Introduction
(I) Specified chromatic inflections in vocal sources

> (II) The theorists' statements

(III) Instrumental tablatures
(IV) Doubling the subtonic
(V) General conclusion

 
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Fifteenth century

There are further theoretical treatises for the fifteenth century, and many of them eventually introduce the attraction principle. The melodic formulation remains rare; it appears in the following works only:

-Ad sciendum artem discantus (CS III, p. 68)
-Bartolomeo Ramos de Pareia, Musica Practica (ed. Wolf, 1901, .43)
-Franchinus Gaffurius, Practica Musice, 1496 (lib. III, cap. 13)
-Domingo Marcos Durán, Comento sobre lux bella (4th page after d-iiij; 2nd page after e.iij)

Moreover, Gaffurius mentions it in a context which seems to be connected with (Ambrosian) plainsong rather than polyphony.

The harmonic formulation is more noticeable: at least eight clear occurrences thereof may be found. Authors who approach this topic are more or less under the influence of Marchetto. But two points of the latter's doctrine are no longer defended: true chromaticism is rejected by Ramos (1482), and the surprising definition of the c sharp-d natural progression as a fifth of a tone is only briefly alluded to by Tinctoris (in his Diffinitorium -- i.e. musical dictionary -- of 1495), who does not adopt it in his own theoretical works.

[See WOLF, Johannes (ed.), Musica Practica Bartolomei Rami de Pareia Bononiae (1482), Leipzig, Breitkopf & Härtel, 1901 (=Publikationen der Internationalen Musikgesellschaft, Beihefte, Heft II), p. 66. TINCTORIS, Johannes, Terminorum musicae diffinitorium, Treviso, 1495, s.v. "Semitonium"]
 

But something much more interesting and surprising remains to be noted: towards the end of the fifteenth century, the harmonic formulation appears in a strikingly weakened presentation; in his famous treatise Practica Musice (1496), Franchinus Gaffurius first recalls the general principle of alternation between imperfect and perfect consonances. He mentions the case of the sixth, which should preferably be major and resolve to the octave. But he does not call here for the introduction of any accidental, and seems to be content with a resolution by contrary motion of both parts, even without the presence of a half-tone step in any of the voices. This is particularly evident in his musical examples, which introduce several minor sixths expanding to the octave. In his commentary, Gaffurius discusses the case without expressing any surprise or uneasiness:
 

[...] Minor vero sexta ad quintam frequentius revertitur unico motu: altera scilicet cantilenae parte immobili: altera mobili: contrarijs vero motibus ad octavam item pertransit. [...]

"As for the minor sixth, it very often returns to the fifth by one single movement, namely the one part of the composition remaining motionless, the other one moving; likewise, it passes as well to the octave by contrary motion."

ex.: Gaffurius, Practica musice (1496), lib. III, cap. 3

 
[Figures appearing above the staff indicate the number of semibreves counting from the beginning of the example; this is how Gaffurius precisely locates the passage he is discussing.]
 

[...] Dehinc quum ambo ipsi contrariis motibus (toniæo [sic] scilicet vtrinque interuallo) ab inuicem distrahuntur: nonam semibreuem in octauam ipsi sextæ propinquiorem constituunt. Atque ex vndecima semibrevi in sextam similiter ducta ad octauam æquisonantem cum duodecima semibrevi contrarijs prodeunt motibus. [...]

"Then, as both of them [i.e. the voices] move apart by contrary motion (that is, by an interval of a [whole] tone on both sides), they get separated from one another, and they place the ninth semibreve on an octave, which is rather close to that very sixth. And from the eleventh semibreve, [which is] a sixth, led in the same manner, with the twelfth semibreve they progress by contrary motion to the octave, a perfect consonance (aequisonantem)."

[See GAFFURIUS, Practica musice, Milano, Ioannes Petrus de Lomatio, 1496, livre 3, cap. 3 "De Octo mandatis sive regulis Contrapuncti",7th rule, sign. dd ij v°.]

As may be seen, this weakened formulation does not consider the possibility of adding any chromatic inflection. Thus this version of the harmonic formulation seems to be nothing more than an empty shell.
 

Implied accidentals

The existence of implied attraction inflections in the fifteenth century is documented by Ramos, Gaffurius and by the anonymous author of "Ad sciendum artem discantus".

[-Ramos: see WOLF, Johannes (ed.), Musica Practica Bartolomei Rami de Pareia Bononiae (1482), Leipzig, Breitkopf & Härtel, 1901 (=Publikationen der Internationalen Musikgesellschaft, Beihefte, Heft II), p. 67.
-GAFFURIUS, Fr., Practica musice, Milano, Ioannes Petrus de Lomatio, 1496; livre 3, cap.13, "De Fictae musicae contrapunto", sign. ee iij r.
-"Ad sciendum artem discantus": see COUSSEMAKER, E. de, Scriptorum de musica medii aevi novam seriem a gerbertina alteram..., Paris, Durand, 1864-76, vol. 3 (=CS III), p. 73a.]
 

