John O Gallagher. Twelve-Tone Improvisation A Method for Using Tone Rows in Jazz

Transcription

1 John O Gallagher Telve-Tone Improvisation A Method for Using Tone Ros in Jazz

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3 John O Gallagher Telve-Tone Improvisation A Method for Using Tone Ros in Jazz

4 2013 y advance music International copyright secured Layout: Harald Wingerter, musiklektoratde Cover art y Schultz + Schultz Mediengestaltung, Wien, Austria Photograph: J C Hernandez Order No ADV UPC ISBN

5 5 TABLE OF CONTENTS Play-Along CD Track Listings 7 Introduction 8 Acknoledgements 9 1 Telve-Tone Music 10 2 The Trichord 13 3 Analysis of Trichord Types 15 4 Considerations in Trichordal Improvising 18 5 The Telve Basic Ros 24 Non-Symmetric Trichords 26 6 Trichord Trichord 1+2 and 2+1 Cominations from the Ro 37 8 Diatonic Applications of Trichord Ro Related Ros Trichord Trichord 1+3 and 3+1 Cominations from the Ro Diatonic applications of Trichord Ro Trichord Trichord 1+4 and 4+1 Cominations from the Ro Diatonic Applications of Trichord Ro Trichord Trichord 1+5 and 5+1 Cominations from the Ro Diatonic Applications of Trichord Ro Trichord Trichord 2+3 and 3+2 Cominations from the Ro Diatonic Applications of Trichord Ro Trichord Trichord 2+4 and 4+2 Cominations from the Ro Diatonic Applications of Trichord Ro Trichord Trichord 3+4 and 4+3 Cominations from the Ro Diatonic Applications of Trichord Ro Symmetric Trichords Trichord Trichord 2+5 and 5+2 Cominations from the Ro Diatonic Applications of Trichord Ro Trichord Trichord 1+1 Cominations from the Ro Diatonic Applications of Trichord Ro Trichord Trichord 2+2 Cominations from the Ro Diatonic Applications of Trichord

6 6 46 Ro Trichord Trichord 4+4 Cominations from the Ro Diatonic Applications of Trichord Ro Tetrachord Chord Exercises 255 Suggested Reading 272

7 7 PLAY-ALONG CD TRACK LISTINGS Track C Instruments Tuning Note B Concert 1/1 Track B Instruments Track E Instruments Trichord 1+2 Exercise 1/2 1/3 1/4 35 Trichord 1+3 Exercise 1/5 1/6 1/7 77 Trichord 1+4 Exercise 1/8 1/9 1/ Trichord 1+5 Exercise 1/11 1/12 1/ Trichord 2+3 Exercise 1/14 1/15 1/ Trichord 2+4 Exercise 1/17 1/18 1/ Trichord 3+4 Exercise 1/20 1/21 1/ Trichord 2+5 Exercise 1/23 1/24 1/ Trichord 1+1 Exercise 1/26 1/27 1/ Trichord 2+2 Exercise 2/2 2/3 2/4 233 Trichord 4+4 Exercise 2/5 2/6 2/7 245 Page Track Page C Instruments Page B Instruments Page E Instruments 2/8 Minor Exercise /9 Minor Exercise /10 Dominant Exercise /11 Dominant Exercise /12 Major Exercise /13 Major Exercise /14 II-V7-I Exercise /15 V79 to Im Exercise /16 Blues Exercise Demonstration Tracks 2/17 Trichord 1+2 2/18 Trichord 1+3 2/19 Trichord 1+4 2/20 Trichord 1+5 2/21 Trichord 2+3 2/22 Trichord 2+4 2/23 Trichord 3+4 2/24 Trichord 2+5 2/25 Trichord 1+1 2/26 Trichord 2+2 2/27 Trichord 4+4 2/28 Minor Chords Using 1+2 Note Example 1/17 = CD 1, Track 17 2/8 = CD 2, Track 8 John O Gallagher Alto Saxophone Russ Lossing Piano Johannes Weidenmuller Bass Dan Weiss Drums

8 8 INTRODUCTION In a typical jazz education, students are taught to improvise using chords and their related scales as they are applied to the standard jazz repertoire This functional harmonic approach relies on the ear perceiving order ecause of cadences and chord progressions that estalish tonality using a hierarchy of tones ased on a diatonic system of scales When applying telve-tone concepts to improvisation there is a fundamental difference in the ay the ear perceives continuity of the harmony and lines In telve-tone music, the interval content is the key ordering principle The distance from pitch to pitch determines the tonal space and structural relevance that the ear perceives This ook ill present a method for using the 12 trichord types and their derived ros in jazz improvisation The trichord a group of three pitches ill e the principal means to descrie intervallic space in a clear harmonic ay By comining four trichords of one type, telve-tone ros ill e created that fully express the harmonic space each trichord occupies Each of the telve ros has structural relationships to others, creating a family of ros sharing common interval connections As a harmonic and melodic principle, telve-tone music stands on its on as a complete system of music Telve-tone improvisation ill e approached in to ays ithin this ook First, as a system that generates musical lines and chords independent from traditional harmony Secondly, in a method that applies this material to functional harmony Individual trichords and trichord pairs extracted from telve-tone ros ill e used as harmonic and melodic material on diatonic chord qualities Finally, telve-tone ros ill e applied to chord changes This ill e achieved y using the harmonic properties of the trichord pairs in conjunction ith the remaining trichords from their ros in alternate patterns of consonance and dissonance As you ork on these exercises you ill egin to recognize the distinct sound of each trichord and its corresponding ro in the same ay you recognize harmonies from major and minor scales Developing your aility to hear trichords and their interval relationships is crucial The goal in improvising is alays to hear the music you play All of these exercises are intended to acclimate and train the ear to a ne ay of hearing harmonic and intervallic space The information in this method is presented in the context of telve-tone ros, ut should not e vieed as limited exclusively to telve-tone uses Any comination of trichords can produce a musically valid statement ithout using a telve-tone ro You should explore riting compositions inspired y the concepts presented in the folloing chapters Try using oth telvetone and non-telve-tone structures This method is designed to expand your melodic content and understanding of interval relationships Memorization and creative use of these exercises is vital to fully developing this material If practiced diligently, these exercises ill give the improviser the aility to rememer a ro s structure and the techniques to e ale to develop it hile maintaining the integrity of the ro s pitch and interval content In short, this system ill provide you ith the tools in hich to hear, and think, in telve-tone The material presented in this ook assumes that the student has a fundamental understanding of traditional harmony and its applications in jazz improvisation

9 9 ACKNOWLEDGEMENTS I ould like to thank Johannes, Russ and Dan for their eautiful playing on the CD Special thanks to Russ Lossing, Frank Carlerg, Ben Monder and Bruce Arnold for their advice hile I orked on drafts of this ook Lastly, thanks to Veronika Gruer, Harald Wingerter and everyone at Advance Music for all their hard ork

10 10 1 TWELVE-TONE MUSIC In the early tentieth century, composers developed a variety of methods to use chromaticism in their orks Arnold Schoenerg is credited ith the most influential of these methods He descried this system as a method of composing ith telve tones hich are related only ith one another Today it is often referred to as serialism Schoenerg, along ith Alan Berg and Anton Weern, ere the major exponents of this system of composition Each developed a compositional style unique to their artistic visions In general, telve-tone compositional technique can e summarized y a fe asic rules estalished in early telve-tone orks These are: that ros should e careful not to imply any kind of traditional harmonic movement; a composition should e free from any tonal center; and all telve pitches should e presented in an ordered succession efore any pitch is repeated These rules in fact are not set in stone and have een modified or roken during the course of serial music s development Serial music today can use ros ith telve or feer pitches and may imply tonality or not, according to the needs of the composer After more than eighty years as a system of composition, a vast numer of methods for developing ros exist This ook ill use some terminology and concepts used y telve-tone and serial composers Hoever, it is not meant as a treatise on set theory or telve-tone composition Using trichords as the organizing principle for ros is only one approach from the many possile in telve-tone composition The material presented here ill teach you ho to apply telve-tone methods to a jazz improvisational context It might seem that telve-tone structures are too complex to use in improvisation But consider that in traditional harmony there are 84 modes from major keys, 84 modes from harmonic minor keys and 84 modes from melodic minor keys This results in a total of 252 modes and their corresponding chords, not including diminished, hole tone, pentatonic or augmented scales In this method of organizing chromatic harmony, there are only 175 telve-tone ros possile and 12 ase chord types Seven of these chord types are non-symmetric and have partners hich are inversions This results in a total of 220 possile trichord constructions using all transpositions So as you can see, this system is no more complex than that of traditional harmony That eing said, there is a large amount of material here and it does require a different ay of thinking and hearing hich may seem demanding at first I strongly recommend that you read as many ooks as possile on telve-tone and contemporary harmony You can find a suggested reading list at the end of this ook The folloing are some terms e ill e using Trichord Any set or segment of three pitches Tetrachord Any set or segment of four pitches Set A collection of pitches either ordered or unordered Rotation A cyclic permutation of either pitches or sets The first pitch of a set is moved to the last position in the pitch order or the first set is moved to the last position in the set order

11 1 Telve Tone Music 11 Prime form A ro or sets fundamental form from hich all variations are derived (ie root position to use a phrase from traditional harmony) For examples of the prime form please refer to page 13 Set class a collection of sets that elong to the same family WEBERN, BABBITT AND SCHAT This system of using trichords to form telve-tone ros goes ack to the eginning of telve-tone music Anton Weern is knon for using derived ros ased on trichords in his compositions By taking one trichord and performing on it the operations of inversion, retrograde, retrograde inversion and transposition, the other trichords can e found to complete a telve-tone ro The folloing is an example of the ro used in Weern s Concerto for nine instruments, Op 24 Ï Ex 11 P RI 7 R 6 I 1 # Ï Ï # Ï Ï # Ï # Ï Ï nï You ill learn in the folloing chapters that this is called ro 1+3 using steering 5+1 (in mixed trichord rotations) derived from trichord 1+3 The first trichord in this ro is our source trichord The second trichord is its retrograde inversion transposed y 7 semitones The third is its retrograde transposed y 6 semitones The last trichord is its inversion transposed y one semitone (Rememer that our source trichord is B A# D, ith its inversion eing B C A, its retrograde eing D A# B and its retrograde inversion eing A C B All transpositions used to find the trichords for this ro are applied to these four forms) Composer Milton Baitt rote on the cominatorial properties of hexachords (to trichord groupings or six pitch classes) and shoed there are only six all-cominatorial hexachords From these hexachords and their complements (the remaining six pitches) e can realize all of the tone ros possile that are generated from trichords The folloing example shos those hexachords and their complements The numers indicate the position of the respecting pitch ithin a chromatic scale, starting ith c = 0 Ï # Ï nï A B C # # # D All-Cominatorial Hexachord # # # # # # # # # # # # # # # Complement n n

12 # # # 12 1 Telve Tone Music n E F # # # # # # # n # # Ex 12 The folloing is a list of the ros e ill e using in our method that can e found in each of these hexachords and their complements Hexachord A + Complement Ro Ro Ro Ro Hexachord B + Complement Ro Ro Ro Ro Hexachord C + Complement Ro Ro Ro Ro Hexachord D + Complement Ro Ro Ro Ro Hexachord E + Complement Ro Ro Ro Ro Hexachord F + Complement Ro Ro Ro In his ook The Tone Clock, composer Peter Schat proposed that the telve trichords and their ros could provide a complete system for organizing chromatic harmony He states that each trichord is a fundamental harmonic unit capale of generating its on chromatic tonality and thus an entire chromatic palette exists of telve chromatic harmonic regions An important part of his concept as the intervallic relationships that connects the ros hich he called their steering

13 13 2 THE TRICHORD In estern functional harmony the triad is the asic uilding lock for all chords Major, minor, augmented and diminished triads are all utilized in a melodic and harmonic frameork that estalishes tonality in a hierarchy of relationships ithin a diatonic system This leaves nine other possile three note chords unused as fundamental harmonic entities In our method e ill extend this idea of the triad as a asic unit of harmony to include three note chords not used in the diatonic system The term used in telve-tone music to descrie a group of three pitches is trichord This term is used to provide clarity so that no reference to traditional harmony is implied Only telve trichord constructions are possile using all intervals eteen three pitches (not just intervals of a major and minor 3) Trichords ill e identified y the numer of half steps eteen each pitch in prime form Ï # Ï Ï Ï # Ï # Ï Ï # Ï Ï Ï # Ï Ï Ï # Ï # Ï Ï Ï Ï Ï Ï Ï Ï Ï # Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï # Ï Ex21 Prime form (root position) of each trichord is the position in hich there is the least distance eteen the to outer voices This example shos that in the prime version of this trichord, six half steps are eteen the first and last pitch here as the first and second rotations have ten and eight Ï Ï # Ï Ï # Ï Ï #Ï Ï Ï Ex

