Early Music, Vol. xxxv, No. 4 © The Author 2007. Published by Oxford University Press. All rights reserved. doi:10.1093/em/cam088, available online at www.em.oxfordjournals.org

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A ccording to their dedication, Domenico Scarlatti ’ s Essercizi per gravicembalo , which

number 1 to 30 in Kirkpatrick ’ s catalogue and were published in London in 1738 or 1739, were ‘ born under the highest auspices ’ of John V of Portugal, in the service of the king ’ s daughter Maria Barbara and brother Antonio, and therefore between 1719 and 1727, during Scarlatti ’ s residence there. 1

The apparent lack of organization in the Esser-cizi compared to the later Venice and Parma manu-scripts, 2 where most of the sonatas have been arranged in twos or threes with a common tonic, has led almost all writers to the conclusion that the single pair and triptych which do occur ( k9- 10 and k 12 - 14, see Table 1 ), are coincidental, if they acknowledge them at all. 3 If major and minor are lumped together, D and G are the most plentiful keys in the Essercizi , with eight and six examples respectively, so that coincidental groups would most likely involve these keys, and this may be the underlying reason for the general disinclina-tion to accept the two groups. On the assumption, implicit in the earlier discussions, that the collection was randomly assembled, i.e. that all arrangements were equally likely, it is possible to test the hypothesis that the two groups are due to chance by determining the mathematical probability of such an occurrence. It is stipulated beforehand that the hypothesis will be questioned if the probability is less than 0.05 or 1/20 (best read in this context as ‘ 1 in 20 ’ ). It is found that the probability of exactly one pair in D and one trip-tych in G is 0.021 or 1/48. 4 Not only, therefore, was the rejection of these groups ill-considered, but there are

also several manifestations of ordering, some clearly deliberate, which have never been recognized.

If the collection is broken down into two halves, the first half is found to contain four (27 per cent) major keys, the second, nine (60 per cent), this lat-ter proportion being almost identical to that in Ven-ice XV (1749).The probability of including just four major-key sonatas in the first fifteen by chance if the pieces were arranged randomly with respect to mode is 1/25 (again k 30 is left out). In addition, the key sig-natures in the second half tend to be more complex, all but k 17, 18 and 30 having at least two accidentals in the signature, whereas k 11 is the only piece in the first half with more than one. The probability of this distribution resulting from random arrangement with respect to key signature is 1 in 50,000.

These discrepancies between the two halves may reflect an earlier composition date for k 1 – 15, alow ratio of major keys being more typical of Scarlatti ’ s earlier compositions, 5 and simpler key signatures being more representative of an archaic style generally.

Another, more important, aspect of organization, and one which may be in part responsible for the above discrepancies, is represented by various key groupings, whose nature again differs between the two halves.

It will be seen from Table 1 that the first eight sonatas form two four-membered sequences whose tonic keys correspond in all but the second position. This particular order of keys has no obvious a priori significance, but given the first four sonatas in their present order, the probability of the next four, cho-sen randomly from the remaining eleven, giving the

❖ observation ❖

Carl Sloane

A fresh look at Domenico Scarlatti ’ s Essercizi per

gravicembalo , and the ‘ tremulo di sopra ’

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same sequence in positions 1, 3 and 4 is 1/264 if posi-tion 2 can be occupied by any different key, 1/440 if by a major key and 1/1320 if by F major.

k 9 – 12 may constitute a third group with the same outer keys as the previous two, but this group also involves the pair in D minor and the triptych in G, and there are several probabilities which may be determined, but they are more difficult to inter-pret. Assuming k 1 – 8, with D and G minors in their observed positions, the probability of the next four, chosen at random from the remaining seven, hav-ing D and G minors in their observed positions, is 1/105. On the other hand, the probability of the D minor pair and the triptych in G being formed upon random arrangement of the last seven sonatas, if no restrictions are placed on their position, is 1/18, which is too high to reject the hypothesis that they are due to chance, and there is some question in my mind as to what significance, if any, can be given to the probability of these two groups occupying their observed positions. The value 1/105 is small enough to suggest volition, and it is possible that Scarlatti created the pair and triptych within or overlapping a four-membered group to give the player a choice of groupings.

