its harmonic profile, while its form, with two five-measure phrases, extends the four-measure phrase model. Most of the chord changes are regular, as are the cadences. Example 16, taken from level b of Example 10, shows these regularities as providing an overall tonality that mixes C minor and major, which gives rise to structural levels and even a clear primary line. The Davis group may have altered the lead sheet, because its character may have been too straightforward aesthetically. EXAMPLE 16. View largeDownload slide Primary line in “Iris” (draft) EXAMPLE 16. View largeDownload slide Primary line in “Iris” (draft) “Iris,” in the version as recorded by the Davis quintet, also presents problems regarding prolongation, although I have argued for an overall tonality of C minor. The form normalizes the draft’s five-measure phrases, but its harmonic profile is more complex. The primary harmonies appear in Example 17, which is modeled on level b of the full analysis (Ex. 9). After beginning on an Fm9 chord, the piece moves to E♭m7 in m. 4 (which at the foreground becomes G♭M7); the second four-measure phrase completes the first period on the irregular A♭M7(add♯5) chord. I omit Roman numerals for both the E♭m or A♭ chords, given their distant functional relationship to C minor. The Cm7 and D♭7 chords in the piece’s second half, however, may be read as i and subV7 in C minor. These impart a significant C-minor aura to the piece’s second half, which, heard as extending to the piece as a whole, helps to balance the effect of the postbop changes of the first half. The primary cadence is a form of half cadence (i.e., to subV7), which heightens the sense of circularity in the piece, particularly as there is no authentic cadence. Nonetheless, prolongation assisted by PBA helps fix the chords of Example 17 as the principal harmonies within the form. EXAMPLE 17. View largeDownload slide Large-scale prolongations in “Iris” EXAMPLE 17. View largeDownload slide Large-scale prolongations in “Iris” Harmonic prolongation in “Pinocchio” is even more ambiguous than in “Iris.” Whereas the C-minor tonality in the second half of “Iris” seems relatively clear, “Pinocchio” features postbop changes throughout. Its final cadence (mm. 16–17 of Ex. 11, the full analysis) suggests a tonality of B, but this subV7–I does not support conventional cadencing melodic notes; that is, instead of, say, ♭ 2^– 1^, we find ♯ 4^ over C7 followed by 6^ over B7. The principal tonal prolongations emerge most clearly in Example 18, which is taken from level b of Example 11. The opening E♭m 96 is a substitute for the tonic B, hence it is labeled as iii; the cadence of the first half of the tune is to a nonfunctional Gm♯7 chord; at the second half hyperdownbeat of m. 9, we hear C7, the subV7 chord; the quasi-dominant F♯13(sus4) chord enters at the hyperdownbeat of m. 13, which prepares the subV7–I in mm. 16–17.48 Although these harmonic guideposts can be seen as ultimately organizing the more-foreground levels, the lack of chord-progression patterns and the nonfunctional nature of many of the foreground chord changes weaken the establishment of prolongational levels as compared to our previous examples. Nevertheless, as argued earlier, the overall voice leading helps to establish the deep middleground shown in Example 18 by expanding the concept of harmonic prolongation. EXAMPLE 18. View largeDownload slide Large-scale prolongations in “Pinocchio” EXAMPLE 18. View largeDownload slide Large-scale prolongations in “Pinocchio” In the final work to be examined, “Face of the Deep,” harmonic succession is too vague to warrant even a postbop label. In a work such as this, structural levels can be hypothesized, but any such inference would seem to be based on salience. The criteria for salience typically vary, but in “Face of Deep” we hear the following harmonies emphasized: phrase beginnings, phrase endings, and chords of greater duration as compared to surrounding chords. Meter is not projected in the piece’s performance, and PBA seems not to be relevant. The smooth voice leading of the chorale-like structures gives rise to the chord sequence shown in Example 19, which reproduces level a of Example 13. The structural levels culminating in Example 19 were fashioned by first omitting decorative notes (i.e., those mimicking the behavior of non-chord tones in more conventional harmonic environments), then omitting harmonies with clearly less significance according to their positions within the phrase. The resulting chord sequence of Example 19 is analogous