(I) Specified chromatic inflections in vocal sources
(II) The theorists' statements
(III) Instrumental tablatures
> (IV) Doubling the subtonic
(V) General conclusion
> first part
In this section, we shall take into consideration a phenomenon illustrated by the following example:
ex.: Clemens non Papa, Missa "Panis quem ego dabo", Agnus Dei
[See BERNET KEMPERS, K. P. (ed.), Clemens non Papa opera omnia, Rome, American Institute of Musicology, 1951-76 (=CMM 4), vol. 7, p. 123/31-36.]
As can be seen, in this cadence the subtonic (or seventh degree of the mode, i.e. c) is carried by both the uppermost voice (which displays the usual cadence formula, a suspended lower auxiliary note, resolved to the final) and the second voice from the top (where it resolves by downward motion).
Although excluded from the counterpoint of Palestrina's time, this kind of formula is very common indeed in Franco-Flemish polyphony of the first half of the sixteenth century. The phenomenon seems to have been first observed by Maurice Cauchie (1933), who also presented the latent imperfect octave (c-c sharp) as inconceivable in the context of Renaissance music, and consequently suggested the exclusion of all leading notes from Franco-Flemish music until about 1550.
[See CAUCHIE, Maurice, "La pureté des modes dans la musique vocale franco-belge du début du XVIe siècle", Theodor Kroyer Festschrift, Regensburg, 1933, p. 54-61.]
Several years later, E. E. Lowinsky accepted Cauchie's suggestion concerning the imperfect octave, but resisted the latter's radical conclusions. In Lowinsky's opinion, such cases are nothing more than an exception and a restriction of the attraction principle, which they do not fundamentally contradict. For Lowinsky, as opposed to Cauchie, the exclusion of the leading note only applies to cadences with a doubled subtonic; all other cadences require the chromatic inflection necessary to ensure that the final is approached by a half-tone step.
[See LOWINSKY, E. E., "Symposium on problems in editing the music of Josquin des Prez", in Josquin des Prez, Proceedings of the International Josquin Festival-Conference New York 1971, London, Oxford University Press, 1976, p. 721-754; p. 740.]
On the other hand, more recent authors tend to favour a systematic application of the raised subtonic, and tolerate the false relation, mainly on the strength of the statements of Tinctoris (1477) and Correa de Arauxo (1626).
[See for example: TOFT, Robert, Aural Images of lost Traditions. Sharps and Flats in the Sixteenth Century, Toronto-Buffalo-London, University of Toronto Press, 1992, 199 p.; p. 30-32; URQUHART, Peter, "Cross-Relations by Franco-Flemish Composers after Josquin", in Tijdschrift van de Vereniging voor Nederlandse muziekgeschiedenis 43/1 (1993), p. 3-41.]
Before we examine this much vexed question of the false relation, let us first describe the history of the doubled subtonic in more detail.
The origin of the "doubled subtonic"
The doubled subtonic first seems to appear in phrygian cadences, in the second half of the fifteenth century. In such cases, there is no question of raising the subtonic, which would be contrary to the very nature of a phrygian cadence; hence we do not face the risk of an imperfect octave here:
ex.: Johannes Regis (c1430-c1485), O admirabile commercium
[See LINDENBURG, C. (ed.), Johannis Regis opera omnia, 1956 (=CMM 9), vol. 2, p. 53/29.]
Ockeghem was probably the first to use this formula in other types of cadences, where the addition of a leading note would entail a simultaneous false relation:
ex.: Jean Ockeghem (c1420-1497), Missa "Fors seulement", Gloria
[See PLAMENAC, Dragan (ed.), Johannes Ockeghem, Collected Works, New York, 2 vol., 1959-66; vol. 2, p. 70/123; we have found in a selection of Ockeghem's works at least seven cases of this kind, which amounts to one third of all cadences with five voices.]
With the following generations of Franco-Flemish composers (from Obrecht, Isaac and Josquin to Crecquillon, Clemens non Papa, Gombert, Sermisy and Manchicourt), such formulas tend to become absolutely common, and few composers fail to resort to it. But it is used essentially in pieces with many voices (five and more), which could explain why the phenomenon has attracted relatively little attention so far.
The statistical approach confirms the dependence of the doubled subtonic on the number of voices. An enquiry concerning about 1000 final cadences taken from the works of Josquin, Isaac, Clemens and Gombert, shows that this kind of formula tends to be very frequent with five voices (around 30%), and even (from six voices) to outnumber the normal cadence:
Frequency of the doubled subtonic according to the number of voices
(V-I cadences only; number of actual voices)
Number of voices Normal cadences Doubled subtonic Errors 3 voices 60 (98.3%) 0 (0%) 1 (1.6%) 4 voices 320 (98.7%) 4 (1.2%) 0 (0%) 5 voices 124 (71.2%) 50 (28.7%) 0 (0%) 6 voices 35 (38.4%) 56 (61.5%) 0 (0%) Total 539 (82.9%) 110 (16.9%) 1 (0.1%)
On the other hand, the appearance of the doubled subtonic seems unrelated to the genre of the music (sacred or secular):
Frequency of the doubled subtonic according to genre (sacred/secular)
(cadences with five or six actual voices only)
Genre Normal cadences Doubled subtonic Total Secular 32 (60.3%) 21 (39.6%) 53 Sacred 127 (59.9%) 85 (40.1%) 212
This observation is of particular interest, since it tends to disprove Lowinsky's conception: according to him, the doubled subtonic could only be used consciously by the composer, in order to force a modal cadence, and give some variety to the harmonic colour of the composition. If this were the case, one could expect that the modal cadence, with its possible connections with the spirit of grandeur and austerity of plainsong, would have been associated principally with sacred music. As may be seen, the statistical approach does not support this view.
