Melodies in space: Neural processing of musical features A DISSERTATION SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE UNIVERSITY OF MINNESOTA BY Roger Edward Dumas IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Dr. Apostolos P. Georgopoulos, Adviser Dr. Scott D. Lipscomb, Co-adviser March 2013 © Roger Edward Dumas 2013 Table of Contents Table of Contents .......................................................................................................... i Abbreviations ........................................................................................................... xiv List of Tables ................................................................................................................. v List of Figures ............................................................................................................. vi List of Equations ...................................................................................................... xiii Chapter 1. Introduction ............................................................................................ 1 Melody & neuro-imaging .................................................................................................. 1 The MEG signal ................................................................................................................................. 3 Background ........................................................................................................................... 6 Melodic pitch ..................................................................................................................................... 6 Melodic contour ............................................................................................................................... 7 Melodic perplexity .......................................................................................................................... 9 Models of music cognition ............................................................................................. 11 Stable and unstable tones ......................................................................................................... 11 Gravity, magnetism & inertia ................................................................................................... 13 Tonal space ...................................................................................................................................... 14 The Circle of Fifths ....................................................................................................................... 14 The diatonic scale ......................................................................................................................... 16 Diletski’s circle of fifths’ (1679) ............................................................................................. 17 Euler’s tonnetz (1739) ............................................................................................................... 19 i Riemann’s tonnetz (1880) ........................................................................................................ 19 Traditional tonnetz ...................................................................................................................... 20 Longuet-Higgins Harmonic space (1962) .......................................................................... 21 Lubin’s toroidal tonal space ..................................................................................................... 22 The probe tone profile, key-finding torus and self-organizing map ...................... 23 Helical tonal surfaces ...................................................................................................... 28 Chew spiral array model (2000) ................................................................................. 29 Dumas perfect 4th helix (P4h) ...................................................................................... 30 Chapter 2. Materials and Methods ...................................................................... 37 Subjects ................................................................................................................................ 37 Experiment A: Neural processing of pitch ......................................................................... 37 Experiment B: Neural processing of auto-correlation ................................................. 37 Experiment C: Neural processing of interval distance ................................................. 37 Experiment D: Neural processing of next-note probability ....................................... 37 Stimuli .................................................................................................................................. 38 Experiment A .................................................................................................................................. 38 Experiments B, C, and D ............................................................................................................. 40 Task ...................................................................................................................................... 42 All Experiments ............................................................................................................................. 42 Data acquisition ................................................................................................................ 42 All Experiments ............................................................................................................................. 42 Chapter 3. Data Analyses ....................................................................................... 43 Experiment A .................................................................................................................................. 43 ii Experiment B .................................................................................................................................. 44 Experiment C .................................................................................................................................. 46 Euclidean distance (Ed) ............................................................................................................. 48 Ed - Tonal Space #1: Frequency ratio (F, D1) ................................................................... 48 Ed - Tonal Space #2: Longuet-Higgins (LH) harmonic space (1962a) .................. 49 Ed - Tonal Space #3 Krumhansl and Kessler (KK) major key probe tone profile (1982). .......................................................................................................................................... 50 Ed - Tonal Space 4: Parncutt (P88) major key chroma salience profile (2011).51 Ed - Tonal space #5: Chew (CH) Spiral array model (2000). ..................................... 52 Ed - Tonal Space #6: Dumas perfect fourth helix (P4h) (2012). .............................. 53 Experiment D .................................................................................................................................. 55 Chapter 4. Results .................................................................................................... 57 Experiment A .................................................................................................................................. 57 Experiment B .................................................................................................................................. 59 Experiment C .................................................................................................................................. 60 Experiment D .................................................................................................................................. 60 Chapter 5. Discussion .............................................................................................. 62 Chapter 6. Concluding remarks and future directions ................................ 66 Bibliography .............................................................................................................. 67 Appendix A – Experiment B plots ....................................................................... 74 Appendix B: Experiment C MEG sensor plots ................................................. 84 Tonal space #1: -log Frequency ................................................................................... 84 iii Tonal space #2: Longuet-Higgins harmonic space ................................................ 85 Tonal space #3: Dumas perfect 4th helix .................................................................. 86 Tonal space #4: Krumhansl & Kessler probe tone profile ................................. 87 Tonal space #5: Parncutt chroma salience profile ............................................... 88 Tonal space #6: Chew spiral array model ................................................................ 89 iv List of Tables Table 1-1. P4h parameter descriptions and values. ................................................................................................... 34 Table 1-2. P4h dimensions and formulae. ....................................................................................................................... 34 Table 1-3. P4h, key of C. Pitches, P4 steps, angles, coordinates and consonance units for pitches within