to the background and deep middleground levels posited in the analyses of the other Shorter tunes, but is of a qualitatively different type given that it is not derived from harmonic interrelationships facilitated by characteristic voice leading. EXAMPLE 19. View largeDownload slide Salient harmonies in “Face of the Deep” EXAMPLE 19. View largeDownload slide Salient harmonies in “Face of the Deep” The more that jazz compositions deviate from predictable form, functional harmony, and standard cadences, the more difficult it is to apply analysis based on voice leading and prolongation. Eventually, we are confronted with pieces such as “Face of the Deep,” whose harmonic vocabulary departs from postbop practice. Although Neo-Riemannian analysis has been applied to postbop works,49 jazz pieces and performances that border on free jazz would seem to elude fruitful application of such techniques and may best be described by pitch-class sets, in which the presence of structural levels is at least controversial and, ultimately, may not be pertinent. Analysis that posits semitone or common-tone voice leading through the work can help clarify melodic roles, but is insufficient to give rise to the hierarchies that underlie prolongational levels derived harmonically. Structural levels can be hypothesized for such pieces, and they may yield useful analytical results, but foreground salience underlies the choice of events specified at each level. Within jazz, attempts have been made to analyze these repertories by Steve Block, who has applied pitch-class set analysis to Free Jazz,50 but his work seems not to have generated subsequent studies. Other approaches may ultimately prove to be valuable but, so far, have not been forthcoming. Clearly, much remains to be done in the analysis of works such as “Face of the Deep” and others that transcend postbop norms and seem more closely allied to Free Jazz practice. Footnotes 1 Many studies have applied the techniques associated with the work of Heinrich Schenker to the jazz repertory. Publications based directly on Schenkerian principles include Stewart (1974/1975); Larson (1996, 1998, 2009); Heyer (2012); and McFarland (2012). Studies influenced by Schenker include Strunk (1979); Martin (1988, 1996, 2011, 2012–13); Julien (2003, 2009, 2011). The two immediate predecessors of this article are Martin (2011 and 2012–13), references to which will appear in the course of the article. 2 Important studies of Wayne Shorter have appeared in the publications of Patricia Julien, Keith Waters, and Steve Strunk, and my work builds on their many insights. Julien (2003) analyzes the harmony of a selection of Shorter’s early compositions by extending Strunk’s method of viewing bebop harmony on the basis of structural levels and transformations. Julien’s studies help account for Shorter’s harmonic moves as found in his early work. Waters has previously examined the pieces I discuss here, as will become clear. I thank him for the copies he sent me of the Library of Congress manuscript deposits of Shorter’s “Pinocchio” and “Face of the Deep,” for pointing out the relevance of Reese’s work on augmented-sixth chords (2013), for alerting me to the F7 chord at the beginning of m. 10 of “Pinocchio” (which does not appear in his transcription, Waters [2011, 229]), and for helpful comments on earlier drafts of this article. I also wish to thank the anonymous readers, whose excellent suggestions I have adopted throughout. 3 Broze and Shanahan (2013, 41). 4 Because of my focus on the improvisational jazz repertory, any techniques advanced in this article would have to be revised or expanded to apply to large-scale jazz compositions or to other relevant tonal or modal repertory. 5 The Miles Davis group, which first recorded two of the four works discussed in this article, famously altered compositions in the studio. Joe Zawinul’s composition “In a Silent Way,” for example, appears very differently on its premiere recording by Davis (In a Silent Way, Columbia CS9875, recorded 18 February 1969) as compared to Zawinul’s subsequent recording (Zawinul, Atlantic SD1579, recorded 6 August 1970). Although each version may be considered a separate object of analysis—which “Silent Way” is the “piece”? Here, Zawinul’s music direction in the follow-up recording would seem to make it the more authoritative. Moreover, in some instances the “piece” may be even more abstract, i.e., an entity potentially inferable from some combination of lead sheets and authoritative performances. In “Blue in Green,” for example—a piece attributed to Miles Davis and/or to Bill Evans—the melody is too freely performed by Davis on the work’s first recording to be clearly defined. This piece even calls into question the validity of the concept of authorship in jazz works, as discussed in Fyffe (2014). 