Combinatorial Harmony: Concepts and Techniques for Composing and Improvising (Book/CD Set)
30042BCD
This book/CD set is a unique and complete system for exploring endless musical possibilities in any style. This book is a must for the contemporary musician. Despite being a guitar-friendly book with a complete mapping of the fretboard, the book is also useful for improvisers, arrangers, composers, theorists and students interested in the combinatorial approach to music. About 1,000 different voicings in all positions and drops are presented, including complete 3-note and 4-note voicings with specially desi ...more
Product Number:
30042BCD
Format:
Book/CD Set
Skill Level:
Multiple Levels
Notation Type:
Standard Notation and Tab
Pages:
312
Binding:
Perfect Binding
Size:
8.75 x 11.75
ISBN:
0-7866-8488-7
ISBN13:
978-07866-8488-5
Series:
None
Publisher:
Mel Bay Publications, Inc.
Date Published:
3/27/2013
This book/CD set is a unique and complete system for exploring endless musical possibilities in any style. This book is a must for the contemporary musician. Despite being a guitar-friendly book with a complete mapping of the fretboard, the book is also useful for improvisers, arrangers, composers, theorists and students interested in the combinatorial approach to music. About 1,000 different voicings in all positions and drops are presented, including complete 3-note and 4-note voicings with specially designed guitar diagrams. The book also includes all triad-pairs (hexatonics) and their combinations in melodic exercises. The book presents brand new "combinatorial voice-leading", for 21st century chorale writing and contrapuntal exploring for any instrument or arrangement. In 312 pages, the book provides a vast store of material for compositional and improvisational use.
Combinatorial Harmony

ACKNOWLEDGEMENTS

FOREWORD by Nelson Faria 

PREFACE by the Author 

INTRODUCTION 

WHO'S THIS BOOK FOR 

HOW TO STUDY THIS BOOK 

CHAPTER 1

1. INTERVAL CLASSES

1.1 DIATONIC STEP

1.2 ACOUSTIC INTERVAL ROOT

1.3 INTERVAL GEOMETRY

1.3.1 CIRCLES (Chromatic and of Fifths)

1.3.2 CYCLES 

1.3.2.1 DITONE CYCLE 

1.3.2.2 SESQUITONE CYCLE 

1.3.2.3 WHOLE TONE CYCLE 

1.3.2.4 TRITONE 

1.4 MAPPING THE GUITAR

1.4.1 GUITAR FRETBOARD (Notes in Standard Notation)

1.4.1.1 CHORD DIAGRAMS.

1.4.1.2 SCALE/CHORD DIAGRAMS

1.4.1.3 GUITAR FRETBOARD (notes in standard notation)

1.4.1.4 GUITAR FRETBOARD (notes on tablature)

1.4.1.5 FINGER POSITIONS 

1.4.2 FIVE ACTIVITY AREAS (CAGED)

1.4.3 FRETBOARD (Set Theory View)

1.4.4 FRETBOARD (Intervallic View)

1.5 NOTATION CONVENTIONS 

1.5.1 NUMBERING MELODIC DEGREES 

1.5.2 NUMBERING HARMONIC DEGREES 

1.6.1 DEGREE CONVENTIONS  

1.6.2 CHORD SYMBOLS CONVENTION.

1.7 MODULATORY CHARACTERISTIC OF DIATONIC SCALE 

1.7.1 CYCLE OF FIFTHS KEY SIGNATURES OF TONAL CENTERS

1.8 SCALE SUPERIMPOSITION 

 

