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Dryden and Draghi in harmony in the 1687 'Song for St Cecilia's Day.' (John Dryden's poem set to music by Giovanni Battista Draghi)

Dryden's 1687 'Song for St Cecilia's Day' ('From Harmony, from heav'nly Harmony') has been the subject of three illuminating literary analyses, the first by Brennecke in 1934, and then two in quick succession, by Levine in 1965 and by Fowler and Brooks in 1967.(1) The poem (given in Appendix I below) describes the creation of the world in Platonic/Pythagorean terms, and subsequent events leading to the Day of Judgement in increasingly Christian terms, plus the beneficial influence on the world of the musicians Jubal, Orpheus and St Cecilia. Plato had described his theory of the creation and structure of the universe in his Timaeus, which is based on the theories of Pythagoras. Thereafter, proportions and numbers were an important strand running through the philosophy of the Creation,(2) and so it is appropriate that Dryden's poem uses proportions and numbers in its own structure. The poem was set by Giovanni Battista Draghi and first performed on St Cecilia's Day (22 November) 1687 in the Stationers' Hall at the annual celebration organized by the Musical Society.

Fowler and Brooks have shown that Dryden's main numbers are:

(a) 10, symbolizing Pythagoras' tetractys.(3) Dryden makes ten references to instruments: 'corded shell', trumpet (twice), drum, flute, lute, violin, organ (twice) and lyre. These instruments are even divided into families appropriately for the tetractys (1 + 2 + 3 + 4), there being one percussion instrument (drum), two brass (trumpet mentioned twice), three wind (organ mentioned twice, flute), and four string ('corded shell' - which is actually a lyre - plus the lyre itself, lute and violin).

(b) 7 and 9, symbolizing respectively the corporeal nature of the world and the spirituality of heaven. These are the numbers of lines in stanzas 7 and 2, which have textual cross-references.

(c) 8 and 15, symbolizing the number of notes in one and two octaves. Compare the number of lines in the first stanza (15) and the number of stanzas (eight, of which the last is unnumbered and makes reference back to the first, thus closing the circle as the return of the tonic does in a scale). Note, too, stanza 1's 'The Diapason [octave] closing full in Man'. The number 8 also symbolizes the Eighth Day - resurrection, regeneration and eternity - and only in the unnumbered eighth stanza does Dryden, having been referring to earthly matters (and having specifically mentioned 'Earth' in the last line of stanza 7), move on to describe the effects, including the musical effects, of resurrection on the Day of Judgement. And indeed, on the simplest level, 8 symbolizes setting out anew, whether biblically (the first day of the second week) or musically (the first note of the next octave as well as the last note of the first octave). The number 15 also symbolizes Man's route to heaven by means not only of the steps of a musical scale but also of Jacob's ladder (Genesis 28: 12), which in Jewish cabbala (though not in Genesis) had fifteen steps.(4)

(d) 4. The four elements listed as 'cold, and hot, and moist, and dry' in stanza 1, then (reordered), each in turn becomes the theme of a later stanza in the guise of the related four temperaments. The four humours, temperaments, elements and elemental characteristics are as follows (in order of mention in stanzas 3-6): bile (angry/hasty; fare; hot; = trumpet (stanza 3); black bile/tears (melancholic; water; moist; = flute (stanza 4); phlegm (sharp; earth; dry; = violin (stanza 5); blood (well-balanced; air; cold; = organ (stanza 6). Note that, whenever the flute is mentioned, the recorder is to be understood.

(e) 4, 5, 6 and 7 taken together and separately are important, given that stanzas 4-7 each have respectively the corresponding number of lines. In stanza 6 the word 'harmonious' is applied to the organ, illustrating the perfection and balance of 6, while in stanza 7 a reference to St Cecilia is finally made, 7 being a number associated with virgins, especially but not exclusively the Virgin Mary.

Dryden's main proportions are:

(a) 2:1, symbolizing the musical interval of the octave. Stanza 1 can be divided into ten and five lines by observing where the repetition of the text occurs. This is also illustrated in a musical, rather than mathematical, way by the fifteen lines of stanza 1 and the eight stanzas of the whole text, fifteen being the number of musical notes in two octaves and eight the number in one.

(b) 4:1. This can be derived from 2:8:2:3, an alternative reading of stanza 1, which, however, is not mutually exclusive of the above analysis;(5) it lays emphasis on the position of the symmetry created by the repeated couplet which exposes the eight intervening lines (so, 8:2) and also emphasizes that Dryden's universe is complete after twelve lines, leaving three at the end, and therefore illustrating 8:2 and 12:3 (both 4:1), the proportion of the double octave.

This repetition within stanza 1 of the couplet beginning 'From harmony' serves to stress symmetry and circularity, two important structural features to which attention is drawn by the word 'Frame'.(6) Symmetry is also found in stanza 2, the first line of which is repeated as its last, and between the first and last stanzas, the first referring to the fact that at the Creation 'The tuneful Voice was heard on high', and the latter confirming that on the Day of Judgement 'The Trumpet shall be heard on high'. Between these two stanzas there is also circularity, in that the same nothingness is assumed to exist after the Day of Judgement as existed before the Creation: the music which tuned the harmony of the spheres at the Creation will untune the sky at the Day of Judgement. Circularity is also exemplified by the fact that the first line of the first stanza has the same rhyme as the last line of the last stanza (Harmony/Sky), the returning rhyme symbolizing the musical scale, whether one octave or two, which returns whence it came (or at least to the same note-name and to a similar sound). Finally, circularity is placed into a specifically musical context by the fact that the final stanza is not numbered '8', as it might be, but is simply entitled 'Grand Chorus', reflecting the fact that the eighth note of the scale is the last note of one octave and also the first note of the next. Another important symmetry occurs between stanzas 2 and 7 (i.e., the second and the penultimate), which are the only two to refer to people: Jubal, the biblical founder of music (Genesis 4: 21) in stanza 2, and Orpheus and St Cecilia in stanza 7. Moreover, Jubal's 'corded Shell' in stanza 2 is the lyre, which is also Orpheus' instrument in stanza 7.