6 Strunk (2005, 328n3). 7 “Now let’s say you’re Coleman Hawkins and you’re going to take a trip down the river on a steamer called ‘The Melody (parent scale) Inferred by each Chord.’ This steamer is a local and will make stops at all the towns along the river… . Lester Young takes an express steamer that makes stops only at the larger ports along the river (the tonic stations)” (Russell 1959, xviii). 8 Pre-1940s jazz occasionally experimented with tonal norms (e.g., Norvo’s “Dance of the Octopus” or Hawkins’ “Queer Notions” [Schuller 1989, 516]), and, by the later 1940s, modernists, such as Lennie Tristano, continued to push the envelope, but it was during the 1950s that widespread innovation in form and tonality began to challenge tonal assumptions. These experiments, in part, provided the motivation for many artists associated with Free Jazz. I also note that, because of the evolution of jazz practice, I feel that there is no single “jazz harmony.” Rather, “jazz harmony” is a catchall term for a number of different practices that depend on the type of jazz being discussed. Consider, for example, the diverse harmonic practices of Louis Armstrong, Art Tatum, Wayne Shorter, and Ornette Coleman. We can further particularize jazz harmony by remembering to separate considerations of chord progression from chord type. While this may be obvious, I do note that the routine use of the term “jazz harmony” seems to presume a single practice. 9 Other theorists have suggested modifications to and expansions of the three Schenkerian Ursätze as well. See, for example, Neumeyer (2009). Emendations to Schenker’s theory, as presented in Schenker 1935 , have appeared as soon as his original teaching began to spread in the mid-twentieth century. An early important work that expands Schenkerian theory is Salzer (1962), a corrected republication of the original edition in 1952. 10 Martin (2012–13). 11 See Martin (1980, 33–38). Other discussions of PBA can be found in Martin (1988, 12–25), Martin (1996, 9–10), and Martin (2012–13, 199–202). 12 “Autumn Leaves” (Kosma-Prévert-Mercer, 1946). 13 The second section of the tune also confirms E minor, as the section begins with a V7–i progression to E minor followed by standard chord changes that can be directly read in the key of E minor. 14 “Sweet Georgia Brown” (Bernie-Pinkard-Casey, 1925). 15 The pattern of dominant sevenths cycling through the circle of fifths to reach an ultimate tonic has been called “funnel tonality” (Johns 1993). Johns lists several well-known songs with this plan, including “Ballin’ the Jack” (Smith 1914) and “Up a Lazy River” (Arodin-Carmichael 1930). The harmonies, as it were, funnel down to converge on a tonic at the end of a predictable time span. Johns, however, does not pursue the possibility of the cycle as generating prolongation and structural levels. 16 At m. 16, the chords in parentheses at level d (Fm7–B♭7) create a turnaround to the beginning of the tune. Note that my reading of the piece as 8 + 8, which agrees with Waters (2010, 142), presents an alternative to Julien’s view of the work as an irregular 7 + 9 (2011, 176). That is, she views m. 8 as beginning a hypermetrical unit, whereas putting the tonics of the II–V–I patterns on the hyperbar downbeats yields a reading of the piece as a more regular 8 + 8, which then segments to 4 + 4 + 4 + 4. How the positioning of a II–V–I pattern within the four- and eight-measure units of jazz standards affects our understanding of the progression is the subject of Salley and Shanahan (2016). 17 I should note that a work’s inability to be described by prolongational procedures is not a demonstration of its deficiency. Although the use of negative language is sometimes necessary in describing what kinds of harmonic and formal conditions may be lacking, these locutions should not be construed as applying to the work aesthetically. 