Two Mozart Fingerprints
Related to the Becking Conducting Curve

Par 1 This paper constitutes a step along the way towards a larger objective: to differentiate selected composers' musical personalities on the basis of a study of their scores. The selected composers are ones usually considered to be "great" (which might be defined as those who have been able to embody in their music a distinctive personality that is considered to have general value). Other composers, who may have adopted a more formulaic or prosaic approach to composition, perhaps deriving their work from the examples of the front-runners, will not be dealt with, for to distinguish their work from that of the leaders is a special task that would require a close examination in each of the innumerable cases, and by definition results obtained for those composers would have less value. We are thus spared the impossible task of dealing with all of music; but the amount to be dealt with is nevertheless very large.

Par 2 To assist in processing the large amount of data, the notion of a musical "fingerprint" will be adopted. A fingerprint of a given composer is defined here as a compositional pattern occurring in many of the composer's scores and in few scores of other composers; it will be carefully specified in each case and comprises a few notes typically covering about one bar of music. It may happen that several such patterns are found for a given composer and act jointly to distinguish his music from that of other composers. ¹   Further, a fingerprint might not occur often in any one movement, for a single occurrence can place its stamp on a whole movement.

Par 3 It is desired not only to find and document composers' fingerprints, which may be of interest for their own sake, but also to relate these to Becking's (1928) notion of composer-specific conducting shapes. That notion, which will be explained more fully in the next section, has allowed the search for fingerprints to proceed in a directed rather than a haphazard manner. The conducting shape is considered as not fully revealed in any one score examined in isolation, but as latent in the composer's collected scores. Becking dealt on a more or less intuitive basis with several well-chosen individual excerpts but not with a composer's output as a whole, so he was not in a position to point to specific features of the scores that imply the shape of a curve. Evidence implying the composer's conducting curve is deeply hidden in his scores, and involves innumerable features of them; the present attempt to make some of that evidence explicit can hope to produce only relatively crude results, yet the attempt seems worth making. It should be noted that it is not sufficient for the present purpose to find general features typical of the composer's output—for instance, the feature of Mozart's music that its textures are especially spare—for while such features may imply something of a curve's quality they would not imply its shape.

Par 4 A fingerprint was recently proposed for Schubert and documented in 150 excerpts from his works (Nettheim, 1998). That fingerprint was related to Becking's conducting curve for Schubert by matching various features of the excerpts to corresponding features of the curve. A theoretical treatment of metre dealt with the number of bars per curve (B/C), that is, the number of 'nominal' bars (as printed) per 'real' bar (corresponding to one complete conducting curve), a number which needs to be determined if the music is to be understood in conducting terms; implications for the understanding of Schubert's tempo indications were also explored.

Par 5 The present paper continues that line of research by proposing two Mozart fingerprints. Much of the theoretical background was already detailed in the Schubert paper (Nettheim, ibid), so it will be covered a little less fully here. As two composers, Schubert and Mozart, have now been studied in this way, systematic comparison between them is possible and will be pursued. On the other hand, the interesting question of the separation of the Mozart conducting beat from the Haydn one via fingerprints is not a main concern at this stage and will be looked at only briefly. Implications for tempo in performance will follow from the study of the relationship between tempo indications and the number B/C, but implications for the detailed nuances of performance within a given tempo are held over for future work. ²   It should finally be mentioned that the present study is a musicological one; in particular, the point of view of cognitive psychology is not taken up here. ³  

Par 6 The central aspect from which music is to be studied here is the conducting shape which it may induce. According to this approach, associated with a piece or movement of music and running throughout it (with occasional possible exceptions) is a more or less exactly repeated cycle of pressure somewhat analogous to the human pulse. Some people may feel such a cycle internally when in the presence of the music (whether by listening, performing, or silent score-reading). ⁴   The cycle runs not only through notes but also through rests. This notion was thoroughly treated by Becking (1928), for which English-language synopses were provided by Shove & Repp (1995) and Nettheim (1996). To render the internal feeling externally visible, Becking used a small baton, letting the music itself induce the motion, a process which I have suggested calling 'armchair' conducting. It is important to note that the causal direction is thus reversed from the usual one: whereas in an actual performance the conductor influences the rendition, here the musical composition influences the conducting. Becking found that the curves observed differ markedly between composers, nationalities and historical times.

Par 7 Becking presented two-dimensional diagrams which became known as 'Becking curves', indicating the way his small baton moved in response to the music of each of a number of composers. His curve for Mozart is shown in Figure 1, which gives the view as seen by a right-handed subject. The varying thickness of the curve represents the varying strength applied in the beating (taking into account both agonist and antagonist muscles), and Becking added the verbal description "selbstverständlich abwärts, sorgfältig getönt" (naturally down, carefully shaded), but the varying velocity is not shown graphically. Several distinguishable phases have been indicated along the curve by the present writer for later use: the (D)ownbeat, the move (A)round the bottom, the following (N)otch and finally the (U)pbeat. The motion of the baton starts high on the left side just before the top of the Figure and moves up to the top in a brief preparation for the downbeat which follows. The downbeat falls on the right side freely at first and is then more finely controlled for the careful swing around the lowest area. Next, after some height has been gained, a small rounded notch is traced out forming a secondary low region, not as low as before; this phase is quite refined and may be found to a certain extent delectable. This notching movement creates enough momentum to allow an easy continuation for the upbeat which completes the cycle. The shape is intended to be executed and felt, rather than merely viewed on paper. A more detailed description, especially of the downbeat, is given by Becking (ibid, pp. 23-26) and is outlined in translation in Nettheim (1996, pp. 113-115); an attempt at an animation of the curve is made in Nettheim (2003).

