1 The most extensive discussion of the structure of the Fantasia appears in Anthony Pople, ‘Vaughan Williams, Tallis, and the Phantasy Principle’, Vaughan Williams Studies, ed. Alain Frogley (Cambridge, 1996), 47–80; see also (in chronological order): Edward Evans, ‘Analysis’, issued with the Hawkes Pocket Scores edition (London, 1943; cited in Pople, op. cit., passim); Percy M. Young, Vaughan Williams (London, 1953), 45–7; A. E. F. Dickinson, ‘The Vaughan Williams Manuscripts’, Music Review, 23 (1962), 177–94 (p. 192), and Vaughan Williams (London, 1963), 175–6; Michael Kennedy, The Works of Ralph Vaughan Williams (2nd edn, Oxford, 1980), 124–6; Lionel Pike, ‘Tallis–Vaughan Williams–Howells: Reflections on Mode Three’, Tempo, new ser., 149 (June 1984), 2–13; Wilfrid Mellers, Vaughan Williams and the Vision of Albion (London, 1989), 50–8; James Day, Vaughan Williams (3rd edn, Oxford, 1998; originally published 1961), 35, 99, 178, 256; William Brooke Joyce, ‘Listening Inside the Memory Palace’ (Ph.D. dissertation, Princeton University, 2005), i, 24–50 (with Vaughan Williams's dates given as ‘1874–1956’ – recte 1872–1958). Among the Vaughan Williams biographers/hagiographers, Dickinson alone expresses reservations about both the structure and the aesthetic quality of the work: ‘the proportions of this work, with so extended a middle section, remain questionable’ (‘The Vaughan Williams Manuscripts’, 192); ‘the odd shape of the music’ (Vaughan Williams, 175).

2 On the terms ‘static’ and ‘dynamic’ symmetry, see the classic study by Jay Hambidge, Elements of Dynamic Symmetry (New York, 1926; repr. 1967), xi–xvii.

4 Vaughan Williams came upon Tallis's melody (see Example 1 below) in Archbishop Matthew Parker's The Whole Psalter Translated into English Metre (London, 1567), where, as the third of Tallis's nine four-part psalm settings, it sets Psalm 2 and begins: ‘Why fum'th in sight: the Gentil's spyght’. For a transcription of Tallis's four-part setting, which places the famous tune (made so by Vaughan Williams) in the tenor, see Pike, ‘Tallis–Vaughan Williams–Howells’, 3–4, and Vaughan Williams and the Symphony, Symphonic Studies, 2 (London, 2003), 16–17. Vaughan Williams included Tallis's melody, now placed in the uppermost voice of his own four-part arrangement, as no. 92 in the English Hymnal, which he co-edited with Percy Dearmer; here it appears with a hymn text by Joseph Addison, ‘When rising from the bed of death’ (London, 1906; rev. edn, 1933), with Martin Shaw now among the editors; for the harmonization, see also Frank Howes, The Music of Ralph Vaughan Williams (London, 1954), 88. In editing the Hymnal, Vaughan Williams – and eventually Shaw – supervised the music, while Dearmer edited the texts.

5 Mellers, Vaughan Williams and the Vision of Albion, wavers about the function of E.1–4: after first calling the passage a ‘codetta’ to the A section (p. 53) – which is how I hear it – he later refers to E.1 as the point at which the bridge itself begins (p. 57); Pople, ‘Vaughan Williams, Tallis, and the Phantasy Principle’, 69, too, seems to consider those four bars as part of the bridge. Yet I would argue that the articulation at E.5 is far more profound than that at E.1, and that the sense of something new getting under way at E.5 finds a structurally important analogue – with the same melodic, harmonic and rhythmic motive – at T.5, which is unambiguous in terms of its function as the beginning of bridge 2 (see below).

6 Young, Vaughan Williams, 45, describes this section as the ‘fantasia proper’; Mellers, Vaughan Williams and the Vision of Albion, 53, refers to it as an ‘anti-development’; Evans, ‘Analysis’, writes that only the material from M.1 to R.7 of this section constitutes the ‘development’ (cited in Pople, ‘Vaughan Williams, Tallis, and the Phantasy Principle’, 71, note 54); Pople, ibid., 49, simply calls it the ‘central section’, and refers to Evans's analysis as ‘innocent’, a charge that strikes me as a bit unfair. Both Young and Pople draw parallels with the structure of the sixteenth- and seventeenth-century English ‘Fancy’ (see Pople, 47–50, on the relevance of the relationship).