18 Similarities can be demonstrated between PBA and the Lerdahl-Jackendoff Time-Span Reduction as well as the Schenkerian concept of the Auxiliary Cadence. The latter, for example, involves a culmination of harmonic and melodic processes without initial establishment of the harmony in question. Nevertheless, the relative simplicity of PBA makes it directly applicable to the regular and strophic metrical structures found in popular standards and jazz tunes. For the Time-Span Reduction, see Lerdahl-Jackendoff (1983, 124–78). Regarding the auxiliary cadence, Schenker writes: “The transition from harmony to harmony is made smoother by the omission of the [initial] I, the first one of the bass arpeggiation. When this tone, which generates and underlies the development, is omitted, the following abbreviated forms arise” (1935, 1:88), with reference to vol. 2 (Supplement), figure 110. These figures consist of V–I forms preceded by another harmony, such as II, III, or IV. Schenker anticipates in his figure 110(e) the significance of the II–V–I progression in jazz. Note Burstein’s summary description of the concept and how it also characterizes PBA: “Thus, the typical auxiliary cadence derives its tonal meaning within the larger context from its final chord alone; only the final chord plays a role on the deeper levels of voice leading. In this sense, the opening, later-level harmonies are ‘auxiliary’ to the final tonic” (2005, 162). 19 “El Toro,” The Freedom Rider, Blue Note BLP4156; recorded 27 May 1961; Lee Morgan, trumpet; Shorter, tenor saxophone; Bobby Timmons, piano; Jymie Merritt, bass; Art Blakey, drums and leader. 20 The analyses in this article adopt Steve Larson’s “strict use” of analytical notation (Larson 1996). In “strict use,” slurs in the prolongational levels show groupings and dependency and not direction, and only notes with stems can be advanced to a deeper structural level. While Larson (1996) is the primary source for “strict use,” Larson (2012) provides a succinct introduction to its essential principles. 21 The E7 chord in m. 14 that tonicizes A major in m. 15 is played by the ensemble, but the Library of Congress deposit of the tune, which appears in Julien (2003, 195), shows G♭7 rather than E7. As pointed out earlier, the recording takes precedence. Also, strictly speaking, the harmonic sequence is also abandoned in m. 14, as E7 (V7) is not preceded by Bm7 (ii7). 22 Waters notes the sequence of major thirds, the centrality of A major as helping to motivate the D minor of the tune’s beginning, the harmonies related by major third (beginning at m. 7 and continuing through the hyperdownbeat of m. 9, which overrides a neat division of the tune into two halves), and the tonicization of D♭ at m. 7 that helps prioritize it over A major (2010, 144–45). The tune’s second half (beginning at the pickup harmonies in m. 8) can also be seen as characterized by a circle-of-fifths progression with occasional omissions, as pointed out by one of this article’s anonymous readers: i.e., B, E, A, [D], G, C, F, [B♭], E♭, A♭, D♭, [G♭, B], E, A. With an arrival at A at m. 15, one could invoke PBA to argue for an overall prolongation of A as dominant of D minor through the piece’s second half, again motivating the D minor at the top and even suggesting an overall D-minor tonality. While this reading is intriguing, I find the prolongation of D♭ in mm. 7–13 makes it a more convincing tonal center. 23 Reese (2013) is a study of this chord as it is found in the music of Debussy and Ravel. 24 Julien writes, “‘El Toro’ exhibits four structural keys, with no sonority or tonal region exhibiting fundamental influence over the composition as a whole. Utilizing an asymmetrical AB form, the piece begins in D minor, the A section concludes in D-flat major, and the B section is governed by A major, F major, and D-flat major. The harmonic (tonal) plateaus in ‘El Toro’ do not reveal themselves to be part of a larger tonal scheme but, instead, are self-sufficient and irreducible” (2011, 176). Julien (2003, 183) expresses a similar view. Elsewhere, Julien, citing Satyendra (1992), suggests that a sequence of tonicizations linked by major third cannot result in tonal prolongation, and hence the organization is “bifocal,” as “… differing organizational principles govern different structural levels” (2009, 110–11). PBA, on the other hand, helps us to expand the kinds of relationships among chords that may result in harmonic prolongation, including third-related tonicizations. Also, as pointed out earlier (n. 13), I find a symmetrical 8 + 8 reading of the piece preferable to Julien’s 7 + 9. 25 The copyright deposit for the tune in The Library of Congress, as reproduced in Julien (2003, 195), has no key signature. This is a reasonable choice on Shorter’s part, given the chromatic nature of the harmony. 26 “Iris,” E.S.P., Columbia CL2350, 20 January 1965; Miles Davis, trumpet and leader; Wayne Shorter, tenor saxophone; Herbie Hancock, piano; Ron Carter, bass; Tony Williams, drums. 