Par 8 It is natural to ask whether Becking's prescription for Mozart's conducting curve has an underlying authenticity, or whether it instead represents just Becking's personal response to the music. The present study adopts Becking's prescription as an hypothesis in order to pursue its implications and to test it against the scores. That prescription happens to ring true for the present writer, and it will be confirmed to a considerable extent by the work to follow. On the other hand, the successful proposal of an alternative curve prescription is theoretically conceivable; its results could be pursued by the same method as that which will be used here.

Par 9 The present approach clearly requires a decision on where in the score each conducting curve begins and ends, and those places are not always obvious. It is therefore necessary to determine, as far as possible, the number of printed bars per curve (B/C). That quantity, which I will call the curve's 'scope', can in practice take the values 1, ½ or 2 (or perhaps very rarely another value). In this connection I define a 'real' bar as covering one curve, by contrast with a 'nominal' bar as printed; the scope, B/C, is then the number of 'nominal' bars per 'real' bar. Various possible methods for determining the scope were mentioned in Nettheim (1998, section 1); the evidence of carefully defined fingerprints was the main one used there, as will be the case here too. ⁵   To attempt such determinations, we first need to deal with the question of the metrical representation of the music in the score.

Par 10 Any metre appearing in a score can be regarded as resulting from three choices: (i) a 'real' metre, (ii) the number (1, ½ or 2) of notated or 'nominal' bars per curve, and (iii) the note-value chosen as metrical unit. When (i), a 'real' metre, is given, then (ii) and (iii) determine the 'nominal' metre. These choices will now be explored systematically.

Par 11 Two given metres may be essentially different, as for instance 3/4 vs 4/4, or 3/4 vs 6/8. They may instead be non-essentially different, differing just in manner of notation, as for instance 3/4 vs 3/8, or one bar of 6/8 vs two bars of 3/8. This is not to say that there is then no difference between the metres; thus 3/8 might be considered to imply a lighter style of performance than 3/4, and perhaps a quicker tempo. ⁶   The terms 'essentially different' and 'non-essentially different' apply, then, to pairs of metres, whereas the terms 'real' and 'nominal' apply to a single metre.

Par 12 The notion adopted here is that a given (continuous) underlying curve can be manifested in different (discrete) metres. That was to be expected in case the difference between such metres is non-essential. It is, however, true also in the case of essentially different metres: although the corresponding conducting shapes might not then be identical, they will be similar. ⁷   This follows directly from Becking's notion of the curve, for a composer is by no means restricted to just one 'real' metre. It is natural, though, that each composer may show some preference for the 'real' metre or metres in which he can best represent his conducting curve. He may also take his own attitude to the conventions of 'nominal' metre, as well as of the related tempo indications. Thus we must discard text-book approaches to metre, which generally do not distinguish between composers, and instead build up our understanding empirically for each composer separately. ⁸  

Par 13 It turns out that for Mozart, as was found also for Schubert, most of the ground can be covered with just three categories of 'real' metre: simple duple/quadruple, simple triple, and compound duple. The distinction between simple duple and simple quadruple metre in respect of the conducting curve and its representation in the scores, though certainly perceptible, is relatively slight, and will accordingly only be commented upon in passing. Excerpts in different 'real' metres are related to the Mozart curve in Figure 2.

Par 14 Staff A shows an excerpt chosen to represent Mozart's 4/4 conducting shape: the beginning of the Piano Sonata K545-1 (the left hand accompaniment is not shown here, but see later Figure 3). The tempo can provisionally be taken to lie within a range of about 1.5 to 2.0 seconds per curve. When the music is heard or thought an internal feeling is induced, whose corresponding conducting shape may be followed externally. The matching of the curve to the score between Figures 1 and 2 is indicated by means of circled initial letters in each Figure. The letters in the score are intended to correspond only approximately to the start of the indicated phases, not to indicate precise locations (precision has been attempted in Nettheim (2003) but the finer detail is not needed for the present purpose). Indeed, Becking (ibid, p.24) wrote that the downbeat in 3/4 metre lasted for "something less than" ("etwas weniger als") two quarter-notes, again only an approximate indication; the (A) phase is shown in the score commencing a little after the 2nd quarter-note of the bar, subsequent to the carefully executed lower portion of the curve's downbeat. The approximate matching was feasible in this case only because two conditions were satisfied: (i) the number of printed bars per curve was assumed known (B/C = 1) and (ii) the excerpt was both typical of the composer and comparatively simple; for many excerpts the matching would be less transparent.

Par 15 Staff B shows an attempt by the present writer to devise music similar to that in Staff A and yielding as nearly as possible the same conducting curve but now in 3/4, a metre which is essentially different from the 4/4 of staff A. To make such an attempt, the first requirement is a change of mental attitude to instal the new metre with full conviction. Suitable locations within the bar are then sought for the phases which were distinguished above. The order of the phases is of course maintained in the new metre, but the locations must in some cases be shifted a little, for the metrical divisions differ essentially. Comparison is facilitated by the correct alignment of all staves of the Figure (that is, the spacings are correctly matched for printing, though not exactly proportional to the durations). The new rhythms have been determined not by the present writer's intuition but from a study of Mozart's practice as revealed in his scores, to be documented later. It was clear that two short notes should lead either to the 2nd beat (as 32nd-notes) or to the 3rd beat (as 16th-notes): the latter was chosen because Mozart more often made that choice, though he sometimes used the former (see e.g. Becking, ibid, p.23, bar 4 of Example 3a from K202-1). It is important to note that the (N) and (U) phases, each of which had in duple metre occurred at its own part of the bar, now in triple metre occur together in compressed fashion on the last beat of the bar; this phenomenon was mentioned specifically by Becking (ibid, p.39) (who however did not discuss specifically the conducting of 'real' 6/8 metre).