14 14 2 The Trichord A trichord is harmonically equivalent and elongs to the same family (setclass) as long as it contains the same interval content in prime form = Ï # Ï Ï # Ï Ï Ï Ex 23 In set theory collections of pitches (sets) that elong to the same family (set class) are laeled y using integer notation [example: (013), (015), etc] Because as improvisers e constantly deal ith intervals, and in order to avoid confusion aout trichord set classes that have inversions, all trichord types ill e referred to y their interval content and not their set class using integer notation interval content Ï Ï Ï pitch class set Ex 24 In our method in order to identify a trichord e ill reduce it to prime ascending form Ï # Ï nï Ï correct incorrect # Ï Ï Ï # Ï nï = correct Ï Ï nï Ï Ï incorrect nï Ï Ï Ï Ex 25 =

15 15 3 ANALYSIS OF TRICHORD TYPES There are a fe methods that can e used to analyze trichords in a melodic and harmonic context They can e identified as consecutive trichord chains, consecutive trichord chains ith common tones, or overlapping trichord chains CONSECUTIVE TRICHORD CHAINS # J # # n 3 # # # Œ Ó Ex 31 Ex 32 Trichords reduced to prime form # n # # n # # # The melody aove is a ell knon Charlie Parker line ith an analysis of its trichord structure All of this analysis shos the trichords in prime form Because e are looking at the interval structure and not the implied harmony ithin a diatonic setting, e can no see a familiar line in a ne light Notice the second trichord of the line (1+2) and its repeated pitch B Trichord shapes and repeated pitches ill e discussed in the next chapter Identifying consecutive trichord chains can also e applied to harmonies as ell In these instances the analysis egins on the loest pitch and ascends to the highest and then the trichords are reduced to prime form Ex 33 =

16 16 3 Analysis of Trichord Types TRICHORD CHAINS WITH COMMON TONES AND OVERLAPPING TRICHORDS In some cases the numer of pitches in a chord or melody may appear to resist trichord analysis In these cases e ill use common tones eteen trichords and in some places overlapping trichords to find the trichord structure Be aare that the trichord laeling here indicates its prime form # Ex 34 CHORD ANALYSIS WITH TRICHORD REDUCTIONS # A B C D E n n # # # A = # # = B = = C # # = = D E # # # # # = = n # = = Ex 35

17 3 Analysis of Trichord Types 17 The previous example shos trichord analysis of chords ith four and five pitches Rememer that in these examples the analysis egins on the loest pitch and ascends EXERCISES IN TRICHORD ANALYSIS Ex 36 1 Identify the folloing trichords in their prime form # # # # # # # 2 Analyze the trichord construction of to jazz standard melodies 3 Identify the trichords in these chords # # # # # # # Ex 37 # # # # # # # 4 Take a eop melody and recompose it using trichord analysis to redistriute the pitches Then use similar trichord types or trichords from the corresponding ros to compose ne harmony and/or an alternate melody Refer to the list of telve-tone ros for their construction

18 18 4 CONSIDERATIONS IN TRICHORDAL IMPROVISING The folloing is a list of asic shapes that should e used hen practicing the trichords individually and in comination ith each other Use contrasting shapes and symmetry as ell as varied rhythms and meters as you ascend and descend through the range of your instrument BASIC MELODIC SHAPES 1 Non Repetitive playing each trichord pitch once Ex 41 Each shape should e practiced y itself in all rotations through the full range of your instrument 1 etc 4 5 etc etc Ex 42

19 4 Considerations in Trichordal Improvising 19 2 Repetitive (different octaves) playing one pitch from the trichord tice Repeated notes in different octave as 1st and 4th pitches Ex 43 Repeated notes as 1st and 3rd pitches Ex 44 Repeated notes as 2nd and 4th pitches Ex 45 Repeated notes as 1st and 2nd pitches Ex 46 Repeated notes as 3rd and 4th pitches Ex Ex 48 Repeated notes as 2nd and 3rd pitches

20 20 4 Considerations in Trichordal Improvising 2a Repetitive (same octave) Repeated note as 1st and 4th pitch # # # # # # Ex 49 Repeated note as 1st and 3rd pitch # # Ex 410 Repeated note as 2nd and 4th pitch # # # # # # Ex Multiple Repeated Pitches It is oviously possile to play melodic phrases that contain multiple repeated pitches Some exercises in the folloing chapters ill sho examples of this FIVE AND SEVEN GROUPINGS USING TWO TRICHORDS Try using these three ays of organizing groups of five and seven pitches 1 Five groupings using three pitches from one trichord and to pitches from another trichord from the same ro 2 Seven groupings using four pitches from one trichord (one repeated pitch) and three pitches from another trichord from the same ro 3 Seven groupings using to pairs of incomplete trichords and one complete trichord from the same ro 1 n n complete incomplete complete incomplete complete complete incomplete n n incomplete n n n n n n n

21 n n n n 4 Considerations in Trichordal Improvising 21 2 n n n n n n n 3 incomplete incomplete complete incomplete incomplete complete Ex 412 n n TWO PITCH GROUPINGS Another variation is to select to pitches from each trichord in a ro Ro 1+2 # n Ro 1+2: to notes from each trichord Ex 413 We can also treat each trichord as having three possile to note cominations Three possile dyad cominations ithin a trichord Ex 414 Trichord 1+5 n # # n a # # # # n # n # RHYTHM, METER AND SHAPE Most of the examples and exercises in this ook ill sho the trichords and ros in their prime form or in simple rotations I strongly recommend you vary the rhythms and meters for each exercise When practicing the ros for the first time use a symmetric pattern as you play through the trichords Once you have an understanding of each ro, mix up the shape, direction, and numer of pitches repeated in each trichord to create more complex melodies Our goal is not to learn patterns or licks that e just plug into our improvisations It is to learn the possiilities contained in each trichord and ro and to organically comine them according to our needs and ho e hear them Some examples of different meters and rhythms to use hen practicing c # # c # # 3 3 # # 3 3 # # 3

22 c # # 22 4 Considerations in Trichordal Improvising c # # # # # # c # # 4 6 # # n # # ΠEx With repeated pitches 4 4 # # # # # 4 Ex 416 In 3 and 2 pitch groupings 8 5 # # # n Ex 417 Four trichord pattern using different shapes and numer of pitches (4, 4, 3, 3) Ro 2+3 c n # # # # # n n # # # # # Ex 418 Try using different rhythmic patterns hen practicing the ros Choose one rhythm and play it through the entire ro Mix up the rhythms as you get comfortale

23 4 Considerations in Trichordal Improvising 23 The folloing example uses the trichords from Ro 2+3 in varied shapes and cominations ith a set pattern ABCD, BCDA, CDAB, and DABC and hile using a simple rhythm in 4/4 c Û Û Û Û Û Û c # # # # # # n # # # # Ex 419 This example uses a to measure rhythm hile keeping the trichords from ro 2+3 in a uniform pattern c J Û Û c j J J J J Û Û Û Û Û Û Û J Û Û J Û j # J # # J J J n # J # # J J J J n J J # J # j # j # J # J # J Ex 420

24 24 5 THE TWELVE BASIC ROWS Each ro is constructed from one trichord type and expresses the tonal space of that trichord using all telve pitches Ï # Ï Ï Ï nï Ï # Ï Ï # Ï Ï Ï nï Ï Ï Ï nï nï Ï # Ï Ï Ï # Ï # Ï Ï 1 +3 * * Ï # Ï Ï Ï Ï nï # Ï Ï Ï nï Ï Ï Ï Ï Ï nï Ï Ï nï # Ï Ï # Ï # Ï Ï * Ï # Ï # Ï Ï Ï Ï Ï nï nï nï Ï nï Ï Ï Ï Ï Ï Ï Ï Ï Ï nï nï nï * Ï Ï Ï Ï Ï Ï # Ï # Ï Ï Ï Ï Ï Ï # Ï # Ï # Ï Ï nï Ï nï Ï Ï Ï nï Ï Ï # Ï Ï * ** Ï Ï # Ï Ï Ï Ï nï # Ï nï # Ï # Ï nï Ï Ï Ï nï nï Ï # Ï nï * * Ï Ï Ï Ï Ï Ï nï # Ï Ï # Ï # Ï # Ï Ï Ï # Ï Ï Ï Ï nï # Ï # Ï Ï nï Ï Ex 51 * More than one construction of these ros exists All variations ill e presented in the chapters on each ro ** This ro is the exception to the construction of ros using trichords It is not possile for a telve-tone ro to e created y using four trichords ith the construction of 3+3 A telve-tone ro can hoever e created y using three tetrachords ith the construction of 3+3+3

25 5 The Telve Basic Ros 25 INTERVAL STEERINGS OF THE ROWS The term steering as coined y Peter Schat in his ook The Tone Clock and is a valuale concept to help us understand the relationships eteen the telve ros It refers to the interval distance eteen the roots of each trichord in a telve-tone ro Ro Ï Ï Ï Ï Ï Ï # Ï # Ï Ï Ï Ï Ï Ï Ï #Ï Ï Ex 52 The steering for ro 2+3 aove is 4+2 Notice that the interval distance eteen C - E - F# - B creates a symmetric tetrachord of or hat can also e vieed as to overlapping trichord chains of 4+2 and 2+4 This is true for every ro Each ill have a steering that is a symmetric tetrachord ith to versions of the same trichord in it overlapping With each ro having nested in its construction another trichord type e have a pattern of interconnections running through all of the ros These harmonic relationships can e thought of as eing very similar to harmonic relationships that exist in traditional harmony HARMONIC RELATIONSHIPS TREE The harmonic relationships tree shos the interconnection eteen the telve trichord types and the ros they express Trichords 3+4, 4+4 and 2+5 do not steer any of our telve-tone ros Each trichord in the tree functions as the steering for the trichord ro in next level aove it / / / / / / / / Overvie of Steerings 1+1 steers ro 3+3+3, steers ro steers ro 4+4, steers ro steers ro steers ro steers ro steers ro 4+4, steers ro 3+4, steers ro 4+4, steers ro 2+5, 3+4, 1+2, steers ro steers ro 2+5, 1+1, 2+2, 4+4, 1+4

26 26 Non-Symmetric Trichords

27 27 6 TRICHORD 1+2 The practice techniques descried in the next four chapters are to e used for all the material presented in this ook In order to ecome familiar ith the construction of each trichord and all its transposition possiilities, egin y practicing each trichord individually Non-symmetric trichords are those that are constructed ith different interval distances eteen each pitch (1+2, 1+3, 1+4, 1+5, 2+3, 2+4, 3+4) Symmetric trichords have the same distance eteen pitches (1+1, 2+2, 3+3, 4+4, 2+5) Trichord 2+5 is the exception ecause its symmetry is found in its first rotation Ï Ï Ï Ï nï Ï Ex 61 Aove are examples of trichord 1+2 and 2+1 Every non-symmetric trichord set class has to constructions for its memers that are inversions of each other and are harmonically equivalent in our system When practicing the folloing exercises it is important that you not only play them as melodic lines, ut as chords if it is possile on your instrument Some possile voicings: Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï? Ï Ï Ï Ï Ï Ï Ex 62 Begin y practicing 1+2 and transposing chromatically, ascending and descending through the range of your instrument

28 28 6 Trichord 1+2 P T1 T2 T3 T4 T5 Ï Ï Ï # Ï Ï Ï Ï Ï Ï # Ï Ï # Ï Ï Ï Ï Ï Ï Ï T6 T7 T8 T9 T10 T11 # Ï Ï Ï Ï Ï Ï # Ï Ï Ï Ï Ï Ï Ï nï # Ï Ï Ï Ï Ex 63 The marking P means this is the prime form of this trichord T1 through T11 means these are transpositions of prime form y one half step to eleven half steps Play through all transpositions of 1+2 in all directions Refer to the chapter Considerations in Trichordal Improvising for a variety of shapes and rhythms to e used Chordal instruments should practice these as chord voicings as ell Next, practice oth rotations of trichord 1+2 using the same techniques as prime Rotation 1 Ï Ï Ï Ï Ï # Ï Ï Ï Ï Ï Ï # Ï P T1 T2 T3 T4 T5 Ï Ï # Ï Ï Ï Ï Ï Ï # Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï T6 T7 T8 T9 T10 T11 Ï Ï Ï Ï Ï Ï Ex 64 Rotation 2 Ï Ï Ï Ï # Ï Ï Ï # Ï Ï Ï Ï Ï Ï Ï Ï P T1 T2 T3 T4 T5 Ï # Ï Ï #Ï # Ï Ï Ï Ï Ï Ï Ï Ï T6 T7 T8 T9 T10 T11 Ï Ï Ï Ï Ï Ï Ï Ï Ï Ex 65