27 In Strunk’s F-minor reading, the emphasized C minor of the tune’s second half functions as a minor v chord with quasi-dominant function to the initial F minor (2005, 304–8). Strunk’s interpretation supports his observation that Shorter sometimes employs customary root progressions with unconventional chord qualities. Waters cites Giel (2004, 291–92) as suggesting the piece is in E♭ major, with Giel claiming the opening progression as a substitute for Fm7–F♭7–E♭M7. Overall, E♭ major receives too little support to be considered the key. 28 “Circular” tunes are those in which the “ending,” rather than concluding the tune, connects to the beginning. See Waters (2011, 86). Waters, Larson, Strunk, and Martin (2016) discusses circularity in jazz tunes. 29 Waters (2011, 88) cites Giel (2004, 291–92) as also suggesting this substitution. 30 On level f (the melody), I correct what are probably typos: Shorter omits the eighth rest on the “and” of beat 3 in m. 2 and the triplet bracket on beat 3 of m. 3. That is, the original has 3.5 beats in m. 2 and 4.5 beats in m. 3. 31 The Library of Congress lead sheet appears in Waters (2011, 85). Waters suggests that, because the lead sheet was deposited on 26 January 1965 (a few days after the recording), it may have been for Shorter “somehow definitive” (2011, 86n). The recorded version on E.S.P. has become the definitive “Iris,” however, and I shall refer to it as the “piece” and the Library of Congress lead sheet as a “draft.” Perhaps Shorter had the lead sheet prepared in advance and was not inclined to update it in view of the revisions made at the recording, feeling that it was “close enough.” 32 For more detail on the differences between the harmonic foregrounds, see Waters (2011, 86–89). There, Waters also discusses how the group modifies the structure of the tune for the improvisational frame. 33 “Pinocchio,” Nefertiti, Columbia CS9594, 19 July 1967; Miles Davis, trumpet and leader; Wayne Shorter, tenor saxophone; Herbie Hancock, piano; Ron Carter, bass; Tony Williams, drums. 34 Waters’s discussions of “Pinocchio” (2011, 228–32; and 2010, 154–60) include some of the points made here and provide further insight on motivic relationships at the foreground. Waters also points out that other discussions of the tune rely on the lead sheet that appears in The Real Book, which differs from what is played on the recording. Waters suggests that the six-measure phrase ending the piece “undercuts” the four-measure hypermeter and gives rise to circularity, but also that the circularity “does not seem exceptionally strong” (2011, 230). I agree with his conclusion that the tune is weakly circular. 35 Waters (2010, 154–60) examines the piece from the perspective of a root progression in major thirds, much like the one seen in the second half of “El Toro.” Unlike “El Toro,” however, the major-thirds progression in “Pinocchio” is less sequential. For example, on level g of Ex. 11, the following harmonic roots are related by major thirds: E♭ in m. 1; B in m. 5; G in m. 7; B in m. 10, beat 3; E♭ in m. 11; and B in m. 17. The melody and phrase rhythm do not align with this major-thirds progression and so the influence of “Giant Steps,” while likely, is indirect. Although the major-thirds relationship is surely pertinent, I feel that a B-major tonality may be inferred from the chord changes on the basis of prolongational relationships assisted by PBA. Waters’s discussion of the final B chord in “Pinocchio” (2010, 158–59) suggests that he also thinks of it as implying a quasi-tonic function with resolution proceeding from the weakly dominant F♯sus13 in m. 13. Waters (2011, 228–36) also discusses Shorter’s improvisation on “Pinocchio.” 36 Note the characteristic difficulty of deciding between enharmonic readings within highly chromatic environments. Should the concluding B13 be read as C♭13, or the opening E♭m6/9 as D♯m6/9? Jazz musicians, in such circumstances, tend to choose the simpler chord spelling. Even the use of subV7, a common enough chord in jazz harmony, renders chord spelling problematic. (Do we want to spell subV7 of E♭ as F♭7?) If tonality is vague (as it is in “Pinocchio”), then there seems to be no benefit in spelling all the chords “properly” in relation to some diatonic key. 37 This point continues to confirm Strunk’s observation that Shorter will sometimes use functional root motions but with unconventional chord structures over them. 38 See Waters (2010, 157) and Waters (2011, 231–32), accompanying his discussions of “Pinocchio.” Waters suggests that the progression can be seen as arising from a “sus chord imperative” (2010, 157) in the repertory, and, indeed, the chord in question can appear as a mixed function sus chord—for example, Am7/D. 39 Waters (2010, 158). 