The Subtle Mathematics
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.