Par 16 Staff C shows an implementation, once more by the present writer, in 6/8 metre. The durations are again taken from Mozart's typical practice, although other choices might also be feasible. The rhythm at the beginning of bar 2, for instance, could conceivably have comprised a dotted quarter-note and two 32nd-notes, but that would not have corresponded to his practice. It may be noted that the pair of 16th-notes in 6/8 metre necessarily occupies a larger proportion of the bar than in 4/4 (one sixth vs one eighth). The 6/8 implementation may be felt as not quite so natural for the Mozart Becking curve as was the 4/4 implementation—a certain tautness has been lost—and indeed 'real' 6/8 metre is apparently used relatively less by Mozart, as will be documented later. ⁹  

Par 17 Simple duple metre (2/4) differs in some respects from simple quadruple metre (4/4), but not sufficiently to warrant considering it 'essentially' different for the present purpose. Manifestations of the two metres in the scores seem to be fully comparable, as will later be seen, the distinction arising rather in performance: in 4/4, all four conducting phases are executed distinctly, whereas in 2/4 (and 2/2) the first two phases are more nearly fused, as are also the last two phases. This distinction was described diagrammatically by Becking (ibid, p.40).

Par 18 In considering the possibility of other 'real' metres, we note that 'nominal' 3/4 metre could be used with triplet 8th-notes, as in the Piano Sonata K279-2; then the 'real' metre could be understood either as 9/8 or as 3/4, a question not pursued here. Mozart may exceptionally have used still other 'real' metres, but we have now covered his main ones.

Par 19 Three musical genres were selected for special study in the present paper: piano sonatas (solo), string quartets, and lieder; the scores were consulted in the Bärenreiter edition. ¹⁰   The 'nominal' metres which Mozart used in these genres are shown in Table 1 (other 'nominal' metres than the six appearing there occur very rarely in Mozart's remaining genres). In this study each metre/tempo section is regarded as a separate 'segment' of music, so the total number of segments exceeds the total number of movements; further, all separately published versions of a movement are counted separately. Those factors somewhat bias the Table as an indication of Mozart's practice, but it is suited to the present different purpose. Unnotated changes of effective metre such as hemiola may occur, but these are not tabulated here. Without yet knowing the 'real' metres applying in each case, the significance of the Table cannot properly be judged: it constitutes just a starting point for the investigation.

Par 20 We now take into account the number of bars per curve (B/C). A complete tabulation is not possible, because in some cases that number has not been determined with certainty. The cases found so far in the genres studied are shown in Table 2; these cases will be documented shortly in score excerpts in the Figures indicated in the present Table (Figures 4a(i) etc.). No case of B/C = ¼ has been confirmed, but the Sonata K332-2 might be considered in that respect.

Par 21 A problem arising from Table 2 is that it is quite clear that Mozart sometimes used 'nominal' 2/2 metre with B/C = ½ (this usage was not found in Schubert by Nettheim, 1998). Each half of the 'nominal' bars can then not represent 'real' 1/2 metre but must provide at least two divisions of the curve, that is, two 'nominal' 4th-notes. The question then arises: in the cases where B/C = ½, what difference is intended between 'nominal' 2/2 and 'nominal' 4/4? It seems from some comparisons of excerpts to be shown later, containing virtually the same rhythms and very similar music, that any difference intended is slight.

Par 22 Mozart's extant scores constitute virtually our entire documentary evidence of his music. Therefore, if his musical personality is to be revealed anywhere it must be via his scores, no matter how deeply it may be hidden in them. As we are here adopting the Becking curve as a governing notion, we will search in the scores for evidence of the curve's two key features: its scope (B/C) and its shape, both defined earlier. That evidence cannot sufficiently be seen in any one musical score or excerpt considered by itself, as Becking pointed out (ibid, p.9). The only remaining possibility is that the evidence resides in the scores as a whole œuvre. ¹¹   The rationale to be adopted for the systematic study of the scores of a given composer is that a number of fingerprint patterns are present in various of the composer's scores and that, while no one pattern fully determines or implies the curve's scope and shape, they do so jointly, each one making a partial contribution to the determination. Each such contribution can be expected to focus on just one or a few properties of the curve. Moreover, a fingerprint may appear in a work or movement perhaps just once or a few times, possibly early in it, suggesting that the whole music is to be understood according to the curve shape thus indicated more or less briefly but strongly; the remainder of the music, although it might further reinforce that indication of shape, need not do so—instead, it need only be consistent with it.

Par 23 The tasks, then, are (i) to propose a suitable set of carefully defined fingerprints for the given composer, and (ii) to document them as extensively as possible in the scores. The first of these tasks requires a considerable familiarity with the scores together with musical understanding (involving, perhaps, broad and rapid subconscious processing, cf. Ehrenzweig, 1967). ¹²   The second task is more purely mechanical, and the results will therefore be objectively verifiable, to the extent possible for any results in an artistic discipline. In particular, a fingerprint falsely proposed will not be capable of convincing documentation in the scores of the given composer. Further, the common appearance of a fingerprint of one composer in the scores of another composer does not necessarily deny the value of that fingerprint for either composer, because of the possibility of the joint action of sets of fingerprints as mentioned above (Par 22).

Par 24 A fingerprint is here understood to comprise just a few notes typically covering about one 'real' bar. It is not sufficient for the present purpose to find general features typical of the composer's output—for instance, the feature of Mozart's music that its textures are especially spare. Again, prototypical phrases, as treated by Gjerdingen (1991), are much longer portions of music than the single-bar units that will be considered here, and they accordingly have very different properties. ¹³  

Par 25 Prototypes will be used to represent each proposed fingerprint concisely. They are designed as convenient reference points for the more extensive documentation to be attempted later. A given prototype is shown as a set of excerpts, one excerpt for each 'real' metre. To facilitate identification, at least one of the prototype excerpts is, when possible, chosen to be a rather well-known one.