One final poetic device is used in stanza 1 to illustrate the chaos which was brought to order by the Creation: the first six lines are in chaos because each has no rhyming or metrical partner, and it is only in the next six lines that they are gradually exposed as couplets and paired off (or submitted to order). For the first twelve lines, the rhyme-scheme as inflected by the metre, once revealed as symmetrical and in couplets, is abcdefefcdab, and it is this scheme which provides one way of reading the first stanza (as 12 + 3 lines, or 4:1; although it can also be read as 10 + 5, or 2:1, as discussed above).

So, Dryden's main devices are symmetry, circularity, judicious chaos, the proportions 2:1 and 4:1 appropriate for octaves, and, at particular moments, 10 (representing the Pythagorean tetractys and therefore the creation of the universe), 7 and 9 (the mundane and the spiritual), 8 and 15 (the octave), 4 (the four temperaments and associated musical qualities), 6 (perfection) and 7 (the virgin saint). His aims are to mirror in the structure of the poem elements of the natural world, especially those associated with the Creation, as then understood, and to use the gifts of God, especially our perception of number and proportion, as the means by which Man imperfectly praises the Creator. As an elegant fusion of theory and practice, the poem is a source of great aesthetic and intellectual pleasure.

But how many at the time understood Dryden's structure? Davies has pointed out that there is 'no explicit statement by any of Dryden's contemporaries about the structure of the 1687 ode, and it would be interesting to know whether the nature of this structure was known',(7) although he shows that Shadwell in his 1690 ode understood Dryden's scheme in many particulars. Specifically, we must ask whether Draghi shows any such awareness in his setting, for 'If Musick and sweet Poetry agree, As they must needs (the Sister and the Brother)', to quote Richard Barnfield (1574-1627), he should at least reflect the aesthetic delight of the poem, and, indeed, he is potentially able to add to the allusions by using the structural possibilities of actual music. Brennecke does not believe that Draghi's setting reflects Dryden's poem: 'The music, in properly carrying out the ideas, violates the poetic structure'.(8) 'The last few pages of Draghi's setting contain some passages in which real violence is done to the poem . . . the same sort of clash between poetic and musical form which we observed in the opening stanza is again apparent. This final stanza did not lend itself readily to purely choral treatment.'(9) Winn also considers that Draghi does not show any sympathy with Dryden's poetry:

When the poem was set to music, Draghi's close attention to locally imitative effects often obscured the structure Dryden had built into the poem. In the first stanza, for example, Draghi set the first two lines as a chorus, and repeated that setting exactly when the lines recurred, thus strengthening the outer parts of Dryden's frame. But he set lines 3-6 as a recitative . . . [and gave] line 7 . . . to . . . a boy soprano. The next three lines, about the elements leaping to their stations, he set as a vocal trio in imitative polyphony. All these devices are effective and dramatic, but the music obscures, as it must, the rhymes, the grouping of the lines in pairs, and the metrical structure by which Dryden had made his own imitative 'setting' of his matter, and from which he derived his larger structure. The numerical proportions, already obscure in the text alone, are of course utterly distorted by the musical setting.(10)

Zimmerman, too, felt that Draghi's 'poetic sensibilities and musical powers were not such as to take full and imaginative advantage of the opportunity Dryden had provided'.(11) It is true that some of Dryden's conceits are not susceptible of direct musical treatment, such as the number of lines in stanzas 4-7, but it is worth exploring whether Draghi finds his own, musical, ways in which to allow Milton's 'sphere-born harmonious sisters' to meet in response to the careful structure of Dryden's poem.

Draghi's music survives in six sources, the earliest of which is Chichester, West Sussex Record Office, Cap. VI/1/1, f. 24, 'a carefully annotated score [which] gives the cast for, probably, the first performance'.(12) At a superficial level, Draghi exploits all the illustrative opportunities that present themselves;(13) thus, the 'Atomes' jar in semiquavers, the 'Harmony' runs through all the compass in semiquavers over the range of a ninth, the 'Diapason' closes 'full' on a sudden semibreve and then comes to a cadence with a phrase incorporating an octave of which the last two notes are dominant and tonic (a full close, then as now; this term is at least as old as Morley (1597)).(14) The reference to 'Nature underneath a heap', and the introduction to the 'tuneful Voice . . . heard on high', allow the bass singer to use the extremes of his voice. This singer, named in the Chichester manuscript (and also in Royal College of Music MS 1106, thought to be for a 1694 or 1695 performance), was the celebrated John Gostling, a member of the Chapel Royal, who was famous for the immense range of his voice; all the other named soloists were, or were soon to become, members of the Chapel Royal or of the 'vocall part' of the Private Music at court.(15) When the 'Voice . . . on high' itself enters, it is a treble encouraging the 'more than dead' to arise with an upward scale in semiquavers. Only three singers characterize the four temperaments in stanza 1, but, as in stanzas 3-6, it is the instruments and their accepted characteristics, rather than the voices (still less the number of voices), that are most significant.(16) In stanza 2 'Musick' raises 'Passion' with an upward semiquaver phrase; trumpets and flutes (recorders) make their predictable appearance in stanzas 3 and 4; the violins return in stanza 5; and all instruments except the continuo (which must therefore be for organ, St Cecilia's instrument) disappear in stanza 6. In the last two stanzas, Gostling's fabled range raises 'the wonder high'r', the choir illustrates the 'Living' in semiquavers while Gostling descends to his famous low C to illustrate their dying, and for 'Musick shall untune the Sky' Draghi uses a chromatic phrase. The cumulative effect of these illustrative devices, set in the context of a rich five-part string ensemble (supplemented as appropriate by recorders and trumpets) produces a most effective and pleasing work. Furthermore, and as Holman has shown in discussing the influence of this work on Purcell's odes, it is of great importance, 'a turning-point in the development of the ode', with its Italianate prelude and Italianate counterpoint rather than French overture and French dance patterns, while 'several aspects of the orchestral writing were new in 1687'.(17) Martin Adams, too, acknowledges the 'assertively Italian' nature of the work, while also recognizing that 'Draghi's style was deeply influenced by English practice', which, in view of our structural investigation, is interesting.(18)