40 Interestingly, authoritative alternate versions of “Pinocchio” exist. There are two notation sources, one of them a Library of Congress deposit dated 13 March 1968 (about eight months after the premiere Davis recording) and the other a lead sheet that appears in a volume of Davis memorabilia (Bessières 2010, 129). The latter may have been a trumpet part, although it is in concert and not marked as such (as are some of the other trumpet parts that appear in the volume). Shorter eventually recorded the piece again, but not until 1978 (a decade or so after the premiere recording), when he was co-leading Weather Report with Joe Zawinul. It appears on the album Mr. Gone (Columbia JC35358, 1978). The most significant harmonic difference between the two notated versions and the premiere recording that we’ve just analyzed is that the second half of the piece shows a B♭M7 chord at m. 9. Although this differs from the subV7 (C13) played on the premiere recording, it can be read as a weak dominant (a form of VII) that eventually gives way to the subV7 in m. 16. (Moreover, both notated versions have an F♯7 chord, the standard dominant, at m. 16.) Both notated versions have a form of G♭M7 chord in m. 1 that can be seen as a substitute for the E♭m6/9 that appears on the premiere recording. The most interesting formal difference is that the lead sheet extends the final two measures by two measures: F♯m9/B bass (two measures) to FM7/B (two measures), the latter as a turnaround. The lead sheet has a thick bar line after m. 18, which suggests that Shorter may have added the two measures as an afterthought, probably to complete the four-measure unit at the end. The two added measures, of course, were not played on the premiere recording. (Also, the notated versions show that the downbeats of m. 1 and m. 9 are anticipated on the “and” of the preceding fourth beats; a pickup to m. 1 has F tied to the F on the downbeat; and, in m. 8, an A tied to the A on the downbeat of m. 9. These syncopations do not affect the analysis.) When Shorter re-records the piece in 1978, the extra two measures at the end of the piece are played, extending the piece to twenty measures. This may not be surprising, however, as the high-powered jazz-rock performance on Mr. Gone is more readily performable with four-measure symmetry. The harmony is mostly nonexistent as the recording continually cycles the melody in unison and octaves (with electronic effects), and there is no improvisation. On the second chorus, which begins at 0:58, Pastorius’s bass line, in departing from the melody, continues a C harmony at m. 8 into m. 9 and also provides an F♯–B resolution at the end of the chorus. Thus, again a B tonality is affirmed. All in all, while there are differences, the two notated versions and the jazz-rock recording do not beg for separate analyses or change how we might wish to analyze the premiere recording; the differences are much less notable, for example, than the draft and recorded versions of “Iris.” 41 “Face of the Deep,” The All-Seeing Eye, Blue Note BLP4219, 15 October 1965. Freddie Hubbard, trumpet; Grachan Moncur III, trombone; James Spaulding, alto saxophone; Shorter, tenor saxophone and leader; Herbie Hancock, piano; Ron Carter, bass; Joe Chambers, drums. 42 Again, we find an authoritative recording taking precedence over the manuscript. 43 Hentoff also quotes Shorter’s general conception of The All-Seeing Eye as a “search for added dimensions … ‘about life and the universe and God.’” “Face of the Deep,” in particular, “… is God reflecting on what He has created and on what man has done within that creation. ‘The piece,’ says Shorter, ‘is pensive and being in minor, it may not sound as if it’s very hopeful since we’re accustomed to hearing hope in music in major scales and chords. But actually “Face of the Deep” is hopeful. As you’ll hear, it doesn’t really end in the usual sense. At the close, I tried to keep away from traditional cadences. The indication is that we don’t know what will happen and, therefore, there is still hope. Also, the sounds in this piece are straight out because, in that way, I wanted to indicate that God’s thought processes are so powerful that He can overcome all of the goofs of man, and some of the goofs may be His, too—and that possibility is raised in “Chaos” as well—I mean that if He had wanted to create a world without conflict, He could have done it.’” (Liner notes, The All-Seeing Eye; “Chaos” is another piece on the album.) 