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Pitch-Class Transformation in Free JazzAuthor(s): Steven BlockSource: Music Theory Spectrum, Vol. 12, No. 2 (Autumn, 1990), pp. 181-202Published by: on behalf of the Society for Music TheoryStable URL: http://www.jstor.org/stable/746167 .Accessed: 03/04/2014 09:44

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Pitch-Class Transformation in Free Jazz

Steven Block

Pitch-Class Transformation in Free Jazz

Steven Block

Pitch-Class Transformation in Free Jazz

Steven Block

Pitch-Class Transformation in Free Jazz

Steven Block

Free jazz originated with performances at the Five Spot Cafe by Cecil Taylor in 1957 and by Ornette Coleman in 1959, both of whom were then in the early stages of their careers.1 Taylor, Coleman, and John Coltrane helped to forge a new era in jazz, characterized by the introduction of harmonic, rhyth- mic, and timbral freedoms that affected the nature of jazz in a manner analogous to the great changes in Western concert mu- sic at the turn of the twentieth century. But while concert music of the formative first quarter of the twentieth century has re- ceived considerable analytical attention, particularly with re- spect to pitch and compositional design, hardly any analyses of free jazz compositions have attempted to go beyond merely de- scriptive commentary.2

The term "free jazz" comes from Coleman's landmark al- bum of the same title, issued in 1960. In this work, which fea- tures the realization of Coleman's ideas about freedom in music to their fullest extent, two quartets perform a 36-minute im- provisation using nontonal material without the benefit of a fixed meter or fixed entries of the ensemble. One can hear this

'Ronald M. Radano, "The Jazz Avant-Garde and the Jazz Community: Action and Reaction," Annual Review of Jazz Studies 3 (1985), 72.

2Gunther Schuller, who sponsored Coleman's work for a time, is the author of A Collection of the Compositions of Ornette Coleman (New York: MJQ Mu- sic, 1961), which contains transcriptions of and commentaries on Coleman's music. Ekkehard Jost's Free Jazz (Vienna: Universal, 1974) must be regarded as the primary work on the subject; it consists mostly of commentary on the music of several artists but also includes a few transcriptions.

Free jazz originated with performances at the Five Spot Cafe by Cecil Taylor in 1957 and by Ornette Coleman in 1959, both of whom were then in the early stages of their careers.1 Taylor, Coleman, and John Coltrane helped to forge a new era in jazz, characterized by the introduction of harmonic, rhyth- mic, and timbral freedoms that affected the nature of jazz in a manner analogous to the great changes in Western concert mu- sic at the turn of the twentieth century. But while concert music of the formative first quarter of the twentieth century has re- ceived considerable analytical attention, particularly with re- spect to pitch and compositional design, hardly any analyses of free jazz compositions have attempted to go beyond merely de- scriptive commentary.2

The term "free jazz" comes from Coleman's landmark al- bum of the same title, issued in 1960. In this work, which fea- tures the realization of Coleman's ideas about freedom in music to their fullest extent, two quartets perform a 36-minute im- provisation using nontonal material without the benefit of a fixed meter or fixed entries of the ensemble. One can hear this

'Ronald M. Radano, "The Jazz Avant-Garde and the Jazz Community: Action and Reaction," Annual Review of Jazz Studies 3 (1985), 72.

2Gunther Schuller, who sponsored Coleman's work for a time, is the author of A Collection of the Compositions of Ornette Coleman (New York: MJQ Mu- sic, 1961), which contains transcriptions of and commentaries on Coleman's music. Ekkehard Jost's Free Jazz (Vienna: Universal, 1974) must be regarded as the primary work on the subject; it consists mostly of commentary on the music of several artists but also includes a few transcriptions.

Free jazz originated with performances at the Five Spot Cafe by Cecil Taylor in 1957 and by Ornette Coleman in 1959, both of whom were then in the early stages of their careers.1 Taylor, Coleman, and John Coltrane helped to forge a new era in jazz, characterized by the introduction of harmonic, rhyth- mic, and timbral freedoms that affected the nature of jazz in a manner analogous to the great changes in Western concert mu- sic at the turn of the twentieth century. But while concert music of the formative first quarter of the twentieth century has re- ceived considerable analytical attention, particularly with re- spect to pitch and compositional design, hardly any analyses of free jazz compositions have attempted to go beyond merely de- scriptive commentary.2

The term "free jazz" comes from Coleman's landmark al- bum of the same title, issued in 1960. In this work, which fea- tures the realization of Coleman's ideas about freedom in music to their fullest extent, two quartets perform a 36-minute im- provisation using nontonal material without the benefit of a fixed meter or fixed entries of the ensemble. One can hear this

'Ronald M. Radano, "The Jazz Avant-Garde and the Jazz Community: Action and Reaction," Annual Review of Jazz Studies 3 (1985), 72.

2Gunther Schuller, who sponsored Coleman's work for a time, is the author of A Collection of the Compositions of Ornette Coleman (New York: MJQ Mu- sic, 1961), which contains transcriptions of and commentaries on Coleman's music. Ekkehard Jost's Free Jazz (Vienna: Universal, 1974) must be regarded as the primary work on the subject; it consists mostly of commentary on the music of several artists but also includes a few transcriptions.

Free jazz originated with performances at the Five Spot Cafe by Cecil Taylor in 1957 and by Ornette Coleman in 1959, both of whom were then in the early stages of their careers.1 Taylor, Coleman, and John Coltrane helped to forge a new era in jazz, characterized by the introduction of harmonic, rhyth- mic, and timbral freedoms that affected the nature of jazz in a manner analogous to the great changes in Western concert mu- sic at the turn of the twentieth century. But while concert music of the formative first quarter of the twentieth century has re- ceived considerable analytical attention, particularly with re- spect to pitch and compositional design, hardly any analyses of free jazz compositions have attempted to go beyond merely de- scriptive commentary.2

The term "free jazz" comes from Coleman's landmark al- bum of the same title, issued in 1960. In this work, which fea- tures the realization of Coleman's ideas about freedom in music to their fullest extent, two quartets perform a 36-minute im- provisation using nontonal material without the benefit of a fixed meter or fixed entries of the ensemble. One can hear this

'Ronald M. Radano, "The Jazz Avant-Garde and the Jazz Community: Action and Reaction," Annual Review of Jazz Studies 3 (1985), 72.

2Gunther Schuller, who sponsored Coleman's work for a time, is the author of A Collection of the Compositions of Ornette Coleman (New York: MJQ Mu- sic, 1961), which contains transcriptions of and commentaries on Coleman's music. Ekkehard Jost's Free Jazz (Vienna: Universal, 1974) must be regarded as the primary work on the subject; it consists mostly of commentary on the music of several artists but also includes a few transcriptions.

music as both a reaction to and an extension of be-bop. The principal differences between free jazz and be-bop are: (1) the elevation of the rhythm section from its formerly subsidiary role to a status equal to that of the melodic instruments; (2) im- provisations that are no longer based upon chord changes; and (3) a harmonic language that does not necessarily incorporate "jazz tonality." The idea of "playing outside"-that is, of not basing an improvisation upon chord changes-is the primary distinction between free jazz and tonal jazz.3

Analysis of free jazz compositions by Coleman, Coltrane, Taylor, and the younger composer Anthony Braxton- compositions that are wholly different in style and tonal emphases-shows that pitch organization in free jazz can be very sophisticated; even ostensibly tonal compositions in this style cannot be adequately understood simply by reference to the harmonic underpinnings of the more tonal sections or to some surface-generative process of motivic invention. As in the analysis of early twentieth-century music, set-theoretical tools prove to be very useful in the analysis of free jazz.

Taylor's music has been labeled atonal by many of his peers. This label may be appropriate to Taylor's compositional de- signs, which are often at least superficially similar to those of Bartok and Stravinsky, but it is misleading in its implication

3It should be understood that functional tonality used in jazz by the be-bop era had evolved to incorporate implications (both in voice-leading and in root progression) that were different from those of the common-practice period in Western music.

music as both a reaction to and an extension of be-bop. The principal differences between free jazz and be-bop are: (1) the elevation of the rhythm section from its formerly subsidiary role to a status equal to that of the melodic instruments; (2) im- provisations that are no longer based upon chord changes; and (3) a harmonic language that does not necessarily incorporate "jazz tonality." The idea of "playing outside"-that is, of not basing an improvisation upon chord changes-is the primary distinction between free jazz and tonal jazz.3

Analysis of free jazz compositions by Coleman, Coltrane, Taylor, and the younger composer Anthony Braxton- compositions that are wholly different in style and tonal emphases-shows that pitch organization in free jazz can be very sophisticated; even ostensibly tonal compositions in this style cannot be adequately understood simply by reference to the harmonic underpinnings of the more tonal sections or to some surface-generative process of motivic invention. As in the analysis of early twentieth-century music, set-theoretical tools prove to be very useful in the analysis of free jazz.

Taylor's music has been labeled atonal by many of his peers. This label may be appropriate to Taylor's compositional de- signs, which are often at least superficially similar to those of Bartok and Stravinsky, but it is misleading in its implication

3It should be understood that functional tonality used in jazz by the be-bop era had evolved to incorporate implications (both in voice-leading and in root progression) that were different from those of the common-practice period in Western music.

music as both a reaction to and an extension of be-bop. The principal differences between free jazz and be-bop are: (1) the elevation of the rhythm section from its formerly subsidiary role to a status equal to that of the melodic instruments; (2) im- provisations that are no longer based upon chord changes; and (3) a harmonic language that does not necessarily incorporate "jazz tonality." The idea of "playing outside"-that is, of not basing an improvisation upon chord changes-is the primary distinction between free jazz and tonal jazz.3

Analysis of free jazz compositions by Coleman, Coltrane, Taylor, and the younger composer Anthony Braxton- compositions that are wholly different in style and tonal emphases-shows that pitch organization in free jazz can be very sophisticated; even ostensibly tonal compositions in this style cannot be adequately understood simply by reference to the harmonic underpinnings of the more tonal sections or to some surface-generative process of motivic invention. As in the analysis of early twentieth-century music, set-theoretical tools prove to be very useful in the analysis of free jazz.