Par 26 In looking for a first figure suitable as a Mozart fingerprint I concentrated attention on the characteristic (N)otch phase of the curve, therefore paying particular attention to the corresponding places in the scores (certainly there is no comparable phase in the Schubert curve, shown later in Figure 8, so this might be expected to lead to clear differentiation between Mozart and Schubert, if not also between Mozart and other composers). The resulting prototypes are shown in Figure 3.

The bar lying between the vertical dashed lines, here the second bar in each excerpt, is the one considered prototypical. The main feature of interest is the positioning of the two short notes just before the middle of the 'real' bar, or before the 3rd beat in 'real' triple metre (which is again as near the middle of the bar as the simple divisions of the metre allow). This proposed fingerprint will therefore be called for convenience the 'middle twiddle'. That admittedly almost childish appellation was chosen because such novelty provides an advantage when one undertakes a rather large task of score processing—that is, it will "stand out" well as a name among the names of various other fingerprints which may arise in future work involving a number of composers and their fingerprints. The matching of the score to the curve is again shown by means of circled letters in the Figure so that, for instance, the two short notes seem to lead in to the (N)otch phase of the curve. The Figure illustrates, as did Figure 2, the relationship between the three 'real' metres, this time with Mozart's own music. Although the vertical alignment in this and other Figures shows the progress through the printed score correctly, the relationships to the curve differ between staves, as may also the tempo of whole bars and of the music within each bar; thus the horizontal axis does not in general reflect uniform chronometric time. The relationship of the score to chronometric time is relevant in performance studies, not treated here.

Par 27 The definition of M1 will be written in terms of the 'nominal' metres 4/4, 6/8 and 3/4, assuming B/C = 1. The corresponding specifications for other metres follow readily.

Definition of M1—the four phases:

Definition of M1—general requirements:

Remarks on the definition of M1:
Close variants of M1:

More distant variants of M1:

Par 28 A collection of examples of the fingerprint M1 is given as score excerpts in Figures 4a-e. The examples are taken from the chosen genres, which are distinguishable by the appearance of a brace for piano music, a bracket for string quartets, and vocal text for lieder (except for the accompanimental solo excerpt from K468 with M1 and later, with M2, K474, K531 and K597). The collection is organized hierarchically according to the three categories mentioned earlier: (i) 'real' metre, (ii) bars per curve (B/C), (iii) metrical unit, and finally (iv) the Köchel catalog order (which is approximately chronological). Each example covers two curves; attention is focussed on the music between the dashed vertical lines, for it is there that M1 is found. The collection is therefore further organized according to whether it is the first or the second curve that contains M1, thereby allowing the vertical alignment of the fingerprints. A movement (more precisely a tempo/metre segment) may contain several examples of M1, in which case only one example is shown here. ¹⁴  

Par 29
'Real' simple duple/quadruple, B/C = 1
We begin with 31 examples in this category. Since B/C = 1, 'real' and 'nominal' metres coincide here.
The first 13 examples have metre 4/4 (Figure 4a(i)). In most of these the 16th-notes move by step, but a quite characteristic drop of a 6th is seen in K080-2, K157-1 and KAnh074, the latter two of which have identical melodies and harmonies. Appoggiaturas, apparently harmless to M1, are seen in K333-1 (close variant d1). The quartet K387-1 also shows signs of the fingerprint M2 (see later).

The next 12 examples have metre 2/4 (Figure 4a(ii)). In this metre the two short notes are 32nds. In 7 cases motion to the (N) note is conjunct, in the other 5 disjunct. K597 has an initial grace-note, indicating a singing nuance (close variant d1).

The next 6 examples have metre 2/2 (Fig. 4a(iii)).

'Real' simple duple/quadruple, B/C = ½
Figure 4b shows 7 examples in this category; the first four have metre 4/4, the other three 2/2. In some of these the printed bar is shifted by half a bar, by comparison with some of the others. The difference of nominal metre between 4/4 and 2/2 seems to have no effect in respect of K570-2 (in 4/4) and K468 & K570-3 (in 2/2), for the music is very similar in these cases. In K332-2 the 1st bar is the cleaner example, having no appoggiatura, but the 2nd bar was more convenient for alignment; this pair of bars confirms the close variant d1.

'Real' simple duple/quadruple, B/C = 2
Only one example in this category has been found in the chosen repertoire, shown in Figure 4c. The presence of a trill on the downbeat note means that the relevance of this example here is somewhat uncertain.

'Real' simple triple, B/C = 1
Figure 4d shows 8 examples in this category. In four of them further notes follow the (N) note (close variant u1).

'Real' simple triple, B/C = ½
No examples were found in this category (and for this 'real' metre B/C = 2 cannot exist).

'Real' compound duple, B/C = 1
Figure 4e shows 4 examples in this category (fingerprints for this 'real' metre were not found with other values of B/C). The movement of the short notes is disjunct in KAnh072 (close variant a1). Strong similarity is noticed between K311-3, K576-1 and KAnh073.

An instructive case which was excluded is K331-1 bars 3-4 (see Figure 5). Here the value of B/C is apparently not 1 but ½. Features arguing against B/C = 1 are the smoothly prolonged continuation from the 6-4 chord at the middle of nominal bar 4 and the dynamic markings (the sf seems to suggest the crisp upbeat phase and the p a new gesture); confirmation will later be seen in the clear instance of M2 with B/C= ½ found in bar 34 of the same movement (shown in Figure 5 and later in Figure 7e). Most cases did not require such detailed investigation.

Par 30 The incidence of the examples documenting the fingerprint M1 is shown in Table 3 by date of composition and genre (together with the incidence for M2, which will be referred to later). The counting in the Table includes all tempo/metre segments, even in cases where an initial tempo/metre combination resumes after a possibly brief departure; thus the Table underestimates the true incidence a little. The overall incidence of M1 as tabulated is 23%. From the percentages in the Table's margins it is seen that the incidence is well-distributed over time through Mozart's output and also between the three genres treated here (excepting only that the incidence in Lieder is lower, that category having however the fewest total segments and therefore providing the least reliable estimates). A lack of uniformity is noticed between the cells within the body of the Table, and in particular the high incidence in the early String Quartets compared with the zero incidence in the early Piano Sonatas; rather than immediately attempt to draw conclusions from that observation, it will be preferable to await corresponding data from other genres of Mozart's œuvre.