The last point to be considered in this statistical study is the dependence on mode. For some modes (Lydian, Ionian), the subtonic already lies a half-tone from the final; in such cases, doubling the seventh degree cannot result in an imperfect octave. So it is interesting to see whether the composers of that time tend to make a difference between these two kinds of modes, and to display particular carefulness for the modes with a subtonium (i.e. a whole tone beneath the final). We shall examine here the situation for the two most frequent finals, g and f:
Frequency of the doubled subtonic according to the final (g/f)
a) Cadences with five actual voices:
Final Normal cadences Doubled subtonic g 74 (71.1%) 30 (28.8%) f 34 (87.1%) 5 (12.8%) Total 108 (75.5%) 35 (24.4%)
b) Cadences with six actual voices:
Final Normal cadences Doubled subtonic g 17 (34.6%) 32 (65.3%) f 12 (50%) 12 (50%) Total 29 (39.7%) 44 (60.2%)
It is surprising to observe that these results run counter to our expectations: the doubling of the subtonic is slightly more frequent for cadences on g. Thus it seems that the risk of an imperfect octave did not prevent composers from doubling the seventh degree, quite the contrary.
How could such an unexpected result be accounted for? Here is the only explanation I could find: let us suppose that the raising of the subtonic does not apply to this repertory (which of course will be discussed in every detail below). In a great number of cases, the subtonic is not only doubled at the cadence, it is furthermore suspended in one voice, at the same time as it is actually heard in another one:
ex.: Josquin Desprez, motet Cantate Domino canticum novum
[See SMIJERS, A. (ed.), Werken van Josquin Desprez, Amsterdam, 1921-; Afl. 45, N° 72, p.13/95.]
In the special case of a cadence in g (as in this last example), there arises a temporary dissonance of a major second (or ninth): f-g. But if the cadence were in f, this second (or ninth) would be a minor one (e-f), which is much more dissonant:
ex.: Heinrich Isaac, Missa de Beata Virgine (I), Sanctus
[See LERNER, E. R. (ed.), Henrici Isaac opera omnia, American Institute of Musicology, 1974- (=CMM 65), vol. /2, p. 68/109.]
Thus, contrary to our initial supposition, doubling the subtonic entails harmonic consequences which are more noticeable for cadences in f than in g. This could be the reason why composers are seen to be more cautious about the former than the latter.
In short, our statistical studies show that the doubling of the subtonic mainly corresponds to technical, not to stylistic criteria.
After a long period when it remained dormant in the fifteenth century, the Italian polyphonic school was revived around 1500, especially with composers like Costanzo Festa, or the Italy-based Franco-Flemish composers Verdelot, Arcadelt, Willaert, and later Lassus.
At its start, this new Italian school assimilated the Flemish technique of the doubled subtonic, as can be seen in many an early work by these composers:
ex.: Adrian Willaert, Verbum bonum et suave (published 1519)
[See ZENCK, H., GERSTENBERG, W. (ed.), Adriani Willaert opera omnia, Rome, American Institute of Musicology, 1950- (=CMM 3), vol. 4, p. 24/183 (final cadence).]
Later on, however, this characteristic would be excluded from this repertoire, at the very same time as explicit leading notes were seen to reappear in it. This evolution also corresponds to the restoration of the attraction principle in the Italian theoretical literature of the time (on this topic, see the second section of the present article).
Willaert's evolution is particularly instructive. Indeed, several printed collections specifically devoted to his works appeared from 1536, thus enabling us to follow closely the progress of his practices in this respect. In the first of these publications (1536), it may be observed that the doubling of the subtonic (which he had applied in a systematic way in the above-quoted Verbum bonum of 1519) is already almost completely avoided. As for Lassus, who was educated in Italy around mid-century, he seems from the start to be unaware of the existence of the doubled subtonic, although (like Willaert) he still favours the conception of implied leading-note accidentals.
France & Flanders
It was only twenty or thirty years later that the doubled subtonic was in turn eliminated from Franco-Flemish counterpoint. Whereas one still can find a few doubled subtonics (but no explicit attraction accidental) in masses by Goudimel and Certon published by Le Roy in 1558, Claude le Jeune's "Dialogue à Sept parties" of 1564 no longer uses this old Franco-Flemish technique, and already contains many explicit leading note accidentals. Thus the time of transition for the Franco-Flemish composers could be set around 1560. An examination of Jacob Vaet's case (c1529-1567) confirms this view. Among the works of this composer, one will find pieces in the old Franco-Flemish style, alongside others in the new Italianate manner (i.e. with many explicit leading-notes, and no doubled subtonic). Chronological data are missing for a proper dating of these different types of works, but the year of Vaet's death (1567) seems to match perfectly the terminus ante quem suggested by Le Jeune's "Dialogue" (1564).
Later publications unambiguously side with the explicit conception of accidentals, and avoid doubling the subtonic. Jacob Regnart's Sacrae aliquot cantiones (1575), or George de la Hèle's masses published by Plantin in Antwerp (1578) could be mentioned in this context, as well as Paschal de l'Estocart's Octonaires de la Vanité du Monde (1582): in all these works, leading note accidentals tend to be written down in a systematic way, and doubled subtonics are no longer to be found. Moreover, imperfect octaves are not attested in this repertoire, except for one case in l'Estocart's Octonaires, a work of surprising boldness from the harmonic point of view (it includes many instances of augmented sixths).
Continued: (IV) Doubling the subtonic (second part) >>>
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