Taylor's music has been labeled atonal by many of his peers. This label may be appropriate to Taylor's compositional de- signs, which are often at least superficially similar to those of Bartok and Stravinsky, but it is misleading in its implication

3It should be understood that functional tonality used in jazz by the be-bop era had evolved to incorporate implications (both in voice-leading and in root progression) that were different from those of the common-practice period in Western music.

music as both a reaction to and an extension of be-bop. The principal differences between free jazz and be-bop are: (1) the elevation of the rhythm section from its formerly subsidiary role to a status equal to that of the melodic instruments; (2) im- provisations that are no longer based upon chord changes; and (3) a harmonic language that does not necessarily incorporate "jazz tonality." The idea of "playing outside"-that is, of not basing an improvisation upon chord changes-is the primary distinction between free jazz and tonal jazz.3

Analysis of free jazz compositions by Coleman, Coltrane, Taylor, and the younger composer Anthony Braxton- compositions that are wholly different in style and tonal emphases-shows that pitch organization in free jazz can be very sophisticated; even ostensibly tonal compositions in this style cannot be adequately understood simply by reference to the harmonic underpinnings of the more tonal sections or to some surface-generative process of motivic invention. As in the analysis of early twentieth-century music, set-theoretical tools prove to be very useful in the analysis of free jazz.

Taylor's music has been labeled atonal by many of his peers. This label may be appropriate to Taylor's compositional de- signs, which are often at least superficially similar to those of Bartok and Stravinsky, but it is misleading in its implication

3It should be understood that functional tonality used in jazz by the be-bop era had evolved to incorporate implications (both in voice-leading and in root progression) that were different from those of the common-practice period in Western music.

This content downloaded from 143.107.200.196 on Thu, 3 Apr 2014 09:44:10 AMAll use subject to JSTOR Terms and Conditions

182 Music Theory Spectrum 182 Music Theory Spectrum 182 Music Theory Spectrum 182 Music Theory Spectrum

that Taylor's music is not really jazz and in its implication that Taylor's music has no tonal references. In an article published in 1965, Taylor describes his music as "constructionistic," meaning "based on the conscious working-out of a given mate- rial."4 The working-out of material is an additive or subtractive process in which motives or pitch material are not only reinter- preted and reworked but also altered slightly from phrase to phrase in a chain of progression that may span a long period of time. The final material may not, therefore, necessarily be un- derstood as related to the original except in the sense that it lies at the opposite end of a musical process.

An excerpt from Taylor's Air above Mountains (1976) illus- trates the additive surface transformation that is typical of Tay- lor's improvisations (see Ex. la).5 The passage has been di- vided into the three primary gestures which alternate in the music, each of which represents a different musical lexicon. The first gesture is chromatic, the second whole tone, and the third diatonic in that it is the 3-9[0,2,7] trichord arranged as as- cending fifths.

For the most part, each gesture is distinct and each one, as it is sounded, is permuted or reiterated in different ways. The first chromatic gesture remains consistent throughout the music and almost always occurs as the tetrachord C#-D-D#-E. The C~ which is added briefly in the opening statement and more prominently in the third statement (second system) expands this tetrachord to a chromatic pentachord. The third, diatonic gesture is always heard as ascending fifths from Ct. The second gesture is the most flexible in that it is first heard as a 3-8[0,2,6] trichord, D-E-Bb, and is always scored as a whole tone plus a tritone, even when it appears as a subset of later gestures. In the second statement of this motive (labeled 2a) this becomes a

4Tom Darter, "Piano Giants of Jazz: Cecil Taylor," Contemporary Key- board (May 1981), 56.

5The transcription in Example la appeared originally in Darter, "Piano Gi- ants of Jazz," 57. The transcribed passage begins about 4'30" into Side 1 of Air above Mountains (Buildings Within) (Inner City IC-3021).

that Taylor's music is not really jazz and in its implication that Taylor's music has no tonal references. In an article published in 1965, Taylor describes his music as "constructionistic," meaning "based on the conscious working-out of a given mate- rial."4 The working-out of material is an additive or subtractive process in which motives or pitch material are not only reinter- preted and reworked but also altered slightly from phrase to phrase in a chain of progression that may span a long period of time. The final material may not, therefore, necessarily be un- derstood as related to the original except in the sense that it lies at the opposite end of a musical process.

An excerpt from Taylor's Air above Mountains (1976) illus- trates the additive surface transformation that is typical of Tay- lor's improvisations (see Ex. la).5 The passage has been di- vided into the three primary gestures which alternate in the music, each of which represents a different musical lexicon. The first gesture is chromatic, the second whole tone, and the third diatonic in that it is the 3-9[0,2,7] trichord arranged as as- cending fifths.

For the most part, each gesture is distinct and each one, as it is sounded, is permuted or reiterated in different ways. The first chromatic gesture remains consistent throughout the music and almost always occurs as the tetrachord C#-D-D#-E. The C~ which is added briefly in the opening statement and more prominently in the third statement (second system) expands this tetrachord to a chromatic pentachord. The third, diatonic gesture is always heard as ascending fifths from Ct. The second gesture is the most flexible in that it is first heard as a 3-8[0,2,6] trichord, D-E-Bb, and is always scored as a whole tone plus a tritone, even when it appears as a subset of later gestures. In the second statement of this motive (labeled 2a) this becomes a

4Tom Darter, "Piano Giants of Jazz: Cecil Taylor," Contemporary Key- board (May 1981), 56.

5The transcription in Example la appeared originally in Darter, "Piano Gi- ants of Jazz," 57. The transcribed passage begins about 4'30" into Side 1 of Air above Mountains (Buildings Within) (Inner City IC-3021).

that Taylor's music is not really jazz and in its implication that Taylor's music has no tonal references. In an article published in 1965, Taylor describes his music as "constructionistic," meaning "based on the conscious working-out of a given mate- rial."4 The working-out of material is an additive or subtractive process in which motives or pitch material are not only reinter- preted and reworked but also altered slightly from phrase to phrase in a chain of progression that may span a long period of time. The final material may not, therefore, necessarily be un- derstood as related to the original except in the sense that it lies at the opposite end of a musical process.

An excerpt from Taylor's Air above Mountains (1976) illus- trates the additive surface transformation that is typical of Tay- lor's improvisations (see Ex. la).5 The passage has been di- vided into the three primary gestures which alternate in the music, each of which represents a different musical lexicon. The first gesture is chromatic, the second whole tone, and the third diatonic in that it is the 3-9[0,2,7] trichord arranged as as- cending fifths.

For the most part, each gesture is distinct and each one, as it is sounded, is permuted or reiterated in different ways. The first chromatic gesture remains consistent throughout the music and almost always occurs as the tetrachord C#-D-D#-E. The C~ which is added briefly in the opening statement and more prominently in the third statement (second system) expands this tetrachord to a chromatic pentachord. The third, diatonic gesture is always heard as ascending fifths from Ct. The second gesture is the most flexible in that it is first heard as a 3-8[0,2,6] trichord, D-E-Bb, and is always scored as a whole tone plus a tritone, even when it appears as a subset of later gestures. In the second statement of this motive (labeled 2a) this becomes a

4Tom Darter, "Piano Giants of Jazz: Cecil Taylor," Contemporary Key- board (May 1981), 56.

5The transcription in Example la appeared originally in Darter, "Piano Gi- ants of Jazz," 57. The transcribed passage begins about 4'30" into Side 1 of Air above Mountains (Buildings Within) (Inner City IC-3021).

that Taylor's music is not really jazz and in its implication that Taylor's music has no tonal references. In an article published in 1965, Taylor describes his music as "constructionistic," meaning "based on the conscious working-out of a given mate- rial."4 The working-out of material is an additive or subtractive process in which motives or pitch material are not only reinter- preted and reworked but also altered slightly from phrase to phrase in a chain of progression that may span a long period of time. The final material may not, therefore, necessarily be un- derstood as related to the original except in the sense that it lies at the opposite end of a musical process.

An excerpt from Taylor's Air above Mountains (1976) illus- trates the additive surface transformation that is typical of Tay- lor's improvisations (see Ex. la).5 The passage has been di- vided into the three primary gestures which alternate in the music, each of which represents a different musical lexicon. The first gesture is chromatic, the second whole tone, and the third diatonic in that it is the 3-9[0,2,7] trichord arranged as as- cending fifths.

For the most part, each gesture is distinct and each one, as it is sounded, is permuted or reiterated in different ways. The first chromatic gesture remains consistent throughout the music and almost always occurs as the tetrachord C#-D-D#-E. The C~ which is added briefly in the opening statement and more prominently in the third statement (second system) expands this tetrachord to a chromatic pentachord. The third, diatonic gesture is always heard as ascending fifths from Ct. The second gesture is the most flexible in that it is first heard as a 3-8[0,2,6] trichord, D-E-Bb, and is always scored as a whole tone plus a tritone, even when it appears as a subset of later gestures. In the second statement of this motive (labeled 2a) this becomes a

4Tom Darter, "Piano Giants of Jazz: Cecil Taylor," Contemporary Key- board (May 1981), 56.

5The transcription in Example la appeared originally in Darter, "Piano Gi- ants of Jazz," 57. The transcribed passage begins about 4'30" into Side 1 of Air above Mountains (Buildings Within) (Inner City IC-3021).

four-note whole-tone collection, 4-25[0,2,6,8], arranged as two tritones surrounding a major second. In m. 3, gesture 2a is re- peated and further extended into the whole-tone pentachord (2b). Thus, both whole-tone and chromatic gestures are addi- tively developed as pc collections.

The relationship between these gestures, however, is more complex than a threefold alternation and variation scheme. There is a strong sense of a tonic D since it is the one pitch, in the first gesture, to which the music constantly returns and since in gesture 2, which is heard in several registers, D is always in the lowest octave. The third gesture features the lowest note of the passage, C,, scored in three octaves and always resolved to D in each of these registers by the music that follows. The final notes of the passage are clearly cadential; each gesture has a cadential formula built into it as well (Ex. lb).