Par 31 For the next fingerprint, attention is shifted to another property of Mozart's conducting shape: its incisiveness and clarity. As with M1, this property is not shared by Schubert's conducting shape, so again a ready distinction between the two composers can reasonably be hoped for. When the fingerprint M2 occurs it is usually in the bass part of cadences; prototypes are shown in Figure 6. Although the pattern contains relatively little detail and might not so well reflect other properties of Mozart's curve, it can nevertheless make an important contribution in helping to determine the value of B/C.

Par 32 The definition is presented according to the same scheme as was that of M1.

Definition of M2—the four phases:

Definition of M2—general requirements:
These are the same as for M1.

Remarks on the definition of M2:

Close variant of M2:

To be distinguished from M2:

Par 33 Examples for M2 are presented in Figures 7a-f in the same manner as earlier for M1 (see Par 28).

'Real' simple duple/quadruple, B/C = 1
Figure 7a(i) shows 9 examples in nominal 4/4 metre. In K155-1 the specified pattern appears in the viola rather than the cello part. Variant pitch patterns appear in K080-2, K160-1, K387-1 and K428-1. Two examples happen to show also M1: K157-1 and K387-1.
Figure 7a(ii) shows 11 examples in nominal 2/4 metre. Variant pitch patterns appear in K529 and K597.

Figure 7a(iii) shows 4 examples in nominal 2/2 metre. The pitch pattern is ascending in the top voice in K281-3, in which the grace notes seem not to interfere with the fingerprint.

'Real' simple duple/quadruple, B/C = ½
Figure 7b shows the only example found in this category, the very clear case K283-2.

'Real' simple duple/quadruple, B/C = 2
Figure 7c shows two examples in this category, both having variant pitch patterns.

'Real' simple triple, B/C = 1
Figure 7d shows 9 examples in this category. Variant pitch patterns appear in K170-2 and K589-3. An example from the Minuet of K173-3 is shown but, to avoid double-counting, one from the Trio of the same movement was excluded.

'Real' simple triple, B/C = ½
Figure 7e shows the only example found: K331-1. This confirms that the temptation to assign B/C = 1 on the basis of bars 3-4 representing M1 should be avoided—see the earlier discussion of Figure 5.

('Real' simple triple with B/C=2 cannot exist.)

'Real' compound duple, B/C = 1
Figure 7f shows 2 examples (the lowest 2). In K421-4 the appoggiaturas in the second violin and viola help to confirm the identification. The pitch pattern and even the number of notes is varied in K428-2, but the effect seems clearly that of M2.

'Real' compound duple, B/C = 2
Figure 7f shows, in the upper system, the only case found in this category: K283-3. This categorization is supported by the pianist Wanda Landowska's insertion into the score of one nominal bar (bar 131a, prolonging the a#-b alternation) where it was required to maintain the 'real' metre with B/C = 2 (see Nettheim, 1999, pp. 27-28).

Incidence of the examples
Par 34 Table 3, given earlier, shows the incidence of M2 as well as of M1. The incidence of the union of these is also shown (thus avoiding double-counting of the 17 segments that contain separate examples of each fingerprint). In four cases both M1 and M2 are seen in a single example: K157-1 bars 33-34 (Fig. 7a(i)), K387-1a bar 10 (Fig. 7a(i)), K589-3 bars 7-8 (a variant of M1, Fig. 7d), K421-4 bars 23-24 (again a variant of M1, Fig 7f); these too have been counted only once. The overall incidence of the union of M1 and M2 is 33%, reasonably high considering the restrictive approach taken to the definitions in this first study. The Table's margins show fair uniformity over time and genre, while the individual cells naturally show some variability. On the whole, the collection of examples seems fairly convincing to me. Formal comparison with the incidence of the Schubert fingerprint proposed in earlier work is not available, because in that work the sampling, though wider ranging and more extensive than here, was unavoidably less controlled; an informal estimate was indicated as 50% overall (Nettheim, 1998, section 3).

Par 35 For each 'real' metre the number of segments having at least one fingerprint example is shown in Table 4 for each value of B/C (the use of the union of the set of examples of M1 and the set of examples of M2 avoids double counting). The totals show that 83.7% had B/C = 1, while 12.2% had B/C = ½ and 4.1% B/C = 2. These percentages are not necessarily indicative of the percentages in the population of Mozart's segments; an estimate of that is not available as we have not yet ascertained the value of B/C for all segments in the population. They may nevertheless serve as a preliminary estimate. It was perhaps to be expected that B/C = 1 would predominate, the less direct notations appearing less frequently. The percentages found here are quite similar to those found in the examples of the Schubert fingerprint proposed in earlier work: 74.7%, 16.0% and 9.3% respectively (Nettheim, 1998, Section 3, Table 3a).

Par 36 For each 'nominal' metre and each value of B/C, the number of segments having an example of M1 or M2 or both is shown in Table 5. Again necessarily restricting attention to the examples so far collected, it is seen that two metres, 2/2 and 3/4, always show B/C = 1, so that 'real' and 'nominal' metre are the same. Whether future research will confirm that Mozart's music in these metres provides reliable clues to the determination of the value of B/C remains, however, to be seen.