7 Note that although the two bridge sections begin in parallel fashion, they function differently – that is, they move in structurally opposite directions – in terms of establishing and/or breaking down both tonal and thematic stability. Whereas the unstable beginning of bridge 1 continues to lead away from both Tallis's theme and the stability on G, that of bridge 2 slowly re-establishes the tonal/modal centre on G and leads to the final statement of Tallis's melody.

8 There are differences of opinion with respect to the point at which the coda begins: Pople, ‘Vaughan Williams, Tallis, and the Phantasy Principle’, 77, places it at U.2 (my A′) and refers to it as a ‘developed coda’; Kennedy, The Works of Ralph Vaughan Williams, 125, speaks of an ‘eight-bar coda’, thus placing it at the solo violin's F minor arpeggio at Z.2; in his article ‘Fancy, Fantasy, or Phantasy’, Grove's Dictionary of Music and Musicians, 2nd edn, ed. John Alexander Fuller Maitland, 5 vols. (London, 1904–11), ii (1906), 638, Fuller Maitland discusses the form of the ‘Fantasy’ in such a way that he would no doubt begin the coda where I do, at X.5 (see Pople, op. cit., 77); finally, Mellers, Vaughan Williams and the Vision of Albion, 56, refers to the entire section starting at around U as constituting a ‘coda-recapitulation’.

3 All references are to the miniature score issued by Boosey & Hawkes, plate number 8838 (1921; repr. 1999). I cite passages by rehearsal letter and bar number following (and, except for locations before rehearsal A, without the prefatory ‘bar’).

9 The date appears on page 38 of the autograph manuscript, which is now London, Royal Academy of Music, MS 7; I am grateful to Ms Kathryn Adamson, Librarian of the Royal Academy, and Ms Aida Garcia-Cole, Print Licensing Manager, Music Sales Corporation/G. Schirmer, for helping me to obtain a microfilm of the manuscript. On the importance of the major music festivals for the careers of Vaughan Williams and other composers, see especially Charles McGuire, ‘Vaughan Williams and the English Music Festival’, Vaughan Williams Essays, ed. Byron Adams and Robin Wells (Aldershot, 2003), 235–68, and ‘A History of the Festival: Victorian Progress, the People, and Charity vs. Competition’, paper read at the Third Biennial Conference of the North American British Music Studies Association, Toronto, 2 August 2008. Professor McGuire's article forms the basis of one of the chapters of his book The History of the English Musical Festival, 1700–1914, currently in progress.

10 Only the revision of 1919 was published, in 1921 (see note 3). For a discussion of the sequence of cuts and revisions in Vaughan Williams's autograph manuscript, see Pople, ‘Vaughan Williams, Tallis, and the Phantasy Principle’, passim, and Table 8 below.

11 Though I subtract the ‘silent seconds’ that sometimes precede the first downbeat, I do include the few seconds of silence at the end, during which the sound still reverberates as we (at least I) exhale in relief.

12 Jonathan D. Kramer, The Time of Music: New Meanings, New Temporalities, New Listening Strategies (New York, 1988), 327.

13 See Kramer, The Time of Music, 327, who justifies his own clock-time analyses of proportions on the basis of musical stasis: ‘In the absence of large-scale changes in any parameter, there is little to make subjective time seem faster or slower than clock time.’

14 In referring to timings gleaned from Vaughan Williams's metronome indications, I have added two seconds to account for the Luftpause after bar 2 and another two seconds for the fermata in the penultimate bar of the piece.

15 For a discussion of the various methods that have been used to analyse proportions, see Roy Howat, ‘Review-Article: Bartók, Lendvai and the Principles of Proportional Analysis’, Music Analysis, 2 (1983), 69–95.

16 Note that ArkivMusic.com lists 78 in-print recordings of the Fantasia, though that number includes some that are merely ‘repackagings’ of the same performance.