One hears an interpenetration of these collections most clearly in m. 6, where the gesture of ascending perfect fifths is briefly transformed (GO mapped into A) into a transposition of gesture 2. This first appearance of the diatonic gesture con- cludes with an enunciation of the interval C#-D# (leading tone and enharmonically respelled ,2, respectively) in three regis- ters. When this gesture is repeated in m. 6 and Cf and DO are paired once more, an A joins them to form a 3-8 whole-tone trichord one semitone lower than the 3-8 of gesture 2. The dia- tonic gesture has therefore been transformed into a whole-tone gesture. One can thus make a case for the most important map- pings of this passage being the chromatic trichord CSt-D-D-, the diatonic trichord C#-D(-G#, and the whole-tone trichord C# -Dt-A (see Ex. Ic). The relationship between the chromatic and diatonic trichord here is the T6MI relationship.6 The rela-

6This has already been shown to have importance in tonal jazz since it maps a chromatic circle to the circle of fifths and underlies a particularly important relationship for chord progression in tonal jazz, the tritone substitution. See Robert Morris, review of John Rahn, Basic Atonal Theory, Music Theory Spectrum 4 (1982), 152-154; Henry J. Martin, "Jazz Harmony" (Ph.D. disser- tation, Princeton University, 1980).

four-note whole-tone collection, 4-25[0,2,6,8], arranged as two tritones surrounding a major second. In m. 3, gesture 2a is re- peated and further extended into the whole-tone pentachord (2b). Thus, both whole-tone and chromatic gestures are addi- tively developed as pc collections.

The relationship between these gestures, however, is more complex than a threefold alternation and variation scheme. There is a strong sense of a tonic D since it is the one pitch, in the first gesture, to which the music constantly returns and since in gesture 2, which is heard in several registers, D is always in the lowest octave. The third gesture features the lowest note of the passage, C,, scored in three octaves and always resolved to D in each of these registers by the music that follows. The final notes of the passage are clearly cadential; each gesture has a cadential formula built into it as well (Ex. lb).

One hears an interpenetration of these collections most clearly in m. 6, where the gesture of ascending perfect fifths is briefly transformed (GO mapped into A) into a transposition of gesture 2. This first appearance of the diatonic gesture con- cludes with an enunciation of the interval C#-D# (leading tone and enharmonically respelled ,2, respectively) in three regis- ters. When this gesture is repeated in m. 6 and Cf and DO are paired once more, an A joins them to form a 3-8 whole-tone trichord one semitone lower than the 3-8 of gesture 2. The dia- tonic gesture has therefore been transformed into a whole-tone gesture. One can thus make a case for the most important map- pings of this passage being the chromatic trichord CSt-D-D-, the diatonic trichord C#-D(-G#, and the whole-tone trichord C# -Dt-A (see Ex. Ic). The relationship between the chromatic and diatonic trichord here is the T6MI relationship.6 The rela-

6This has already been shown to have importance in tonal jazz since it maps a chromatic circle to the circle of fifths and underlies a particularly important relationship for chord progression in tonal jazz, the tritone substitution. See Robert Morris, review of John Rahn, Basic Atonal Theory, Music Theory Spectrum 4 (1982), 152-154; Henry J. Martin, "Jazz Harmony" (Ph.D. disser- tation, Princeton University, 1980).

four-note whole-tone collection, 4-25[0,2,6,8], arranged as two tritones surrounding a major second. In m. 3, gesture 2a is re- peated and further extended into the whole-tone pentachord (2b). Thus, both whole-tone and chromatic gestures are addi- tively developed as pc collections.

The relationship between these gestures, however, is more complex than a threefold alternation and variation scheme. There is a strong sense of a tonic D since it is the one pitch, in the first gesture, to which the music constantly returns and since in gesture 2, which is heard in several registers, D is always in the lowest octave. The third gesture features the lowest note of the passage, C,, scored in three octaves and always resolved to D in each of these registers by the music that follows. The final notes of the passage are clearly cadential; each gesture has a cadential formula built into it as well (Ex. lb).

One hears an interpenetration of these collections most clearly in m. 6, where the gesture of ascending perfect fifths is briefly transformed (GO mapped into A) into a transposition of gesture 2. This first appearance of the diatonic gesture con- cludes with an enunciation of the interval C#-D# (leading tone and enharmonically respelled ,2, respectively) in three regis- ters. When this gesture is repeated in m. 6 and Cf and DO are paired once more, an A joins them to form a 3-8 whole-tone trichord one semitone lower than the 3-8 of gesture 2. The dia- tonic gesture has therefore been transformed into a whole-tone gesture. One can thus make a case for the most important map- pings of this passage being the chromatic trichord CSt-D-D-, the diatonic trichord C#-D(-G#, and the whole-tone trichord C# -Dt-A (see Ex. Ic). The relationship between the chromatic and diatonic trichord here is the T6MI relationship.6 The rela-

6This has already been shown to have importance in tonal jazz since it maps a chromatic circle to the circle of fifths and underlies a particularly important relationship for chord progression in tonal jazz, the tritone substitution. See Robert Morris, review of John Rahn, Basic Atonal Theory, Music Theory Spectrum 4 (1982), 152-154; Henry J. Martin, "Jazz Harmony" (Ph.D. disser- tation, Princeton University, 1980).

four-note whole-tone collection, 4-25[0,2,6,8], arranged as two tritones surrounding a major second. In m. 3, gesture 2a is re- peated and further extended into the whole-tone pentachord (2b). Thus, both whole-tone and chromatic gestures are addi- tively developed as pc collections.

The relationship between these gestures, however, is more complex than a threefold alternation and variation scheme. There is a strong sense of a tonic D since it is the one pitch, in the first gesture, to which the music constantly returns and since in gesture 2, which is heard in several registers, D is always in the lowest octave. The third gesture features the lowest note of the passage, C,, scored in three octaves and always resolved to D in each of these registers by the music that follows. The final notes of the passage are clearly cadential; each gesture has a cadential formula built into it as well (Ex. lb).

One hears an interpenetration of these collections most clearly in m. 6, where the gesture of ascending perfect fifths is briefly transformed (GO mapped into A) into a transposition of gesture 2. This first appearance of the diatonic gesture con- cludes with an enunciation of the interval C#-D# (leading tone and enharmonically respelled ,2, respectively) in three regis- ters. When this gesture is repeated in m. 6 and Cf and DO are paired once more, an A joins them to form a 3-8 whole-tone trichord one semitone lower than the 3-8 of gesture 2. The dia- tonic gesture has therefore been transformed into a whole-tone gesture. One can thus make a case for the most important map- pings of this passage being the chromatic trichord CSt-D-D-, the diatonic trichord C#-D(-G#, and the whole-tone trichord C# -Dt-A (see Ex. Ic). The relationship between the chromatic and diatonic trichord here is the T6MI relationship.6 The rela-

6This has already been shown to have importance in tonal jazz since it maps a chromatic circle to the circle of fifths and underlies a particularly important relationship for chord progression in tonal jazz, the tritone substitution. See Robert Morris, review of John Rahn, Basic Atonal Theory, Music Theory Spectrum 4 (1982), 152-154; Henry J. Martin, "Jazz Harmony" (Ph.D. disser- tation, Princeton University, 1980).

This content downloaded from 143.107.200.196 on Thu, 3 Apr 2014 09:44:10 AMAll use subject to JSTOR Terms and Conditions

Transformation in Free Jazz 183 Transformation in Free Jazz 183 Transformation in Free Jazz 183 Transformation in Free Jazz 183

Example la. Gestural analysis of an excerpt from Cecil Taylor's Air above Mountains (Buildings Within). Transcription by Jim Aikin

Example la. Gestural analysis of an excerpt from Cecil Taylor's Air above Mountains (Buildings Within). Transcription by Jim Aikin

Example la. Gestural analysis of an excerpt from Cecil Taylor's Air above Mountains (Buildings Within). Transcription by Jim Aikin

Example la. Gestural analysis of an excerpt from Cecil Taylor's Air above Mountains (Buildings Within). Transcription by Jim Aikin

Accidentals apply only to the note they precede. A

Accidentals apply only to the note they precede. A

Accidentals apply only to the note they precede. A

Accidentals apply only to the note they precede. A

(2) 3-8 (1) (2) 3-8 (1) (2) 3-8 (1) (2) 3-8 (1)

) (1) 4-1 ( a) 5-1 (1) 3 '

B

(2a) 4-25

(2b) 5-33 (3) 3

; j'jjj^ja^ ^ ?H' j .r? Tf (la)

3

9f: Li,[--:' L 3

(2) (2b) (2) i I (1)

|.. (2a) (3) i , # m

. P,;:J. J.

::r^^S^ffl nf 17 r h

) (1) 4-1 ( a) 5-1 (1) 3 '

B

(2a) 4-25

(2b) 5-33 (3) 3

; j'jjj^ja^ ^ ?H' j .r? Tf (la)

3

9f: Li,[--:' L 3

(2) (2b) (2) i I (1)

|.. (2a) (3) i , # m

. P,;:J. J.

::r^^S^ffl nf 17 r h

) (1) 4-1 ( a) 5-1 (1) 3 '

B

(2a) 4-25

(2b) 5-33 (3) 3

; j'jjj^ja^ ^ ?H' j .r? Tf (la)

3

9f: Li,[--:' L 3

(2) (2b) (2) i I (1)

|.. (2a) (3) i , # m

. P,;:J. J.

::r^^S^ffl nf 17 r h

) (1) 4-1 ( a) 5-1 (1) 3 '

B

(2a) 4-25

(2b) 5-33 (3) 3

; j'jjj^ja^ ^ ?H' j .r? Tf (la)

3

9f: Li,[--:' L 3

(2) (2b) (2) i I (1)

|.. (2a) (3) i , # m

. P,;:J. J.

::r^^S^ffl nf 17 r h I j I 1 I j I 1 I j I 1 I j I 1 16 V t Tt I I

16 V t Tt I I

16 V t Tt I I

16 V t Tt I I

I? I? I? I?

#:t :; #; $_

#:t :; #; $_

#:t :; #; $_

#:t :; #; $_

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184 Music Theory Spectrum 184 Music Theory Spectrum 184 Music Theory Spectrum 184 Music Theory Spectrum

Example lb. Cadential patterns within the gestures of Example la Example lb. Cadential patterns within the gestures of Example la Example lb. Cadential patterns within the gestures of Example la Example lb. Cadential patterns within the gestures of Example la

4-1

4-T eit

4-25

AM ,t.