Par 37 It is of interest to examine the relationship between Mozart's tempo indications and the values of B/C occurring in his scores, to see whether the indications correspond to 'real' or to 'nominal' bars (or to neither of those). Data covering Mozart's whole output is available in Marty (1988) for the tempo indications but is unfortunately not presently available for the values of B/C (Marty did not systematically treat these latter, instead attempting to find systematic behaviour in the relation between the indications and the note values used in the compositions). We therefore investigate this relationship just in the present examples of M1 and M2: the data, read off from the examples in Figures 4 and 7, is summarized in Table 6. ¹⁵  

Par 38 We now briefly discuss the entries in the Table's cells. When B/C = ½ it is seen from Table 4 that 9 segments are involved; of these, the only case that is faster than Andante is K570-3 at Allegretto. When B/C = 2, 3 segments are involved, admittedly a small number, whose tempos are Presto, Presto and Allegro assai. These two extremes, the first and last rows of Table 6, are the most revealing for the present purpose. It remains to consider the (less critical) middle row, where B/C=1. In simple duple/quadruple metre 41 segments are involved; the great majority of these have a variety of Allegro or a slightly slower tempo, the only apparently differing ones being K597 Etwas langsam and K589-2 Larghetto. In simple triple metre 15 segments are involved, showing only one case of a non-central tempo: K169-1 at Molto allegro. In compound duple metre 6 segments are involved, showing 3 Allegros, an Andante con moto and two with no tempo indication—there are no extremes here.

Par 39 For a more thorough investigation, the authenticity of all the published tempo indications would need to be checked, as well as any other relevant circumstances applying in particular cases. But the conclusion seems inescapable, though drawn just from the present limited data, that Mozart's tempo indications correspond in general not to 'real' but to 'nominal' bars. Thus Presto means that it is the notated bars that proceed rapidly, the 'real' bars proceeding only half as rapidly. Similarly for Andante and slower tempos it is the notated bars that proceed at the indicated speed, the 'real' bars proceeding only half as slowly. It is to be noted that the same general conclusion had been reached earlier for Schubert's verbal tempo indications (Nettheim, 1998, Section 4). These conclusions have practical importance, for they imply that the conducting tempos for both composers vary less than if the indications had corresponded to 'real' bars. More specifically, for these composers Presto music is generally not as fast, when B/C=2, as might have been assumed if the B/C factor had not been taken into account, and similarly Larghetto is generally not as slow, when B/C=½, as might have been assumed.

Par 40 It might be tempting to draw a further conclusion from the Table by reversing the direction of implication: that in order to determine the value of B/C one need only look at the tempo indication, except when 'real' simple triple metre is a possibility. To draw that conclusion would, however, be risky until further data is available to confirm the relationships suggested by the Table and, even then, it is unlikely to apply without exceptions arising; a separate investigation of the prevailing musical features therefore remains the preferred method for determining the value of B/C for a given segment.

Par 41 Now that the works of two composers have been studied from the present point of view (with a fair though not complete coverage), the two sets of results may be compared.

Par 42 A cross-match is regarded here as a passage found in the scores of one composer that could convincingly be executed according to the conducting curve of another composer. It is to be expected that many excerpts containing more or less neutral material could have been written by either composer; this material may in an extreme case consist simply of a whole ('real') bar's rest, or in less extreme cases a simple chord or scale or repeated-note passage. Such neutral excerpts are not of interest here, and we will pass them by. Even a non-neutral cross-match does not by itself constitute a refutation of the approach taken in this paper: instead, it challenges the researcher to look closely enough into the excerpts to find features distinguishing the two musical personalities involved. If, of course, one were unable to find such features, the approach would to that extent have failed.

Par 43 The search for cross-matches requires, in the present case, the attempt to work through Schubert's scores after having mentally (and perhaps physically) installed Mozart's conducting curve, so as to see whether any excerpts from those scores are to a fair extent compatible with Mozart's curve. That is a somewhat unnatural task for a musician, but for this purpose it must be carried out diligently. The subjectivity of the method will be minimized, as before, by carefully examining the excerpts thus brought to light in relation to the already defined fingerprints and curve characteristics.

Par 44 The definitions of M1 and M2 will need to be modified to some extent for the purpose of finding instances of them in a work by Schubert. For instance, the textures of the writing will usually differ between composers, in some cases even the available instruments or their range, and that alone may make strict cross-matches unlikely. Further, the value of B/C will need to be known, not as it may be determined according to the writing of Schubert, even though Schubert was in fact the composer, but, if it were possible, according to the writing of Mozart, the 'null hypothesis' composer.

Par 45 The field of the comparison must be determined too: the null hypothesis may be that all of Schubert's output could have been written by Mozart, ¹⁶   that a given work could have been, a given movement, segment, portion of a segment, excerpt covering just one conducting curve (of what would be Mozart's shape), or an even smaller unit. If the music of a single curve is at issue it follows that, as one cannot determine B/C from just one curve, one must determine it by conducting also the surrounding material as if it were by Mozart, even though that single curve might be the only one whose music appears to fit the Mozart curve.

Par 46 The problems just discussed seem to rule out the possibility of a strict definition of a cross-match. I therefore decided to search in Schubert's works for instances which might informally be described as "something like" the Mozart fingerprints. It is of interest to obtain a (necessarily informal) idea of the frequency of such instances; in order to err on the side of overestimating that frequency, I noted cases of even slight similarity, and accordingly use the term 'cross-match candidate'.

Par 47 Cross-match candidates of M1 in Schubert are shown in Figures 8a-e. The survey is confined to the solo piano sonatas.

Par 48
'Real' simple duple/quadruple
Three candidates were found with B/C = 1 (Figure 8a). In D566-1 bars 3-6, 63-66, the melody note held throughout the 3rd and 4th beats is not typical of Mozart's M1 figure and fits it less well. In D845-1 bar 162, 165 many features contradict M1. Finally, in D459-1 bars 1, 3, the opening RH figure is the same as in K576-3 bars 1, 3 (see Figure 9, which is placed within the series 8a-e). Schubert's crescendo/diminuendo swelling across the 2nd and 4th bar-lines is one feature differentiating the gesture from Mozart's as it suggests a less crisp downbeat. That opening figure is apparently not very important to Schubert, for it never recurs in the movement (the recapitulation begins at bar 80 with plain RH octaves).

