Roots of the Classical: The Popular Origins of Western Music

By Peter Van Der Merwe | Go to book overview

1
The Subtle Mathematics
of Music

Life is not an illogicality; yet it is a trap for logicians. It looks just a little
more mathematical and regular than it is; its exactitude is obvious, but
its inexactitude is hidden; its wildness lies in wait

G. K. Chesterton1

At an open-air service on the island of Skye, Ralph Vaughan Williams once heard a sermon in Gaelic, a language he did not understand. As he later explained, this ignorance enabled him to devote all his attention to the tones of the preacher's voice: 'The fact that he was out of doors forced him to speak loud, and that, coupled with the emotional excitement which inspired his words, caused him gradually to leave off speaking and actually, unconsciously of course, to sing. '2 At first the preacher was content with a monotone, but as his excitement grew he gradually developed certain clearly defined melodic formulas, which Vaughan Williams quotes in musical notation as e–a–b–a, a–b–c+–b–a, and a–b–a–g–a.3

He was probably mistaken in assuming that this gradual heightening of speech into song was unconscious, but perfectly justified in drawing a connection between musical pattern and emotional emphasis. Not only preachers and orators, but all human beings incline towards song when excited. Similar forms of oratory might have been observed in Africa, in the southern United States, and in many other parts of the world. What is much more remarkable, these speech tunes bear a strong family likeness to one another, regardless of language or culture. Again and again we find the same limited set of rhythms and intervals, expressible in the same simple mathematical ratios.

This proves the closeness of speech to song and the impossibility of drawing a clear distinction between the two. It proves, too, the fundamental importance

1 'The Paradoxes of Christianity' (third sentence), in Orthodoxy.

2The Making of Music, ch. 2, 'What is Music?' (in National Music and Other Essays), 207.

3 In another passage, evidently referring to the same incident, Vaughan Williams gives the notes as
being 'a, b, a, g, a, with an occasional drop down to e'. See National Music and Other Essays, ch. 2, 'Some
Tentative Ideas on the Origins of Music', 17.

-7-

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Roots of the Classical: The Popular Origins of Western Music
Table of contents

Table of contents

  • Title Page iii
  • Preface v
  • Acknowledgements vii
  • Contents ix
  • List of Figures xi
  • A Note on Terminology and Notation xii
  • A Note on the Musical Examples xvi
  • Abbreviations xviii
  • Introduction 1
  • Part One - The Melodic Foundations 5
  • 1: The Subtle Mathematics of Music 7
  • 2: The Ramellian Paradigm 19
  • 3: The Children's Chant 27
  • 4: The Pentatonic Scale 38
  • Part Two - The Harmonic Revolution 51
  • 5: Primitive Harmony 53
  • 6: The Discovery of Tonality 66
  • 7: Rivals to Tonality 86
  • 8: Dissonance and Discord 106
  • 9: The Evolution of Tonality 116
  • Part Three - The Melodic Counter-Revolution 129
  • 10: The Rude, the Vulgar, and the Polite 131
  • 11: The Debt to the East 144
  • 12: The Dances of Central Europe 231
  • 13: The Nineteenth–century Vernacular 271
  • 14: Romanticism 339
  • 15: Modernism 376
  • 16: The Popular Style 426
  • Epilogue 461
  • List of Musical Examples 467
  • Glossary 485
  • Bibliography 502
  • Index 515
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