4-1

4-T eit

4-25

AM ,t.

4-1

4-T eit

4-25

AM ,t.

4-1

4-T eit

4-25

AM ,t. -..---B U

3-9

Example lc. Mapping of the important trichords from Example la

-..---B U 3-9

Example lc. Mapping of the important trichords from Example la

-..---B U 3-9

Example lc. Mapping of the important trichords from Example la

-..---B U 3-9

Example lc. Mapping of the important trichords from Example la

3-1

X #~ 1

3-7 i :

(m. 6)

3-8

3-1

X #~ 1

3-7 i :

(m. 6)

3-8

3-1

X #~ 1

3-7 i :

(m. 6)

3-8

3-1

X #~ 1

3-7 i :

(m. 6)

3-8

tionship between the other two trichords, though, is undefined. From trichord to trichord, the leading tone and 2 remain in- variant. It is D[ , the tonic, which can be perceived as mapping into 4 in moving to the whole-tone trichord and mapping into #4 when the circle of fifths dyad is enunciated. The transforma- tion is still tonally suggestive, especially in its relation to the blues.

The passage taken from Air above Mountains shows imme- diate relationships between differing chord forms in different languages. Taylor's composition "Tales (8 Whisps)" (1966),

tionship between the other two trichords, though, is undefined. From trichord to trichord, the leading tone and 2 remain in- variant. It is D[ , the tonic, which can be perceived as mapping into 4 in moving to the whole-tone trichord and mapping into #4 when the circle of fifths dyad is enunciated. The transforma- tion is still tonally suggestive, especially in its relation to the blues.

The passage taken from Air above Mountains shows imme- diate relationships between differing chord forms in different languages. Taylor's composition "Tales (8 Whisps)" (1966),

tionship between the other two trichords, though, is undefined. From trichord to trichord, the leading tone and 2 remain in- variant. It is D[ , the tonic, which can be perceived as mapping into 4 in moving to the whole-tone trichord and mapping into #4 when the circle of fifths dyad is enunciated. The transforma- tion is still tonally suggestive, especially in its relation to the blues.

The passage taken from Air above Mountains shows imme- diate relationships between differing chord forms in different languages. Taylor's composition "Tales (8 Whisps)" (1966),

tionship between the other two trichords, though, is undefined. From trichord to trichord, the leading tone and 2 remain in- variant. It is D[ , the tonic, which can be perceived as mapping into 4 in moving to the whole-tone trichord and mapping into #4 when the circle of fifths dyad is enunciated. The transforma- tion is still tonally suggestive, especially in its relation to the blues.

The passage taken from Air above Mountains shows imme- diate relationships between differing chord forms in different languages. Taylor's composition "Tales (8 Whisps)" (1966),

provides an opportunity to study a more sophisticated transfor- mation over a longer span of time. Here the transformation is similar to a type that often occurs in Bartok, in which a passage previously octatonic is reshaped in the diatonic yet remains rec- ognizable. In "Tales," an eight-movement work for seven play- ers, the outer sections are clearly related on the surface by in- strumentation, texture, and gesture.

The opening measures of "Tales" are shown in Example 2a. On one level, this passage is a florid elaboration of an El blues scale with the important notes clearly emphasized. First, the 3 and 4 3 are emphasized in mm. 1-2, followed by the dominant which then twice arpeggiates up to the tonic in m. 3 of the ex- ample. The next pitches to occur are 4 and 04 in mm. 4-5; this phrase ends with the leading tone. The motion from leading tone to tonic is picked up again in mm. 8-9. As in the previous Taylor excerpt, the development of material here follows an additive course.

Despite these tonal emphases, the basis of "chord" changes to come are evident from a tetrachordal segmentation of the primary gestures of the opening (Ex. 2b). In this mostly chro- matic environment, the segmentation of these tetrachords fol- lows a general pattern whereby semitone dyads and, more rarely, whole-tone dyads are arranged around some inner in- terval to form a larger pitch grouping.

At the end of the composition, the gestures are not distinctly or overtly related to those of the opening because the connec- tions can only be understood as parts of a developmental proc- ess. Example 3a shows the conclusion of "Tales" with some pitch-class and gestural analysis. The first gesture, in all its vari- ations, is a diatonic 5-20[0,1,5,6,8] pentachord; gesture 2 is a more general category used for extended "chromatic" ges- tures; gesture 3 is octatonic; gesture 4 is made up of the Z- related 6-Z6[0,1,2,5,6,7] and 6-Z38[0,1,2,3,7,8] hexachords; and gesture 5 represents the cluster passages, both whole-tone and chromatic, at the conclusion. Using this labeling, one can follow some of the simultaneously unfolding processes. The

provides an opportunity to study a more sophisticated transfor- mation over a longer span of time. Here the transformation is similar to a type that often occurs in Bartok, in which a passage previously octatonic is reshaped in the diatonic yet remains rec- ognizable. In "Tales," an eight-movement work for seven play- ers, the outer sections are clearly related on the surface by in- strumentation, texture, and gesture.

The opening measures of "Tales" are shown in Example 2a. On one level, this passage is a florid elaboration of an El blues scale with the important notes clearly emphasized. First, the 3 and 4 3 are emphasized in mm. 1-2, followed by the dominant which then twice arpeggiates up to the tonic in m. 3 of the ex- ample. The next pitches to occur are 4 and 04 in mm. 4-5; this phrase ends with the leading tone. The motion from leading tone to tonic is picked up again in mm. 8-9. As in the previous Taylor excerpt, the development of material here follows an additive course.

Despite these tonal emphases, the basis of "chord" changes to come are evident from a tetrachordal segmentation of the primary gestures of the opening (Ex. 2b). In this mostly chro- matic environment, the segmentation of these tetrachords fol- lows a general pattern whereby semitone dyads and, more rarely, whole-tone dyads are arranged around some inner in- terval to form a larger pitch grouping.

At the end of the composition, the gestures are not distinctly or overtly related to those of the opening because the connec- tions can only be understood as parts of a developmental proc- ess. Example 3a shows the conclusion of "Tales" with some pitch-class and gestural analysis. The first gesture, in all its vari- ations, is a diatonic 5-20[0,1,5,6,8] pentachord; gesture 2 is a more general category used for extended "chromatic" ges- tures; gesture 3 is octatonic; gesture 4 is made up of the Z- related 6-Z6[0,1,2,5,6,7] and 6-Z38[0,1,2,3,7,8] hexachords; and gesture 5 represents the cluster passages, both whole-tone and chromatic, at the conclusion. Using this labeling, one can follow some of the simultaneously unfolding processes. The

provides an opportunity to study a more sophisticated transfor- mation over a longer span of time. Here the transformation is similar to a type that often occurs in Bartok, in which a passage previously octatonic is reshaped in the diatonic yet remains rec- ognizable. In "Tales," an eight-movement work for seven play- ers, the outer sections are clearly related on the surface by in- strumentation, texture, and gesture.

The opening measures of "Tales" are shown in Example 2a. On one level, this passage is a florid elaboration of an El blues scale with the important notes clearly emphasized. First, the 3 and 4 3 are emphasized in mm. 1-2, followed by the dominant which then twice arpeggiates up to the tonic in m. 3 of the ex- ample. The next pitches to occur are 4 and 04 in mm. 4-5; this phrase ends with the leading tone. The motion from leading tone to tonic is picked up again in mm. 8-9. As in the previous Taylor excerpt, the development of material here follows an additive course.

Despite these tonal emphases, the basis of "chord" changes to come are evident from a tetrachordal segmentation of the primary gestures of the opening (Ex. 2b). In this mostly chro- matic environment, the segmentation of these tetrachords fol- lows a general pattern whereby semitone dyads and, more rarely, whole-tone dyads are arranged around some inner in- terval to form a larger pitch grouping.

At the end of the composition, the gestures are not distinctly or overtly related to those of the opening because the connec- tions can only be understood as parts of a developmental proc- ess. Example 3a shows the conclusion of "Tales" with some pitch-class and gestural analysis. The first gesture, in all its vari- ations, is a diatonic 5-20[0,1,5,6,8] pentachord; gesture 2 is a more general category used for extended "chromatic" ges- tures; gesture 3 is octatonic; gesture 4 is made up of the Z- related 6-Z6[0,1,2,5,6,7] and 6-Z38[0,1,2,3,7,8] hexachords; and gesture 5 represents the cluster passages, both whole-tone and chromatic, at the conclusion. Using this labeling, one can follow some of the simultaneously unfolding processes. The

provides an opportunity to study a more sophisticated transfor- mation over a longer span of time. Here the transformation is similar to a type that often occurs in Bartok, in which a passage previously octatonic is reshaped in the diatonic yet remains rec- ognizable. In "Tales," an eight-movement work for seven play- ers, the outer sections are clearly related on the surface by in- strumentation, texture, and gesture.

The opening measures of "Tales" are shown in Example 2a. On one level, this passage is a florid elaboration of an El blues scale with the important notes clearly emphasized. First, the 3 and 4 3 are emphasized in mm. 1-2, followed by the dominant which then twice arpeggiates up to the tonic in m. 3 of the ex- ample. The next pitches to occur are 4 and 04 in mm. 4-5; this phrase ends with the leading tone. The motion from leading tone to tonic is picked up again in mm. 8-9. As in the previous Taylor excerpt, the development of material here follows an additive course.

Despite these tonal emphases, the basis of "chord" changes to come are evident from a tetrachordal segmentation of the primary gestures of the opening (Ex. 2b). In this mostly chro- matic environment, the segmentation of these tetrachords fol- lows a general pattern whereby semitone dyads and, more rarely, whole-tone dyads are arranged around some inner in- terval to form a larger pitch grouping.