17 On this progression, in which all voices move by semitone, see Richard Cohn, ‘Uncanny Resemblances: Tonal Signification in the Freudian Age’, Journal of the American Musicological Society, 57 (2004), 285–323 (pp. 285–6), who characterizes it as consisting of ‘hexatonic poles’. On Vaughan Williams's use of the progression see Alain Frogley, Vaughan Williams's Ninth Symphony (New York, 2001), 290–1, note 73, who seems to be the first to have noted its presence in the composer's works. My thanks to Blake Howe, a doctoral candidate in musicology at The Graduate Center, The City University of New York, for calling my attention to the relevance of Cohn's article and for permitting me to adopt his very appropriate characterization of the music at the beginning of bridge 1 as being ‘unhinged’.

18 Clearly, what is ‘insignificant and imperceptible’ for one listener might not be so for another. Thus whereas Kramer, The Time of Music, 332, cites studies that permit the ‘imperceptible’ to range from as much as 8% to 16% of the total duration (note that these figures deal with minuscule time spans of 4–30 seconds, so that the percentages are understandably bloated), David Epstein, Shaping Time: Music, the Brain, and Performance (New York, 1995), 498–9, claims that discrepancies of more than 5% begin to become apparent (though he offers no parameters in terms of total duration), while Mario Livio, an astrophysicist, permits no deviation at all when discussing the Golden Section (The Golden Ratio: The Story of Phi, the World's Most Astonishing Number (New York, 2002), 159–94). Finally, whatever our definition of ‘imperceptible’ might be, we should bear the obvious in mind: we perceive large-scale proportions in a piece of music only through reflection after experiencing the entire piece, and usually upon more than a few hearings.

19 Day, Vaughan Williams, 99, refers to ‘a series of four massive, grinding chords’.

20 Known to the Pythagoreans in the fifth century BC, and invested with divine and Christian mystical attributes by Luca Pacioli and Johannes Kepler in the sixteenth and seventeenth centuries respectively, the Golden Section is unique in dividing a length in such a way that the ratio of the length in its entirety to the longer section is equal to the ratio of the longer section to the shorter section. We can determine the Golden Section of a given length by multiplying that length by 0.618 (since the proportion is an irrational number, the decimal places could go on indefinitely). The literature on both the Golden Section and the closely related Fibonacci sequence is enormous. Here I cite only three recent and particularly useful items (all with good bibliographies): Livio, The Golden Ratio (see note 18); Richard Padovan, Proportion: Science, Philosophy, Architecture (London and New York, 1999); and Roger Herz-Fischler, A Mathematical History of the Golden Number (New York, 1999; originally published as A Mathematical History of Division in Extreme and Mean Ratio (Waterloo, ON, 1987)). There is also a large literature on the Golden Section and music, with a quartet of ‘responsible’ starting points consisting of Roy Howat, Debussy in Proportion: A Musical Analysis (Cambridge, 1983); Kramer, The Time of Music, 303–21 (with an extensive bibliography that includes a number of important psychological studies); Allan W. Atlas, ‘Stealing a Kiss at the Golden Section: Pacing and Proportion in the Act I Love Duet of La Bohème’, Acta musicologica, 75 (2003), 269–91; and Ruth Tatlow, ‘The Use and Abuse of Fibonacci Numbers and the Golden Section in Musicology Today’, Understanding Bach, 1 (2006) – the web journal of Bach Network UK, online at <http://www.bachnetwork.co.uk/understandingbach> (accessed 17 April 2009) – which questions the methods and claims of earlier studies, including one of my own.

21 Mellers, Vaughan Williams and the Vision of Albion, 55, 57, hears the change in character as a shift from ‘ecclesiastical devotion into pastoral lyricism […] people's prayer into the open fields’; Pople, ‘Vaughan Williams, Tallis, and the Phantasy Principle’, 70, characterizes the viola's opening statement as being ‘folksong-like’ and marking ‘a significant transformation of genre’.

22 I use ‘short’ Golden Section (SGS) to describe the Golden Section when the short segment precedes the long segment, while ‘long’ Golden Section (LGS) describes the opposite situation; in both instances we are moving from beginning to end/left to right.