29 6 Trichord Next practice 2+1 using the same method as 1+2 P T1 T2 T3 T4 T5 Ï Ï Ï # Ï # Ï Ï Ï Ï Ï Ï Ï Ï Ï # Ï Ï Ï Ï Ï T6 T7 T8 T9 T10 T11 # Ï # Ï Ï Ï Ï Ï # Ï # Ï Ï Ï Ï Ï Ï Ï Ï Ï # Ï Ï Ex 66 Rotation 1 Ï Ï Ï # Ï Ï # Ï Ï # Ï Ï Ï #Ï Ï Ï Ï Ï Ï Ï Ï P T1 T2 T3 T4 T5 # Ï Ï # Ï Ï # Ï Ï Ï Ï Ï Ï Ï T6 T7 T8 T9 T10 T11 Ï Ï Ï Ï # Ï Ï Ï Ex 67 Rotation 2 Ï Ï Ï Ï # Ï # Ï Ï # Ï # Ï Ï Ï Ï Ï Ï Ï Ï # Ï # Ï Ï Ï Ï Ï Ï Ï Ï Ï # Ï P T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 Ï Ï Ï Ï Ï Ï Ï Ï # Ï Ex 68 Once you are comfortale ith the transpositions of trichord 1+2 and 2+1, play longer patterns on each transposition for oth 1+2 and 2+1 Example: P Ï Ï T1 # Ï nï Ï nï Ï Ï #Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï # Ï Ï Ï # Ï Ï # Ï Ï Ï # Ï Ï Ï Ï Ï Ï ú Ï # Ï Ï Ï # ú T2 Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï ú

30 30 6 Trichord 1+2 # Ï nï nï #Ï Ï Ï # Ï Ï Ï Ï Ï Ï # Ï Ï Ï # Ï Ï Ï # ú T2 Ï Ï Ï T3 # Ï # Ï nï Ï Ï Ï Ï Ï Ï #Ï #Ï Ï # Ï # Ï Ï # Ï # Ï Ï Ï Ï Ï #Ï Ï Ï Ï Ï # Ï # Ï Ï Ï Ï Ï #Ï #Ï Ï ú Ï # Ï # ú T4 Ï Ï nï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï ú T5 Ï Ï T6 Ï # Ï nï nï Ï Ï #Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï # Ï Ï Ï # Ï Ï # Ï Ï Ï # Ï Ï Ï Ï Ï Ï ú Ï # Ï Ï Ï # ú T7 Ï Ï T8 # Ï nï Ï nï Ï Ï #Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï # Ï Ï Ï # Ï Ï # Ï Ï Ï # Ï Ï Ï Ï Ï Ï ú Ï # Ï Ï Ï # ú T9 Ï Ï Ï T10 # Ï # Ï nï T11 Ï Ï nï Ï Ï Ï Ï Ï Ï #Ï #Ï Ï # Ï # Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï # Ï #Ï # Ï Ï Ï Ï Ï Ï Ï Ï # Ï # Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï #Ï #Ï Ï Ï ú Ï # Ï # ú Ï Ï Ï Ï ú Ex 69 All of these exercises must e practiced from memory hile using varied shapes and directions The next step in the process of learning trichord 1+2 involves comining to transpositions of 1+2 in a pattern that alternates eteen oth trichords Begin y playing P and T1 These are preliminary exercises intended to acclimate you to the methods e ill e using

31 6 Trichord Example of to trichord comination using 1+2: Ï Ï P + T Ï Ï Ï Ï # Ï nï nï nï nï #Ï Ï Ï Ï nï rotation 1 rotation 2 Ï Ï #Ï Ï Ï Ï # Ï nï Ï nï nï Ï Ï nï Ï # Ï Ï nï # Ï Ï Ï Ï Ï Ï Ï # Ï nï Ï nï # Ï nï Ï Ï Ï Ï #Ï nï Ï nï Ï Ï Ï nï # Ï Ï Ï nï nï # Ï Ï Ï nï Ï #Ï nï Ï Ï Ï Ï nï nï # Ï Ï Ï Ex 610 The aove example shos 1+2 prime form and T1 comined y alternating eteen the to All rotations of the trichords are used in a ascending and descending pattern through the full range of your instrument Next, repeat the previous exercise using P and T1 of trichord 2+1 Example of to trichord comination using 2+1: Ï Ï Ï # Ï Ï Ï # Ï # Ï nï nï Ï Ï Ï # Ï # Ï nï nï nï nï Ï Ï # Ï # Ï # Ï Ï Ï Ï nï Ï Ï # Ï # Ï nï # Ï Ï # Ï nï nï Ï nï Ï # Ï # Ï Ï # Ï # Ï nï Ï Ï Ï Ï # Ï nï # Ï nï Ï Ï Ï # Ï # Ï nï nï Ï # Ï # Ï Ï Ï nï Ï # Ï nï # Ï Ï Ï Ï nï # Ï # Ï nï nï Ex 611

32 32 6 Trichord 1+2 All of the remaining possile cominations of transpositions can e a source of study ut are not used in our system of telve tone organization I ould suggest coming ack to these at some point in the future after orking on the material presented in the folloing chapters When you choose to ork on these cominations, rite them out until you can do them mentally Cominations ith repeated pitches create interesting melodies and can e challenging to organize Practice them sloly and visualize each trichord as it is played Belo are the remaining 1+2 cominations ith prime folloed y a chart shoing all the other cominations possile using all transpositions Ï Ï Ï Ï P + T2 P + T3 P + T4 Ï Ï nï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï # Ï nï # Ï nï # Ï Ï Ï P + T5 P + T6 P + T7 nï Ï Ï Ï Ï nï nï Ï Ï Ï Ï Ï Ï P + T8 Ï # Ï nï nï Ï Ï P + T9 P + T10 P + T11 Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï nï Ï nï Ex 612 Trichord Cominations Chart T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T1+T2 T2+T3 T3+T4 T4+T5 T5+T6 T6+T7 T7+T8 T8+T9 T9+T10 T10+T11 T1+T3 T2+T4 T3+T5 T4+T6 T5+T7 T6+T8 T7+T9 T8+T10 T9+T11 T1+T4 T2+T5 T3+T6 T4+T7 T5+T8 T6+T9 T7+T10 T8+T11 T1+T5 T2+T6 T3+T7 T4+T8 T5+T9 T6+T10 T7+T11 T1+T6 T2+T7 T3+T8 T4+T9 T5+T10 T6+T11 T1+T7 T2+T8 T3+T9 T4+T10 T5+T11 T1+T8 T2+T9 T3+T10 T4+T11 T1+T9 T2+T10 T3+T11 T1+T10 T2+T11 T1+T11 Ex 613 TRICHORD ROTATIONS FROM COMMON TONES One technique used y Stravinsky and other composers to develop a ro takes each possile rotation of a ro and starts it from the same pitch Example: Six note ro ith to rotations Prime from ro Rotation 1 Rotation 2 Ï Ï # Ï # Ï Ï Ï Ï # Ï # Ï Ï Ï Ï # Ï # Ï Ï Ï Ï nï Ex 614 Ï Ï # Ï # Ï Ï Ï Ï # Ï # Ï Ï Ï Ï Rotation 2 Ï Ï Ï Ï # Ï Ï

33 Ï Ï # Ï # Ï Example: Six note ro ith rotations from a common pitch Ï Ï # Ï # Ï Ex 615 Ï Ï Ï Ï Ï # Ï # Ï Prime from ro Rotation 1 Ï # Ï # Ï Ï Ï Ï Ï Ï Ï # Ï # Ï Rotation 2 Ï Ï Ï Ï Ï Ï Ï # Ï nï Ï 6 Trichord This is a technique you have proaly used efore hen practicing modes or chords starting from a common tone This same method can e used ith trichords Using the first, second and third pitch as our common tones, e ill express all the intervals from the rotations of prime rotation 1 rotation 2 C common tone prime rotation 1 rotation 2 D common tone rotation 1 rotation 2 prime # E common tone rotation 2 prime rotation 1 n # Ex 616 Notice that if e reduce each ne trichord to its prime form, it results in root movements that express three transpositions of 2+1 and an even larger nesting of 1+2 Ex 617 n n n n n C common tone D common tone E common tone n #

34 34 6 Trichord 1+2 This technique gives us another method for organizing our trichord choices even though it s not using a telve-tone ro IMPROVISATION ON THE MATERIAL After practicing the transpositions of 1+2 and 1+2 in various shapes and rotations, spend time freely improvising ith them Use common tones as connections eteen trichords or freely comine 2, 3, or more trichords Experiment ith setting up tonal centers y repeating one trichord and contrasting it ith others or y modulating chromatically through several Start y only using 1+2 and then proceed to using 2+1 Then comine 1+2 and 2+1 freely The next chapter ill egin comining 1+2 and 2+1 in cominations derived from the ro 1+2 freely comined 4 Ï Ï Ï Ï J Ï Ï J Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï # Ï j#ï Ï Ex using common tones to connect trichords * * * * 4 4 # # # # (* marks the common tones) Ex using one trichord as tonal center contrasting ith others 8 6 # J # J # J # # Ex 620

35 6 Trichord TRICHORD 1+2 EXERCISE The folloing exercise is ill familiarize your ear to the sound of this trichord Cue up the track on the play-along CD that corresponds to the key your instrument is pitched in and egin to improvise using the trichords from Line 1 These are the trichords that form ro 1+2 The rhythm section is playing the first trichord of each staff system Explore the tonal character of this ro y playing the contrasting trichords over that hich is eing played y the rhythm section Be sure to use a variety of shapes and rhythms as you play through this exercise Next, improvise using the trichords from Line 2 These are the trichords rotations from common tones Shon aove each group of three trichords is the common tone they share The first trichord in each staff system is the one all others for that system are derived from These trichords ill have a varying degree of consonance and dissonance in relation to the trichord eing sounded y the rhythm section Track 1/2 1/3 1/4 Trichord 1+2 Exercise- CD Ro 1+2 ABCD C n n n n D # # # E n n n n # 4x? Ro 1+2 BCDA # n # n n # # D E F # # # n n 4x? # # # n n

36 36 6 Trichord Ro 1+2 CDAB # # # # n n # F G A # n # # # n n # n n n # n? # # 4x 1 2 Ro 1+2 DABC n n A n n # # n n n B n n n n # n n n B n # n? n 4x Ex 621 SUMMARY OF TRICHORD EXERCISES The exercises descried in this chapter should e applied to every type of trichord in this ook 1 Practice root position trichords chromatically in various directions 2 Practice first rotation trichords chromatically in various directions 3 Practice second rotation trichords chromatically in various directions 4 Practice longer patterns of each trichord using all rotations 5 Practice trichord rotations from common tones 6 Practice freely comining the various transpositions and rotations 7 (Optional) Practice all to trichord cominations possile using all transpositions

37 37 7 TRICHORD 1+2 AND 2+1 COMBINATIONS FROM THE ROW Every trichord can e found in specific positions in a prime form ro as set A B C or D All the possile to set cominations extracted from the ro are shon Folloing the interval construction of each trichord pair, a numer in parenthesis ( ) ill give the distance in half steps eteen the root of each trichord Comination 1 (Set A+B or C+D) 1+2, 2+1 (2) P T1 T2 T3 n n # n # # # n T4 T5 T6 T7 # # n n # # # n n T8 T9 T10 T11 # n # n n # # Ex 71 Play through each transposition in varied patterns, rhythms and rotations through the range of your instrument

38 38 7 Trichord 1+2 and 2+1 Cominations from the Ro Ex 72 Notice that the preceding example egan ith the second trichord of the pair (2+1) It is important hen practicing these to egin from oth trichords Maintain rotational consistency as you ascend or descend through the trichords If you play a chordal instrument practice these cominations as simultaneities in different orders and voicings Experiment ith clusters and changing ass pitches to realize the color possiilities? 1+2, 2+1 (2) 4 4 n Ex 73 Comination 2 (Set A+C) 1+2, 1+2 (6) P T1 T2 # # # T3 T4 T5 # # Ex 74 This comination only has six transpositions ecause of its symmetry at the tritone You may notice that this comination creates a partial diminished scale

39 7 Trichord 1+2 and 2+1 Cominations from the Ro 39 Comination 3 (Set B+D) 2+1, 2+1 (6) P T1 T2 # # # # # # T3 T4 T5 # # # # Ex 75 Comination 4 (Set D+A or B+C) 2+1, 1+2 (4) P T1 T2 T3 n # # # n T4 T5 T6 T7 # # n # # # # # T8 T9 T10 T11 n n # # # Ex 76 These four cominations are to e the focus of practice and are found in the construction of our 1+2 telve-tone ro When you are practicing the to trichord cominations, egin orking on at least one transposition of the related ro at the same time This ill help you understand the to trichord cominations and their relationship to the ro The next chapter ill examine the harmonic properties of trichord 1+2 and ill use these four cominations as applications on common chords