At the end of the composition, the gestures are not distinctly or overtly related to those of the opening because the connec- tions can only be understood as parts of a developmental proc- ess. Example 3a shows the conclusion of "Tales" with some pitch-class and gestural analysis. The first gesture, in all its vari- ations, is a diatonic 5-20[0,1,5,6,8] pentachord; gesture 2 is a more general category used for extended "chromatic" ges- tures; gesture 3 is octatonic; gesture 4 is made up of the Z- related 6-Z6[0,1,2,5,6,7] and 6-Z38[0,1,2,3,7,8] hexachords; and gesture 5 represents the cluster passages, both whole-tone and chromatic, at the conclusion. Using this labeling, one can follow some of the simultaneously unfolding processes. The

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Transformation in Free Jazz 185

Example 2a. Opening measures of Cecil Taylor's "Tales (8 Whisps)." Transcription by the author from Unit Structures (Blue Note BST-84237)

Transformation in Free Jazz 185

Example 2a. Opening measures of Cecil Taylor's "Tales (8 Whisps)." Transcription by the author from Unit Structures (Blue Note BST-84237)

Transformation in Free Jazz 185

Example 2a. Opening measures of Cecil Taylor's "Tales (8 Whisps)." Transcription by the author from Unit Structures (Blue Note BST-84237)

Transformation in Free Jazz 185

Example 2a. Opening measures of Cecil Taylor's "Tales (8 Whisps)." Transcription by the author from Unit Structures (Blue Note BST-84237)

Piano Piano Piano Piano

J =176 (tempo somewhat free)

1 , .

~drum v I v (D rr s r s

~

! i7 I rq rrrirrrq . r f h-i--I--i 1 LI f' ~

J =176 (tempo somewhat free)

1 , .

~drum v I v (D rr s r s

~

! i7 I rq rrrirrrq . r f h-i--I--i 1 LI f' ~

J =176 (tempo somewhat free)

1 , .

~drum v I v (D rr s r s

~

! i7 I rq rrrirrrq . r f h-i--I--i 1 LI f' ~

J =176 (tempo somewhat free)

1 , .

~drum v I v (D rr s r s

~

! i7 I rq rrrirrrq . r f h-i--I--i 1 LI f' ~ l.U!1 3~1 ! i ! |I _ ! 1 .

Piano A: bbbbb

3 14 15

Drum Set7 -

poco accel. > (may be a fist cluster) =34 p , Poco accel. > > >' >,-=304

P,iano

bbbbbb

3 3 1 7 3 8

)\' b bbbb ' f 17 ?rf 8 :bb;bbbb u r 1' r

Drum Set:

drummer only: IP =264

Piano 9 >

Drum Set -- -

l.U!1 3~1 ! i ! |I _ ! 1 .

Piano A: bbbbb

3 14 15

Drum Set7 -

poco accel. > (may be a fist cluster) =34 p , Poco accel. > > >' >,-=304

P,iano

bbbbbb

3 3 1 7 3 8

)\' b bbbb ' f 17 ?rf 8 :bb;bbbb u r 1' r

Drum Set:

drummer only: IP =264

Piano 9 >

Drum Set -- -

l.U!1 3~1 ! i ! |I _ ! 1 .

Piano A: bbbbb

3 14 15

Drum Set7 -

poco accel. > (may be a fist cluster) =34 p , Poco accel. > > >' >,-=304

P,iano

bbbbbb

3 3 1 7 3 8

)\' b bbbb ' f 17 ?rf 8 :bb;bbbb u r 1' r

Drum Set:

drummer only: IP =264

Piano 9 >

Drum Set -- -

l.U!1 3~1 ! i ! |I _ ! 1 .

Piano A: bbbbb

3 14 15

Drum Set7 -

poco accel. > (may be a fist cluster) =34 p , Poco accel. > > >' >,-=304

P,iano

bbbbbb

3 3 1 7 3 8

)\' b bbbb ' f 17 ?rf 8 :bb;bbbb u r 1' r

Drum Set:

drummer only: IP =264

Piano 9 >

Drum Set -- - Y. p?a f

*

^1)0 Y. p?a f

*

^1)0 Y. p?a f

*

^1)0 Y. p?a f

*

^1)0

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186 Music Theory Spectrum 186 Music Theory Spectrum 186 Music Theory Spectrum 186 Music Theory Spectrum

Example 2b. Tetrachordal segmentation of opening measures of "Tales" Example 2b. Tetrachordal segmentation of opening measures of "Tales" Example 2b. Tetrachordal segmentation of opening measures of "Tales" Example 2b. Tetrachordal segmentation of opening measures of "Tales"

m.2 4-7 m.2

I I I I

m.2 4-7 m.2

I I I I

m.2 4-7 m.2

I I I I

m.2 4-7 m.2

I I I I

4-9 m.4 I I

I _

4-9 m.4 I I

I _

4-9 m.4 I I

I _

4-9 m.4 I I

I _

I I I - _L 4-7 4-1 4-3

ideas of additive and subtractive variation are present, but they are not always on the level of the musical surface. Here it is pitch-class metamorphoses which control the structure. Several pairs of sets, for instance, are related by T2. These sets are out- lined in gestures 2 and 2a (7-5[0,1,2,3,5,6,7] chromatic sets), both in m. 2; in gesture 2b (the abstract complement of 7-5) in m. 7 and in the included pentachord in 2a; in gesture 4 (the 6-Z6 hexachord) in m. 4 and in gesture 4' in m. 16; and ;n gesture 4a (6-Z38) in m. 5 and in 4b in m. 8. Another T2 relation, not shown in the score, exists between the 6-Z38 hexachord in 4c and the 6-Z38 hexachord outlined in the upper register notes of the first measure of this transcription.

There are more subtle ways in which these gestures are re- lated as well. The diatonic 5-20 pentachord is a subset of a hexa- chord, 6-Z38, a hexachord which one cannot abstractly hear as diatonic. Thus, the addition of one pitch class can transform a smaller octatonic or whole-tone collection into a chromatic one. In general, a set associated with one superset can be chro- matically inflected to connect it with a different superset. In this light, one might conclude that the clusters which are so preva- lent in Taylor's music, yet are so often dismissed as mere tex- tural devices, in fact play a real structural role, since these are the elements from which any of the gestures in the final passage (or, as shown previously, the openings blues passage) can be derived.

Example 3b is a reduction of mm. 9-11, which can be thought of as a gestural summary of this movement. A subtler transformation emerges from an interpretation of the tetra-

I I I - _L 4-7 4-1 4-3

ideas of additive and subtractive variation are present, but they are not always on the level of the musical surface. Here it is pitch-class metamorphoses which control the structure. Several pairs of sets, for instance, are related by T2. These sets are out- lined in gestures 2 and 2a (7-5[0,1,2,3,5,6,7] chromatic sets), both in m. 2; in gesture 2b (the abstract complement of 7-5) in m. 7 and in the included pentachord in 2a; in gesture 4 (the 6-Z6 hexachord) in m. 4 and in gesture 4' in m. 16; and ;n gesture 4a (6-Z38) in m. 5 and in 4b in m. 8. Another T2 relation, not shown in the score, exists between the 6-Z38 hexachord in 4c and the 6-Z38 hexachord outlined in the upper register notes of the first measure of this transcription.

There are more subtle ways in which these gestures are re- lated as well. The diatonic 5-20 pentachord is a subset of a hexa- chord, 6-Z38, a hexachord which one cannot abstractly hear as diatonic. Thus, the addition of one pitch class can transform a smaller octatonic or whole-tone collection into a chromatic one. In general, a set associated with one superset can be chro- matically inflected to connect it with a different superset. In this light, one might conclude that the clusters which are so preva- lent in Taylor's music, yet are so often dismissed as mere tex- tural devices, in fact play a real structural role, since these are the elements from which any of the gestures in the final passage (or, as shown previously, the openings blues passage) can be derived.

Example 3b is a reduction of mm. 9-11, which can be thought of as a gestural summary of this movement. A subtler transformation emerges from an interpretation of the tetra-

I I I - _L 4-7 4-1 4-3

ideas of additive and subtractive variation are present, but they are not always on the level of the musical surface. Here it is pitch-class metamorphoses which control the structure. Several pairs of sets, for instance, are related by T2. These sets are out- lined in gestures 2 and 2a (7-5[0,1,2,3,5,6,7] chromatic sets), both in m. 2; in gesture 2b (the abstract complement of 7-5) in m. 7 and in the included pentachord in 2a; in gesture 4 (the 6-Z6 hexachord) in m. 4 and in gesture 4' in m. 16; and ;n gesture 4a (6-Z38) in m. 5 and in 4b in m. 8. Another T2 relation, not shown in the score, exists between the 6-Z38 hexachord in 4c and the 6-Z38 hexachord outlined in the upper register notes of the first measure of this transcription.

There are more subtle ways in which these gestures are re- lated as well. The diatonic 5-20 pentachord is a subset of a hexa- chord, 6-Z38, a hexachord which one cannot abstractly hear as diatonic. Thus, the addition of one pitch class can transform a smaller octatonic or whole-tone collection into a chromatic one. In general, a set associated with one superset can be chro- matically inflected to connect it with a different superset. In this light, one might conclude that the clusters which are so preva- lent in Taylor's music, yet are so often dismissed as mere tex- tural devices, in fact play a real structural role, since these are the elements from which any of the gestures in the final passage (or, as shown previously, the openings blues passage) can be derived.

Example 3b is a reduction of mm. 9-11, which can be thought of as a gestural summary of this movement. A subtler transformation emerges from an interpretation of the tetra-

I I I - _L 4-7 4-1 4-3

ideas of additive and subtractive variation are present, but they are not always on the level of the musical surface. Here it is pitch-class metamorphoses which control the structure. Several pairs of sets, for instance, are related by T2. These sets are out- lined in gestures 2 and 2a (7-5[0,1,2,3,5,6,7] chromatic sets), both in m. 2; in gesture 2b (the abstract complement of 7-5) in m. 7 and in the included pentachord in 2a; in gesture 4 (the 6-Z6 hexachord) in m. 4 and in gesture 4' in m. 16; and ;n gesture 4a (6-Z38) in m. 5 and in 4b in m. 8. Another T2 relation, not shown in the score, exists between the 6-Z38 hexachord in 4c and the 6-Z38 hexachord outlined in the upper register notes of the first measure of this transcription.