Johannes Legrense and his pupil Nicolas Burtius also state that it is not mandatory to write down all accidentals, but only in the context of the b fa b mi (b flat -- b natural).

[-LEGRENSE, Johannes, Ritus canendi vetustissimus et novus (before 1473), in COUSSEMAKER, E. de, Scriptorum de musica medii aevi novam seriem a gerbertina alteram..., Paris, Durand, 1864-76, vol. IV, p. 361a.
-BURTIUS, Nicolaus, Musices opusculum... cum defensione Guidonis aretini adversus quendam hyspanum veritatis prevaricatorem, [1487], tract. I, cap. xx.]
 

Finally, as we have seen for the fourteenth century, it should be noted that many fifteenth-century treatises do not approach the question of attraction; among these are the works of some of the most celebrated theorists of the time, for example Tinctoris, Hothby, Guillelmus Monachus or Adam von Fulda. It is interesting to observe that these writers are mainly Northeners: an Englishman, a Fleming and a German, plus an Italian reflecting mostly English practices (Guillelmus Monachus).
 

Sixteenth century

The Germanic tradition

The geographical distinction to which we just have alluded will be found to hold for the sixteenth century as well, and is even more striking than in the fifteenth century. Indeed, among the eleven Germanic treatises which we have examined, only one will be seen to include the very idea of attraction, namely "Tetrachordon Musices" by Johannes Cochlaeus (1511), a relatively minor work, which proposes a brief melodic formulation.
   Most other Germanic theorists simply ignore the concept of attraction; among them may be found the most celebrated figures of the time, for example Sebald Haydn (De arte canendi, 1540), Andreas Ornithoparchus (De arte cantandi micrologus, 1533), Heinrich Glarean (Dodecachordon, 1547), Hermann Finck (Musica practica, 1556), Heinrich Faber (Ad musicam practicam introductio, 1550) and Gregor Faber (Musices practicae erotematum libri II, 1552).
   One of these Germanic theorists, Adrien Petit Coclico, who presents himself as a pupil of Josquin, even goes as far as to criticize the principle of alternation between perfect and imperfect consonances, which is the very basis of the harmonic formulation of the attraction principle:
 

Sunt qui asserant unisonum requirere tertiam, Tertiam autem quintam, Quintam vero sextam, Sextam etiam octavam, Octavam quintam aut decimam. Sed Iosquinus haec non observavit.

"Some state that the unison requires the third, and the third the fifth, the fifth the sixth, and the sixth the octave, the octave the fifth or tenth. But Josquin did not comply with such rules."

[See COCLICUS, Adrianus Petit, Compendium musices..., Norimberga, J. Montanus & U. Neuber, 1552, 3 pages after Liij.]

 

Italy

As explained above, Gaffurius (1496) had presented a weakened harmonic formulation, which possibly amounted to a relinquishing of the very idea of attraction. During the first half of the sixteenth century, this weakened formulation was to be progressively corrected, and the original idea finally restored.
   Thus Lanfranco (1533) takes up Gaffurius' rules, without altering them; but he does not quote the musical example given by his predecessor. And in another part of his treatise, he gives another, more explicit harmonic formulation, which mentions the presence of sharps in such cases.

[See LANFRANCO, Giovan Maria, Scintille di musica, Brescia, Lodovico Britannico, 1533, p. 116; p. 126-7.]
 

Writing the same year as Lanfranco, Stephano Vanneo is even clearer: although he does not mention the name of Gaffurius, he distinctly states that the minor sixth must resolve to the fifth, and that it is not allowed to draw it toward the octave:
 

Huiusmodi namque notularum situ, haec maior & minor Sexta perbelle incedit, sed Tenore descendente, Supranoque ascendente, cupienti decorum in cantilena servare, superiore maioris Sextae cum Octava utendum erit connexione.

"For in this layout of notes [a sixth before a fifth, the upper voice moving downwards by one step], this major or minor sixth fits beautifully; but if the tenor moves downwards, and the soprano upwards, whoever wants to preserve the propriety of the composition shall use the progression from the major sixth to the octave, as stated above."

[See VANNEO, Stephano, Recanetum de musica aurea, Rome, Valerius Doricus, 1533, f.75v.]

Several years later, Luigi Dentice (1553) was to even go as far as to challenge Gaffurius' authority, stating that the latter's harmonies were no longer fashionable:
 

[...] Onde per la settima regola si vede, che non astringe il componitore, che dalle specie imperfette vada alle perfette con la specie più propinqua ad essa perfetta, mà che dalle specie imperfette vada alle più propinque perfette Come possete vedere allo essempio. Perloche non si può dire che compone falso chi si fonda & si regola per li precetti d’esse regole. Ser. Gliè vero, mà non possete negare, che all’orecchie nostre non piaccia più quel modo, [...]

"[...] So you can see from the seventh rule that he [Gaffurius] does not request the composer to go from the imperfect consonances to the perfect consonances with the consonance which is closest to this perfect consonance; but to go from the imperfect consonances to the closest perfect consonances; as you can see in the example [Dentice quotes exactly Gaffurius' example, see above]. So you cannot say that he who bases himself on the directions of these rules composes incorrectly.
Ser. That is true, but you cannot deny that this manner no longer pleases our ears."