In the second half of the volume, there are two couples in E major – D major. If one couple is assumed, and it is required that the two couples and the remaining sonata in D be isolated from one another, as they are, the probability of chance occur-rence of a second couple is 1/24.

Table 1 Essercizi per gravicembalo , showing Kirkpatrick number and key

Kirkpatrick no. Key

Kirkpatrick no. Key

Kirkpatrick no. Key

1 d 11 c 21 D 2 G 12 g 22 c 3 a 13 G 23 D 4 g 14 G 24 A 5 d 15 e 25 f 6 F 16 B 26 A 7 a 17 F 27 b 8 g 18 d 28 E 9 d 19 f 29 D 10 d 20 E 30 g (fuga)

In addition, there are two exactly analogous tri-ples, k 16 – 18 and k 23 – 5, which can be expanded to quadruples if mode is disregarded. Since the key sequence has an a priori significance, it is legitimate to calculate the probability of both groups rather than just that of the second given the existence of the first. For the two triples, this probability is 1/4000, for the quadruples, 1/360,000. Given the triples, the probability that sonatas in F minor and A major would each end up where they do by chance is 1/56 if the E – D couples are also assumed in advance, which they should be if the triples are assumed.

The above probabilities are small enough to show beyond reasonable doubt that the Essercizi have been extensively organized, and to obviate any argu-ment which attempts to use their supposed random arrangement as proof that the pairs in Venice and Parma are due to the scribe (see Boyd ’ s caution in note 3). The groupings themselves would seem to be of an experimental nature, and one is bound to wonder if they are part of Scarlatti ’ s ‘ ingenious jest-ing with Art ’ ; those in the first half may be founded in modal theory — D minor is tono primo , and G minor tono primo irregolare . 6 The rationale in k 16 - 18 and k 23 – 5, or the corresponding quadruples, seems obvious, at least to a point, but both they and the E – D couples may reflect a desire to create contrast by exploiting the temperament. Until someone presents a more convincing argument to the contrary than any I have seen so far, I am compelled to believe that Scarlatti used mean-tone, 7 and although some writ-ers are dismissive of what they regard as hair-split-ting divisions of the comma, I doubt whether any of them would extend their point of view to mean-tone. There is also an association between E and D majors in Venice, particularly in the early volumes, and in the later volumes E major tends to be found in conjunction with A major/minor. The two obser-vations suggest that there may be a higher level of organization in Venice and Parma as well.

The groupings in the Essercizi can probably be considered the immediate forerunners of the pairs in Venice and Parma, and the precedent of the Esser-cizi may help to explain why each member of a pair retains its own title and number, in contrast to the two-movement Italian sonata, which Sheveloff estimates to have arrived in Spain around 1745, and which he thinks may have provided the motivation

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for Scarlatti ’ s sonata pairing, while not causing him to discard the separate title and numbering. 8

The groups would have gone unnoticed if they had not been duplicated in some form. While they may have been inherently more apparent to Scar-latti ’ s contemporaries, it still seems strange that he made no attempt to define them clearly. Duplica-tion may always have been the key to their identifi-cation, and it should be noted that there are very few explicit indications of pairing in Venice and Parma either (which may, in fact, have been intended for publication), and often, especially in the earlier vol-umes, the pairs are not consistent from one source to the other, even when the members are explicitly linked in one of them. 9 There does not appear to be any relation between the groupings in the Essercizi and the inconsistent handling of the repeat signs, 10 or the variable compass in the bass.

The ‘ tremulo di sopra ’

Some readers will recall a short discussion in this journal of a passage in a Portuguese treatise of 1764, which explains the ‘ tremulo ’ , an ornament used by Scarlatti in about two dozen of his sonatas, mostly in the early volumes. 11 The treatise makes a clear dis-tinction between the tremulo and the trill, stating that the tremulo uses the lower auxiliary, whereas

the trill always uses the upper. Sheveloff and Neu-mann have arrived at much the same interpretation reasoning from 17th-century Italian practice.