And yet, in addition to the innovatory orchestral and formal features, the influence on Purcell, and the fact that this music sounds pleasing, there is more to be found under the surface. At first sight, it appears that the structure of Draghi's setting favours the primordial chaos over the Platonic order, for it opens with an overture comprising a chordal introduction and a fugue (22 + 64 minims),(19) a symphony leading into the opening phrase of the text (30 + 24 minims), and a fugue and closing symphony of 36 + 34 minims. These three combined passages - 86, 54 and 70 minims - do not appear to have much in common, and the injunction from 'on high' (24 + 20 = 44) does not at first sight give them any additional shape. However, it quickly becomes clear that an important contribution to our understanding of the work is to be provided by the overture and symphonies which provide variety of sound and also define Draghi's structure; these were still relatively new features punctuating the structure of extended English vocal works in the 1680s. At first, as we have seen, their presence is of no assistance in presenting any discernible structure, so we need to remove them temporarily to begin to identify Draghi's structure, although we shall, of course, restore them in due course. This is in tune with Dryden's hint in line 6 of stanza 1, where he concentrates on the 'tuneful Voice'; he does not turn his attention to instruments until stanza 2. So for the moment we shall focus precisely on the 'tuneful' voices.

In the first stanza, Draghi is unable actually to replicate musically the resolution (after line 6) of the initially chaotic rhyme-scheme, but he does attempt to provide the musical equivalent, by setting the lines as follows (see also the annotated text in Appendix I, below). If we ignore the symphonies and ritornellos, line 1 (rhyme a) has 24 minims, and line 2 (rhyme b) 36, a clear 2:3. On the return of these rhymes, which is also a precise repetition of the text, line 11 (rhyme a) has 18 minims and line 12 (rhyme b) 36, a clear 1:2. Musically, this 36 is the fugal section repeated exactly from earlier in the stanza, but the material that precedes it ('From Harmony . . .') is abbreviated upon its return; from 24 to 18 minims in length (4:3). Lines 3-6 (rhymes c, d, e, f) are set continuously for bass solo in such a way that musically they form a structural unit comprising 24 minims (and therefore consistent with the 18, 24 and 36's noted already). Although the musical structure of these four lines demands that they be run together (i.e., they form a continuous movement for bass), the cadences produce an internal structure of 4 + 4 + 6 + 10 minims, a sequence capable of different harmonious interpretations depending on the combinations taken: 8 + 16 (1:2) or 4 + 10 + 10. This might, without being too fanciful, be equated with the chaos of the rhymes as the listener/reader tries to decide what goes with what. Line 6 alone, containing the description of the 'Voice . . . on high', has 10 minims, derived from the Pythagorean 10 (the tetractys, symbolizing the Creation and used by Dryden in this sense in this stanza as the number of lines (10) in its first part; see above). Now, at line 7, Dryden begins to clarify his rhyme-scheme: with the instructions to the chaotic elements to arrange themselves, the chaotic rhymes apparently follow suit. Draghi, likewise, begins to clarify his structural scheme. The line containing this command (line 7, rhyme e) has 20 minims, also, of course, derived from the Pythagorean 10 and related to the preceding 10. The further institution of order (lines 8-10, rhymes f, c, d) has 32 minims, which are related to the 24's and 36's already noted (32:24 is 4:3, and 32:36 is 8:9, both being Pythagorean and Platonic proportions, the former the interval of a perfect fourth and the latter a whole tone; see below). It is at this point that Dryden repeats the opening couplet, as noted already, although Draghi abbreviates the setting of the opening line. So the vocal representatives of the 'tuneful Voice' alone have their own logic.

However, the instrumental material is also an important part of the movement, and so it is necessary to reinstate it in order to examine what structural role it plays. If we therefore restore the instrumental music we can see how Dryden's chaos (lines 1-6) which submits to order (starting in line 7) is mirrored by Draghi's 'chaos' of 86, 54, 70 and 24 (including the instrumental material) submitted to order by 20 (in line 7), after which 32, 18 and 36 turn out to be related to the 24's and 36's achieved by separating the vocal material from the instrumental, as instructed by Dryden. Furthermore, we have not yet fitted the last three lines of the stanza into our scheme (8 + 24 + 62 = 94). There are two other large combinations of 94, one following the initial symphony at the beginning of the stanza (24 + 36 + 34 = 94) and another incorporating the symphony in the middle of the stanza (20 + 32 + 24 + 18 = 94). This analysis would produce for the whole stanza (excluding the overture and the opening and closing symphonies) a structure of 94-24-94-36-94, pleasingly symmetrical around 24 and 36 (2:3). If we now include more of the instrumental material, an even clearer and cleverer scheme appears, where the overture (86) is as 1:2 to the whole of the second part of the stanza, excluding the final ritornello (24 + 18 + 36 + 8 + 24 + 62 = 172). We have seen that the overture (86) is followed by a symphony and the setting of the first line (30 + 24 = 54), making a large paragraph of 140 minims (86 + 54). This is promptly answered by 'This universal Frame' and its symphony (36 + 34 = 70), making a 2:1 proportion (140:70). Indeed the first movement, excluding the overture but now including the final ritornello, is 400 minims in length, divided into 200 + 200, the division coming at the return of 'From Harmony, from heav'nly Harmony', a division that is clear in the text and is identified by Fowler and Brooks.(20) The first half comprises 30 + 24 + 36 + 34 + 24 + 20 + 32 = 200; the second half 24 + 18 + 36 + 8 + 86 + 28 = 200. Finally, the total length of the first stanza, including the overture and therefore all the instrumental music as well as the 'tuneful' voices, is 486 minims, an important symbolic number to which we shall return.

The symbolism of stanzas 2 and 7, which are linked in various ways pointed out above and by Fowler and Brooks, suggests that they should be taken together, hence 96 + 94 = 190. This is 19 x 10, with 19 representing music (this is the theoretical number of notes possible according to the Guidonian Hand) and 10, as we have seen, representing the Creation (via Pythagoras' tetractys).(21) Hence the role of music (19) in creation (10) is stressed. The portion of stanza 1 that is most apposite to stanzas 2 and 7 is that which finally gets round to linking natural harmony to man, that is, the last two lines ('Through all the compass . . .'; 86 + 28 (symphony) = 114). This is 19 x 6, with 19 still representing music, and 6 representing Man because it was on the sixth day that Man was created; hence, 19 and 6 represent very precisely the 'Diapason closing full in Man'. This 114 is also as 3:5 to the combined length of stanzas 2 and 7 (190).