40 40 8 DIATONIC APPLICATIONS OF TRICHORD 1+2 This chapter ill examine the harmonic properties of trichord 1+2 and 2+1 as chord voicings over a ass pitch as ell as the applications of individual trichords and trichord pairs extracted from the telve-tone ros on minor, dominant and major chords TRICHORDS AS CHORD VOICINGS OVER A BASS The folloing chord qualities result from trichord 1+2 and 2+1 eing played over a ass note It can e very difficult to lael every chord ith a conventional chord symol Some ill e complete chords hereas others ill imply certain chord qualities ut ith missing chord tones Because of this it is possile to lael some of these chords in multiple ays Belo is an example of this in Chord numer 2 It could e laeled as Dmaj7 or D maj7 In these cases here no third is present, chord symols ill e laeled as major ecause of the major third in the overtone Others ill defy conventional harmonic laeling so they ill e laeled in unorthodox ays or as harmonically amiguous Play these and listen to the tonal quality of each Rememer that changing the voicing of the trichord pitches ill change the sound of the chord 1+2 c ? c ? Ex 81 1 C Phrygian 5 D-maj7 (no5, 9)/E 9 Asus4 (add3) 2 D Maj7 (9, no3, no5) 6 F7 (no3, 13) 10 A (5, #9) 3 Harmonically Amiguous 7 G6 (no3, #11) 11 B (no5, 9, 11) 4 E7 (13, no3, no5) 8 E7 (no5, 13)/G 12 B (no5, 9, 9)

41 8 Diatonic Applications of Trichord ? c c 1 2 # ? # Ex 82 1 C (no5, 9) 7 D7 (n o 5, 9)/F# 2 Harmonically amiguous 8 C - (9)/G 3 D79 (no3, no5) 9 A (#11) 4 Emaj7 (no3, no5, 13) 10 Adim (add 11) 5 Emaj7 #5 (no3, 7) 11 C-9 (no5)/b 6 F7 (no3, 13) 12 C-maj7 (no5, 9)/B USING ONE TRICHORD ON A CHORD QUALITY The folloing examples sho the possile harmonic applications using a single trichord 1+2 and 2+1 on minor, dominant and major chords These examples only use the chord tones and tensions from the associated modes for these chords Other single trichord applications are possile that use cominations of pitches from different modes Those applications ill e introduced in the to trichord cominations Applications for G Minor (Dorian, Phrygian, Aeolian, Harmonic Minor, Melodic Minor) R maj7 R 9 R # R maj7 R 7 R 9 # Ex 83

42 42 8 Diatonic Applications of Trichord 1+2 Applications for C7 (Mixolydian, Mixolydian 2 6, Whole tone, ½ h Diminished, Altered, Lydian 7, Mixolydian 6, Sus4 chords) 1+2 # # # R n # # # 13 7 R 2+1 # # # # # # # # # R 9 Ex 84 Applications for F Major (Ionian, Lydian, Lydian #5) # # maj7 R maj7 # # # 13 maj7 R # # Ex 85 Exercise using one trichord on a chord quality Choose one trichord application from those previously listed for a chord quality Then select a play along exercise from Chapter 52 for that chord Practice using the trichord application you have selected on all chords in the exercise This exercise is useful for not only soloists, ut also for accompanists to learn ho to use one trichord structure as a voicing on all the chord changes of a tune The folloing example shos one trichord application eing used (1+2 from 9th of minor 7) for the first four chords in Minor Exercise 2 from chapter 52 Melodic example using 1+2 from 9th of a minor 7 chord D 4 7 j j J C j Œ J F # # j J # G J Œ Ex 86 Exercise using one trichord for varied chord qualities We can develop on the idea of the previous exercise y using one trichord structure on chord changes of different types Take a jazz standard and select 1+2 or 2+1 trichords that are appropriate for its chord changes Write out and then practice using those trichords as a melody and as

43 8 Diatonic Applications of Trichord harmonic accompaniment if possile on your instrument The folloing example uses the chord changes to the first four measures of Moments Notice The trichords used are 1+2 from the 9th of the minor 7th chords and 1+2 from the #11th of the major 7 chord Notice that the application used on minor also functions as 1+2 from the 13th of the dominant seventh chords c # E 7 A7 F 7 B7 E D A 7 D7 Ex 87 Also try using to different applications for the minor and dominant chords The folloing example uses 1+2 starting on the #9 of the dominant 7th chords This application has #9 and #11 as tensions E 7 A7 c úú ú # úú ú F 7 B7 úú ú úú #ú E D A 7 úúú D7 úú ú Ex 88 Understanding an individual trichord s possile harmonic implications is very important Our goal is to e ale to use one, to and three trichords as ell as complete telve-tone ros according to our musical needs METHODOLOGY FOR TWO TRICHORD APPLICATIONS The folloing applications on minor7, dominant 7, and major 7 chords are found in the to trichord cominations from ro 1+2 Because the construction of trichords and ros are ithout regard to key or tonality, all of the trichords pitches spelled incorrectly in a traditional harmonic context should e considered equivalent to their correct enharmonic spelling (example: E = D# = #9 on C7, C# = D = 9 on C7) In this and the folloing chapters there are numerous applications possile for each comination presented Spend your time practicing the cominations that you like the most When transposing these applications to other keys rememer that the first pitch of each application is the scale degree from hich to start on Use Chapter 52 for practicing the harmonic applications on chord changes The to trichord cominations e ill e using elong to three general categories 1 To trichord cominations here all six pitches function as chord tones/tensions as found in traditional harmony These ill e marked ith a 2 To trichord cominations that have a mixture of chord tones/tensions that function in a traditional harmonic ay hile also having dissonant pitches that function as chromatic approach tones These chromatic tones may e in the same trichord or in different trichords from their target pitches 3 To trichord cominations in hich one trichord functions as a dissonant in relation to the second trichord hich functions diatonically as a consonant on the chord quality These cominations often move chromatically from the dissonant trichord to the consonant and sometimes function in a dominant to tonic ay Some of these cominations ill give a typical sound for the chord quality in question hile other cominations ill give an unorthodox sound implying other colors ith a high amount of chromaticism These applications may have pitches normally considered as rong notes on the chord quality Rememer that the unifying principle of this system is the ear perceiving order due to the interval content of the music Even hen played in a diatonic harmonic context the sound

44 44 8 Diatonic Applications of Trichord 1+2 of non-diatonic trichords or non-diatonic pitches in a trichord retain a structural significance and are heard as relevant in relation to their diatonic partners Be aare that the perceived level of dissonance in these trichord cominations is affected y the melodic and rhythmic development of the musical phrase and its resolution to the consonant pitches of the chord Telve-Tone ros on Minor, Dominant and Major In order to use complete telve-tone ros on chord changes, e ill alternate eteen one trichord pair as consonance and one pair as dissonance on a chord quality This suject is covered in detail in Chapter 52 APPLICATIONS ON MINOR CHORDS All of the minor applications in this ook contain chord tones and tensions from the various modes of minor (Dorian 7, 9, 11, 13; Phrygian 7, 9, 11, 13; Aeolian 7, 9, 11, 13; Harmonic Minor 9, 11, 13, maj7; Melodic Minor 9, 11, 13, maj7) as ell as chromatic approach tones In many cases an application may contain pitches from to minor modes (eg 9 and 9, 13 and 13, 7 and maj7) In these cases, choice of hich pitch to emphasize as consonant ill depend on the type of minor chord it is applied to and its context Those applications here 9 and 13 have no chromatic relationships to any other pitches in the to trichords should e considered as exclusively for use on III-7 or VI-7 chords Some applications ith 13 are marked ith a ecause of its importance in defining the sound of harmonic minor and natural minor There are some applications here 5 is present ith no chromatic relationships to other pitches These are exceptions to our methodology and are included ecause they have a quasi lues sound Tensions ill e ritten aove the applications only hen they have no chromatic relationship to any other pitches APPLICATIONS ON DOMINANT 7TH CHORDS The applications for dominant may have a comination of tensions from different modes (eg 13 and 13 or 9 and 9) Choice of hat to emphasize as consonant ill depend on the chord in question and the context Applications here 11 has no chromatic relationship to other pitches should e considered as for use exclusively for sus4 chords All tensions contained in the application ill e shon APPLICATIONS ON MAJOR CHORDS The applications for major 7 may contain the tensions 9, #11, 13 and #5 as found in the Ionian, Lydian and Lydian #5 modes as ell as chromatic approach tones There are some applications here 3 is present ith no chromatic relationships to other pitches These are exceptions to our methodology and can function in three ays; as a quasi lues sound, as diminished major 7 (E/F) as a delay in resolution to I major7, or as a major triad sustitution at a distance of a major third (C#maj/Fmaj) implying a symmetric augmented sound Tensions ill e ritten aove the applications only hen they have no chromatic relationship to any other pitches

45 8 Diatonic Applications of Trichord MINOR CHORDS 1 Set A+B or C+D-1+2, 2+1 (2) G # n # # # # # # # # n # # # n # # # # # n # n # # # n # # Ex 89 2 Set A+C -1+2, 1+2 (6) G # # # 9, maj7, 11 Blues 9 # # # Ex Set B+D -2+1, 2+1 (6) G maj7, 11 Blues 9 9, 13 # # # # # # 13 # Ex 811

46 46 8 Diatonic Applications of Trichord Set D+A or B+C -2+1, 1+2 (4) G n , 11 # # n n 9, 13 9, 13 7 # # # n Ex 812 DOMINANT 7TH CHORDS 1 Set A+B or C+D-1+2, 2+1 (2) C 7 # 9, 9, #9 9, 9, #9, #11 9, #9, #11 #9, #11 13 n # # # # # # # # n #11, 13, 13 #11, 13, 13 #11, 13, 13 13, 13 # # # n # # # # # n # Ex 813 9, 13, 13 9, 9, 13 9, 9, #9 9, 9, #9 n # # # n # # 2 Set A+C -1+2, 1+2 (6) C 7 9, #9, #11, 13 9, 9, 13 #9, #11, 13 9 # # # # # # Ex 814 9, #11, 13

47 8 Diatonic Applications of Trichord Set B+D -2+1, 2+1 (6) C 7 9, #9, #11, 13, 13 9, #9, 13 9, 13 #9, #11, 13 # # # # # # 9, #11 # Ex Set D+A or B+C -2+1, 1+2 (4) C 7 9, #9 9, #9, #11, 13 9, #11,13 #9, #11, 13 n 11, 13, 13 9, #11, 13, 13 9, 13 9, #9, 13 n # # # # # # # n # # # 9, 9, 13 9, 9, #9, 11 # n Ex 816 MAJOR CHORDS 1 Set A+B or C+D-1+2, 2+1(2) F # n # # # # # # # # n # # # n # # # # # n # n # # # n # # Ex 817

48 48 8 Diatonic Applications of Trichord Set A+C -1+2, 1+2 (6) Ex 818 F # #11 #5, 9 Blues n 3 Set B+D -2+1, 2+1 (6) Ex 819 F # # #5, 9 Blues #11 # # # 4 Set D+A or B+C-2+1, 1+2 (4) F # maj7 9 C#/F 13 n # # # # # maj7, #11 9, 13 # # n n Ex 820 It is interesting to note that y looking at the harmonic properties of the unused trichords from the corresponding ro, functional applications can sometimes e found in conjunction ith the primary comination The folloing example demonstrates this ith the primary trichords eing 1+2, 1+2 (6) from the major 7 of F major This comination gives the sound of #5 and #11 ith natural 11 as a passing/approach tone Note that the remaining trichords from this ro can function in a dominant ay as C7 ith 9, #9, #11, 13 and 13 C 7 9, #9, #11, 13, 13 #5, 9, #11 F # # # n n # Ex 821 The next example uses 2+1, 1+2 (4) from the 3rd of F major as the primary application This comination gives the sound of 5, maj7, #5, #11 and 13 The non-harmonic trichords from the ro can also function in a dominant ay although slightly different than our previous comination The 4th degree is functioning as an approach tone

49 8 Diatonic Applications of Trichord Ex 822 C 7 # #9, #11, 13 #5, #11, 13 F 3 n # These to trichord cominations for the qualities of minor, dominant and major have unconventional cominations of chord tones and passing tones that give a unique quality to their sound As you learn applications from the other trichord types you ill hear the variety of colors possile for each of these common chords COMBINATION AS CHORDS The cominations used in all the exercises in this ook should also e used as chord voicings played either simultaneously or in succession If you don t play a chordal instrument it is still important to play these on the piano to hear their color Arpeggiating the chords can also give a different sense of alance and color to the cominations Play the same rotations together as simultaneities first and then mix up the rotations and voicings to explore all the color possiilities When using these cominations as accompaniment, careful consideration must e given in selecting applications that ill harmonically support the soloist The folloing to examples sho some to trichord comination possile as voicings for C minor Notice that neither voicing contains the third of the chord Example as simultaneities 2+1, 1+2 (4) from 5th? c c C 7 Ex 823 The example aove shos chord voicings that use oth 7 and major 7 on C minor Example as successions 2+1, 1+2 (4) from 11th The folloing example shos a comination in hich e have oth 13 and 13 on C minor In this example the 13 acts as an approach leading to 13 hen played in succession If played as simultaneity the chord ould have oth tensions and consideration ould have to e given to the voicing and context used? c c Ex 824 C 7 n

