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Use of pregroups for recognition of chord sequences

Use of pregroups for recognition of chord sequences. Richard G. TERRAT Lirmm Ircam Montpellier Paris Blues for Alice (Charlie Parker). Why Grammars in Music ?. Knowledge representation Composition structure Rhythmic structure Melodic structure Harmonic structure

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Use of pregroups for recognition of chord sequences

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  1. Use of pregroups for recognition of chord sequences Richard G. TERRAT Lirmm Ircam Montpellier Paris Blues for Alice (Charlie Parker)

  2. Why Grammars in Music ? • Knowledge representation • Composition structure • Rhythmic structure • Melodic structure • Harmonic structure • Performance : Generative Grammars • Aid to (human) improvisation • Automatic composition by computers

  3. Why Recognition Grammars ? • Harmonic Analysis (musical sense) • Education • Classification Restricted to Tonal Western Music Jazz Chord Sequences

  4. Syntax vs. Semantics • Syntax • Rewriting rules • Categorial Grammars • Pregroup Grammars • Semantic Theories • Mathematical : Pythagore, Euler, Zarlin, … • Physical : Helmoltz, Fourrier, .. • Psycho-Physio-Acoustic : Rameau, Flecher, Sauveur, Longuest-Higgins,…

  5. Steedman’s Grammar (1984) A Generative Grammar for Blues Notations Roman Numbers (I to VII) : diatonic degrees D (x) Dominant of x (V(x)) Sd (x) Sub-dominant of x (IV(x)) St (x) Super-tonic of x (II(x)) M(x) Mediant of x (III(x)) L(x) Leading tone of x (VI(x)) [m] if m (minor) is present left side, it must be present right side [7] idem with 7th. Meta-Rule Duration of whole chords left side = Duration of whole chords right side

  6. Six Rewriting Rules • R0 S12[m]  I[m] , I7 , IV[m] , I[m] , V7 , I[m] • R1 x[m][7]  x[m] , x[m][7] • R2 x[m][7]  x[m][7] , Sd(x) * • R3 y, x7  D(x)[m]7 , x7 y , xm7  D(x)7 , xm7 ** • R4 D(x)7 , x[m][7]  bSt(x)[m][7] , x[m][7] • R5 x, x, x  x, St(x)m , M(x)m D(x) D(x) • R6 x[m], x[m], St(x)m7  x[m] , #x°7 , St(x)m7 L(x)m7L(x)m7

  7. Other Rules • Context sensitivity • * May be applied only to the right branch of the metric tree sequence • ** w may not be a 7th. dominant chord • The root of w must not have been changed by a previous rule • Embellishment Rules • x  xM7 | x7' | x9 | x13 • x7  xb9 | xb10 | x7+5 • xm  xm7' | xm6 • xm7  xm9 | x°7

  8. Blues for AliceCharlie Parker

  9. The Blues Chord Sequencewith turnover

  10. Cadence extension Rule 1 (Bars : 4, 12 ) Rule 3 (Bars : 4l, 3, 2 ; 9, 8, 7, 6 ; 12l, 11r )

  11. Tritone substitution Rule 4 (Bars : 3r, 6, 8 )

  12. Subdominant addition Rule 2 (Bars : 6r, 7r, 8r )

  13. Embellishments (Bars : 1, 2, 6r, 7r, 8r, 11l) )

  14. A Pregroup Grammar for Chord Sequences Types Basic types We use the traditional notation for chords using the simple modes : major (omitted) or minor (m) and the seventh (7). X is called the root of the chord, i the alteration and j the mode possibly with the seventh Xij X  {A, B, C, D, E, F, G} i  {b, , #} j  { , m, 7, m7} Ex A, Bm, Gm7, C7

  15. A Pregroup Grammar for Chord Sequences Order Some sevenths are minor sevenths and don’t act as dominant ones. If this is the case they have to be rewritten as simple triads ; the typing rules will treat differently this two types of sevenths : Xi7  Xi Xim7  Xim (Dis-)Embellishments XM7  X Xm6  Xm X7b9  X7 Xm9  Xm7 X9  X X7#9  X7 Xm7b5  Xm7 X13  X X7#5  X7

  16. A Pregroup Grammar for Chord Sequences Functions used in typing The typing rules will make use of the distances between roots of chords. These distances will be represented by functions using roman numbers as diatonic distances possibly with chromatic alterations (b or #) as prefix. The mode, possibly with a seventh, is added as suffix. F(x) x  {A, B, C, D, E, F, G} F  {b, , #} x {I, II, III, IV, V, VI, VII} x { , m, 7, m7} Ex: bIIm(E) = Fm VI7(C) = A7

  17. A Pregroup Grammar for Chord Sequences Typing Chords Simple types x I(x) Identity Vr(x) V(x) IV deletion Vmr(x) Vm(x) " V7r(x) V7(x) " Vm7r(x) Vm7(x) " bIIr(x) IV7(x) I(x) Tritone substitution bIImr(x) IV7(x) I(x) "

  18. A Pregroup Grammar for Chord Sequences xm Im(x) Identity bVIIr(x) bVII(x) IIIml(x) IIm & IIIm deletion bIIr(x) IV7(x) Im(x) Tritone substitution bIImr(x) IV7(x) Im(x) ” x7 I7(x) Identity V7r(x) I7(x) Perfect cadence Vm7r(x) I7(x) " bII7r(x) I7(x) Tritone substitution bIIm7r(x) I7(x) "

  19. A Pregroup Grammar for Chord Sequences xm7 Im7(x) Identity V7r(x) Im7(x) Perfect cadence bII7r(x) Im7(x) Tritone substitution bIIm7r(x) Im7(x) " x°7 VIIr(x) VII(x) bIIm(x) bIIml(x) °7 deletion VIIr(x) VII(x) V(x) Vl(x) " VIIr(x) VII(x) VIm(x) VIml(x) "

  20. Typing

  21. Contraction

  22. Conclusion • A typical chord sequence from Be-bop fifties can be classified as « Blues » with a pregroup grammar. • Typing can be done step by step to classify blues chord sequences by periods of time : New Orleans, Dixieland, Chicago, Be-bop, Hard Bop, …. • But : • Typing is actually insufficient to recognize « all » types of blues • Other typing must be considered to classify other types of Jazz music : Rag, Anatole, …

  23. References Pregroups • DEGEILH Sylvain, PRELLER Anne (2003) - Pregroups and the French noun phrase - LIRMM, rapport de recherche n° 03023, 2003 - to be published in: JLLI, 2004 • LAMBEK Joachim (2000) - An algebraic approach to English sentence - unpublished lecture notes, McGill University, QC, Canada Chords and Grammars • CHEMILLIER Marc (2004) – Grammaires, automates et musique – BRIOT, PACHET (éd) – Informatique musicale, IC2 Hermes – to appear • CHEMILLIER Marc (2004) – Steedman's grammar for jazz chord sequences – Soft Computing, special issue on Formal Systems and Music – to appear • PACHET François (1998) – Sur la structure algébrique des séquences d’accord de Jazz – JIM 1998, Agelonde • STEEDMAN Mark (1984) – A Generative Grammar for Jazz Chord Sequences – Music Perception 2, 52-77 1984 • STEEDMAN Mark (2004) – Pattern and Grammar in Music – AI2 Jan. 2004 • TERRAT Richard (2002) – CFML : Chord Files Markup Language – JIM 2002 Marseille • TERRAT Richard (2004) – Pregroup Grammars for Chords – submitted to ISMIR 2004

  24. Acknowledgments • Anne Preller : Pregroups • Mark Steedman : « The blues and the abstract truth » • And ….. Charlie Parker

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