 CHAPTER 2

2. FUNCTIONAL HARMONY

2.1 FUNCTIONAL NOTATION

2.2 SUPERIMPOSITION OF THIRDS CHORD MODEL

2.3 TONAL SYSTEM - AXES

2.3.1 TONAL CYCLE / CHORD PROGRESSION

2.4 MAJOR TONALITY - FUNCTIONAL AXES 

2.4.1 TONIC AXIS IN [C:]

2.4.2 DOMINANT AXIS in [C:]

2.4.2.1 TRITONE (LEADING TONES ) 

2.4.3 SUBDOMINANT AXIS in [C:]

2.5 MINOR TONALITY - FUNCTIONAL AXES 

2.5.1 TONIC AXIS in [a:]

2.5.2 DOMINANT AXIS IN [a:] 

2.5.3 SUBDOMINANT AXIS IN [a:]

2.6 SYMMETRICAL AXES  

2.6.1 OCTATONIC DOMINANT AXIS

2.6.2 OCTATONIC DIMINISHED AXIS

2.6.3 WHOLE TONE DOMINANT AXIS

2.7 USUAL CHORD SYMBOLS RELATED TO HARMONIC FUNCTION

2.8 SCALE /FUNCTION RELATIONSHIP

 

CHAPTER 3

3. CARDINALITY 3 - THREE NOTE CHORDS.

3.1 "A" TYPOLOGY - TRIADS

3.2 "B" TYPOLOGY - QUARTAL CHORDS

3.3 "C" TYPOLOGY - SEVENTH WITHOUT THE FIFTH CHORDS

3.4 "D" TYPOLOGY - SEVENTH WITHOUT THE THIRD CHORDS.

3.5 "E" TYPOLOGY - CLUSTERS (THREE NOTE SEGMENTS)

3.6 CARD 3 - TYPOLOGY

3.6.1 7-35 DIATONIC SCALE 

3.6.2 7-32a HARMONIC MINOR SCALE 

3.6.3 7-34 MELODIC MINOR SCALE 

3.6.4 7-32b HARMONIC MAJOR SCALE 

3.6.5 8-28 OCTATONIC SCALE  

3.6.6 9-12 NONATONIC SCALE 

3.6.7 AUXILIARY SCALES TYPOLOGIES 

6-35 WHOLE TONE SCALE 

6-20 AUGMENTED SCALE 

3.6.8 TRICHORDS - GENERIC INTERVALS 

3.6.9 TRICHORDS - GENERIC INTERVALS THROUGH DIATONIC STEPS

3.6.10 TRICHORDS - STEPS THROUGH SYMMETRICAL SCALES 

TRICHORDS - STEPS THROUGH 8-28 OCTATONIC SCALE STEPS

TRICHORDS - STEPS THROUGH 9-12 NONATONIC SCALE STEPS

3.7 CARD 3 - THREE -NOTE CHORDS

See the Pitch Class Sets Index on page 309

 

CHAPTER 4

4. CARDINALITY 4 - FOUR-NOTE CHORDS

4.1 "A" TYPOLOGY - SEVENTH CHORDS

4.2 "B" TYPOLOGY - QUARTAL CHORDS

4.3 "C" TYPOLOGY - TRIADS WITH AN ADDED NINTH OR IN THE BASS (SUS)

4.4 "D" TYPOLOGY - TRIADS WITH AN ADDED FOURTH OR IN THE BASS 

4.5 "E" TYPOLOGY - T 3 7 + (9) FOUR-NOTE SEGMENTS

4.6 VOICING THEORY. 

4.6.1 CLOSED POSITION CHORDS

4.6.2 OPEN POSITION CHORDS

4.6.2.1 DROP 2 VOICINGS

4.6.2.2 DROP 3 VOICINGS

4.6.2.3 STRING TRANSFERENCE

4.6.2.4 VOICINGS (SUMMARY TABLE )

4.7 THEORY OF GENERIC INTERVALS 

4.7.1 TABLE OF GENERIC INTERVALS

4.8 GENERIC INTERVALS FORMULAE

4.8.1 GENERIC INTERVALS FORMULAE TABLE 

4.9 CARD 4 - TYPOLOGY

4.9.1 7-35 DIATONIC SCALE

4.9.2 7-32a HARMONIC MINOR SCALE

4.9.3 7-34 MELODIC MINOR SCALE

4.9.4 7-32b HARMONIC MAJOR SCALE

4.9.5 8-28 OCTATONIC SCALE

4.9.6 9-12 NONATONIC SCALE 

4.9.7 AUXILIARY SCALES TYPOLOGIES 

6-35 WHOLE TONE SCALE

6-20 AUGMENTED SCALE 

4.10 CARD 4 - FOUR-NOTE CHORDS

See the Pitch Class Sets Index on page 311

 

