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Chapter 10

Figure 10.1.1. (a) A basic nineteenth-century voice-leading schema, linking fifth-related diatonic triads by stepwise voice leading.  (b) The same schema, now interpreted as the upper four voices of a sequence of ninth chords.  (c) A variant that suspends the ninth of the ii chord into V, forming a thirteenth; the note B in the Cmaj9 chord is also replaced with A, so that all four upper voices move down by step from V to I.

Figure 10.1.2.  The “left hand voicings” in their A and B forms.

Figure 10.1.3.  The basic voice-leading structure of the ii-V-I.  As long as these contrapuntal motions are clear, the schema can be embellished with a large variety of additional notes.

Figure 10.1.4.  The schema in Figure 10.1.3 need not always be presented in its entirety.  In (a) the root of the V chord is transposed by tritone; while in (b) the leading tone is absent from the V chord, producing a suspended chord.  In both examples, the open noteheads show tones that are central to the basic schema in Figure 10.1.3.

Figure 10.1.5.  A and B voicings in classical music.  (a) Ravel, “Forlane” from Le tombeau de Couperin, m. 130, presenting the A voicings on V and IV (upper staff).  (b) Grieg’s Lyric Piece “Salon,” Op. 65 No. 4, m. 1 outlines the dominant B voicing with its final sixteenth notes.  (c) The same piece has a variant of the A dominant voicing, in which the root of the chord replaces the ninth.  (d) Scriabin’s Etude, Op. 65 No. 3.  The four highest notes of the G7 chord outline an A voicing.

Figure 10.1.6. Concert-music chords that omit the jazz “avoid notes.” The first three examples present tonic voicings that omit the fourth above the root.  (a) Debussy’s “Sirènes,” m. 8.  (b) Ravel Jeux d’eau m.1 (c) Reich, Different Trains, movement 1. (d) A ii 11-V sus-I in Ravel's “Rigaudon,” from Le tombeau de Couperin, mm. 1-2.  The dominant voicing is a suspended chord, analogous to Figure 10.1.4 ( b); as in jazz practice, the leading tone becomes the “avoid note” in the suspended chord. ( e) An extended predominant in Ravel’s Pavane pour une infante défunte,  mm. 67-68. ( f) Altered dominant chords in the opening of Reich’s The Desert Music, movement 1, all conspicuously omitting the fourth above the root.  ( g) Debussy, Prelude to “The Afternoon of a Faun,” R10, is similar.

Figure 10.2.1.  The dominant and tonic A voicings reinterpreted as stacks of fourths. In (c) the stacks are extended until they reach an “avoid note.”

Figure 10.2.2.  Quartal predominant voicings.  (a) The “So What” voicing.  (b) The same voicing with the bass note doubled in the soprano.  This is a complete stack of pentatonic thirds: D-F-G-A-C-D-F-G-A-C-D.  (c)  Other inversions of the “'So What' chord” begin the stack of thirds on a different note of the F pentatonic scale.  Each voicing has four perfect fifths and one four-semitone “near fifth.”

Figure 10.2.3. Quartal ii-V-I voicings played with both hands (a) and with the left hand alone (b).

Figure 10.2.4.  Two passages from Keith Jarrett’s solo on “You and The Night and The Music,” which exploits stacks of fourths.

Figure 10.2.5.  The opening of “Freedom Jazz Dance” begins by arpeggiating the Ef pentatonic scale, adds a D to create a diatonic hexachord, and concludes with the Df pentatonic scale.

Figure 10.2.6. (a) An extended sequence of melodic fourths will generate notes that clash with the underlying harmony or scale. (b–c) To correct this problem one can add a “near fourth,” producing a pentatonic or diatonic collection.

Figure 10.3.1. (a) A familiar seventh-chord ii-V-I voice-leading schema.  (b) The dominant chord can be replaced with its tritone transposition so as to preserve the notes in the upper staff, moving those in the lower staff by semitone.

Figure 10.3.2. Tritone substitution as applied to the quartal version of the A voicing.  The notes in the middle staff are preserved, while those in the upper staff move by semitone.

Figure 10.3.3. Tritone substitution produces a fˆ7→ˆ5 leap reminiscent of the fˆ7→fˆ6→5 motion in classical minor-key harmony.

Figure 10.3.4. (a) Tritones can be linked to their tritone transpositions by zero-semitone voice leading, while perfect fourths can be linked to their tritone transpositions by semitonal voice leading.  (b) These facts reflect the geometry of two-note chord space.  

Figure 10.3.5. Tritone substitution applied to tonic (b) and predominant (c) chords.  The tonic substitution is not very effective, while the predominant substitution is somewhat more so.

Figure 10.3.6. Diatonic third-substitution (a) and chromatic tritone-substitution (b).  Both substitutions preserve important notes in the first chord while moving the remaining notes by short distances.

Figure 10.3.7. Classical chord progressions that can be understood as tritone substitutions. (a) The augmented sixth chord can be seen as a tritone substitution for V7/V. (b) The central chord progression in Till Eulenspiegel can be seen as a tritone substitution for a common viiø$→I progression.  (c) The initial progression of Tristan can be seen as a tritone substitution for iiø$ →V. (d) In the “Forlane” from Le tombeau de Couperin, Ravel embellishes a descending-fifth sequence with tritone transpositions.

Figure 10.3.8. Voice leading between fifth-related (a) and tritone-related (b) dominant seventh chords.  The two voice leadings are individually T-related, and are nearly the same size.