50 50 9 ROW 1+2 There is only one construction of this ro ith a steering of 2+4 Steering 2+4 (six transpositions) P n n # # # T1 # n n n T2 n # # T3 # # n n n # T4 # # n n T5 n n n # # Ex 91 T6 Symmetric at the tritone # # # n n P n n # # # Ex 92 Because of this ro s symmetry at the distance of a tritone, there are only six unique transpositions We ill lael the four trichords as set A B C or D according to their position in a prime form ro The tonal color of this ro is that of diminished If e comine set A ith C, and set B ith D e can see to partial diminished scales one hole step apart A B C D A C B D n n Ex 93 # # # # C half hole diminished n n n # # D hole half diminished

51 9 Ro These to partial diminished scales can function in a dominant to tonic ay as V7 to I7 We can see that all the usual applications of the diminished scale and minor third chord sustitutions apply hen using this ro This harmonic aspect of this ro can e oscured hen using other trichord cominations that don t reference the diminished sound in such an ovious ay # # Ex 94 V7 # # ## E G B C # A C E 7 # 9 # F # # # # # # I7 # B D A C as chords #? Ex 95 This ro also can function in a dominant to tonic ay as V7 to I maj7 #5 Notice the chromatic approach to the #11 on the folloing Maj7 #5 application # # Ex 96 B # # A D7 9 # 9 # D By changing the order of the trichords e can also see to possile harmonic progressions of V7 to I minor or I major using only three of the four trichords A D maj G maj7 5 9 # 11 # # # # C Ex 97 C F # # # # # # F-maj7 or B-maj7 Fmaj7 Bmaj7 # # A C B D E 7 # 9 # A7 # 9 # # D- or G#- # # A C B D

52 52 9 Ro 1+2 BASIC OPERATIONS ON THE ROW There are three operations composers typically applied to telve-tone ros They are orth mentioning ecause they demonstrate a relationship eteen to transpositions of ros in our method These operations are inversion, retrograde, and retrograde inversion of a ro Prime Ro 1+2 Retrograde of P1+2 n n # # # # # n n # n Inversion of P1+2 Retrograde Inversion of P1+2 Ex 98 n # # n n n If e reduce these ros to their prime ascending form it results in to transpositions of ro 1+2 (prime and retrograde) P n n # # # T1 (inversion and retrograde inversion) # n n n Ex 99 Aareness of these relationships can add another level of structure to your use of transposition hen improvising and composing TWO, THREE AND FOUR TRICHORD COMBINATIONS The method used hen practicing the to trichord cominations ill e continued here ith the addition of one and to more trichords It is our goal to e flexile in our aility to comine the to, three and four trichords according to our melodic and harmonic needs As alays use a variety of directions and rhythms The folloing is a list of all the various cominations that can e derived from the four trichords in a ro in all rotations The to trichord cominations have een covered in the previous chapter ut ill e included here as ell AB AC AD To Trichord Cominations n n A B A B A B # n A C A C A C n # # n n # # #

53 9 Ro AD BC n A C A C A C n # # # n n n # A D A D A D # # n # # a BD n CD # n Ex 910 B C B C B C n # # # # n n # # # # # n B D B D B D # n C D C D C D # # # # ABC ACD BCD Three Trichord Cominations Ex 911 n n # # # # # # # n BDA # # n n n n n When you feel comfortale ith these cominations feely comine the three trichords from each comination in hatever pattern you like By stressing to trichords out of the three you can create a sense of tonality that contrasts ith the third trichord n n n n # # # # A # # # # # n A B C A B C A B C n n n n n n n # n a n # # A a # # A C D A C D A C D # # B C D B C D B C D B D A B D A B D A

54 54 9 Ro 1+2 ABCD n Four Trichord Cominations n # # # nnn# # # nn # # # n # nn Ex 912 n # # n nn n n # # n # n # # # nn n n nn n n n n n n n Within these six cominations there are three additional set rotations availale to apply to each ro This results in 24 possile permutations Belo is a list of all the set rotations Because of the large amount of material, as alays pick the cominations you like most and egin orking on those Notice that 6, 3, and 5 have retrograde set relationships to 1, 2 and 4 # n n # # # nn n # # n # n # n # # n # # # n n n n n # # n n # # nn n # n n n n n # n # # A B C D A B C D A B C D ABDC ACDB ACBD ADBC nn n # # n A B D C A B D C A B D C n # # # n # # n A C D B A C D B A C D B # n n n # n nn n # # A C B D A C B D A C B D nn # n n n A D B C A D B C A D B C ADCB A D C B A D C B A D C B n n n # # # n n nn n Retrograde of each other Ex ABCD BCDA CDAB DABC 2 ABDC BDCA DCAB CABD 4 ACBD CBDA BDAC DACB 6 ADCB DCBA CBAD BADC 3 ACDB CDBA DBAC BACD 5 ADBC DBCA BCAD CADB Retrograde of each other

55 9 Ro APPROACHES TO PRACTICING ROWS When practicing the ros, use these methods for organizing the set patterns and rotations of the trichord sets Vary your routine hen practicing and egin the exercises from your highest as ell as your loest note Because of the range limits of your instrument you may find that you can t alays complete a ro s pattern Rememer to practice all transpositions of this ro and use the techniques from Chapter 4 These examples are only the asic frameork to egin your studies on this material 1 Prime form trichords in a fixed set pattern n n # # # n n # # # A B C D A B C D n n # # # n n # # # A B C D A B C D A B n n Ó Ex st rotation trichords in a fixed set pattern n n # # # # # # n n # Ó # A B C D A B C D A B C D A B # Ex nd rotation trichords in a fixed set pattern n # # # n # # # Ex 916 A B C D A B C D n # # # A B C D A B n Ó

56 56 9 Ro 1+2 n n 4 All trichord rotations in a fixed set pattern n # # # n # # # 1st rotation n n 2nd rotation # # # n # # # A B C D A B C D A B C D # # # n # # # A B C D A B C D A B C D n n # # # n # # # n # # # A B C D A B C D A B C D n n Ex 917 # # # * n # # # n n #* n Ó # A B C D A B C D A B C D A B # Because of the range limits of your instrument, you may have to change the octave in hich some trichords are played Notice in the preceding example that in the third measure from the end trichord C (marked *) has een raised one octave n 5 Prime form trichords in a rotating set pattern n # # # # # # # # # A B C D B C D A C D A B # # n n # n n n n n # # # # # # D A B C A B C D B C D A n n # n n n #

57 9 Ro # # # n n # # n n # n n # # # C D A B D A B C A B C D # # # # # # n n n # # n n # B C D A C D A B D A B C n n # # # # # # # # # n n n A B C D B C D A C D A B Ex st rotation trichords in a rotating set pattern # # n # # # # # # n n # # # # A B C D B C D A C D A B n n # # # # # # n D A B C A B C D B C D A Ex 919 # # # n # # n n C D A B D A B C # 7 2nd rotation trichords in a rotating set pattern n # # # # # # # # # n n # # A B C D B C D A C D A B n n # n # # # # # # D A B C A B C D B C D A # # # # #

58 58 9 Ro 1+2 # # # Ex 920 n # # C D A B D A B C n # n 8 All trichord rotations in a rotating set pattern n # # # A B C D # # # B C D A # # # n n # # # # # # n # # # n n n # # # # # # # # # n n C D A B # # n n # # # n n # # # n n # D A B C n n # # # A B C D # # # B C D A # # # n n C D A B n n # # # # # # # # # n # # # # # # n # # # n # # # n

59 9 Ro # # n n # n n # # n # n # # n # n D A B C Ex 921 An alternative to keeping a fixed set pattern or rotating set pattern is to treat the set pattern as retrogradeale hen you change the overall direction of the line This is actually easier in some ays ecause it complements the construction of the ro FIXED SET PATTERN Ex 922 n n n n # # # n n # # # A B C D A B C D # # # n n # # # A B C D A B C D A B n n Ó RETROGRADE SET PATTERN AT DIRECTION CHANGE n n # # # n n # # # n n # # retrograde A B C D A B C D A B A D # n # # # n C B A D C B A Œ Ex 923 Another approach to the set patterns is to group the trichord sets in pairs and rotate them as you play through them Use all trichord rotations as ell

60 60 9 Ro 1+2 ROTATING SET PAIRS # # n n # # # # n B D A C D B C A n # # # # # n Ex 924 n # # # n n n n # # # # n B D A C D B C A # # # # B D C A D B A C B D C A D B Also practice this rotating pattern using three sets of the four in an additive pattern as you play through all four sets rotations n Ó # ADDITIVE ROTATING THREE SET PATTERN n n # n # # # n # # n n n n n # n # # A B C B C D C D # # # n A D A B A B C B n # # n n n n # # # # # # n # # n C D C D A D A B n # n A D C D C B C B

61 9 Ro n n # # # # n n # # # A B A D A D C D # n # n C B C B A Ex 925 Ó Œ The preceding example shos the set pattern ABCD as the line ascends and DCBA (retrograde) as the line descends You can use all the mixed set patterns ith this approach TWO TRICHORD COMBINATIONS USING ALL SETS FROM ROW 1 Mixed Rotations A n n # B B n # C A # n D # A # n # C B D B A # # # C # n A # # # n # # C B D A C D D B n n

62 62 9 Ro 1+2 n D n B n D C # n # # n n # A B A C # # A D # # # # # ΠB A n n n n B D B C n n # # # A # # D # # # A C # # # A B D C n n n # # # # # # n # # n D # # # # B

63 9 Ro # # # # D A # # C # n B # C # A # # C # D # # n # # # n n # # B A n n n n B D # # # # # # B # C # # A D # # # # # A # B A # C n # Ó Ex 926 The preceding example shos all the to set cominations (A Ac Ad, Bc Bd Ba, Cd Ca C, Da D Dc) ithin an overall set pattern of ABCD Notice that hen the line descends I use the retrograde set pattern (Ba Bd Bc, Ad Ac A, Dc D Da, C Ca Cd, Ba Bd Bc, etc) as ell as the reverse order of the trichord rotations (prime, second rotation, first rotation) This ordering of the trichord rotations orks ell ecause of the structure of the ros Practice your ros using this method in all transpositions

64 64 9 Ro 1+2 Next, try a variation on the preceding example In this exercise e ill keep the same rotation of pitches as e play each cycle of trichord pairs Prime 1st rotation 2nd rotation A Ac Ad A Ac Ad A Ac Ac etc Again hen descending use the retrograde set pattern and reverse order of rotations 2 Uniform Rotations n n # # # n # # # # # # n # n # # # # # n n # # # # # # # n n # # # # n # n n # # # # # # # # # # # # # n # # # n # # # # # n # # #

65 9 Ro n n # # # n # # # # # # n # # # # n # # # # # # # n # # n # retrograde set pattern starting on set B n # # # n n # # # n # # n # # # # # # # n # # n # n # # # n n # #

66 66 9 Ro 1+2 # # # # # n # # # # n # # # # # # # # # # # # # # n # # # n # # # n n # # n # n # # n # # # # # # n # # # n # n Ex 927 Pianists should also play the previous to exercises as chord voicings using the to trichord cominations presented as simultaneities in the various rotations Consider the the octave placement of the to trichords Arpeggiating the trichords can soften the dissonance and change the character of the sound Experiment ith comining different rotations of each trichord comination to understand the sound of each comination Some ros and the cominations ill e more dissonant than others The folloing example has a high amount of dissonance

67 9 Ro a Uniform rotations as simultaneities # ## # # # # ## # ##? # # # # ## ## nn # # n? # #? ## # n nn ## # n # # # n ## # Ex 928 The folloing exercise shos a linear ay of using the trichords from the ro in an ascending and descending shape When changing from one trichord set to the next use the next closest neighoring tone and continue the direction of the line You ill e using a mixture of rotations depending on hat pitch you start on and here you change the direction of the line This example uses a fixed set pattern of ABCD n # # # # # # n n # # # n # # #

68 68 9 Ro 1+2 Ex 929 # # # TRANSPOSITIONS OF ROW 1+2 After ecoming familiar ith all the transpositions of ro 1+2, spend some time freely improvising and modulating through them Use common tones as pivot points for your modulations or select a pattern of transpositions to play P # # j # J j T1 j # J j T10 # J # Ex 930 We can adapt the trichord rotation from the common tone exercise in Chapter 8 to modulate to transpositions of ro 1+2 Take the trichords from the page 31 example and add the remaining sets from the ro to hich they elong Source Trichord 1+2 Ex 931 Trichords elo are the rotations from common tones C, D, and E n n n n n n # Ex 932