One candidate was found with B/C = 2 (Figure 8b). In D625-4 bars 35-36, 210-211 the duplication of the (N) figure in the LH produces a less nimble effect than in Mozart.

'Real' simple triple
Four distinct candidates were found, all with B/C=1 (Figure 8c). In D557-1 bars 2, 6 the continuation does not fit well with item u1 of the definition of M1. In D567-1 bars 45, 53, 171, 179 = D568-1 bars 45, 53, 190, 198 (in which we refer to the 'real' bar-line with B/C = 1, understanding this music according to Mozart, whereas possibly B/C = 2 according to Schubert) the crescendo/diminuendo across the bar-line seems un-Mozartean, as it did in Figure 9. ¹⁷   The remaining candidates are D894-2 bar 141 (in octaves), 143, 144 and D960-2 bars 36, 40, 129, 133; the context provided by the surrounding material seems to differentiate these from Mozartean writing, yet by themselves they match M1 reasonably well.

'Real' compound duple
Two candidates were found with B/C = 1 (Figure 8d). D568-4 bars 95, 97 and D604 bars 2, 35 introduce no features beyond those seen in earlier candidates.

Three candidates were found with B/C = 2 (Figure 8e). In D537-3 bars 210-213, D575-4 bars 81-86, 307-316, and D845-3 bars 1-2 a short repeated figure does not lead to a good match with M1; the latter two candidates contradict item d2 of the definition of M1.

Par 49 Cross-match candidates of M2 in Schubert are shown in Figures 10a-d, where the survey is again restricted to the solo piano sonatas.

Par 50
'Real' simple duple/quadruple
One candidate was found with B/C = 1 (Figure 10a). In D664-1 bar 133 the first bass note is held through, contradicting item d4 of the definition of M2 and thereby losing Mozart's incisiveness.

Two candidates were found with B/C = 2 (Figure 10b). In D157-1 bars 103-104, 250-251 (also in the earlier version D154-1 bars 85-86), the solid chords in the RH make the music more heavy-handed than for Mozart. In D958-2 bars 114-115, the pitch pattern is varied and the last chord is twice as long as in M2.

'Real' simple triple
Two candidates were found, both with B/C = 1 (Figure 10c). In D850-3 bar 51 and D959-3 bar 22 the pitches are inverted. In the first case Schubert appears to be experimenting with B/C = 2 in the RH against B/C = 1 in the LH, creating a special accentuation foreign to Mozart. In the second case the first bass note is held through the bar, contradicting definition item d4.

'Real' compound duple
Three candidates were found. One has B/C = 1 (Figure 10d). D557-3 bars 19-20 is a fairly close match to K428-2 bars 34-35 (shown in Figure 7f) but both have 4 chords rather than 3 and so are not fully convincing representations of M2.

Two have B/C = 2 (Figure 10e): D157-3 bars 19-20, 67-68 and D625-3 bars 47-48, the latter with a different pitch pattern. If it is accepted that compound duple time is Mozart's least congenial one, then these three examples would not have been expected to be very convincing candidates.

Par 51 We must now attempt to grasp Schubert's musical personality. The Becking curve for Schubert is shown in Figure 11, whose accompanying text is "führen und schwingen" (guide and swing). ¹⁸   The Becking curve for Mozart was shown in Figure 1. These curves differ greatly in orientation (vertical vs horizontal), in contour, and in the associated feeling qualities; a reader who executes them with conviction will more fully grasp the significance of the differences between them.

The usage of 'nominal' and 'real' metres by the two composers differs too; we do not reproduce here the details given in Nettheim (1998, section 2) but mention in particular that it seems that, whereas 'real' duple/quadruple suited Mozart specially well, 'real' compound duple suited Schubert better. A Schubert fingerprint, S1, was proposed and defined in detail in Nettheim (1998, section 3) as a 'prepared appoggiatura' figure. The somewhat extensive details of its definition will not be reproduced here, but prototypes for each main 'real' metre are shown in Figure 12 (in each case the second 'real' bar contains S1).

Par 52 Cross-match candidates of S1 in Mozart are shown in Figures 13a-d. The survey is again confined to the solo piano sonatas.

Par 53
'Real' simple duple/quadruple
One candidate was found with B/C = 1 (Figure 13a). In K330-3 bar 169 the texture is thinner than is typical for Schubert, a reservation which will naturally be likely to apply to all or most of these candidates. More significantly it is seen that, whereas Mozart has repeated the note f' on the downbeat of bar 169, Schubert would, according to our knowledge of S1, more likely have moved to e' there, resulting in a smoother progression at the middle of the bar and thereby corresponding better to Schubert's than to Mozart's conducting shape. Such an experiment of re-composing an excerpt from the music of one composer to introduce a feature of the other composer is often instructive.

One candidate was found with B/C = ½ (Figure 13b). In K282-1 bar 36 a Mozartean, rather than Schubertian, feature seems to be the slur over the notes g-ab in the first half of the bar, which does not allow the ab to function as a typical beginning of a Schubertian gesture.

'Real' simple triple
One candidate was found with B/C = 1: K475-1 bars 153-154 (also bar 157) (Figure 13c). The sfp accent in the middle of bar 153 perhaps militates against a Schubertian rendition.

'Real' compound duple
Three candidates were found, all with B/C = 1: K280-2 bars 8, 42, 44, 46 (bar 44 is shown); K332-3 bar 236; and K576-1 bar 129 (Figure 13d). In the first of these, Mozart's rests are a distinguishing feature, the first one acting in opposition to a smooth Schubertian downbeat—this is highlighted in the comparison of similar musical material by the two composers shown in Figure 14. The fact that these three candidates match Schubert somewhat better than those in other 'real' metres might be due in part to 'real' compound duple metre being less sympathetic to Mozart's shape and more sympathetic to Schubert's. Similarly, a close match in Schubert to Mozart had been seen in Figure 9 in simple duple/quadruple metre, a metre less sympathetic to Schubert than to Mozart.