23 The metronome indications in the 1919 revision run as follows. Bar 1: 56; I.1: 66; M.1: 80; O.6: 96; T.5: 44; T.9: 56.

24 Two other pairs come within seconds of agreeing with one another in terms of their total duration: Handley is only four seconds faster than Toscanini, while Barbirolli beats Spano by a mere five seconds.

25 For instance, on Puccini's tendency to change gears at the approximate SGS in various numbers of La Bohème, see Atlas, ‘Stealing a Kiss at the Golden Section’; for a sample of observations about the LGS and climactic moments, including the beginning of the recapitulation in sonata forms, see, among others, Howat, Debussy in Proportion; Clive Pascoe, ‘Golden Proportion in Musical Design’ (Ph.D. dissertation, University of Cincinnati, 1973); J. H. Douglas Webster, ‘Golden-Mean Form in Music’, Music and Letters, 31 (1950), 238–48; and the thoughtful paper by Kris P. Shaffer (a candidate for the Ph.D. in Music Theory at Yale University), ‘The Traditional and Progressive in Béla Bartók's Fifth String Quartet’ (2004; online at <http://www.kris.shaffermusic.com/doc/bartok5.pdf>, accessed 22 November 2009), 7, 24–5.

26 Ralph Vaughan Williams, ‘The Romantic Movement and its Results’, The Musician, 1 (1897), 430–1; the article is reprinted in Vaughan Williams on Music, ed. David Manning (Oxford, 2008), 13–16 (p. 14).

27 Neither Vaughan Williams's writings about music nor his published letters offer evidence of any interest on his part in such mathematical-structural, pre-compositional planning; for the letters, see the large selection in Letters of Vaughan Williams, 1895–1958, ed. Hugh Cobbe (Oxford, 2008), and the biographical studies cited in note 1 above.

28 If we omit the speedy Mitropoulos, and the rather slow Stokowski and even slower Bernstein, the nine remaining recordings give us an average total duration of 15:20/920.

29 For an informal (and not very scientific) experiment that tries to test our ability to perceive the Golden Section over the course of a much shorter span (approximately four minutes), see Atlas, ‘Stealing a Kiss at the Golden Section’, 284–5, which shows that, once instructed about what to listen for, four listeners (all musicians) improved dramatically in their ability to judge the durational proportion defined by the performance-time SGS in the Act 1 love duet of La Bohème; perhaps, then, ‘perception’ sometimes needs a little guidance (they are not mutually exclusive). Obviously, the entire matter is fraught with difficulty, and I know of nothing that adds to Kramer's observation about it: ‘neither music theory nor psychology has offered many answers to these intriguing questions’ – and none, I would add, that are meaningful in terms of ‘real’ listening experiences; for Kramer's statement, see The Time of Music, 321.

30 Without drawing any firm conclusions about the matter one way or another, I would like to point to still another large-scale SGS in the Fantasia, though one that is non-linear in nature. It was simply curiosity that led me to compare the proportional balance between those sections of the piece in which the solo quartet is playing either alone or at least independently of the two string orchestras with those in which it doubles them. If we agree that the quartet is independent at I.1–P.1, U.2–W.7 and Z.2–6, the data is as follows (based on Vaughan Williams's metronome indications and the recordings by Neel, Barbirolli and Boult, each of whom, we might note, enjoyed a close working relationship with the composer):

I offer this information with the thought that perhaps we should begin to look at proportions in terms other than the strictly linear. Perhaps we should consider them in connection with such parameters as tonal areas, dynamics or any other element that contributes to the way we perceive the structure of a piece. A few words about the solo quartet: the Boosey & Hawkes score (see note 3) misleads by inserting the indication ‘div.’ (divisi) in the solo parts of the opening bars; Vaughan Williams's autograph score (see note 9) indicates only that the solo parts are to be played ‘col tutti’ at that point, but obviously without the divisi (impossible for the solo quartet) called for in each of the two orchestras. In fact, Vaughan Williams has crossed out the four- and five-stave systems of both the soloists and the second orchestra (the latter being told to play ‘col orch. I’). Further, the title page of the autograph bears the following note to the copyist: ‘The parts for the solo instruments are the same parts as the first orchestra’, with the Boosey & Hawkes score adding: ‘The Solo parts are to be played by the leader of each group [of Orchestra I].’