69 9 Ro Ros using these trichords P T11 T9 n # # n n # # # # n n n # n T10 2 T1 n n # n # # n n n 3 Ex 933 T2 T3 n n # # n n n n # This results in related transpositions of ro P1+2 at T9, T11, T1, T10, T2 and T3 This may seem complicated at first ut it is actually not difficult once you kno all the transpositions of ro 1+2 ecause each trichord elongs to only one ro Other ros can e more complex ecause of the numerous transpositions and steerings they have Notice that ro T3 and T9 are the same ro, starting on a different set rotation Practice playing the ros to the corresponding source trichords P 1+2, T1 1+2, T2 1+2, T3 1+2, T4 1+2, T5 1+2 Also use trichord 2+1 as the source trichord Practice playing the ros to the corresponding source trichords P 2+1, T1 2+1, T2 2+1, T3 2+1, T4 2+1, T5 2+1 Practice the source trichord and its related trichords from the common tone as the first to e played in each ro Then later change the order in hich you play the source trichord and its relatives Since there are only six unique transpositions of this ro, e are using all transpositions using this approach This gives structural importance to our modulation choices as opposed to some random pattern of modulation (hich is fine too)

70 70 9 Ro 1+2 SUMMARY OF ROW EXERCISES All of the exercises are to e practiced in all transpositions and using various rhythms and meters If you play a chordal instrument play these exercises as simultaneities as ell 1 Prime form trichords in a uniform and retrogradale set pattern 2 1st rotation trichords in a uniform and retrogradale set pattern 3 2nd rotation trichords in a uniform and retrogradale set pattern 4 All trichord rotations in a uniform and retrogradale set pattern 5 Prime form trichords in a rotating and retrogradale set pattern 6 1st rotation trichords in a rotating and retrogradale set pattern 7 2nd rotation trichords in a rotating and retrogradale set pattern 8 All trichord rotations in a rotating and retrogradale set pattern 9 Rotating set pairs of trichords in prime form 10 Rotating set pairs of trichords in 1st rotation 11 Rotating set pairs of trichords in 2nd rotation 12 Rotating set pairs of trichords in all rotations 13 Additive rotating three set pattern using prime form trichords 14 Additive rotating three set pattern using 1st rotation trichords 15 Additive rotating three set pattern using 2nd rotation trichords 16 All to trichord cominations ith mixed rotations 17 All to trichord cominations ith uniform rotations 18 Modulations ased on rotations of source trichord and its pitches When eginning, pick one exercise and practice it using all transpositions of the ro All of the ros presented in this ook should e practiced using these methods and played from memory

71 RELATED ROWS The relationships eteen our telve different ro types can e approached in either a general or specific ay A general relationship exists eteen ro 1+2 and ro 2+4 ecause the steering of ro 1+2 is to overlapping 2+4 and 4+2 trichords In other ords, trichords 2+4 and 4+2 are nested in the construction of ro 1+2 A general approach ould utilize oth ro 1+2 and 2+4 in a melodic and harmonic ay ithout regard to the transpositions each ro uses Specific relationships that exist eteen ros depend on the transpositions used and the set position in a ro (A, B, C or D) the steering trichord occupies Ro 1+2 A B C D n n # # # Ex 101 The steering of ro 1+2 is a tetrachord that can e divided into to overlapping trichords of 2+4 and 4+2 Rotating this tetrachord results in to additional trichords of 2+4 and 4+2 at a distance of a tritone from the original # # Å Å Ex 102 There are no to transpositions of oth trichords 2+4 and 4+2 hich can e used as memers of ro 2+4 # # Ex # # 4 + 2

72 Related Ros Each of the trichords aove elongs to a specific transposition of ro 2+4 in a specific set position (set A, B, C or D) With three steering constructions for ro 2+4, there ill e eight transpositions for each of the different steerings This results in 24 versions of ro 2+4 possile Ro 2+4, steering 1+3 P2+4 A # n # # n T6 A n # # n # n Ex These to transpositions of ro 2+4 use the trichords that steer ro 1+2 in set position A The remaining ros are as follos T11 Set Position B # # n B # n T5 # # B n # # n Ex 105 Set Position C T10 n # # # T4 C C n # # n n # # Ex 106 Set Position D T9 # n D T3 D # # n # # # n Ex 107 Ro 2+4 steering 3+1 Set position A P A # n n # # n # T6 A # # # n Ex 108

73 Related Ros 73 T9 Set position B # n # # n # # B T3 B # # n # Ex 109 Set position C T10 # # n C # # n T4 # # n # C n # Ex 1010 Set position D T7 # n n # n D # # T1 n # # n n D Ex 1011 Ro 2+4 steering 4+1 Set position A P A # # # n n n # # T6 A # # n # Ex T7 Set position C # # n Ex 1013 n # # # C T1 C # # Set position B T10 Ex 1014 # # T4 B B n n # # # n # #

74 Related Ros Set position D T5 # # n n D # # T11 # n # # D Ex 1015 In the folloing chapters the student should ork on all telve ros and achieve a level of proficiency on each efore methodically exploring the relationships eteen them Try using these relationships in compositions and then later in improvisations

75 75 11 TRICHORD 1+3 There are to versions of trichord 1+3 Ex 111 # n n as chord voicings # n # #? # n n Ex 112 Use the same method for practicing these trichords as in Chapter trichords in prime form P T1 T2 T3 T4 T5 # # # Ex 113 # # T6 T7 T8 T9 T10 T11 # # #

76 76 11 Trichord 1+3 # # Rotation 1 P T1 T2 T3 T4 T5 # # # T6 T7 T8 T9 T10 T11 # # # # Ex 114 Rotation 2 P T1 T2 T3 T4 T5 # T6 T7 T8 T9 T10 T11 # # # # # # Ex 115 n 3+1 prime form trichords P T1 T2 T3 T4 T5 # # # # # n T6 T7 T8 T9 T10 T11 # # Ex 116 Rotation 1 n # # n # P T1 T2 T3 T4 T5 n # # # # # T6 T7 T8 T9 T10 T11 n # # # # n n # Ex 117

77 11 Trichord # Rotation 2 P T1 T2 T3 T4 T5 # # # T6 T7 T8 T9 T10 T11 # # # Ex 118 Practice all these to trichord cominations in the same manner as in Chapter 6 TRICHORD 1+3 EXERCISE This exercise is practiced in the same manner as in Chapter 6 Begin y improvising using the trichords from Line 1 These are the trichords that form ro 1+3 Be sure to use a variety of shapes and rhythms as you play through this exercise Next, practice improvising using the trichords from Line 2 These are the trichords rotations from common tones Shon aove each group of three trichords is the common tone they share The first trichord in each staff system is the one all others for that system are derived from Track 1/5 1/6 1/7 Trichord 1+3 Exercise 1 2? c c Ro 1+3 -ABCD # n # n # C n j # n n n D n # n # n Π# # n n n # # n n j # E # n n j # J n 4x J

78 78 11 Trichord ? Ro 1+3 -BCDA n n # # n # n # # F A A j n n # # n 4x 1 2? Ro 1+3 -CDAB # n # # # # # # j n # F # G B # # n # Πn n # # # j # n n j n j j 4x 1 2? Ro 1+3 -DABC # # # # n # B D E # n n # n # n n # n # # 4x Ex 119

79 79 12 TRICHORD 1+3 AND 3+1 COMBINATIONS FROM THE ROW There are to versions of ro 1+3 ith different steerings The first cominations presented are from steering 2+3 hich are then folloed y those from steering 5+1 FROM ROW WITH STEERING 2+3 Comination 1 (Set A+B) 1+3, 1+3 (2) P # # # # # # # n # # # n Ex T1 T2 T3 # # # T4 T5 T6 T7 # # # # # # # T8 T9 T10 T11 Comination 2 (Set A+C or B+D) - 1+3, 3+1 (5) (also in steering 5+1) You may recognize this comination as your symmetric augmented scale (or a truncated version of Messiaen s 3 mode of limited transposition) P # # n T1 T2 T3 # # # # n # # # n n T4 T5 T6 T7 # # # n n # # # n #

80 80 12 Trichord 1+3 and 3+1 Cominations from the Ro # # n # # # # T8 T9 T10 T11 n # Ex 122 Notice that P, T4 and T8 are the same scale as are T1, T5, T9 and T2, T6, T10, and T3, T7, T11 This comination is also in steering 5+1 Comination 3 (Set D+A) - 3+1, 1+3 (5) P T1 T2 T3 n # # # # # # # T4 T5 T6 T7 n n n # n n # # # n # # # n T8 T9 T10 T11 Ex 123 Comination 4 (Set B+C) - 1+3, 3+1 (3) P # T1 T2 T3 n # # # # n # n # n T4 T5 T6 T7 # # # # n # n # # T8 T9 T10 T11 # Ex 124 Comination 5 (Set C+D) 3+1, 3+1 (2) P T1 T2 T3 n # # # # # # n # n

81 12 Trichord 1+3 and 3+1 Cominations from the Ro 81 T4 T5 T6 T7 # n n n # # n n # # # # n # # n n T8 T9 T10 T11 # n Ex 125 FROM ROW WITH STEERING 5+1 Comination 6 (Set A+C) - 1+3, 1+3 (6) P 1+3 # # 1+3 T1 T2 T3 # # # # n # # # T4 n # T5 Ex 126 Comination 7(Set B+D) - 3+1, 3+1 (6) P 3+1 n 3+1 # T1 T2 T3 # n # # # # T4 n T5 n Ex 127 Comination 8 (Set D+A or B+C) - 3+1, 1+3 (1) P n T1 T2 T3 # # # # n n # # # # # # n T4 T5 T6 T7 # # n n #

82 82 12 Trichord 1+3 and 3+1 Cominations from the Ro # # # n n # # n T8 T9 T10 T11 # n Ex 128 All of the previous to trichord cominations should e practiced in the same manner as in Chapter 7 In all the folloing chapters on the remaining trichords and ros the methods for practicing are the same as used for trichord 1+2 and ro 1+2 Refer ahead to the chapter on ro 1+3 to etter understand the cominations e are using and their relationship to the ros

83 83 13 DIATONIC APPLICATIONS OF TRICHORD 1+3 Chord qualities resulting from 1+3 and 3+1 over a ass note 1+3 c # # # # # #? c # # # # # # #? # # Ex Chord qualities 1 C# -maj7 (no5)/c 7 F#7 (no3, #11) 2 C# -maj7 (no5) 8 C# dim maj7/g 3 C# -maj7 (no5)/d 9 C# -maj7/g# 4 C# -maj7 (no5)/e 10 A (add #9) 5 C# -maj7(no5)/e 11 B dim (add 9) 6 Fmaj7 (no3, 13) 12 C# -maj7 (no5)/b

84 84 13 Diatonic Applications of Trichord c ? c # ? # Ex Chord qualities 1 C (no5,add #9) 7 F#75 (no3, 13) 2 C# -maj7 (no5, 9) 8 C (add #9)/G 3 D7(no3, no5, 9, 9) 9 A (add 13) 4 Emaj7#5 (no3)/e 10 A (add #11) 5 Emaj7#5 (no3) 11 C7 (no5, #9)/B 6 Fmaj7 (no3, 7) 12 Emaj7#5 (no3)/b USING ONE TRICHORD ON A CHORD QUALITY Use the exercises presented in chapter 8 for the folloing trichords Applications for G Minor (Dorian, Phrygian, Aeolian, Harmonic Minor, Melodic Minor) 1+3 # Ex 133 maj7 R 3 # maj7 13 maj7 R # maj7 9 3 # Applications for C7 (Mixolydian, Mixolydian 2 6, Whole tone, ½ h Diminished, Altered, Lydian 7, Mixolydian 6, Sus4 chords) 1+3 # # R n # # # # # #

85 3+1 Ex 134 # # n Applications for F Major (Ionian, Lydian, Lydian #5) # # # # n # R # 5 13 R # 5 maj7 R # # 13 Diatonic Applications of Trichord # # 13 R 9 Ex APPLICATIONS ON COMMON CHORD TYPES Use Chapter 52 for practicing these harmonic applications on chord changes MINOR CHORDS Refer to Chapter 8 for the methodology used for applications on minor chords from steering Set A+B 1+3, 1+3 (2) G maj7 9 9 # # # # # # # n # # # # # # # n 13 7 # # # Ex 136

86 86 13 Diatonic Applications of Trichord Set A+C or B+D 1+3, 3+1 (5) G # # # # # # # n # # n # n # n # n # # n # # # # n # Ex Set D+A 3+1, 1+3 (5) G n n 9, 11 Blues 11, 13 Blues # # # # # # 7 maj7, , 9 n # n n # n # # maj7, 9 n # # # Ex Set B+C 1+3, 3+1 (3) G # n # # # # n n # # # # n # # n # n # # # Ex 139