In stanzas 2 and 7, Draghi has also responded directly to Dryden's focus on the numbers 9 and 7. He emphasizes 9 in his setting of stanza 2 by using phrases of 18 minims for the three portions of this stanza which refer to the 'corded Shell' (lines 1-2, 6, 7-8), while the remaining lines (3-4, 5, 9) are set respectively to 16, 16 and 10, a total of 42, which is a multiple of 7. This also means that the 'Shell' lines (3 x 18 = 54) and the others (42) are as 9:7 (x 6). Stanza 7 also places emphasis on multiples of 9, the first three lines being set to a passage of 36 minims and the next couplet ('But bright Cecilia') to 18 (so 2:1), leaving only the final couplet which reflects the 1:2 proportions of the early part of this stanza: 'An Angel heard' has 10 minims, 'Mistaking Earth' has 20, and finally there is a symphony of 10. This Angel, referring again to the Pythagorean creation number of 10 and its multiple, 20, is presumably also to be taken as the 'tuneful Voice' of stanza 1, which produced a 10 and 20. It should also be noted that stanzas 2 and 7 both end with 10-minim passages.

Stanzas 3 and 4 (142 + 118 = 260) are as 2:1 to stanza 5 (130), while stanza 6 (90) balances the solo portion of stanza 3 (36 + 54 = 90). Incidentally, stanza 4 is indeed 118 (dotted) minims in length: Brennecke rightly states that it consists of eleven statements of a ground which is ten dotted minims in length (= 110 dotted minims);(22) the additional eight dotted minims are short links to get the music from C minor to the three statements in G minor and back again.

The final Grand Chorus, which is linked textually to the first stanza (with references to 'on high' etc.), begins with a 64-minim section for the first four lines (NB 64 again, which was found in the Overture), followed by its symphony of 16 (therefore 4:1), making a total of 80 minims, followed by a trio (32) and final full section (88) which together make 120; this 80:120 makes a large 2:3 proportion, which may be compared with the 2:1 (140:70) at the beginning of the opening stanza. The last movement is further linked to the first in that its length is 200 minims, compared with the total length of the first chorus, excluding the overture, of 400 minims. Thus the double 'Diapason' (or double octave) of the first stanza, with fifteen lines representing the fifteen notes of two octaves, has twice the length of the single octave of the final stanza (400:200), the eighth stanza reflecting the eight notes of a single octave.

As for the overall structure of Draghi's setting, he has a total length for the whole of the overture and stanza 1 of 486 minims, as we have already seen; this is answered by the length of stanzas 2-5 (96 + 142 + 118 + 130 = 486), leaving the remainder of the work (stanzas 6-8) as 90 + 94 + 200 = 384. These numbers (486, 384) are as 81:64 (x 6), or [9.sup.2]:[8.sup.2], and they are also Crantor numbers (sometimes called Platonic/Pythagorean numbers; see Appendix II, below). The point of division comes at 'But oh!' (stanza 6), which agrees with Fowler and Brooks's analysis of the poetry. Even within this, Draghi contrives to make the length of the four 'numerological' verses (i.e., stanzas 4-7, which have, respectively, four to seven lines) 432 minims (118 + 130 + 90 + 94), another Crantor number which provides the missing link between the 486 and 384 identified above, for 432:384 is 9:8 and 432:486 is 8:9. Until the sixteenth century, 384 represented the highest theoretical note in real music (e-la) and is so described not only by Crantor but also by Jacques de Liege in his Speculum musicae of c. 1330.(23) Thus the numbers 384, 432 and 486 represent the actual notes e[double prime] d[double prime] and c[double prime] (see Appendix II for further details).

Draghi sets Dryden's text using structural techniques that were familiar to composers up to 250 years earlier in Italy and England. Crantor numbers and carefully proportioned lengths were used by Dufay and Dunstable and many other fifteenth-century composers almost as a matter of course, especially when writing a work reflecting religious concepts (at that time, Masses, antiphons etc.), and their use continued extensively during the first half of the sixteenth century, and to a slightly lesser extent during the latter half. But we must ask how common it was to write carefully proportioned music in 1687. Draghi may be using the same broad techniques as Dufay or Dunstable, but it is by no means easy to establish a continuous thread through the ages, for there is a gap in our knowledge of the use of proportion and number between about 1610 and the early part of the eighteenth century, a gap which this work helps to fill while at the same time raising many interesting problems. In the early years of the seventeenth century, Monteverdi certainly used a significant number (147) once, in his Vespers of 1610, and in England Gibbons was still using carefully judged proportions in his Madrigalls and Motetts of 1612.(24) In filling the gap between 1610 and the 1680s, it should also be remembered that Gibbons's son, Christopher, was himself a composer, although at present there is no proof that he understood this side of his and his father's craft. We need to discover much more of the musical upbringing of Draghi and his Italian contemporaries, as well as the English into whose world he moved, before we can assume a purely musical motive for setting the text in this way. On the other hand, it is difficult to imagine a musical structure of such complexity as Draghi's emerging from nowhere (and there is sufficient musical idiosyncrasy, such as the Crantor numbers, to make it clear that his inspiration does not stem purely from the structure of Dryden's poem). Whatever the case, the work is clearly both a compliment and a complement to Dryden's formal construction, substituting musical devices when the literary device cannot be imitated directly. Just as Dryden uses his best (literary) gifts to reflect praise back to the Creator, Draghi's best (musical) gifts add a new dimension and use a new human capability (music) to add to the pleasure of the listener and (one hopes) the Creator.

I have already noted that some writers have wondered which contemporaries understood Dryden's structural approach. As we have seen, Shadwell is one poet who seems to have recognized something of it, and I have now shown that certainly one musician, Draghi, understood it well. Was he alone? What about Blow and Purcell? Holman has identified several ways in which Purcell assimilated and developed Draghi's musical ideas, starting only a month after the first performance of this ode with his anthem 'Behold, I bring you glad tidings' (Z.2) for Christmas Day 1687, which picks up the arpeggios of Draghi's opening in its introductory symphony.(25) It is now possible to see that in this work Purcell also uses carefully proportioned structure, together with symmetry (see Appendix III, below). Another possible candidate, from the choice of subject matter, is the occasional ode 'Celestial music did the gods inspire' (Z.322) ('A Song that was perform'd at Mr Maidwell's, a schoolmaster, on the 5th of August, 1689, the words by one of his scholars'),(26) but this work does not use well-proportioned structure with any consistency, though there are some passages which are related to each other; the analysis given in Appendix III, below, demonstrates, rather, that when a work does not contain careful structuring, no amount of playing with the numbers will make it do so. Mr Maidwell's scholar approaches celestial music from a different angle from Dryden, and with rather more slender poetic resource, and consequently Purcell is not perhaps as inspired as Draghi. But as the analysis shows, it seems that in this ode Purcell was not prepared to apply this compositional technique.