There are more subtle ways in which these gestures are re- lated as well. The diatonic 5-20 pentachord is a subset of a hexa- chord, 6-Z38, a hexachord which one cannot abstractly hear as diatonic. Thus, the addition of one pitch class can transform a smaller octatonic or whole-tone collection into a chromatic one. In general, a set associated with one superset can be chro- matically inflected to connect it with a different superset. In this light, one might conclude that the clusters which are so preva- lent in Taylor's music, yet are so often dismissed as mere tex- tural devices, in fact play a real structural role, since these are the elements from which any of the gestures in the final passage (or, as shown previously, the openings blues passage) can be derived.

Example 3b is a reduction of mm. 9-11, which can be thought of as a gestural summary of this movement. A subtler transformation emerges from an interpretation of the tetra-

4-3

chords within the segmented phrases as divided into semitone dyads. From this vantage point, one sees a type of pitch-class condensation taking place in this passage: a 4-9[0,1,6,7] tetra- chord, or two semitone dyads surrounding a perfect fourth, is reduced to a 4-8[0,1,5,6] tetrachord (two semitone dyads sur- rounding a major third), which in turn is transposed up a semi- tone, and finally is reduced to a 4-3[0,1,3,4] tetrachord (two semitone dyads surrounding a whole tone). This contraction may not seem as "natural" as the kinds of extensions or reduc- tions that occur on the surface pitch level from gesture to ges- ture; but, since within the process itself two or three pitch classes are invariant from gesture to gesture, it is quite conceiv- able that the artist consciously composed these structural connections.

The concluding cluster passages in Example 3a may be heard as moving from an overall whole-tone sonority to a more chromatic gesture centering on chromatic trichords to a mix- ture of the two. The registral separation in m. 17 segments ges- ture 5b' into a 4-10[0,2,3,5] tetrachord (two whole-tone dyads surrounding a semitone), and a 4-3[0,1,3,4] tetrachord which is the same collection of pitches that concluded the summary pas- sage just discussed (Ex. 3b). As this cluster gesture becomes further condensed, the final sound can be heard as a V7 of G. This seems puzzling, since if one were to hear this final passage as tonal, Dl, would be the tonic since that pitch is segmented out by register, often in the bass. Moreover, gesture 3 returns twice in the guise of a dominant ninth of Db . It does seem pref- erable, on the whole, to hear Taylor's music as nontonal even

4-3

chords within the segmented phrases as divided into semitone dyads. From this vantage point, one sees a type of pitch-class condensation taking place in this passage: a 4-9[0,1,6,7] tetra- chord, or two semitone dyads surrounding a perfect fourth, is reduced to a 4-8[0,1,5,6] tetrachord (two semitone dyads sur- rounding a major third), which in turn is transposed up a semi- tone, and finally is reduced to a 4-3[0,1,3,4] tetrachord (two semitone dyads surrounding a whole tone). This contraction may not seem as "natural" as the kinds of extensions or reduc- tions that occur on the surface pitch level from gesture to ges- ture; but, since within the process itself two or three pitch classes are invariant from gesture to gesture, it is quite conceiv- able that the artist consciously composed these structural connections.

The concluding cluster passages in Example 3a may be heard as moving from an overall whole-tone sonority to a more chromatic gesture centering on chromatic trichords to a mix- ture of the two. The registral separation in m. 17 segments ges- ture 5b' into a 4-10[0,2,3,5] tetrachord (two whole-tone dyads surrounding a semitone), and a 4-3[0,1,3,4] tetrachord which is the same collection of pitches that concluded the summary pas- sage just discussed (Ex. 3b). As this cluster gesture becomes further condensed, the final sound can be heard as a V7 of G. This seems puzzling, since if one were to hear this final passage as tonal, Dl, would be the tonic since that pitch is segmented out by register, often in the bass. Moreover, gesture 3 returns twice in the guise of a dominant ninth of Db . It does seem pref- erable, on the whole, to hear Taylor's music as nontonal even

4-3

chords within the segmented phrases as divided into semitone dyads. From this vantage point, one sees a type of pitch-class condensation taking place in this passage: a 4-9[0,1,6,7] tetra- chord, or two semitone dyads surrounding a perfect fourth, is reduced to a 4-8[0,1,5,6] tetrachord (two semitone dyads sur- rounding a major third), which in turn is transposed up a semi- tone, and finally is reduced to a 4-3[0,1,3,4] tetrachord (two semitone dyads surrounding a whole tone). This contraction may not seem as "natural" as the kinds of extensions or reduc- tions that occur on the surface pitch level from gesture to ges- ture; but, since within the process itself two or three pitch classes are invariant from gesture to gesture, it is quite conceiv- able that the artist consciously composed these structural connections.

The concluding cluster passages in Example 3a may be heard as moving from an overall whole-tone sonority to a more chromatic gesture centering on chromatic trichords to a mix- ture of the two. The registral separation in m. 17 segments ges- ture 5b' into a 4-10[0,2,3,5] tetrachord (two whole-tone dyads surrounding a semitone), and a 4-3[0,1,3,4] tetrachord which is the same collection of pitches that concluded the summary pas- sage just discussed (Ex. 3b). As this cluster gesture becomes further condensed, the final sound can be heard as a V7 of G. This seems puzzling, since if one were to hear this final passage as tonal, Dl, would be the tonic since that pitch is segmented out by register, often in the bass. Moreover, gesture 3 returns twice in the guise of a dominant ninth of Db . It does seem pref- erable, on the whole, to hear Taylor's music as nontonal even

4-3

chords within the segmented phrases as divided into semitone dyads. From this vantage point, one sees a type of pitch-class condensation taking place in this passage: a 4-9[0,1,6,7] tetra- chord, or two semitone dyads surrounding a perfect fourth, is reduced to a 4-8[0,1,5,6] tetrachord (two semitone dyads sur- rounding a major third), which in turn is transposed up a semi- tone, and finally is reduced to a 4-3[0,1,3,4] tetrachord (two semitone dyads surrounding a whole tone). This contraction may not seem as "natural" as the kinds of extensions or reduc- tions that occur on the surface pitch level from gesture to ges- ture; but, since within the process itself two or three pitch classes are invariant from gesture to gesture, it is quite conceiv- able that the artist consciously composed these structural connections.

The concluding cluster passages in Example 3a may be heard as moving from an overall whole-tone sonority to a more chromatic gesture centering on chromatic trichords to a mix- ture of the two. The registral separation in m. 17 segments ges- ture 5b' into a 4-10[0,2,3,5] tetrachord (two whole-tone dyads surrounding a semitone), and a 4-3[0,1,3,4] tetrachord which is the same collection of pitches that concluded the summary pas- sage just discussed (Ex. 3b). As this cluster gesture becomes further condensed, the final sound can be heard as a V7 of G. This seems puzzling, since if one were to hear this final passage as tonal, Dl, would be the tonic since that pitch is segmented out by register, often in the bass. Moreover, gesture 3 returns twice in the guise of a dominant ninth of Db . It does seem pref- erable, on the whole, to hear Taylor's music as nontonal even

m.1 rn m.l I m.1 rn m.l I m.1 rn m.l I m.1 rn m.l I nm.1-2

I_ nm.1-2

I_ nm.1-2

I_ nm.1-2

I_ b .- E b .- E b .- E b .- E -4 :

_

V F: 'O- 1 - 11 dph I 1-I ? I

4 .-e I ML NL I I I -

-4 : _

V F: 'O- 1 - 11 dph I 1-I ? I

4 .-e I ML NL I I I -

-4 : _

V F: 'O- 1 - 11 dph I 1-I ? I

4 .-e I ML NL I I I -

-4 : _

V F: 'O- 1 - 11 dph I 1-I ? I

4 .-e I ML NL I I I -

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Transformation in Free Jazz 187

Example 3a. Final measures of "Tales" segmented into related gestures and pc sets. Transcription by the author

Transformation in Free Jazz 187

Example 3a. Final measures of "Tales" segmented into related gestures and pc sets. Transcription by the author

Transformation in Free Jazz 187

Example 3a. Final measures of "Tales" segmented into related gestures and pc sets. Transcription by the author

Transformation in Free Jazz 187

Example 3a. Final measures of "Tales" segmented into related gestures and pc sets. Transcription by the author

accel ------ tempo accel ------ tempo accel ------ tempo accel ------ tempo

=240 accel. - - - tempo

3 ^ . L_

=240 accel. - - - tempo

3 ^ . L_

=240 accel. - - - tempo

3 ^ . L_

=240 accel. - - - tempo

3 ^ . L_

( 7 / 1, 1 12 1 ' I I

/

L; 12b subset of gestures 2 4

b

79:2 n ..... ~ ! , ,ue ,,t^ k V (1) 5-20, diatonic i i (la) literal subset i i (2) 7-5, chromatic of gesture 1 (2a) 75, related by (3) ctatonic I/Adomiant inth 1

s u beT2 to gesture 2 (4) 6-Z6 (4a) 6-Z38 T

~j^I . ~: : . b?~~~~~~~~~~~

( 7 / 1, 1 12 1 ' I I

/

L; 12b subset of gestures 2 4

b

79:2 n ..... ~ ! , ,ue ,,t^ k V (1) 5-20, diatonic i i (la) literal subset i i (2) 7-5, chromatic of gesture 1 (2a) 75, related by (3) ctatonic I/Adomiant inth 1

s u beT2 to gesture 2 (4) 6-Z6 (4a) 6-Z38 T

~j^I . ~: : . b?~~~~~~~~~~~

( 7 / 1, 1 12 1 ' I I

/

L; 12b subset of gestures 2 4

b

79:2 n ..... ~ ! , ,ue ,,t^ k V (1) 5-20, diatonic i i (la) literal subset i i (2) 7-5, chromatic of gesture 1 (2a) 75, related by (3) ctatonic I/Adomiant inth 1

s u beT2 to gesture 2 (4) 6-Z6 (4a) 6-Z38 T

~j^I . ~: : . b?~~~~~~~~~~~

( 7 / 1, 1 12 1 ' I I

/

L; 12b subset of gestures 2 4

b

79:2 n ..... ~ ! , ,ue ,,t^ k V (1) 5-20, diatonic i i (la) literal subset i i (2) 7-5, chromatic of gesture 1 (2a) 75, related by (3) ctatonic I/Adomiant inth 1

s u beT2 to gesture 2 (4) 6-Z6 (4a) 6-Z38 T

~j^I . ~: : . b?~~~~~~~~~~~ ~]-eL-r r- L, ' M T " 1 m ~]-eL-r r- L, ' M T " 1 m ~]-eL-r r- L, ' M T " 1 m ~]-eL-r r- L, ' M T " 1 m