44 If Shorter thinks of the piece as “in minor” but without “traditional cadences,” we might speculate on what minor key he had in mind. If we view the soprano melody apart from the chords, F minor arises as a possibility. Measures 1–4 are directly from an F natural-minor scale and cadence to 1^. The rising E–G–C figure in m. 6 creates a dominant. Measures 7–8 are out of an F natural-minor scale, but, beginning in m. 8, a descending diminished (octatonic) scale proceeds from C♯5 to D4 at the end of the tune. This diminished scale could be seen as expanding the tune’s F–G–A♭ motive as well as the F melodic-minor scale. Moreover, level a of Ex. 13 shows that many of the melodically emphasized notes are from F minor. (Interestingly, arrival at ^1 of F minor in m. 4, one-third of the way through the piece, suggests circularity.) Although F minor is present melodically through the piece, analysis of the harmonies and voice leading via this key is subverted by the nonfunctional nature of its chord progression and voicings. 45 Problems of post-tonal prolongation are discussed in Straus (1987). Straus (2003) provides a theory of atonal voice leading that might yield prolongational structures applicable to works such as this. Again, the issue is the difference in meaning between structural weight emerging from events with clear foreground salience versus seeing such events as the product of prolongation. 46 In jazz practice, however, key signatures are often omitted when they are cumbersome (too many sharps or flats) or the key of the work is not obvious. 47 The numbers that suggest a range in each style category do not appear in Martin (2012–13), although they are suggested there (217). Moreover, under Category II (Foreground harmonies) and Category V (Structural levels), the possibility of “postbop” is added: this designation refers to the kinds of harmonies that appear in “Pinocchio” that are sometimes called “modal.” For such harmonies, “postbop” may be a more accurate designation, since they tend to be tonally unclear—sometimes in chord formation, but often in progression. For more on the usages of “postbop,” see Waters (2016, 38) and Waters (2013, 575). 48 The irregular form of eighteen measures gives us only two measures of the tonic B, however the lead sheet from Bessières (2010, 129) and the jazz-rock version of the tune on Mr. Gone further reinforce the B tonality by expanding the two-measure arrival on B at the end of the tune to four measures. 49 Strunk (2003) may have been the first study to apply Neo-Riemannian techniques to jazz analysis. 50 See Block (1990). Block has published other articles as well that use set theory to analyze free jazz closely. Works cited Bessières Vincent. 2010. We Want Miles: Miles Davis vs. Jazz . New York: Skira Rizzoli. Block Steven. 1990. “Pitch-Class Transformation in Free Jazz.” Music Theory Spectrum 12 ( 2): 181– 202. Google Scholar CrossRef Search ADS Broze Yuri, Shanahan Daniel. 2013. “Diachronic Changes in Jazz Harmony: A Cognitive Approach.” Music Perception 31 ( 1): 32– 45. Google Scholar CrossRef Search ADS Burstein L. Poundie. 2005. “Unraveling Schenker’s Concept of the Auxiliary Cadence.” Music Theory Spectrum 27 ( 2): 159– 85. Google Scholar CrossRef Search ADS Fyffe Jamie. 2014. “Uniqueness, Signifyin(g) and Compositional Process in ‘Blue and Green’.” Jazz Perspectives 8 ( 2): 185– 208. Google Scholar CrossRef Search ADS Giel Lex. 2004. The Music of Miles Davis . Milwaukee, WI: Hal Leonard. Heyer David J. 2012. “Applying Schenkerian Theory to Mainstream Jazz: A Justification for an Orthodox Approach.” Music Theory Online 18 ( 3). Johns Donald. 1993. “Funnel Tonality in American Popular Music, ca. 1900–70.” American Music 11 ( 4): 458– 72. Google Scholar CrossRef Search ADS Julien Patricia. 2003. “The Structural Function of Harmonic Relations in Wayne Shorter’s Early Compositions: 1959–1963.” Ph.D. diss., University of Maryland. Julien Patricia. 2009. “‘Sakeena’s Vision’: The Trifocal Organization of Harmonic Relations in One of Wayne Shorter’s Early Compositions.” Theory and Practice 34: 107– 40. Julien Patricia. 2011. “Harmonic Plateaus in Two of Wayne Shorter’s Compositions.” Jazz Perspectives 5 ( 3): 163– 83. Google Scholar CrossRef Search ADS Larson Steve. 1996a. “The Art of Charlie Parker’s Rhetoric.” Annual Review of Jazz Studies 8: 141– 66. Larson Steve. 