The treatise, however, leaves open the meaning of ‘ tremulo di sopra ’ , which occurs only once in the entire corpus (Venice xv -6, k 96). Sheveloff and Neu-mann are convinced that in this particular case the upper auxiliary is required, but they do not explain why Scarlatti chose this method of notation instead of a simple trill sign with ties, as in k 82. 12 In my opinion, ‘ di sopra ’ should be understood in the sense of ‘ di sopra in sotto ’ ( ‘ from above downward ’ ), by analogy with ‘ di sotto in su ’ ( ‘ from below upward ’ ), which is seen, for example, in the writing of the 20th-cen-tury novelist Alberto Moravia. This interpre tation is supported by a passage in a 17th-century Neapolitan treatise cited in a more recent issue of Early Music : the article ’ s author translates the phrase ‘ nella sec-onda linea di sopra ’ as ‘ on the second line down ’ . 13

It is a curious fact that the ‘ tremulo di sopra ’ represents the first appearance of the tremulo in any form in Venice, and the suspicion thus arises that the qualifying phrase has more to do with the sonata ’ s location than with the ornament itself. In other words, this tremulo is probably identical with the normal tremulo, and the qualifier is nothing more than a prompt on the first occurrence to emphasize the distinction between tremulo and trill.

Carl Sloane graduated in Pharmacy from the University of Toronto, but worked for many years as a translator. He is an amateur harpsichordist and has written on theoretical and practical aspects of key-board temperament in various journals, including Harpsichord and Fortepiano , The Diapason and Journal of Sound and Vibration. carlsloane@yahoo.ca

1 G. Doderer, ‘ New aspects concerning the stay of Domenico Scarlatti at the court of King John V (1719 – 1727) ’ , in the preface to Libro di tocate per cembalo: Domenico Scarlatti (Lisbon, 1991), pp.7 – 52, cited in W. D. Sutcliffe, The keyboard sonatas of Domenico Scarlatti and eighteenth-century musical style (Cambridge, 2003), p.69, and in J. H. van der Meer, ‘ Os instrumentos de tecla na propriedade de D. Maria Bárbara, Rainha de Espanha ’ , Revista Portuguesa de Musicologia , ii (1992), pp.161 – 9, at p.161.

2 Two series of volumes copied by professional scribes, starting in 1742 with what is now referred to as Venice xiv . The numbers xiv and xv attached to the two earliest volumes in Venice are not original.

3 R. Kirkpatrick, Domenico Scarlatti (Princeton, 1953, R 1983), pp.141 – 2, 162; H. Keller, Domenico Scarlatti, ein Meister des Klaviers (Leipzig, 1957), p.34; J. Sheveloff, ‘ Domenico Scarlatti: tercentenary frustrations ’ , Musical Quarterly , lxxi (1985), pp.399 – 436, at p.431; C. Rousset, ‘ Approche statistique des sonates ’ , in Domenico Scarlatti: 13

recherches , Cahiers de la Société de Musique Ancienne de Nice, no. 1 (Nice, 1985), pp.68 – 87, at p.71; F. Hammond, ‘ Domenico Scarlatti ’ , in Eighteenth-century keyboard music , ed. R. L. Marshall (New York, 2/2003), pp.154 – 90, at p.181; M. Boyd, Domenico Scarlatti: master of music (London, 1986), p.165; M. Flannery, A chronological order for the keyboard sonatas of Domenico Scarlatti (1685 – 1757) (Lewiston, NY, 2004), p.192n (p.190 in a later printing). Hammond is undecided about the groups, Boyd seems to accept them, but even he hedges, remarking

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that ‘ the ordering . . . cannot be taken as proof that the later pairs did not originate with the composer ’ . Flannery, besides not accepting the groups, mis-states the overall keyboard compass required by the Essercizi (p.48). For a recent expression of doubt as to Scarlatti ’ s role in the pairings see Sutcliffe, The keyboard sonatas of Domenico Scarlatti , p.371.

4 The probability of a chance event, such as the adjacency of two D minor sonatas, or a tossed coin coming up heads, can be expressed as a decimal or rational fraction between 0 and 1, 1 being certainty, or as a per cent from 0 to 100. Thus 0.05, 1/20 and 5 per cent are equivalent ways of stating the same probability. For the reader with betting proclivities, a probability of 1/20 corresponds to odds of 19 to 1 against. This particular value is the one at or below which it is generally felt that chance can reasonably safely be rejected as the cause (see J. S. Rosenthal, Struck by lightning (Toronto, 2005), p.101). The calculation is based on the first 29 sonatas only, since the position of k 30, a fugue, is undoubtedly deliberate (see Boyd, Domenico Scarlatti , p.288). The basic approach used was to divide the total number of distinguishable arrangements into the number of distinguishable arrangements possible when the relevant conditions are satisfied.