However, Purcell also wrote three odes for St Cecilia's Day; perhaps he reserved well-proportioned writing for such texts? Of these, by far the best known is 'Hail, bright Cecilia' (Z.328) of 1692, but there are two smaller works, one of which, 'Welcome to all the pleasures' (Z.339), was written for the 1683 London celebration by the Musical Society, and the other, a Latin ode, 'Laudate Ceciliam' (Z.329), was also written in 1683.(27) Since these three odes, of 1683 and 1692, neatly sandwich Draghi's of 1687, they may show what effect Draghi had. Blow's 1684 ode, 'Begin the song', if it represents the undiluted native tradition, sets the scene usefully, because there is no hint of careful proportional structure in it.(28) Likewise, Blow's 'Ode on the Death of Mr Henry Purcell',(29) even though it is to a text by Dryden and includes a reference to the scale of music up which Purcell was ascending, contains no numerological references.

Purcell's 'Welcome to all the pleasures' (1683; see Appendix I, below) is to a text by Christopher Fishburn which does not address the Creation as Dryden was to do in his 1687 poem. However, although Purcell does not have a profoundly allusive text, he does write a fairly well-proportioned piece. The opening Symphony (144) is 4:3 to stanza 1 (108). Stanza 2 is divided musically into two movements ('Here the deities' and 'While joys') separated by a short link of two minims; the former portion (114) is as 3:2 to the latter (76, including the link passage). Stanza 3 is rather more irregular, although it still makes references to other sections; it opens with 48, which balances the 48's in stanzas 2 and 4, but the 23 appears to be outside any scheme until one takes it with the preceding two passages (13 + 20 + 23 = 56), which now balances the end of the first half of stanza 2 (54 + 2 = 56) and the fifth and final stanza of the work (15 + 41 = 56). The final 8 of this stanza is not excluded, because it may be combined with the following 48 to make another 56. The shape of stanza 4 is very straightforward (48 + 48); the place of stanza 5 (56) in the scheme has already been described.

This scheme is clarified and actually carried further when we separate the instrumental material from the vocal:

[Mathematical Expression Omitted]

In the instrumental category 144:48 is 3:1, and the various 48's are self-evident, but one of them contributes to a 56 (8 + 48) balancing an earlier 56 (54 + 2). In the vocal category, the 60's and 56's are self-evident, and the former are each as 4:1 to the 15 and as 5:4 to the 48, while the 26 is as 1:4 to the last two passages combined (48 + 56 = 104). So it seems that Purcell was able to write a well-proportioned work in 1683.

'Laudate Geciliam' (see Appendix I, below), also composed in 1683 according to the note in its holograph source,(30) is constructed simply, with repeated vocal and instrumental sections punctuating the structure. The opening symphony (26 + 55 = 81) is as 3:1 to the opening verse and chorus ('Laudate Ceciliam' = 27); both recur later in the work, and the verse and chorus does so a third time at the end.(31) Between these punctuating sections are passages of 38 + 6 + 16 ('Modulemini psalmum') and 34 + 14 + 30 ('Dicite virgini') which form sections of 60, 48 and 30; these are interspersed with the refrain of 27 + 81 = 108 giving 5:8:10:18 for 30:48:60:108, which includes 1:2 for 5:10 and 4:5 for 8:10. As with 'Welcome to all the pleasures' and indeed 'From Harmony, from heav'nly Harmony', it is again revealing to separate instrumental music from vocal. The vocal sections are:

27 38 16 27 34 14 30 27

in which 38 + 16 = 54, which is not only as 2:1 to the 27's already noted but also as 9:8 to 34 + 14 = 48, while 38 alone is as 2:3 to the 30 + 27 = 57 at the end. In these punctuating sections of 38 + 6 + 16 and 34 + 14 + 30, prominence is also given to 22 and 44 (38 + 6, 14 + 30, 6 + 16), perhaps referring to St Cecilia's Day as being 22 November.

It is difficult to analyse 'Hail, bright Cecilia' (1692) because of the mensural variety used, notably the time-signatures ranging from 3/8 to 3/2, which make it difficult without extensive further work to decide exactly what should be counted. However, there are moments without attendant mensural problems that show careful structure. In the third movement ('Soul of the world' and 'Thou tun'st', appropriately enough) the chorus (85) is related to the following symphony, soprano solo and chorus (34 + 34 + 34; the further relationship between these three passages is presumably not coincidental) as 5:6 (85:102). This appears to be related to the end of the work, which has 144 + 60 = 204 for 'The fife and all', followed by the final Grand Chorus ('Hail, bright Cecilia'; 50 + 42 + 28 + 50 = 170), this 204 and 170 being related to the earlier 102 and 85.

In 'Hail, bright Cecilia', nevertheless, as in 'Celestial music did the gods inspire', it is not clear that Purcell uses well-proportioned structure as a deliberate and consistent technique, despite the appearance of some internally-related lengths. In 'Behold, I bring you glad tidings' and the two odes 'Welcome to all the pleasures' and 'Laudate Ceciliam', on the other hand, it appears that he does lay out his structure with balances, symmetry and careful proportion. Clearly, an overall view of Purcell's attitude to this composing technique must await further research. Similarly, although the use of numerology (as distinct from the well-judged proportion familiar to medieval musicians) in the eighteenth century is certainly recognized, notably in music by Bach, it does not at present seem that Handel used the technique; Handel set Dryden's 'Song for St Cecilia's Day' in 1739, but as far as I can see he shows no sign of having any knowledge either of Draghi's setting or of Dryden's literary subtleties.