87 13 Diatonic Applications of Trichord Set C+D 3+1, 3+1 (2) G n # # # # n n # n n 7 maj7 9 n # # n n # # # # 9 n # # n n Ex 1310 steering Set A+C 1+3, 1+3 (6) from 5+1 steering G # # 13 maj7, 11 Blues 9 9, 13 # # # n # # # n Ex Set B+D 3+1, 3+1 (6) from 5+1 steering G n maj7, 11 Blues 9 9, 13 # 13 n # n # # # # Ex 1312

88 88 13 Diatonic Applications of Trichord Set D+A or B+C 3+1, 1+3 (1) from 5+1 steering G n # # # # # # # # n # n n # # # n n # # # # n n # # n # n Ex 1313 DOMINANT 7TH CHORDS Refer to Chapter 8 for the methodology used for applications on dominant chords 1 Set A+B 1+3, 1+3 (2) C 7 9, 9, #9, #11 9, 9, #9 9, #9, #11, 13 #9, #11, 13 # # # # # # # n # # #11, 13 #11, 13, 13 9, 13, 13 9, 13, 13 # # # # # # 9, #9, 13 9, 9 9, 9, #9, 11 n # # # Ex Set A+C or B+D 1+3, 3+1 (5) Notice that this comination results in a symmetric augmented scale Each column uses the same pitch content in three different expressions of 1+3, 3+1 (5) C 7 9, 13, 13 9, 9, #11, 13 9, #9, #11 #9, 13 # # # # # # # n # # n # n # n # n

89 # # # # # # # 9, 13, 13 9, 9, #11, 13 9, #9, #11 #9, 13 n # n # n n # # 13 Diatonic Applications of Trichord # n 9, 13, 13 9, 9, #11, 13 9, #9, #11 #9, 13 # # n # # # # n # Ex Set D+A 3+1, 1+3 (5) C 7 #9, #11, 13 9, #11 #9, #11, 13, 13 9, 13, 13 n # # # 9, 11, 13, 13 #9, #11, , 9, 11, 13 n n n # n 9, 9, #9, #11, 13 9, 9, #9 # # # # # # n # n # # Ex Set B+C 1+3, 3+1 (3) C 7 # 9, #9, #11 9, 9, 13 9, #9, #11, 13, 13 #9, #11, 13 n # # # # n 13 #11, 13, 13 9, #11, 13 9, 9, 13 # n # 9, #9, 13, 13 9, #9, 13 9, 9 9, #9, #11 # n n # # # # # # n # Ex 1317

90 90 13 Diatonic Applications of Trichord Set C+D 3+1, 3+1 (2) C 7 9, #9, #11 9, #9, #11 9, #11, 13 #9, #11, 13, 13 n # # # # # # # n #11, 13, 13 11, 13, 13 #11, 13, 13 9, 13 # n n n # # n n n # 9, 9, 13 9, 9, #9, 13 9, 9, #9 # # # n # # n n Ex Set A+C 1+3, 1+3 (6) from 5+1 steering C 7 # 9, #11 9, #9, #11, 13, 13 9, #9, 13 9, 13 # #9, #11, 13 # # # n # # # n Ex Set B+D 3+1, 3+1 (6) from 5+1 steering C 7 #9, #11, , #11, 13 9, #9, #11, 13 n # 9, 9, 13 n # n # # # # Ex 1320

91 13 Diatonic Applications of Trichord Set D+A or B+C 3+1, 1+3 (1) from 5+1 steering C 7 9, 9, #9 9, 9, #9, #11 9, #9, #11 #9, #11, 13 n # # # # # # # # n #11, 13, 13 #11, 13, 13 #11, 13, 13 13, 13 # n n # # # n n # 9, 13, 13 9, 9, 13 9, 9, #9 9, 9, #9 # # # n n # # n # n Ex 1321 MAJOR CHORDS Refer to Chapter 8 for the methodology used for applications on major chords 1 Set A+B 1+3, 1+3 (2) F # # 9 Blues #11 # # n # # # # # # # #5 13 maj7 # # # # # Ex Set A+C or B+D 1+3, 3+1 (5) F # # # # # # # n # # n # n # n # n # # n # # # # n #

92 n Diatonic Applications of Trichord 1+3 # n # n # n # # n # # # # n # Ex Set D+A 3+1, 1+3 (5) F n # #11, 13 maj7, #5 13 # maj7, 9 C#/F dim, maj7 n # n # # n n n Ex Set B+C 1+3, 3+1 (3) F # n # # # # n n # # # # n # # n # n # # # Ex Set C+D 3+1, 3+1 (2) F n n # n #5 13 maj7 # # # # n 9 #11 # n # n # n Ex 1326

93 13 Diatonic Applications of Trichord Set A+C 1+3, 1+3 (6) from 5+1 steering F # # #11 #5, 9 Blues # # # n Ex Set B+D 3+1, 3+1 (6) from 5+1 steering # Ex 1328 F #5, 9 Blues #11 n # n 8 Set D+A or B+C 3+1, 1+3 (1) from 5+1 steering F n # # # # # # # # n # n n # # # n n # # # # n n # # n # n Ex 1329

94 94 14 ROW 1+3 There are to constructions possile for ro 1+3 One has a steering of 2+3 and the other has a steering of 5+1 Steering 2+3 (telve transpositions) P # # # n n n T1 # # # # n T2 # # n n n # T3 n # # # # T4 # n # n # T5 # # n n T6 # # n # # T7 # n n # T8 # # # # # T9 n n # n # T10 n # # # n n T11 # n # # # Ex 141

95 14 Ro Steering 5+1 (six unique transpositions) Because of the construction of this ro and its symmetry at the distance of a tritone, there are only six unique transpositions Transpositions T6 to T11 are the same ros in a rotation starting on set C P # n # n # T1 # # # n T2 # # n # # T3 n n n # T4 n n n # # T5 # n n Ex 142 As as mentioned efore, oth steerings of this ro can e looked at as to symmetric augmented scales at a distance of a hole step Steering 2+3 A B C D # # # n n n A C B D # n # # n Steering 5+1 A B C D # n # n # Ex 143 A B # n rotation of hexachord # # n In steering 2+3 you can see the to symmetric augmented scales hen e change the set order to ACBD We can also get a partial diminished scale y comining set B+C from steering 2+3 In steering 5+1 you can clearly see oth symmetric augmented scales I rotated trichords C and D as a hexachord to sho the scale from the same root as in steering 2+3 Because of the construction of this ro e have a limited numer of different cominations Ros starting on P, T2 T4 T6, T8 and T10 all can e thought of as different segmentations of the same to symmetric augmented scales This follos as ell for T1, T3 T5, T7, T9 and T11 Even though these ros share this characteristic, they each have distinct trichord cominations that give different melodic contours hile using the same general pitches Practice this ro using the methods outlined in Chapter 9

96 96 14 Ro 1+3 SUMMARY OF ROW EXERCISES All of the exercises are to e practiced in all transpositions and using various rhythms and meters If you play a chordal instrument play these exercises as simultaneities as ell 1 Prime form trichords in a uniform and retrogradale set pattern 2 1st rotation trichords in a uniform and retrogradale set pattern 3 2nd rotation trichords in a uniform and retrogradale set pattern 4 All trichord rotations in a uniform and retrogradale set pattern 5 Prime form trichords in a rotating and retrogradale set pattern 6 1st rotation trichords in a rotating and retrogradale set pattern 7 2nd rotation trichords in a rotating and retrogradale set pattern 8 All trichord rotations in a rotating and retrogradale set pattern 9 Rotating set pairs of trichords in prime form 10 Rotating set pairs of trichords in 1st rotation 11 Rotating set pairs of trichords in 2nd rotation 12 Rotating set pairs of trichords in all rotations 13 Additive rotating three set pattern using prime form trichords 14 Additive rotating three set pattern using 1st rotation trichords 15 Additive rotating three set pattern using 2nd rotation trichords 16 All to trichord cominations ith mixed rotations 17 All to trichord cominations ith uniform rotations 18 Modulations ased on rotations of source trichord and its pitches When eginning, pick one exercise and practice it using all transpositions of the ro All of the ros presented in this ook should e practiced using these methods and played from memory

97 97 15 TRICHORD 1+4 There are to versions of this trichord Ex Possile chord voicings ? Ex trichords in prime form P T1 T2 T3 # # # # T4 T5 T6 T7 # # # T8 T9 T10 T11 # # # # Ex 153

98 98 15 Trichord 1+4 Rotation 1 P T1 T2 T3 # # # # Ex 154 T4 T5 T6 T7 # # # # T8 T9 T10 T11 # # # Rotation 2 P T1 T2 T3 # # # # Ex 155 T4 T5 T6 T7 # # # # # T8 T9 T10 T11 # # 4+1 trichords in prime form P # T1 T2 T3 # T4 T5 T6 T7 # # T8 T9 T10 T11 # # Ex 156

99 15 Trichord Rotation 1 P T1 T2 T3 # # T4 T5 T6 T7 # # T8 T9 T10 T11 # # Ex 157 Rotation 2 P T1 T2 T3 # # # T4 T5 T6 T7 # # # Ex 158 T8 T9 T10 T11 # #

100 Trichord 1+4 TRICHORD 1+4 EXERCISE Track 1/8 1/9 1/10 Play this exercise in the same manner as in the previous chapters Use various shapes and rotations and mix the order in hich you play the trichords Begin y improvising using the trichords from Line 1 These are the trichords that form ro 1+4 Explore the tonal character of this ro y playing the contrasting trichords over that hich is eing played y the rhythm section Next, practice improvising using the trichords from Line 2 These are the trichords rotations from common tones Shon aove each group of three trichords is the common tone they share The first trichord in each staff system is the one all others for that system are derived from These trichords ill have a varying degree of consonance and dissonance in relation to the trichord eing sounded y the rhythm section 1 2 Ro 1+4 -ABCD C E # # # n # # F # 4 5? Ro 1+4 -BCDA # # D # # n E # # n # # # G #? 2 «1 2 Ro 1+4 -CDAB # # # n # # # n # # # # # n F B B n # # #? # # # # #

101 15 Trichord Ro 1+4 -DABC # # n # # n # # n # # # # G A C # # # # n # # # #? # # j # # j # # 2 «Ex 159

102 TRICHORD 1+4 AND 4+1 COMBINATIONS FROM THE ROW There are three different steerings for this ro There are some to trichord cominations that each of these steerings has in common FROM ROW WITH STEERING 2+2 Comination 1- (Set A+B) 1+4, 1+4 (2) P T1 T2 T3 # # # # # n # # # # T4 T5 T6 T7 # # # # # # n # # # # n # # # # # # T8 T9 T10 T11 Ex 161 Comination 2 - (Set A+C or B+D) 1+4, 4+1 (4) (in common ith steering 2+4) P 1+4 # # 4+1 T1 T2 T3 # # n # # # # n T4 T5 T6 T7 # # n # # # # # n # # # # # n #

103 # # n # # # 16 Trichord 1+4 and 4+1 Cominations from the Ro 103 # # n # # # # # n # T8 T9 T10 T11 Ex 162 Comination 3 - (Set A+D) 1+4, 4+1 (6) P 1+4 # # # 4+1 T1 T2 T3 # # # # # T4 T5 T6 T7 # # # # # # # # # # # # # T8 T9 T10 T11 Ex 163 Comination 4 - (Set B+C) 1+4, 4+1 (2) P # # T1 T2 T3 # # n # # # T4 T5 T6 T7 # # # # # n # T8 T9 T10 T11 # # n # # # # # # Ex 164 Comination 5 - (Set C+D) 4+1, 4+1 (2) P # T1 T2 T3 # # # # # n # # # n # # #

104 # # # # Trichord 1+4 and 4+1 Cominations from the Ro # # n # # # T4 T5 T6 T7 n n # # # # n T8 T9 T10 T11 # # # # # Ex 165 FROM ROW WITH STEERING 2+4 Comination 6 (Set A+B) 4+1, 1+4 (2) P T1 T2 T3 # # # # n # # n T4 T5 T6 T7 # # n # # # n # T8 T9 T10 T11 n # # n # # n # Ex 166 Comination 7 (Set A+C) 4+1, 4+1 (6) (Set A+C or B+D in common ith steering 3+3) P T1 T2 T3 # # # # # # n # T4 # T5 n # Ex 167