5 C. Sloane, ‘ Some new reflections on Domenico Scarlatti ’ s sonatas ’ , Revista de Musicología , xxiv (2001), pp.107 – 13. It is unlikely that the second half is exactly contemporary with Venice xv , despite the similar proportions of major and minor keys. Most (88 per cent) of the sonatas in Venice xv ascend to d � � � , while none in the Essercizi rises above c � � � . If Scarlatti made his selection from a pool consisting only of Venice xv (42 sonatas, 5 to c � � � ) plus the 14 sonatas from the Essercizi , the probability of his choosing 14 sonatas ascending no higher than c � � � is 1 in 500 million if the sonatas were drawn randomly with respect to compass. This is a model that did not occur to me in my earlier article, and results in a much higher probability than the one given there, but one which is still

vanishingly small. The argument that Scarlatti deliberately chose pieces not exceeding c � � � in order to satisfy purchasers with a narrow-compass harpsichord is unconvincing, since nine, almost a third of the collection, go below C in the bass, which is probably the lowest note that Scarlatti could count on a purchaser having. The overall compass of the Essercizi is 54 notes if a chromatic keyboard is assumed, 53 otherwise, G � not being required.

6 See ‘ Studio primo ’ , in Francesco Durante, Sonate per cembalo, divise in studii e divertimenti (Naples, 1732). Vicente Rodriguez ’ s Libro de Tocatas para címbalo (Ms. 1744) also opens in D minor, then ascends chromatically, omitting those keys not suited to the temperament, probably with some allowance for retuning (sonatas in A , B and D majors are included).

7 C. Sloane, ‘ The case for meantone in Scarlatti ’ , Continuo , xvi/6 (1992), pp.15 – 16; Sloane, ‘ Some new reflections on Domenico Scarlatti ’ s sonatas ’ ; Sloane, ‘ The persistence of meantone in the Iberian peninsula ’ , Revista de Musicología , xxv (2002), pp.471 – 5.

8 J. Sheveloff, ‘ Domenico Scarlatti, tercentenary frustrations ’ , at p.431.

9 In Venice xv , for example, k 99 and 100 are unified by a ‘ Volti subito ’ and subsumed under one number, yet in Parma they appear as two singletons, and k 99 also appears in Venice ii as the third member of a triptych which does not include k 100. The almost invariable number of 30 sonatas per volume, particularly in Parma, has been seen as an indication that Scarlatti planned on publishing the entire series (see Boyd, Domenico Scarlatti , p.165). There are even a couple of places near the end of the catalogue where the pairing has been sacrificed on this account, illustrating once more the labile nature of the pairs.

10 See P. Cienniwa, ‘ Repeat signs and binary form in François Couperin ’ s Pièces de claveçin ’ , Early Music , xxx (2002), pp.94 – 103, at p.102.

11 C. Sloane, ‘ Domenico Scarlatti ’ s “ tremulo ” ’ , Early Music , xxx (2002), p.158. Two citation errors should be

corrected: ‘ intende ’ should read ‘ entenda ’ , and ‘ espresso ’ should read ‘ expresso ’ .

12 J. Sheveloff, ‘ Domenico Scarlatti: tercentenary frustrations ’ , p.102; F. Neumann, Ornamentation in Baroque and post-Baroque music (Princeton, 1978), pp.352 – 4. See also E. Fadini, ‘ La grafia dei manoscritti scarlattiani: problemi e osservazioni ’ , in Domenico Scarlatti e il suo tempo , Chigiana xl (Florence, 1985), pp.183 – 206, at p.205. Fadini not only favours the upper auxiliary, she also advocates an upward shift of the ornament as each higher note enters, but Scarlatti ’ s failure to use standard trill signs would be even more surprising in this case.

13 S. Picerli, Specchio secondo di musica (Naples, 1631), p.192, cited in A. Johnstone, ‘ “ High ” clefs in composition and performance ’ , Early Music , xxxiv (2006), pp.29 – 53, at p.48.

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