We should finally consider how Draghi came to set Dryden's poem at all, for despite being described by John Evelyn as an 'excellent and stupendious Artist' on the keyboard(32) he was hardly in the mainstream of the typical 'English' Chapel Royal side of English musical life. He is assumed to have come to England soon after the Restoration of Charles II. During Charles II's reign a Catholic chapel was kept for his wife, Catherine of Braganza, as indeed it had been at the beginning of the century for Charles I's wife, Henrietta Maria. Draghi was made first organist of the queen's chapel in 1673 over the head of Locke, and organist of James II's private 'Popish' chapel in 1687, and it may have been on the strength of his rising star, combined with that of the Catholic party, that he was selected to compose the music for the poem of his fellow Catholic, and that he was able to engage the services of the best Chapel Royal soloists (and presumably the complete Chapel for the full passages). He was gradually assimilated into the musical life of the court and country, and it is notable that he stayed on in England even when the Catholic chapel was closed at the accession of William and Mary in 1688, ending his life on a pension from Queen Anne. It is difficult to state, without substantial further research, whether Draghi was being deliberately old-fashioned in his structural approach or was setting the text in the only way he knew; few of his works survive, and little is known of his training in Italy. In 1687, Dryden had recently converted to Catholicism, so perhaps we may see a political dimension in this poem, the choice of its poet and composer representing a temporary success for the Catholic party. It has been suggested that 'political and religious concerns may have been in Dryden's mind when he wrote this song' and that the notion that 'Musick shall untune the Sky' reflected the political disharmony untuning the reign of James II.(33) The announcement in December 1687 of the queen's pregnancy and the birth in June 1688 of a Catholic heir (James, who eventually became the Old Pretender) brought down the curtain on James II's reign and the Catholic party. Further research is needed to determine whether this untuning of the sky also marked the end of this kind of well-proportioned compositional technique.



Crantor Numbers

Crantor (c.340-c.280 BC) was a Greek philosopher-mathematician who brought together the theories of both Pythagoras (c.580-c.500 BC) and Plato (427-347 BC). As is the case with many Greek philosophers, few of his actual writings survive, but he is fairly copiously quoted and referred to by later writers, notably Plutarch (first century AD). Crantor's numbers are derived from Pythagoras' tetractys - 1, 2, 3, 4 - which was itself the source of Plato's sequence 1, 2, 3, 4, 9, 8, 27; the latter was used to describe the creation of the universe in the Timaeus.(1) Plato also describes how these lengths of 'soul-stuff' (i.e., the material out of which the fabric and soul of the universe were made) were filled in by the creator with carefully proportioned strips of matter - thus: 1, 4/3, 3/2, 2 - corresponding to the physics of the musical intervals of a perfect fourth (4:3), perfect fifth (3:2), and octave (2:1). In due course, the intervening notes of the scale were added, providing the musical metaphors for creation, the universe, the harmony of the spheres etc. Plutarch explains how and why Crantor multiplied this sequence by 6, so that whole numbers, rather than fractions, represent the fourth and fifth degrees of the scale.(2) Thus, instead of Plato's 1, 4/3, 3/2, 2 we find 6, 8, 9, 12, which allowed a new number sequence to be developed, deriving the numbers for the intervening degrees of the scale (such as the tone, 9:8) and extrapolating these numbers into further octaves.(3) This sequence used to be called Pythagoreo-Platonic before it was realized that Crantor was responsible: 'Whenever one meets ratios of the series etc. it is safe to presume that this was not casual, but the result of reflections which directly or indirectly depend on the Pythagoreo-Platonic division of the musical scale'.(4) These numbers are extrapolated through further octaves, each replicating the proportions of the initial 6:8:9:12 and with further degrees of the diatonic scale (and therefore intervening numbers and proportions) entering as they become whole numbers. The octave beginning 384 (= 64 x 6) continues 432, 486, 512 (= 64 x 8), 576 (= 64 x 9), 648, 729, 768 (= 128 x 6, an octave lower than 384); it is the first to have all eight notes of the diatonic scale (the last degree, the major seventh finally reaching a whole number, 1458/2 or 729).(5) The full system is given in Table I, below.



Two More Purcell Works

The counting criteria (minims or dotted minims) follow those adopted in Appendix I, above. As before, an asterisk indicates instrumental music.

(a) 'Behold, I bring you glad tidings'
Symphony                    12(*) + 56(*) + 56(*)

Behold I bring you          56                      B verse

Glad tidings of great joy   62 + 36(*)              CtTB verse

Glory to God on high        58 + 24(*)              verse/full

Alleluia                    48                      full

Glory to God on high        14                      full

The correct version of the extended opening symphony is found in only one source (the Gostling Manuscript, see n. 12, above; facs. edn., Austin, Texas, & London, 1977, pp. 95-104 (front end)); that of London, Royal College of Music, MS 2011 lacks one breve's worth of music: the fugal portion is repeated (56 + 56), and for once the repetition appears significant. The overall scheme is:
instr.    12    56    56              36        24

chor.                      56    62        58        48    14

The opening symphony (124) is as 2:1 to the closing Alleluia (62), and the opening bass verse (56) picks up the fugato portion of the Symphony (56). Between the 124 and the 62 are two combined passages of 118 (56 + 62 followed by 36 + 58 + 24, the latter itself exhibiting a 3:2 ratio between 36 and 24). Alongside this division is a parallel arrangement whereby the symphony and opening verse (124 + 56 = 180) is balanced by the next sections (62 + 36 + 58 + 24 = 180), leaving the final chorus of 62 outside the scheme. These two 180's (= 360) represent perfection, the circle closed, in medieval and Renaissance allusive number symbolism, which is appropriate for a Christmas anthem. The second 180 comprises choral passages (62 + 58 = 120) alternating with their symphonies (36 + 24 = 60). Thus, multiples of 12 and 14 define all the lengths (12, 24, 36, 48, 60, 120, 180; 14, 56).