CHAPTER 5

5. CARDINALITY 5 - TYPOLOGY

5.1 7-35 DIATONIC SCALE

5.2 7-34 MELODIC MINOR SCALE

5.3 7-32a HARMONIC MINOR SCALE

5.4 7-32b HARMONIC MAJOR SCALE

5.5 CARD 5 - MELODIC EXERCISES 

5.5.1 PENTATONIC SUBSETS OF 8-28 SCALE 

 

CHAPTER 6

6. COMBINATORIAL VOICE LEADING OF HEXATONICS

6.1 Melodic and harmonic exercises

 

CHAPTER 7

7. CADENCES AN D CHORD PROGRESSIONS 

7.1 TONAL AXES

7.2 CADENTIAL GRAVITY

7.3 ALL TONAL CENTERS - FUNCTIONAL SUMMARY

7.4 CADENTIAL MODELS 

7.5 LIST OF CADENTIAL MODELS

7.6 CONNECTING CADENTIAL MODELS 

7.7 CHORD PROGRESSIONS 

7.7.1 SAME CHORD TYPE THROUGH THE SESQUIDITONE CIRCLE 

7.7.2 V-I THROUGH THE SESQUIDITONE CIRCLE

7.7.3 V-I THROUGH THE DITONE CYCLE 

7.7.4 V-I THROUGH THE SESQUITONE CYCLE 

7.7.5 V-I THROUGH THE WHOLE TONE CYCLE 

7.7.6 II-V THROUGH THE SESQUIDITONE CIRCLE 

7.8 HARMONIC PLURALITY

7.9 HARMONIC ANALYSIS

7.9.1 SECONDARY DOMINANTS

7.9.2 SECONDARY SUBV7

7.9.3 SECONDARY II - V

7.9.4 SECONDARY II - SubV7

7.9.5 EXTENDED DOMINANTS

7.9.6 INTERPOLATED CHORDS

7.9.7 ADJACENT II - V´s

7.9.8 MODAL INTERCHANGE

7.9.8.1 MODAL BORROWING

7.9.8.2 CHROMATIC MEDIANTS

7.9.9 DIMINISHED CHORDS

7.9.10 AUGMENTED CHORDS

7.10 SCALE FINGERINGS (GUITAR)

7.10.1 SCALE 7-35 (DIATONIC)

7.10.2 SCALE 7-32a (HARMONIC MINOR)

7.10.3 SCALE 7-32a (MEL ODIC MINOR)

7.10.4 SCALE 7-32b (HARMONIC MAJOR)

 

CHAPTER 8

COMPOSITIONS 

SONATA (to Ben Monder)

AINDANÃO (not yet)

serial matrix used on "ainda não " composition.

 

TECHNICAL APPENDIX (MUSICAL SET THEORY) 

A. BASIC DEFINITIONS 

A.1 PITCHES  

A.2 PITCH CLASSES 

A.3 CIRCULARITY

A.4 PITCH CLASS SETS

A.5 PRIME FORMS.

A.6 INTERVAL VECTOR

A.7 FORTE´S TABLE 

A.7.1 REDUCING THE SCOPE

A.7.2 THE 3-1 SE T (0,1,2)

A.7.3 REMOVING THE 3-1 (0,1,2) THRICORD FROM THE SYSTEM

A.7.4 TABLE OF THE SETS WITHOUT THE 3-1 TRICHORD

A.7.5 SETS WITHOUT THE 3-1

 

END NOTES

REFERENCES

ABOUT THE AUTHOR

PITCH CLASS SETS INDEX 

CD TRACKS INDEX 

 
Series: None
Combinatorial Harmony

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