Figure 10.4.1. An improviser who plays diatonically will need to handle the “avoid notes” with care, for instance by making them into passing or neighboring notes.  Another alternative is to raise the avoid notes by semitone, in which case they can be used more freely.  The resulting ii-V-I progression uses three different scales.

Figure 10.4.2. (a) The lydian-dominant mode of the acoustic scale combines a whole-tone lower tritone with an octatonic upper tritone.  (b) Here, the pianist makes a tritone substitution, playing the Df lydian dominant mode, while the bass player does not.  (c) The result is a G altered scale, which combines an octatonic lower tritone with a whole-tone upper tritone.

Figure 10.4.3. (a) A harmonic minor scale with an additional (neighboring) fˆ7.  (b) The resulting notes are very similar to the altered scale.

Figure 10.4.4. There are four ways to combine octatonic and whole-tone upper and lower tritones, producing one whole tone scale, one octatonic scale, and two modes of the acoustic scale.

Figure 10.4.5. Scales that are compatible with common altered-dominant chords.

Figure 10.4.6. These seven scales contain all the sets that do not themselves contain a chromatic subset such as{C, Cs, D}, and hence all of the common extended or altered tonal harmonies.

Figure 10.4.8.  Other scales commonly played in jazz.  Pentatonic scales are often used over ii, V, and I.  The hexatonic scale can be played against a major seventh.  The acoustic scale often appears over iiø7 in the “locrian s2” mode; the same scale sometimes appears against a bare tonic triad (without the seventh).  Harmonic minor is sometimes used for minor-key dominant chords, as in classical music, and harmonic major can be used over a major-seventh tonic.

Figure 10.5.1.  Bass substitution and upper-voice substitution.  Here either the bass player or pianist makes the substitution, but not both.  In either case, the effect is to transform a diatonic voicing containing the seventh, ninth, third, and thirteenth above the root into an altered voicing containing third, flat thirteenth, seventh, and sharp nine.

Figure 10.5.2. Upper-voice substitution leaves the whole-tone and octatonic scales unchanged (top two lines), exchanges the lydian dominant and altered modes of the acoustic scale (line three), and sends the diatonic scale to its tritone transposition (bottom line).

Figure 10.5.3.  Independent applications of the tritone transposition can clash with purely diatonic voicings.  Here, the diatonic notes C and D clash with the bass player’s (tritone substitute) Df; similarly, the unsubstituted G in the bass clashes with the pianist’s Gf diatonic.

Figure 10.5.4.  Chromatically descending voicings can always accompany descending-fifths patterns in the bass.  In effect, tritone transposition is applied to every other chord in the sequence.

Figure 10.5.6.  Impressionist composers prefigured many central ideas of jazz harmony.  In (a), from Prelude to "The Afternoon of a Faun," mm. 61-62, Debussy uses an acoustic scale over V7, as in Figure 10.4.1.  In (b), from Ravel's "Ondine," bass substitution is applied to the dominant chord at the end of m. 46 and m. 51.  In (c), from the Prelude "La danse de Puck," Debussy applies something that resembles upper-voice substitution, moving between altered and diatonic dominant voicings.  In (d), from Six épigraphes antiques, No. 4, Debussy uses descending-semitone voicings over a descending-fifths bass line, applying the upper-voice tritone substitution to every other chord in the sequence.

Figure 10.6.1.  The blues often features polyscalar clashes between melody and harmony.

Figure 10.6.2. Out-of-key playing in Warne Marsh’s solo on “Smog Eyes.”  Marsh plays an E-major figure over an Ef harmony; the A is an upper-neighbor to the Gs, and the entire E-major triad resolves downward to Ef.

Figure 10.6.3.  Sidestepping in Chopin.  (a)  In the first Nocturne (Op. 9 No. 1), Chopin shifts suddenly from Df major to D major, in the middle of the phrase.  (b)  In the second Nocturne(Op. 9 No. 2), he returns from Bf to Ef by way of E major.

Figure 10.6.4.  Harmonic motion in “Passion Dance” largely consists in oscillations between in-key and out-of-key playing.

Figure 10.6.5.  “Upper structure” dominant voicings combine root, fifth, and seventh in the bass with a foreign triad in the upper voices.  Upper-voice tritone substitution leaves the lowest three notes unchanged, transposing the triad by tritone.  This provides a convenient way to remember and categorize these voicings.

Figure 10.7.1.  Sonny Rollins’ tune “Oleo,” as played by Bill Evans.

Figure 10.7.2.  The first chorus of Evans’ solo.

Figure 10.7.3.  Measures 47-49 articulate an efficient voice leading between Bf and G major triads.  However, the G represents the upper notes of an extended Aø7 chord.

Figure 10.7.4.  The second chorus of Evans’ solo.

Figure 10.7.5.  The first phrase of the chorus linearizes a collection of four-note voicings, similar to those discussed earlier in the chapter.

Figure 10.7.6.  The second phrase of the chorus displaces the accent: on its own, the melody would be heard with the registrally accented notes on strong beats (lower line); as played, however, the notes are rhythmically weak, creating a kind of polyrhythm.

Figure 10.7.7.  The third chorus of Evans’ solo.

Figure 10.7.8.  The rhythm of the dotted sixteenth-note figure articulates three-measure groups.  However, the pitches articulate a nine dotted-quarter sequence.

Figure 10.7.9.  The fourth chorus of Evans’ solo.

Figure 10.7.10. Motivic development at the opening of the fourth chorus.

Figure 10.7.11.  Development of the bluesy motif.

Figure 10.7.12. With augmented triads, ascending minor thirds and descending semitones produce the same sequence of chords.

Figure 10.8.1. A simple jazz progression incorporates techniques from the entire history of tonality.

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