31 Perhaps it is time for a word about Vaughan Williams's metronome indications and the total duration in which they would result if followed scrupulously. With a total duration of 11:27/687, they seem rather on the fast side, 1:13/73 faster than the fastest of our recordings (that by Mitropoulos, whose total duration of 12:40/760 exceeds the next fastest, Frühbeck's 14:08/848, by a very significant 1:28/88). To express this in three other ways: Vaughan Williams's 11:27/687 is (1) a little more than four minutes faster than our median timing of 15:34/934, which we find on the recordings of both Neel and Slatkin (and with which timing Vaughan Williams must have been satisfied, since he was present at the Neel recording), (2) approximately the same amount faster than our average timing of 15:20/920 (which we get if we omit Mitropoulos, Stokowski and Bernstein – see note 28), and (3) almost seven minutes faster than Bernstein's leisurely 18:12/1,092. This, of course, raises the question of just how far apart – and in terms of what total duration – the fastest and slowest performances of a given piece can be without one or the other distorting or falsifying the integrity of the work. For instance, has Bernstein, whose recording would be 59% longer than a performance that followed Vaughan Williams's metronome indications exactly, distorted the work? To appreciate the magnitude of this difference, see the interesting discussion of tempo and duration in José Antonio Bowen, ‘Tempo, Duration, and Flexibility: Techniques in the Analysis of Performance’, Journal of Musicological Research, 18 (1996), 111–56 (pp. 129–30), who suggests that we can generally tolerate no more than about a 30% difference between fastest and slowest performances, though slow movements – and Vaughan Williams's Fantasia falls into that category – can stand a greater degree of difference. Bowen goes on to note that there are those who will tolerate much less than that; thus Joachim Braun, ‘Beethoven's Fourth Symphony: Comparative Analysis of Recorded Performances’, Israel Studies in Musicology, 1 (1978), 54–76 (p. 60), argues for limits of±17%, and writes: ‘We may suggest that in performances where the slowing down of Beethoven's tempo is as much as 20% or more […] a major distortion of Beethoven's idea takes place’. Now, while some might well argue that Bernstein's 18:12/1,092 goes beyond the breaking point, to say that he has crossed some hypothetical limit and thus distorted or falsified the Fantasia is clearly a matter of personal taste. It is a fascinating topic that deserves more attention, as does the analysis of tempo and proportion in general.

36 Ursula Vaughan Williams, R.V.W.: A Biography of Ralph Vaughan Williams (London, 1964), 88.

32 Young, Vaughan Williams, 45.

33 Day, Vaughan Williams, 134.

34 Hubert Foss, Ralph Vaughan Williams: A Study (London, 1950), 118.

35 Mellers, Vaughan Williams and the Vision of Albion, 53. See also Kennedy, The Works of Ralph Vaughan Williams, 126. Pople, ‘Vaughan Williams, Tallis, and the Phantasy Principle’, 50–3, reviews this aspect of the reception of the Fantasia.

37 Auguste Choisy, Histoire de l'architecture (Paris, 1899; repr. Geneva, 1983), ii, 403; cited and discussed in Padovan, Proportion, 190, 192.

38 The measurements are cited after H. J. L. J. Massé, Cathedral Church of Gloucester: A Description of its Fabric and a Brief History of the Episcopal See, Bell's Cathedral Series (London, 1900), not paginated; Massé's study appears online at <http://vrcoll.fa.pitt.edu/medart/image/England/Gloucester/cathedral/maingloucester.html> (accessed 17 April 2009).

39 The 34-foot width of the nave is echoed in the two transepts, each of which is between 33 and 34 feet long, while the choir is approximately 30 feet wide, or the equivalent of the two aisles; see Massé, Cathedral Church of Gloucester, and David Welander, The History, Art and Architecture of Gloucester Cathedral (Stroud, 1991), 547.