I I I (not clear) I_ (3a) Octatonic I (4b) 6-Z38, related by T2 (3) rearrangement, upper register preserved

to gesture 4a (2c') extension of 2c Summary Passage ^=200 1 E .I )I .I I I= 336 k - ~ ~ ~ ~ ~ ~ ~ ~ ~~~e = 200 , -' C' a~-33

I I I (not clear) I_ (3a) Octatonic I (4b) 6-Z38, related by T2 (3) rearrangement, upper register preserved

to gesture 4a (2c') extension of 2c Summary Passage ^=200 1 E .I )I .I I I= 336 k - ~ ~ ~ ~ ~ ~ ~ ~ ~~~e = 200 , -' C' a~-33

I I I (not clear) I_ (3a) Octatonic I (4b) 6-Z38, related by T2 (3) rearrangement, upper register preserved

to gesture 4a (2c') extension of 2c Summary Passage ^=200 1 E .I )I .I I I= 336 k - ~ ~ ~ ~ ~ ~ ~ ~ ~~~e = 200 , -' C' a~-33

I I I (not clear) I_ (3a) Octatonic I (4b) 6-Z38, related by T2 (3) rearrangement, upper register preserved

to gesture 4a (2c') extension of 2c Summary Passage ^=200 1 E .I )I .I I I= 336 k - ~ ~ ~ ~ ~ ~ ~ ~ ~~~e = 200 , -' C' a~-33

a =336 A

a =336 A

a =336 A

a =336 A 3 3 3 3 I 0-t1 I 0-t1 I 0-t1 I 0-t1

1 (inclusion of previous 5-20 is literal)

1 (inclusion of previous 5-20 is literal)

1 (inclusion of previous 5-20 is literal)

1 (inclusion of previous 5-20 is literal)

-2 -2 -2 -2

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188 Music Theory Spectrum

3a (cont.)

= 240

188 Music Theory Spectrum

3a (cont.)

= 240

188 Music Theory Spectrum

3a (cont.)

= 240

188 Music Theory Spectrum

3a (cont.)

= 240

175 ,1,1 ~ --- ! ', (5) Clusters (whole tone) 6f --

'1' ' e Tr r r :=r===

175 ,1,1 ~ --- ! ', (5) Clusters (whole tone) 6f --

'1' ' e Tr r r :=r===

175 ,1,1 ~ --- ! ', (5) Clusters (whole tone) 6f --

'1' ' e Tr r r :=r===

175 ,1,1 ~ --- ! ', (5) Clusters (whole tone) 6f --

'1' ' e Tr r r :=r=== (5a) Clusters (chromatic) (5a) Clusters (chromatic) (5a) Clusters (chromatic) (5a) Clusters (chromatic)

(5b) (5b) (5b) (5b) (5b') (5b') (5b') (5b') (5b) condensation (5b) condensation (5b) condensation (5b) condensation

Example 3b. Reduction of mm. 9-11 from Example 3a 4-9 4-8 4-8 1 I 11 4.-8 1 1 1 1 11 1 A I I I 4-RIf I I I I I I4 -

Example 3b. Reduction of mm. 9-11 from Example 3a 4-9 4-8 4-8 1 I 11 4.-8 1 1 1 1 11 1 A I I I 4-RIf I I I I I I4 -

Example 3b. Reduction of mm. 9-11 from Example 3a 4-9 4-8 4-8 1 I 11 4.-8 1 1 1 1 11 1 A I I I 4-RIf I I I I I I4 -

Example 3b. Reduction of mm. 9-11 from Example 3a 4-9 4-8 4-8 1 I 11 4.-8 1 1 1 1 11 1 A I I I 4-RIf I I I I I I4 - 4-3 ! 4-3 ! 4-3 ! 4-3 ! I I

"^y '~.w-4 - 1 #0- f f "- - I i I

I /

i T 5-20 6-Z38 5-20

I l I I l I l l l I

Q__b- b^ __ b,^ bw bb, _ b. b _,,

I I

"^y '~.w-4 - 1 #0- f f "- - I i I

I /

i T 5-20 6-Z38 5-20

I l I I l I l l l I

Q__b- b^ __ b,^ bw bb, _ b. b _,,

I I

"^y '~.w-4 - 1 #0- f f "- - I i I

I /

i T 5-20 6-Z38 5-20

I l I I l I l l l I

Q__b- b^ __ b,^ bw bb, _ b. b _,,

I I

"^y '~.w-4 - 1 #0- f f "- - I i I

I /

i T 5-20 6-Z38 5-20

I l I I l I l l l I

Q__b- b^ __ b,^ bw bb, _ b. b _,, r r r r * - * - * - * - r r r r

though it often contains tonal jazz references. Nevertheless, taking the cue from the final five notes of the piece being M- related to the important 5-20 pentachord in this passage, one can hear the closing notes as a T6MI chord substitution for the dominant of D,. Therefore, these final cluster passages can be understood as summaries of the measures in the entire excerpt, both in terms of derivational structure and tonal orientation.

though it often contains tonal jazz references. Nevertheless, taking the cue from the final five notes of the piece being M- related to the important 5-20 pentachord in this passage, one can hear the closing notes as a T6MI chord substitution for the dominant of D,. Therefore, these final cluster passages can be understood as summaries of the measures in the entire excerpt, both in terms of derivational structure and tonal orientation.

though it often contains tonal jazz references. Nevertheless, taking the cue from the final five notes of the piece being M- related to the important 5-20 pentachord in this passage, one can hear the closing notes as a T6MI chord substitution for the dominant of D,. Therefore, these final cluster passages can be understood as summaries of the measures in the entire excerpt, both in terms of derivational structure and tonal orientation.

though it often contains tonal jazz references. Nevertheless, taking the cue from the final five notes of the piece being M- related to the important 5-20 pentachord in this passage, one can hear the closing notes as a T6MI chord substitution for the dominant of D,. Therefore, these final cluster passages can be understood as summaries of the measures in the entire excerpt, both in terms of derivational structure and tonal orientation.

Though Coltrane emerged as an important jazz artist before Taylor and Coleman, he turned to his own free jazz style only during his last period (1964-67), after Taylor's and Coleman's music had become widely known. Coltrane's first solo in Ascen- sion is a good example of his use of two primary generative de- vices within a quasi-modal framework: interval cycles and tri- chordal source sets. Coltrane's improvisations have

Though Coltrane emerged as an important jazz artist before Taylor and Coleman, he turned to his own free jazz style only during his last period (1964-67), after Taylor's and Coleman's music had become widely known. Coltrane's first solo in Ascen- sion is a good example of his use of two primary generative de- vices within a quasi-modal framework: interval cycles and tri- chordal source sets. Coltrane's improvisations have

Though Coltrane emerged as an important jazz artist before Taylor and Coleman, he turned to his own free jazz style only during his last period (1964-67), after Taylor's and Coleman's music had become widely known. Coltrane's first solo in Ascen- sion is a good example of his use of two primary generative de- vices within a quasi-modal framework: interval cycles and tri- chordal source sets. Coltrane's improvisations have

Though Coltrane emerged as an important jazz artist before Taylor and Coleman, he turned to his own free jazz style only during his last period (1964-67), after Taylor's and Coleman's music had become widely known. Coltrane's first solo in Ascen- sion is a good example of his use of two primary generative de- vices within a quasi-modal framework: interval cycles and tri- chordal source sets. Coltrane's improvisations have

accel.------- nt.------------- accel.------ rit.------- accel.------- nt.------------- accel.------ rit.------- accel.------- nt.------------- accel.------ rit.------- accel.------- nt.------------- accel.------ rit.-------

I I I I I I I I

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Transformation in Free Jazz 189 Transformation in Free Jazz 189 Transformation in Free Jazz 189 Transformation in Free Jazz 189

traditionally been described in terms of modal shifts as the pri- mary indicators of harmonic movement and the modes them- selves as the primary generators of pitch material. However, this kind of description fails to clarify whether Coltrane heard the modes simply as source collections or whether he exploited the structural properties of the mode to emphasize, for in- stance, the modal final and the dominant.7

At the opening of Ascension, Coltrane's tenor sax line is si- multaneously imitated in the same register by the other players (see Ex. 4a for a transcription of Coltrane's opening line). Overall, the rhythmic emphasis marks the opening as a "Bb blues" statement with the scale enunciated from i to 5 and in- cluding both l,3 and | 3. The ensemble, as a whole, ignores t 3; thus one primarily hears Bl, D,, and Eb, which constitute a 3-7[0,2,5] trichord. The added Dt, which occurs only in Col- trane's part, forms a 3-2[0,1,3] trichord with the upper portion of the scale and a 3-3[0,1,4] moving down to the Bb tonic.

When Coltrane later begins his first solo (see Ex. 4b), these same trichords are fundamental to the pitch progression within the mode.8 The solo is launched from the 3-7 trichord now formed by the seventh, tonic, and third of the mode and an al- ternation between 3-2 and 3-3 trichords is the subject of the next 15 bars. The pitches explored here are not those from the opening but, instead, the lowest third of the B b scale with the leading tone.

The second part of the B, Aeolian solo features a longer play on the first trichord of the solo, 3-7; the entire passage, in fact, can be segmented into 3-7 trichords. One interesting rela- tionship is that of the tetrachord formed in the first part by the

7Such a problem arises, for example, when Jost (Free Jazz, 92-93) catego- rizes the first part of the solo as being in B Aeolian with an added A as a leading tone. Considering the generality of this description, Bb minor seems equally suitable as a classification; but in either case, no real insight is gained into Coltrane's choice of specific pitch structures.