(b) 'Celestial music did the gods inspire'


The opening symphony is from Purcell's coronation anthem 'My heart is inditing' (1685); each half is to be repeated, and actually two minims are lost in the second-time bar, so the length would be 52 + 50 + 42 + 42 if repeated, but as before I take a single statement as my basis. 'Her charming strains', if well proportioned, would be 56 + 28, but an extra dotted minim appears at the end, calling into doubt whether even this simple 2:1 was intended. In 'Whilst music' the ritornello is the same music as that of the sung portion, except that one section is not marked to be repeated, a possibility which is entirely plausible in musical terms; in this event, the length of the ritornello would be 16 + 32 = 48 instead of 16 + 16 + 32 = 64 (both lengths are listed above). The final full section of 'Let Phillis', if well proportioned, would be 24 + 36, but it is actually 25 + 36 = 61, as marked. If by a leap of imagination we adjust these minor discrepancies and take the supposed intentions, then we still have to indulge in some imaginative combining, but we can find a 1:2 for the 70 (the last three segments, 48 + 32 + 60 = 140), while the 28 for 'Celestial music' is related to the 56 and assumed 28 of 'Her charming strains'. However, we are still without a relationship for the opening symphony, for 'Hence he by right' and for 'Whilst music did improve', so our bid must be regarded as a failure. There is, however, the very faintest possibility that Purcell has introduced some half-understood reference to Draghi's work, for the length of the opening Symphony (94), and the lengths 70 and 140, mentioned above, are found in Draghi's 'Song for St Cecilia's Day'. It could be argued that the symphony, coming as it does from' another work, should not need to be regarded as part of the structure, but in that case a foreign piece should not be imported in the first place. Thus this ode shows no use of careful proportion.

1 See in particular Jacob Obrecht: Opera omnia; Missae, vii, ed. Marcus van Crevel, Amsterdam, 1964, pp. lx-lxxvii; Margaret Vardell Sandresky, 'The Continuing Concept of the Platonic-Pythagorean System and its Application to the Analysis of Fifteenth-Century Music', Music Theory Spectrum, i (1979), 107-20. The chart in this appendix is based on Sandresky's.

2 Plutarch, On the Generation of the Soul in the Timaeus (Peri tes en Timaioi psychogonias), 1027F, 1017C-1020D; see Plutarch's Moralia, xiii/1, trans. & ed. Harold Cherniss, Cambridge, Mass., & London, 1976, pp. 269-303.

3 The interval of the tone is derived from two fifths (a ninth) - so [(3/2).sup.2] = 9/4 - brought back within the same octave: so 9/4 [divided by] 2 = 9/8. A sixth is three fifths treated in the same way, and so on through the circle of fifths until the major seventh, v which is five fifths (two octaves and a seventh) - [(3/2).sup5] = 243/32 - brought back by two octaves: so 243/32 [divided by] 4 = 243/128.

4 Rudolf Wittkower, Architectural Principles in the Age of Humanism, London, 1949, p. 112.

5 729, or 1458/2, is of course 243/128 x 6 = 1458/128 x 64, just as 384 is Plato's 1 multiplied by Crantor's 6 multiplied by 64 through successive octaves.

1 Ernest Brennecke Jr., 'Dryden's Odes and Draghi's Music', Publications of the Modern Language Association, xlix (1934), 1-36 (I cite the reprint in Essential Articles for the Study of John Dryden, ed. J. Swedenberg Jr., Hamben, Connecticut, 1966, pp. 425-65); Jay Arnold Levine, 'Dryden's "Song for St Cecilia's Day, 1687"', Philological Quarterly, xliv (1965), 38-50; Alastair Fowler & Douglas Brooks, 'The Structure of Dryden's Song for St Cecilia's Day, 1687', Essays in Criticism, xvii (1967), 434-47 (I cite the reprint in Silent Poetry: Essays in Numerological Analysis, ed. Alastair Fowler, London, 1970, pp. 185-200). This is built upon literary techniques found earlier in works such as Spenser's The Faerie Queene, and some of the same features are found in Shadwell's 1690 'Song for St Cecilia's Day'. See also Alastair Fowler, Spenser and the Numbers of Time, London, 1964; H. Neville Davies, 'The Structure of Shadwell's A Song for St Cecilia's Day, 1690', Silent Poetry, ed. Fowler, pp. 201-33. A few additional remarks about Dryden's poem and Draghi's music are to be found in James Anderson Winn, Unsuspected Eloquence, New Haven & London, 1981, pp. 218-20, 224-8. For a recent discussion of proportioned literary composition, see Maren-Sofie Rostvig, Configurations: a Topomorphical Approach to Renaissance Poetry, Oslo & Oxford, 1994.

2 Plato, Timaeus, trans. H. D. P. Lee, Harmondsworth, 1965. See also Plutarch, On the Generation of the Soul in the Timaeus (Peri tes en Timaioi psychogonias); see Plutarch's Moralia, xiii/1, trans. & ed. Harold Cherniss, Cambridge, Mass., & London, 1976; pseudo-Plutarch, De musica, Greek Musical Writings, i: The Musician and his Art, trans. Andrew Barker, Cambridge, 1984, pp. 205-57; Pietro Bongo, Mysticae numerorum significationis liber, Bergamo, 1585 (expanded edn. entitled De numerorum mysteria, Basle, 1618). Modern studies of this subject include Christopher Butler, Number Symbolism, London, 1970; Vincent F. Hopper, Medieval Number Symbolism, its Sources, Meaning and Influence on Thought and Expression, New York, 1938; Raymond Klibansky, The Continuity of the Platonic Tradition during the Middle Ages, London, [1939]; John Macqueen, Numerology, Edinburgh, 1985; Heinz Meyer, Die Zahlenallegorese im Mittelalter: Methode und Gebrauch, Munich, 1975. Studies relating the subject to musical compositions include Brian Trowell, 'Proportion in the Music of Dunstable', Proceedings of the Royal Musical Association, cv (1978-9), 100-141; Jacob Obrecht: Opera omnia; Missae, vii, ed. Marcus van Crevel, Amsterdam, 1964, introduction; and Margaret Vardell Sandresky, 'The Continuing Concept of the Platonic-Pythagorean System and its Application to the Analysis of Fifteenth-Century Music', Music Theory Spectrum, i (1979), 107-20.

3 Davies ('The Structure of Shadwell's A Song for St Cecilia's Day, 1690', p. 201) doubts the significance of 10, but the evidence seems clear.