1996b. “‘Strict Use’ of Analytic Notation.” Journal of Music Theory Pedagogy 10: 31– 71. Larson Steve. 1998. “Schenkerian Analysis of Modern Jazz: Questions about Method.” Music Theory Spectrum 20 ( 2): 209– 41. Google Scholar CrossRef Search ADS Larson Steve. 2009. Analyzing Jazz: A Schenkerian Approach. Hillsdale, NY: Pendragon Press. Larson Steve. 2012. “Expressive Meaning and Musical Structure, Chapter 1 of Schenkerian Analysis: Pattern, Form, and Expressive Meaning.” Music Theory Online 18 ( 3). Lerdahl Fred, Jackendoff Ray. 1983. A Generative Theory of Tonal Music . Cambridge: MIT Press. Martin Henry. 1980. “Jazz Harmony.” Ph.D. diss., Princeton University. Martin Henry. 1988. “Jazz Harmony, a Syntactic Background.” Annual Review of Jazz Studies 4: 9– 30. Martin Henry. 1996. Charlie Parker and Thematic Improvisation . Lanham, MD: Scarecrow Press. Martin Henry. 2011. “Schenker and the Tonal Jazz Repertory.” Tijdschrift voor Musiektheorie 16 ( 1): 1– 20. Martin Henry. 2012–13. “Expanding Jazz Tonality: The Compositions of John Coltrane.” Theory and Practice 37–38: 185– 219. McFarland Mark. 2012. “Schenker and the Tonal Jazz Repertory: A Response to Martin.” Music Theory Online 18 ( 3). Mitchell Jason. 2014. “Shorter Stories: The Music and Life of Wayne Shorter.” M.A. Thesis, Rutgers University, Newark. Neumeyer David. 2009. “Thematic Reading, Proto-Backgrounds, and Registral Transformations.” Music Theory Spectrum 31 ( 2): 284– 324. Google Scholar CrossRef Search ADS 2006. The Real Book , 6th edition. Milwaukee, WI: Hal Leonard. Reese Alan. 2013. “French Sixths: Harmonic Functions and Pitch Types of Augmented Sixth Chords in the Music of Debussy and Ravel.” M.A. Thesis, University of Colorado, Boulder. Russell George. 1959. The Lydian Chromatic Concept of Tonal Organization . New York: Concept Publishing Co. Salley Keith, Shanahan Daniel T. 2016. “Phrase Rhythm in Standard Jazz Repertoire: A Taxonomy and Corpus Study.” Journal of Jazz Studies 11 ( 1): 1– 39. Google Scholar CrossRef Search ADS Salzer Felix. 1962. Structural Hearing: Tonal Coherence in Music . Two vols. New York: Dover. Satyendra Ramon. 1992. “Chromatic Tonality and Semitonal Relationships in Liszt’s Late Style.” Ph.D. diss., University of Chicago. Schenker Heinrich. 1935. Free Composition (Der freie Satz) . Ed. Oster Ernst. New York: Longman. Schuller Gunther. 1989. The Swing Era: The Development of Jazz 1930–1945 . New York: Oxford University Press. Stewart Milton Lee. 1974/1975. “Structural Development in the Jazz Improvisational Technique of Clifford Brown.” Jazzforschung/Jazz Reserach 6–7: 141– 273. Straus Joseph. 1987. “The Problem of Prolongation in Post-Tonal Music.” Journal of Music Theory 31 ( 1): 1– 21. Google Scholar CrossRef Search ADS Straus Joseph. 2003. “Uniformity, Balance, and Smoothness in Atonal Voice Leading.” Music Theory Spectrum 35 ( 2): 305– 52. Google Scholar CrossRef Search ADS Strunk Steven. 1979. “The Harmony of Early Bebop.” Journal of Jazz Studies 6 ( 1): 4– 53. Strunk Steven. 2005. “Notes on Harmony in Wayne Shorter’s Compositions, 1964–67.” Journal of Music Theory 49 ( 2): 301– 32. Google Scholar CrossRef Search ADS Strunk Steven. 2016. “Analytical Approaches to Chick Corea’s Compositions of the 1960s.” Music Theory Spectrum 38 ( 1): 16– 36. Google Scholar CrossRef Search ADS Strunk Steven. 2003. “Wayne Shorter’s Yes and No: An Analysis.” Tijdschrift voor Muziektheorie 8 ( 1): 40– 56. Waters Keith. 2010. “‘Giant Steps’ and the ic4 Legacy.” Intégral 24: 135– 62. Waters Keith. 2011. The Studio Recordings of the Miles Davis Quintet, 1965–68 . New York: Oxford University Press. Google Scholar CrossRef Search ADS Waters Keith. 2013. “Postbop.” In Grove Dictionary of American Music , 2nd edition, vol. 6, 575. Ed. Garrett Hiroshi. New York: Oxford University Press. Waters Keith. 2016. “Centrifugal Forces: Chick Corea and Postbop Harmony (A Response to Steven Strunk).” Music Theory Spectrum 38 ( 1): 37– 57. Google Scholar CrossRef Search ADS Waters Keith, Larson Steve, Strunk Steve, Martin Henry. 2016. “Circular Thinking: A Roundtable on ‘Blue in Green’ and ‘Nefertiti’.” Journal of Jazz Studies 11 ( 1): 105– 20. Google Scholar CrossRef Search ADS © The Author(s) 2018. Published by Oxford University Press on behalf of The Society for Music Theory. All rights reserved. For Permissions, please e-mail: email@example.com. 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Music Theory Spectrum – Oxford University Press
Published: Apr 10, 2018
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