8The transcription in Example 4b is taken from Jost, Free Jazz, 92-93; the analytic summary alongside is my own.

traditionally been described in terms of modal shifts as the pri- mary indicators of harmonic movement and the modes them- selves as the primary generators of pitch material. However, this kind of description fails to clarify whether Coltrane heard the modes simply as source collections or whether he exploited the structural properties of the mode to emphasize, for in- stance, the modal final and the dominant.7

At the opening of Ascension, Coltrane's tenor sax line is si- multaneously imitated in the same register by the other players (see Ex. 4a for a transcription of Coltrane's opening line). Overall, the rhythmic emphasis marks the opening as a "Bb blues" statement with the scale enunciated from i to 5 and in- cluding both l,3 and | 3. The ensemble, as a whole, ignores t 3; thus one primarily hears Bl, D,, and Eb, which constitute a 3-7[0,2,5] trichord. The added Dt, which occurs only in Col- trane's part, forms a 3-2[0,1,3] trichord with the upper portion of the scale and a 3-3[0,1,4] moving down to the Bb tonic.

When Coltrane later begins his first solo (see Ex. 4b), these same trichords are fundamental to the pitch progression within the mode.8 The solo is launched from the 3-7 trichord now formed by the seventh, tonic, and third of the mode and an al- ternation between 3-2 and 3-3 trichords is the subject of the next 15 bars. The pitches explored here are not those from the opening but, instead, the lowest third of the B b scale with the leading tone.

The second part of the B, Aeolian solo features a longer play on the first trichord of the solo, 3-7; the entire passage, in fact, can be segmented into 3-7 trichords. One interesting rela- tionship is that of the tetrachord formed in the first part by the

7Such a problem arises, for example, when Jost (Free Jazz, 92-93) catego- rizes the first part of the solo as being in B Aeolian with an added A as a leading tone. Considering the generality of this description, Bb minor seems equally suitable as a classification; but in either case, no real insight is gained into Coltrane's choice of specific pitch structures.

8The transcription in Example 4b is taken from Jost, Free Jazz, 92-93; the analytic summary alongside is my own.

traditionally been described in terms of modal shifts as the pri- mary indicators of harmonic movement and the modes them- selves as the primary generators of pitch material. However, this kind of description fails to clarify whether Coltrane heard the modes simply as source collections or whether he exploited the structural properties of the mode to emphasize, for in- stance, the modal final and the dominant.7

At the opening of Ascension, Coltrane's tenor sax line is si- multaneously imitated in the same register by the other players (see Ex. 4a for a transcription of Coltrane's opening line). Overall, the rhythmic emphasis marks the opening as a "Bb blues" statement with the scale enunciated from i to 5 and in- cluding both l,3 and | 3. The ensemble, as a whole, ignores t 3; thus one primarily hears Bl, D,, and Eb, which constitute a 3-7[0,2,5] trichord. The added Dt, which occurs only in Col- trane's part, forms a 3-2[0,1,3] trichord with the upper portion of the scale and a 3-3[0,1,4] moving down to the Bb tonic.

When Coltrane later begins his first solo (see Ex. 4b), these same trichords are fundamental to the pitch progression within the mode.8 The solo is launched from the 3-7 trichord now formed by the seventh, tonic, and third of the mode and an al- ternation between 3-2 and 3-3 trichords is the subject of the next 15 bars. The pitches explored here are not those from the opening but, instead, the lowest third of the B b scale with the leading tone.

The second part of the B, Aeolian solo features a longer play on the first trichord of the solo, 3-7; the entire passage, in fact, can be segmented into 3-7 trichords. One interesting rela- tionship is that of the tetrachord formed in the first part by the

7Such a problem arises, for example, when Jost (Free Jazz, 92-93) catego- rizes the first part of the solo as being in B Aeolian with an added A as a leading tone. Considering the generality of this description, Bb minor seems equally suitable as a classification; but in either case, no real insight is gained into Coltrane's choice of specific pitch structures.

8The transcription in Example 4b is taken from Jost, Free Jazz, 92-93; the analytic summary alongside is my own.

traditionally been described in terms of modal shifts as the pri- mary indicators of harmonic movement and the modes them- selves as the primary generators of pitch material. However, this kind of description fails to clarify whether Coltrane heard the modes simply as source collections or whether he exploited the structural properties of the mode to emphasize, for in- stance, the modal final and the dominant.7

At the opening of Ascension, Coltrane's tenor sax line is si- multaneously imitated in the same register by the other players (see Ex. 4a for a transcription of Coltrane's opening line). Overall, the rhythmic emphasis marks the opening as a "Bb blues" statement with the scale enunciated from i to 5 and in- cluding both l,3 and | 3. The ensemble, as a whole, ignores t 3; thus one primarily hears Bl, D,, and Eb, which constitute a 3-7[0,2,5] trichord. The added Dt, which occurs only in Col- trane's part, forms a 3-2[0,1,3] trichord with the upper portion of the scale and a 3-3[0,1,4] moving down to the Bb tonic.

When Coltrane later begins his first solo (see Ex. 4b), these same trichords are fundamental to the pitch progression within the mode.8 The solo is launched from the 3-7 trichord now formed by the seventh, tonic, and third of the mode and an al- ternation between 3-2 and 3-3 trichords is the subject of the next 15 bars. The pitches explored here are not those from the opening but, instead, the lowest third of the B b scale with the leading tone.

The second part of the B, Aeolian solo features a longer play on the first trichord of the solo, 3-7; the entire passage, in fact, can be segmented into 3-7 trichords. One interesting rela- tionship is that of the tetrachord formed in the first part by the

7Such a problem arises, for example, when Jost (Free Jazz, 92-93) catego- rizes the first part of the solo as being in B Aeolian with an added A as a leading tone. Considering the generality of this description, Bb minor seems equally suitable as a classification; but in either case, no real insight is gained into Coltrane's choice of specific pitch structures.

8The transcription in Example 4b is taken from Jost, Free Jazz, 92-93; the analytic summary alongside is my own.

alternation of 3-2 and 3-3 trichords (4-3) and its T8M-related set (4-26[0,3,5,8] formed by the overlapping of two 3-7 trichords in mm. 16-20. This is a result of the transformation that maps the chromatic semitone of leading tone-to-tonic in the first tetra- chord into the perfect fifth dominant-to-tonic in the second tetrachord.

In the final run of the first section, the first whole-tone struc- ture is enunciated in mm. 23-24 when the 3-6[0,2,4] trichord, F-E ,-Dl, is sounded, a harbinger of the subsequent structural importance of the whole-tone cycle. The accumulation of whole-tone structures in the second section proceeds in a way that is analogous to the use of the 3-7 trichord (as major second followed by minor third) at the end of the first section. At the opening of the second section, Coltrane sounds a 3-8[0,2,6] whole-tone trichord and follows in upward scalar motion with a 5-30[0,1,4,6,8] chord (which embeds two 3-8 trichords). This 5-30 is then altered to the whole-tone pentachord 5-33 [0,2,4,6,8], which appears in ascending scalar form in m. 27.

Measures 27-30 mark the beginning of a section which paral- lels the opening of the solo. Here, instead of alternating be- tween trichords, Coltrane primarily reiterates the pitch classes of one whole-tone tetrachord while varying them rhythmically. The tetrachord is scored as a descending whole-tone trichord followed by a downward tritone leap. The repetition and re- working of the chord clearly connect to the opening passage of the solo in section 1. The aural association of the two passages is made obvious through the use of the leap, which preserves con- tour. Coltrane's scoring ensures that one hears the last three notes in the second motive, which form the interval succession of whole tone and tritone, as a 2:1 expansion of the 3-3 trichord at the opening (semitone and minor third). Proceeding from section 1 to section 2, then, the listener notices: (1) the increase in cardinality of the chordal generator-or, at least, of the em- phasized chord; (2) the contour expansion; (3) the intervallic expansion, with the chromatic generators 3-2 and 3-3 being re- placed by whole-tone generators.

alternation of 3-2 and 3-3 trichords (4-3) and its T8M-related set (4-26[0,3,5,8] formed by the overlapping of two 3-7 trichords in mm. 16-20. This is a result of the transformation that maps the chromatic semitone of leading tone-to-tonic in the first tetra- chord into the perfect fifth dominant-to-tonic in the second tetrachord.

In the final run of the first section, the first whole-tone struc- ture is enunciated in mm. 23-24 when the 3-6[0,2,4] trichord, F-E ,-Dl, is sounded, a harbinger of the subsequent structural importance of the whole-tone cycle. The accumulation of whole-tone structures in the second section proceeds in a way that is analogous to the use of the 3-7 trichord (as major second followed by minor third) at the end of the first section. At the opening of the second section, Coltrane sounds a 3-8[0,2,6] whole-tone trichord and follows in upward scalar motion with a 5-30[0,1,4,6,8] chord (which embeds two 3-8 trichords). This 5-30 is then altered to the whole-tone pentachord 5-33 [0,2,4,6,8], which appears in ascending scalar form in m. 27.

Measures 27-30 mark the beginning of a section which paral- lels the opening of the solo. Here, instead of alternating be- tween trichords, Coltrane primarily reiterates the pitch classes of one whole-tone tetrachord while varying them rhythmically. The tetrachord is scored as a descending whole-tone trichord followed by a downward tritone leap. The repetition and re- working of the chord clearly connect to the opening passage of the solo in section 1. The aural association of the two passages is made obvious through the use of the leap, which preserves con- tour. Coltrane's scoring ensures that one hears the last three notes in the second motive, which form the interval succession of whole tone and tritone, as a 2:1 expansion of the 3-3 trichord at the opening (semitone and minor third). Proceeding from section 1 to section 2, then, the listener notices: (1) the increase in cardinality of the chordal generator-or, at least, of the em- phasized chord; (2) the contour expansion; (3) the intervallic expansion, with the chromatic generators 3-2 and 3-3 being re- placed by whole-tone generators.

alternation of 3-2 and 3-3 trichords (4-3) and its T8M-related set (4-26[0,3,5,8] formed by the overlapping of two 3-7 trichords in mm. 16-20. This is a result of the transformation that maps the chromatic semitone of leading tone-to-tonic in the first tetra- chord into th