Par 54 As so few candidates for S1 occur in Mozart's scores, it may be instructive to describe a few cases of appoggiatura figures in Mozart which are not considered to be candidates, together with the reasons for their non-candidature. These reasons are not based on mere pedantry, but ultimately on the extent to which the scores match the given conducting curve, which I have attempted to make explicit with the aid of fingerprint definitions. Some features of many of Mozart's appoggiaturas, compared with many of Schubert's, are shown in Table 7.

Here are a few examples having the tabulated features (a more complete list is available from the author): (A) K279-1 bar 5, (B) K281-1 bar 40, (C) K457-3 bars 175-176, (D) K283-2 bar 4b, (E) K311-1 bar 39, (F) K280-2 bar 24. Many examples have more than one of these features, e.g. K283-2 bar 39b (B,D). In particular, short appoggiaturas are particularly characteristic of Mozart rather than of Schubert. A thorough and systematic examination of Mozart's appoggiaturas lies, however, beyond the scope of the present paper.

Par 55 To conclude the comparison between Mozart and Schubert, we show in Figure 15 an excerpt for each composer, intended to represent each one's curve well (for the Mozart excerpt it is assumed that B/C=1, for the Schubert excerpt 2). These excerpts are thus chosen to be as distinct as possible in the present sense. (On the other hand, the excerpts in Figures 9 and 14 were chosen to be as similar as possible, so those pairs are of the kind so well selected and instructively differentiated by Becking, ibid).

Each excerpt contains a fingerprint, and each composer's "favourite" 'real' metre has been chosen. These excerpts seem to me to sum up the two composers' musical personalities about as well as can be managed in such short excerpts, and to contrast them well. (Other features than the presently-studied fingerprints might play a role here, especially Mozart's short appoggiaturas in bars 2 and 4 mentioned earlier in connection with Table 7.) An attempt to execute either excerpt according the other's curve, whether in performance or in thought, will, I believe, be found to violate the musical character of each composer. This could be assumed to be readily grasped by a person sensitive to this music, but it can now be made more explicit by referring to the matching of features of the excerpts, and especially their fingerprints, to corresponding features of the curves. ¹⁹  

Par 56 The main purpose of this section is to look briefly at the comparison between Mozart and Haydn in respect of the fingerprints M1 and M2. The music of these two composers is usually thought to be somewhat similar in general terms, so the extent to which the present method can distinguish between them is of some interest. However, as this comparison is not central to the purpose of the present paper, we do not attempt a thorough study of Haydn's music at this time, we do not propose a fingerprint for him, and we do not look for Haydn-like figures in Mozart's scores. Instead, we will look for cross-matches of M1 and M2 in Haydn's scores. We will also take the opportunity to notice any evidence in Haydn's scores (however unlikely it may seem a priori) of Schubert's fingerprint S1; that constitutes a secondary purpose of this section. The greater the number of composers involved, the more difficult is the mental task of searching through the scores for all the possible cross-matches (with a certain value of B/C to be determined in each case), so the present task is not entirely easy to carry out. Attention is once again restricted to the solo piano sonatas (Haydn, 1962).

Par 57 To save space, detailed results will not be given here. The general results are that cross-matches in Haydn to the fingerprints M1 or S1 occur only rarely; cross-matches in Haydn to M2 occur somewhat more commonly than that, but still M2 is a good deal less common in Haydn than in Mozart. One example of each of these cross-match candidates is given in Figure 16 (note that H44 has B/C = ½). Here we have shown quite close candidates. However, the more distant candidates, which are more commonly found, may be more instructive (there is not space for them here); for instance, candidates for M1 often show melodic notes following the (N) note, candidates for M2 often have the last bass note twice as long as in M2, and candidates for S1 often have double rather than single appoggiaturas.

It may finally be remarked that Haydn's prepared appoggiaturas often differ from Schubert's through having a much shorter preparation note or through the bass moving at the resolution of the appoggiatura.

Par 58 The basis of the present work has been Becking's notion of the composer-specific conducting curve. To what Becking provided I have attempted to add several features: (a) the fingerprint as an aid to systematic score study and to the matching of scores to curves, (b) the systematic treatment of metre, and (c) the investigation of relations between the number of notated bars per conducting curve (B/C) and tempo. The attempt to encapsulate Mozart's musical personality in terms of fingerprints found in his scores seems to have had a successful beginning here. The contrast with Schubert's musical personality also seems clearly drawn in similar terms. The contrast with Haydn's musical personality has been attempted so far only in a cursory manner. Mozart's tempo indications, like Schubert's, seem to relate generally to notated bars so, when B/C is taken into account, Presto music is in many cases not as fast as might otherwise have been assumed, and conversely the music having slow indications is in many cases not as slow as might have been assumed.

Par 59 It is anticipated that future work will include the attempt to add further fingerprints (M3..., S2...) to the ones already found for Mozart and Schubert, and the expansion of the coverage of those composers' works in the surveys. Other methods of determining the number of notated bars per conducting curve are to be pursued; such methods will be used alongside the fingerprint method. The similar treatment of other composers and comparisons among them should naturally be attempted. Perhaps further into the future, the specification of performance nuances appropriate to the composers studied will be able to be explored on the solid basis of the relationship between the scores and the conducting curves.

Par 60 Ingmar Bengtsson's view was similar to that adopted in the present paper, though he apparently had not followed it up in a similar way; here we provide two relevant excerpts.

Par 61 [A] Bengtsson (1961):

Par 62 [B] Bengtsson (1955):