105 16 Trichord 1+4 and 4+1 Cominations from the Ro 105 Comination 8 (Set B+D) 1+4, 1+4 (6) (Set A+C or B+D in common ith steering 3+3) P T1 T2 T3 # # # # # # # T4 # # T5 n Ex 168 FROM ROW WITH STEERING 3+3 Comination 9 (Set A+B or B+C or C+D or D+A) 4+1, 4+1 (3) P T1 T2 T3 # # # n # # n # # T4 T5 T6 T7 # # # n # # # n # # # T8 T9 T10 T11 # n # Ex 169 Comination 10 (Set A+B or B+C or C+D or D+A) 1+4, 1+4 (3) P T1 T2 T3 # # # # # n # # # n T4 T5 T6 T7 # # # # # # # n # # # n # T8 T9 T10 T11 Ex 1610

106 DIATONIC APPLICATIONS OF TRICHORD 1+4 Chord qualities resulting from 1+4 and 4+1 over a ass note 1+4? c c # # # # # # #? # # # # # # # # Ex Chord qualities 1 C#maj7 (no5)/c 7 F#maj7 (no3, #11) 2 C#maj7 (no5) 8 C#maj7 5/G 3 D 7 (maj7, no5) 9 C#maj7/G# 4 E13 (no3, no5) 0 Aaug (add #9) 5 C#maj7 (no5)/e 11 B (add 9) 6 C#maj7 (no5)/f 12 C#maj7 (no5)/b

107 17 Diatonic Applications of Trichord c ? c #? # Ex Chord qualities 1 Fmaj7 (no3)/c 7 F#maj75 (no3, 7) 2 C#maj7 (no5, #9) 8 G7sus4 (no5, 13) 3 D 9 (no5) 9 A aug (add 13) 4 Fmaj7 (no3)/e 10 Fmaj7/A 5 E Phrygian 11 Bsus2 (#11) 6 Fmaj7 (no3) 12 Fmaj7 #11 (no3)/b USING ONE TRICHORD ON A CHORD QUALITY Use the exercises presented in chapter 8 for the folloing trichords Applications for G Minor (Dorian, Phrygian, Aeolian, Harmonic Minor, Melodic Minor) 1+4 R R # 5 maj7 R 13 R Ex 173

108 Diatonic Applications of Trichord 1+4 Applications for C7 (Mixolydian, Mixolydian 2 6, Whole tone, ½ h diminished, Altered, Lydian 7, Mixolydian 6, Sus4 chords) 1+4 # # 4+1 Ex 174 # # # 5 13 R R 9 # # # R # # Applications for F Major (Ionian, Lydian, Lydian #5) maj7 R 3 # # 11 5 maj # maj7 R # Ex APPLICATIONS ON COMMON CHORD TYPES Use Chapter 52 for practicing the folloing harmonic applications on chord changes As ith the previous chapters, rememer that in some cases one or more pitches may e non-harmonic and may function as a chromatic approach to a chord tone or tension MINOR CHORDS Refer to Chapter 8 for the methodology used for applications on minor from steering Set A+B 1+4, 1+4 (2) G maj7, 13 7 n n n n # n # # n Ex 176

109 17 Diatonic Applications of Trichord Set A+C or B+D 1+4, 4+1 (4) G n # n # n n # n # n n # n # # Ex Set A+D 1+4, 4+1 (6) G # n n # n n n # n n # n n # # n n # Ex Set B+C 1+4, 4+1 (2) G n # n n n # n n # n # n # n n n n # n # n # Ex 179

110 Diatonic Applications of Trichord Set C+D 4+1, 4+1 (2) # Ex 1710 G n # 7, 13 maj7, 13 7 n n # n # # n from steering Set A+B 4+1, 1+4 (2) Ex 1711 G # n 9, # n , 11 7 Set A+C 4+1, 4+1 (6) (or Set A+C or B+D from steering 3+3) G # n # # n n n n n Ex 1712

111 17 Diatonic Applications of Trichord Set B+D 1+4, 1+4 (6) (or Set A+C or B+D from steering 3+3) G # n # # # n n n # n Ex 1713 from steering Set A+B or B+C or C+D or D+A 4+1, 4+1 (3) G 9 11 # n n 13 # n # # n maj7 n Ex Set A+B or B+C or C+D or D+A 1+4, 1+4 (3) G # # # # n # # # # # n 7 maj7 # # # n # Ex 1715

112 Diatonic Applications of Trichord 1+4 DOMINANT 7TH CHORDS Refer to Chapter 8 for the methodology used for applications on dominant from steering Set A+B 1+4, 1+4 (2) C 7 # # 9, 9, #9, 11 9, 9, #9, #11, 13 9, #9, 13 #9, #11, 13 # # # # n # # # #11, 13 9, 13, 13 9, #9, 13, 13 9, 13 n n # n # n n 9, #9, 11 9, 9, #11 # # # # Ex Set A+C or B+D 1+4, 4+1 (4) C 7 9, 13, 13 9, 9, #11, 13 9, #9, #11 #9, 13 n n # n # 9, 13, 13 9, 9, #11, 13 9, #9, #11 #9, 13 9, 13, 13 9, 9, #11, 13 9, #9, #11 #9, 13 n # n # n # # n n # n # # # Ex Set A+D 1+4, 4+1 (6) C 7 # # 9, #11 9, 9, #11 9, 9, #9, 13 9, 9, #9, 13, 13 n n # # n n # # n # # #

113 # # n n # # n n 17 Diatonic Applications of Trichord n 9, #9, 13 #9, #11 #11 9, #11, 13 # # n # # 9, 9, #11, 13, 13 9, #9, 13, 13 #9, 13, n # # n # n # Ex Set B+C 1+4, 4+1 (2) C 7 9, 9, #11 9, 9, #9, #11, 13 9, #9, 13, 13 #9, 13, 13 n # n # # # n #11, 13 #11 9, #11, 13 9, 9, 13, 13 # n # n # # n n n n 9, 9, #9, 13, 13 9, #9, 13 #9 9, #11 n n # n # # Ex Set C+D 4+1, 4+1 (2) C 7 9, #11 9, #9, #11, 13 9, #11, 13, 13 #9, 11, 13, 13 # # # # n # #11, 13, 13 9, 11, 13 9, #11, 13 9, 9, 13 n # n n # n n n 9, 9, #9, 13 9, #9 n # # Ex 1720

114 Diatonic Applications of Trichord 1+4 from steering Set A+B 4+1, 1+4 (2) C 7 9, #9 9, #9, #11, 13 9, #11, 13 #9, #11, 13 # # # # n # # 11, 13, 13 9, #11, 13, 13 9, 13 # n n 9, #9, 13 9, 9, 13 9, 9, #9, 11 n # n # Ex Set A+C 4+1, 4+1 (6) (or Set A+C or B+D from steering 3+3) C 7 # n #11 9, #11 9, 9, #11, 13 9, 9, #9, 13, 13 # 9, #9, 13, 13 #9, 13 n n # # # n n Ex Set B+D 1+4, 1+4 (6) (or Set A+C or B+D from steering 3+3) C 7 9, #11 9, 9, #11, 13 9, 9, #9, 13, 13 9, #9, 13, 13 # n # n # # n #9, 13 #11 n # # n Ex 1723

115 17 Diatonic Applications of Trichord from steering Set A+B or B+C or C+D or D+A 4+1, 4+1 (3) C 7 #9, 13 9, #11, 13, 13 9, #11, 13 #9, #11 13 # # n # n # # n 13, 13 9, 11, 13, 13 9, 9, #11, 13 9, #9 n # n n # 9, #9, 13 9, 9, 13 9, 9, #9, #11 # n # # Ex Set A+B or B+C or C+D or D+A 1+4, 1+4 (3) C 7 9, #9, 13 9, 9, #11, 13 9, #9, #11 13, 13 # # # # n 9, #11 13, 13 9, #11, 13 #9, 13 9, 13, 13 # # # # # # # n 9, 9, 11, 13 9, 9, #9, #11 9, #9 # # # n # Ex 1725

116 Diatonic Applications of Trichord 1+4 MAJOR CHORDS Refer to Chapter 8 for the methodology used for applications on major 1 Set A+B 1+4, 1+4 (2) from steering 2+2 F 13 maj7, n #11 # n # n Ex Set A+C or B+D 1+4, 4+1 (4) F n n # n # n # # n # # n # n # n # n # Ex Set A+D 1+4, 4+1 (6) F # # # Ex Set B+C 1+4, 4+1 (2) F # n n n # n # n # # # # # n #

117 # n n n n 17 Diatonic Applications of Trichord n # # # # # n # n # # n n n # Ex Set C+D 4+1, 4+1 (2) F 9 9 #11 #5, #11 n # # # # # # Ex maj7, 13 # # # from steering Set A+B 4+1, 1+4 (2) F 9, 13 maj7 9 # n 13 maj7, #11 # n # # n Ex Set A+C 4+1, 4+1 (6) (or Set A+C or B+D from steering 3+3) F n # # n # # # n # # Ex 1732

118 Diatonic Applications of Trichord Set B+D 1+4, 1+4 (6) (or Set A+C or B+D from steering 3+3) F n # # # # # Ex 1733 n # n # from steering Set A+B or B+C or C+D or D+A 4+1, 4+1 (3) F 9 dim maj7 # # n # n # #11 #5 13 # # # # n maj7 # Ex Set A+B or B+C or C+D or D+A 1+4, 1+4 (3) F C#/F #11 # # # # n # # # n #5 13 maj7 # # # # # n 9 Ex 1735

119 ROW 1+4 There are three steerings for ro 1+4 These are 2+2, 2+4, and 3+3 Steering 2+2 (telve transpositions) P # n # # # T1 # # # # n n n T n # # T3 # # # # n n # T4 # n T5 # # n # # T6 # # # n n T7 n n # # # T8 # # # # n n # T9 n # # T10 # # # n # # T11 # # n n Ex 181

120 Ro 1+4 Steering 2+4 (six unique transpositions) P # # # n # T1 # # # # n T # n n # T3 # # n # n T4 # # n T5 n # # n # Ex 182 Because this ro is symmetric at the tritone, there are only six unique transpositions Ros starting on T6, T7, T8, T9, T10, and T11 are rotations of P, T1, T2, T3, T4, T5 starting on set C Steering 3+3 (three unique transpositions) This steering has to variations A P # # n # T1 # # # n T2 # n # Ex 183 B P # # # n T1 # # n # # T # # # n # n Ex 184

121 18 Ro This steering only allos for 3 unique transpositions P, T3, T6 and T9 are all different set rotations of the same ro This is the case as ell for T1, T4, T7, T10 and T2, T5, T8, T11 The tonal color of these ros suggests augmented Much like ro 1+3, if e comine Set A and Set C and then Set B and Set D from Steering 2+2 e get to symmetric augmented scales For Steering 2+4 Set A and D form a symmetric augmented scale and B and C form another These ros also suggest the tonal color of Olivier Messiaen s 4th and 5th mode of limited transposition In Steerings 3+3 and 2+4 if e comine Set A and Set C, as ell as Set B and Set D e get to transpositions of Messiaen s 5th mode of limited transposition Steering 3+3 A B C D # # n # A C B D # # n # 5th mode of limited transpostion # # # n # Ex 185 This color is also possile ith steering 2+2 except only y comining trichord A and D The resulting 4th mode of limited transposition is missing to pitches from different non-symmetric points in the scale Steering 2+2 A B C D # n # # # A # # # D Ex 186 4th mode of limited transpostion # ] # Å # Comining Set B and Set C from steering 2+2 also results in another transposition of mode 4 ut missing the last to pitches of the scale This oscures the tonal quality of this set comination Steering 2+2 A B C D # n # # # B n C # Ex 187 4th mode of limited transpostion n # # Å # Å

122 TRICHORD 1+5 There are to versions of this trichord Ex 191 # # n n # Possile chord voicings # # n# n # # n a n? # # # Ex trichords in prime form P T1 T2 T3 # # # # T4 T5 T6 T7 # # T8 T9 T10 T11 # # Ex 193

123 19 Trichord Rotation 1 P # # T1 T2 T3 # T4 T5 T6 T7 # # # T8 T9 T10 T11 # # Ex 194 Rotation 2 P T1 T2 T3 # # # # Ex 195 # # # T4 T5 T6 T7 T8 T9 T10 T11 # 5+1 trichords in prime form # # # Ex 196 P T1 T2 T3 T4 T5 T6 T7 # # n # # # T8 T9 T10 T11 # #

124 Trichord 1+5 Rotation 1 P T1 T2 T3 # # # # # T4 T5 T6 T7 n # # # T8 T9 T10 T11 # # Ex 197 Rotation 2 # Ex 198 P T1 T2 T3 # # # # Practice this trichord using the same method as in chapter 6 # # T4 T5 T6 T7 T8 T9 T10 T11 # # # #

125 19 Trichord TRICHORD 1+5 EXERCISE Play this exercise in the same manner as in the previous chapters Use various shapes and rotations and mix the order in hich you play the trichords Begin y playing the trichords from Line 1 Then continue y playing the trichord rotations from Line 2 Track 1/11 1/12 1/13