4 Ibid., pp. 206-19.

5 Winn, Unsuspected Eloquence, p. 224; Earl Wasserman, 'Pope's Ode for Musick', English Literary History, xxviii (1961), 163-86. See also Brennecke, 'Dryden's Odes and Draghi's Music', p. 465 n. 21, referring to A. W. Verrall, Lectures on Dryden, Cambridge, 1914, pp. 183-5.

6 Winn, Unsuspected Eloquence, loc. cit.

7 'The Structure of Shadwell's A Song for St Cecilia's Day, 1690', p. 204.

8 Brennecke, 'Dryden's Odes and Draghi's Music', p. 446.

9 Ibid., p. 456. Of course, Brennecke was writing many years before scholars began to study the detailed numerology of poetry, though in his reference to Verrall, who was writing in 1914, he reminds us that this approach has a venerable modern history.

10 Winn, Unsuspected Eloquence, pp. 227-8.

11 Franklin B. Zimmerman, Henry Purcell, 1659-95: his Life and Times, 2nd edn., Philadelphia, 1983, p. 147.

12 Peter Holman, Four and Twenty Fiddlers: the Violin at the English Court, 1540-1690, Oxford, 1993, p. 426. I am very grateful to Peter Holman for comments, suggestions and help in various parts of this study. Other copies are at London, Royal College of Music, MSS 1097 and 1106; University of Austin, Texas, Humanities Research Center Library, pre-1700 MS 85 (the Gostling Manuscript); Oxford, Bodleian Library, MS Tenbury 1226 (where it is entitled 'St Ciscaelias Song by [Sen.sup.r] Baptist'), and (incomplete) London, British Library, Add. MS 33287, ff. [221.sup.v]-[229.sup.v] (the latter is the last page of the manuscript).

13 Brennecke describes the music with generous examples showing illustrative effects. As far as I know, there is no generally available modem edition, although there is a good recording by the Playford Consort and the Parley of Instruments, directed by Peter Holman and Richard Wistreich (Hyperion, CDA 66770).

14 Thomas Morley, A Plaine and Easie Introduction to Practicall Musicke (London, 1597), ed. R. A. Harman, London, 1952, p. 244.

15 Holman, Four and Twenty Fiddlers, p. 426.

16 See Fowler & Brooks, 'The Structure of Dryden's Song for St Cecilia's Day, 1687', pp. 188-9, referring to Marin Mersenne's Harmonic universelle (Paris, 1635).

17 Holman, Four and Twenty Fiddlers, pp. 426-9.

18 Martin Adams, Henry Purcell: the Origins and Development of his Musical Style, Cambridge, 1995, p. 44.

19 In all sources there are double bar-lines between the introduction and the fugue and at the end of the fugue, which at this time is usually alone sufficient to denote repetition. Whether repeated or not, however, the structure clearly depends on the length of a single statement as the significant number.

20 Fowler & Brooks, 'The Structure of Dryden's Song for St Cecilia's Day, 1687, p. 191.

21 See Jacob Obrecht: Opera omnia; Missae, vii, ed. van Crevel, pp. cv, lxi. Although there are twenty notes in the compass gam-ut to e-la (G to e"), there are only nineteen countable joints of the hand, and so the twentieth note (e-la) was regarded as being outside the Guidonian Hand proper.

22 Brennecke, 'Dryden's Odes and Draghi's Music', p. 447.

23 Jacobus Leodensis (Jacques de Liege), Speculum musicae, ed. Roger Bragard ('Corpus scriptorum de musica', iii), Rome, 1955-68, pp. lxxx-lxxxi.

24 For Monteverdi, see Roger Bowers, 'Some Reflection upon Notation and Proportion in Monteverdi's Mass and Vespers of 1610', Music & Letters, lxxiii (1992), 347-95, at p. 394. For Gibbons, see Roger Bray, 'Music and Musicians in Tudor England: Sources, Composition Theory and Performance', The Blackwell History of Music in Britain, ii: The Sixteenth Century, ed. Roger Bray, Oxford, 1995, pp. 1-45, at p. 21 (also, p. 328 n. 60).

25 See Peter Holman, Purcell, Oxford, 1994, pp. 170-72, 176-7; 'Behold, I bring you glad tidings', The Works of Henry Purcell, xxviii, ed. Anthony Lewis & Nigel Fortune, London, 1959 (repr. 1967), 1-27. I am grateful to Nigel Fortune for pointing out that the rediscovery of the Gostling Manuscript provides a correct version of the opening symphony by the inclusion of an extra bar's music after bar 14 of the published edition, thus solving a puzzle that had vexed him at the time of editing. A revision of this volume in The Works of Henry Purcell edited by Robert Manning is forthcoming. In an early version of this essay, I stated (following the printed version of the opening symphony that was one bar (two minims) short) that this anthem showed no use of carefully proportioned structure; fellow counters will be encouraged to know how a rediscovered bar can affect one's assessment.

26 The Works of Henry Purcell, xxvii, ed. Arnold Goldsbrough, London, 1957 (repr. 1966), 29-58.

27 'Hail, bright Cecilia', The Works of Henry Purcell, viii, ed. Peter Dennison, Sevenoaks, 1978; the other two St Cecilia Odes are in The Works of Henry Purcell, x, ed. Bruce Wood, London & Sevenoaks, 1990. A third, smaller work, 'Raise, raise the Voice' (also in The Works of Henry Purcell, x), is now thought not to be a St Cecilia ode.

28 London, British Library, Add. MS 33287, ff. 103-[111.sup.v], ed. H. Watkins Shaw, London, 1950.

29 Ed. Walter Bergmann, London, [1962].

30 London, British Library, RM 20.h.8, ff. 190-188 (vol. reversed).

31 In the middle entry of this material the symphony follows the verse, whereas at the beginning it had preceded and led straight into it. The result is an extra cadential beat (56 instead of 55), but presumably the music is intended to be regarded as the same each time. The music is not written out in full; the score simply says: 'Laudate Ceciliam as before then the first [symph.sup.y] & so on'. At the end of the work, again the music is not written out, but the rubric ('Laudate Ceciliam as before to conclude') probably implies that only the verse without the symphony is required.

32 The Diary of John Evelyn, ed. E. S. de Beer, London, 1955, iv. 49.

33 James Anderson Winn, John Dryden and his World, New Haven & London, 1987, pp. 429-30.
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