40 The length is so given in Edward Shaw, Shaw's Civil Architecture; Being a Complete Theoretical and Practical System of Building Containing the Fundamental Principles of the Art, and Illustrated by Eighty-Two Copperplate Engravings (6th edn, Boston, 1852), 139; the book is available online at <http://books.google.com/books?hl=en&id=wtkDAAAAYAAJ&dq=shaw's+civil+architecture&printsec=frontcover&source=web&ots> (accessed 17 April 2009). Note that Welander, The History, Art and Architecture of Gloucester Cathedral, 547, gives the length as ‘approx’ 421 feet, while Massé, Cathedral Church of Gloucester, inexplicably lists it as 407 feet (raising the question of just where he measured from).

41 Shaw, Shaw's Civil Architecture, 139, Massé, Cathedral Church of Gloucester, and Welander, The History, Art and Architecture of Gloucester Cathedral, 547, all of which agree on the length of the nave.

42 Dimensions after Massé, Cathedral Church of Gloucester.

43 At the risk of going beyond extravagance: the height above the nave is 68 feet, that above the aisles 40 feet, so that they miss defining a true LGS, 68:42, by 2.9% (measurements after Welander, The History, Art and Architecture of Gloucester Cathedral, 547), something that strikes me as being at least vaguely parallel to the LGS formed by the proportion of the piece in which the solo quartet is independent and that in which it is not: both are, in a sense, non-linear.

44 Salisbury = 17–34–17 (feet), while Wells = 22–38–22; see, respectively: Illustrated Guide to Salisbury Cathedral, Being a Full Historical and Descriptive Account of the Buildings and Monuments, Brown's Stranger's Handbook, 1 (Salisbury and London, 1884; online at <http://books.google.com/books?id=Ats6AAAAMAAJ&&pg=PA105&dq=salisbury+cathedral+ground+plan>, accessed 17 April 2009), 8, and Percy Dearmer, The Cathedral Church of Wells: A Description of its Fabric and a Brief History of the Episcopal See, Bell's Cathedral Series (London, 1899; online at <http:/books.google.com/books?id=CxZNAAAAMAAJ&pj161&dq=wells+cathedral+dimensions# PPP5.M1>, accessed 17 April 2009), 160–1. Note that the author of the Wells Cathedral study is the Percy Dearmer who co-edited the 1906 English Hymnal with Vaughan Williams (see note 4). Could Dearmer have discussed architectural proportions with Vaughan Williams – both in general and about Gloucester Cathedral in particular – when they collaborated on the Hymnal?

45 See Shaw, Shaw's Civil Architecture, 139 (measurements in feet):

46 Pople, ‘Vaughan Williams, Tallis, and the Phantasy Principle’, 57, writes: ‘Vaughan Williams made jottings in the manuscript to keep track of the total reduction in length and the implication of this for the work's duration in performance.’ When I initially read this (prior to seeing a reproduction of the autograph – see note 9), I took it to mean that Vaughan Williams actually jotted down the amount of time (in seconds) by which each cut would shorten the total duration of the work. This, however, is not the case. Rather, the jottings to which Pople refers appear on the second and third pages of the autograph (right after the title page and both without page numbers). Those on the second page, which is headed ‘Bar scheme’, consist of two columns: (1) a longer one (on the left), which provides the complete series of rehearsal letters (A–Z, with V crossed out), with each letter followed by the number of bars within after the final round of cuts, and (2) a shorter one (to the right), which tallies up the number of bars that were cut (seven entries) and adds up to 33 (though Vaughan Williams incorrectly adds them up to equal ‘23’). The third page bears the following inscription in Vaughan Williams's hand across staves 2–4: ‘11 bars cut = 35 beats = nearly 1 minute’, which must refer to the first round of cuts in 1913. My thanks to Alain Frogley for deciphering Vaughan Williams's notoriously difficult handwriting.

47 Unfortunately there is no recording of the original 1910 version. Note that the restored cuts are timed in accordance with the 1910 metronomic indications, so that I have, admittedly, combined the metronome indications of the 1910 version with those of the 1919 version, which guided Boult's tempos.

48 Cited in Kennedy, The Works of Ralph Vaughan Williams, 94. The reviewer in the Musical Times (51, 1 October 1910, 650) also thought the piece too long: ‘It is a grave work, exhibiting power and much charm of the contemplative kind, but it appeared over long for the subject matter’. On the other hand, The Times's critic (7 September 1910, p. 11) thought the piece ‘remarkable’ from beginning to end. The matter of the work's length remained an issue for some critics even after the cuts of 1919. Thus when Richard Aldrich reviewed the American première of the Fantasia – in New York, Carnegie Hall, 9 March 1922, with Walter Damrosch conducting the New York Symphony Orchestra (which would merge with the New York Philharmonic in 1928) – he wrote, ‘it is in its way imaginative, interesting and impressive up to a certain point; but Mr. Williams [sic] is so entranced with the evolution of his fancy that he forgets to stop before the listening ear is satiated with the gravity and severe decorum of the music’ (New York Times, 10 March 1922, 22, my emphases). Note that my own hypothetical reconstruction estimates that, played at Boult's prevailing tempo, the 1910 version would run just under 18:30 (see Table 9). Kennedy, A Catalogue of the Works of Ralph Vaughan Williams (2nd edn, Oxford, 1996), 55, writes with reference to the 1919 version of the work: ‘Duration. 14½ minutes’, a timing that, among our 12 recordings, only Mitropoulos, Frühbeck and Norrington beat, while Handley and Toscanini come very close to it (see Table 1).

49 I should note that Pople believes that Vaughan Williams may have made the cuts in response to the Journal's review (‘Vaughan Williams, Tallis, and the Phantasy Principle’, 57).

50 See Kennedy, The Works of Ralph Vaughan Williams, 59; Imogen Holst, The Music of Gustav Holst (London, 1951), 147; Michael Short, Gustav Holst: The Man and his Music (Oxford, 1990), 26–7. For the Vaughan Williams–Holst correspondence, see Heirs and Rebels: Letters Written to Each Other and Occasional Writings on Music, ed. Ursula Vaughan Williams and Imogen Holst (London, 1959), which, however, contains no reference to the Fantasia. What makes the Holst-as-critic proposal particularly enticing is that Holst himself was deeply interested in and well informed about the music of Thomas Tallis. In fact, when Holst's Ave Maria for eight-part women's chorus was premièred in 1900, the reviewer in the Minim praised the work and ventured that Holst had ‘studied the compositions of the old writers, such as Tallis and Palestrina’ (quoted in Short, Gustav Holst, 60). On the reception of Tallis's music in Victorian England, see Suzanne Cole, Thomas Tallis and his Music in Victorian England, Music in Britain, 1600–1900 (Woodbridge, 2008), and ‘Who is the Father? Changing Perceptions of Tallis and Byrd in Late Nineteenth-Century England’, Music and Letters, 89 (2008), 212–26.

51 See above, esp. note 27.

52 In the spirit of dismissing other outside influences that some readers might deem possible, particularly with respect to the Golden Section: (1) though Vaughan Williams spent three months in Paris early in 1908 studying with Ravel; and (2) though he (Vaughan Williams) suffered an attack of ‘French Fever’, as exemplified by such works as the String Quartet no. 1 in G minor (1908) and the magnificent song cycle for voice, piano and string quartet On Wenlock Edge (1909); and (3) though Ravel might already have developed either an interest in or his own intuitive feeling for Golden Sections by that time (he certainly seems to have done so by the time he composed Le tombeau de Couperin, 1914–17), there is simply no evidence that discussions about proportions played a part in the lessons, which seem to have focused mainly on matters pertaining to orchestration. On the other hand, who knows what the two composers chatted about during the course of their ‘small talk’? Nor is there any evidence to suggest that Vaughan Williams developed an interest in Golden Sections through contact with Debussy. On Vaughan Williams's lessons with Ravel, see Kennedy, The Works of Ralph Vaughan Williams, 90–1, and, at greater length, Byron Adams, ‘A Little French Polish: Vaughan Williams's Lessons with Ravel’, paper read at the conference ‘Ralph Vaughan Williams (1872–1958): Fifty Years On’, The Graduate Center, The City University of New York, 14 November 2008. On the Golden Sections in Ravel's Le tombeau de Couperin, see Roy Howat, ‘Ravel and the Piano’, The Cambridge Companion to Ravel, ed. Deborah Mawer (Cambridge, 2000), 71–96 (pp. 93–5); on Debussy's interest in and use of Golden Sections, see Howat, Debussy in Proportion.