[See DENTICE, Luigi, Duo dialoghi della musica, Roma, Vincenzo Lucrino, 1553, sign. Kij; see the second and third pages of Kij as well.]

Thus most Italian theorists of that period agree on restoring the full strength of the attraction principle. They are divided, however, on the question of implied accidentals: some of them (Vanneo, 1533; Zarlino, 1558) deny the necessity of writing down every needed chromatic inflection, and trust the performer to provide them. Others (Pietro Aaron, 1529, and Nicola Vicentino, 1555), arguing that even professional singers could not foresee everything the composer has in mind, require the latter to make plain his intentions. Both trends correspond exactly to the general evolution we have been able to observe in the vocal sources themselves: whereas the classical school of Willaert, Lassus and Palestrina appears to be reluctant to explicit accidentals up to the end of the century, composers connected with the development of the madrigal (Verdelot, Arcadelt, Festa) tend to mark their scores in an ever more precise way, from about 1530-40.

[-AARON, Pietro, Toscanello in musica, Venice, Bernardino et Matheo de Vitali, 1529, lib.II, cap. 20; see above all the appendix: "Aggiunta del toscanello a complacenza de gli amici fatta". The passage in question appears on pages 8-9 of this "Aggiunta" (1529 edition), or p. 5-6 (1539 edition).
-VANNEO, Stephano, Recanetum de musica aurea, Rome, Valerius Doricus, 1533, f. 90r.
-VICENTINO, Nicola, L’antica musica ridotta alla moderna prattica, Rome, 1555; facsimile (ed. E. E. Lowinsky), Kassel, Bärenreiter, 1959 (=Documenta musicologica, Erste Reihe, XVII), fol. 53r.
-ZARLINO, Gioseffo, Le Istitutioni harmoniche, Venice, 1558, p. 190.]
 

Even more fascinatingly, one theorist explicitly questions the validity of the attraction principle. This is an isolated case, but it is of particular interest, because the author in question is at the same time a member of the papal chapel, and an avowed supporter of modality. Himself a Flemish in origin, Ghiselin Danckerts claims to stand for the tradition of "our old" masters ("i nostri antichi"). He deserves to be mentioned here mainly because of the treatise he wrote in the 1550s in defense of his views. According to this text, some of the most recent tendencies in sixteenth-century music were a threat to the modal purity of polyphony: diatonic, chromatic and enharmonic genera were thus being confused by "modern composers" ("compositori novelli"). And in the following passages, Danckerts asserts that the attraction principle (in its harmonic formulation) is nothing more than "empty obligations and rules of theirs" ("vane obligationi è leggi loro"), which Josquin and his followers did not apply at all:
 

Costoro troppo inconsideratamente vogliono quasi sempre usare questi alzamenti et abbassamenti delle note, fuora delle lor proprie è naturali intonationi nelle compositioni loro (come ho detto) legandosi con certe vane obligationi è leggi loro, di non volere andare alla consonantia perfetta, se non con la imperfetta piu propinqua, il che si potrebbe supportare quando l’usassero rare volte, et accidentalmente; ma osservandosi questa legge ordinariamente per tutto, et in ogni luogo sempre [(]come fanno li detti Compositori Novelli) verebbe in troppo pregiuditio delli tuoni predetti.

"Those people want too inconsiderately to use almost always in their compositions these raisings and lowerings of notes beyond their proper and natural intonations (as I have said), binding themselves with certain empty obligations and rules of theirs, [saying that] they do not want to go to the perfect consonance except from the closest imperfect one; this might be tolerated if they used it rarely and accidentally; but should this rule be observed ordinarily throughout, and always in every place (as the said Modern Composers do), this would excessively damage the said modes."

[Rome, Biblioteca Vallicelliana, MS R 56, fol. 408r; quoted by ARLETTAZ, Vincent: «'La malconsiderata legge.' La pureté modale selon Ghiselin Danckerts (XVIe siècle)», in: Revue Musicale de Suisse Romande 64/1, mars 2011, p. 20-47; see p. 34-35 (with French translation). The English translation above is closely modelled on Berger's (BERGER, Karol, Musica ficta, Theories of accidental inflections in vocal polyphony from Marchetto da Padova to Gioseffo Zarlino, Cambridge etc., Cambridge University Press, 1987, p. 128; see also p. 230, note 37); but note that "supportare" (modern Italian sopportare) is not to be taken here as an equivalent of the English "to support", but in the usual meaning of the Italian verb ("to endure").]

Disprezzando et biasimando ancho[ra?] essi compositori novelli, con queste lor persuasioni, tutte le dotte opere, composte dalli eccellentissimi e perfettissimi et expertiss: Musici, da i quali essi hanno havuta luce, è senza gli cui essempij, essi non havrebbono saputo formare una consonantia, come sono Josquin desprez: [Giovan?] Mouton: Divitis: Mathurin forestier: Brumel: Richafort: Guascogne: Fevin: Carpentras; Constantio festa; Consilium: Andrea de silva: Morales: Adrian Willart: Jacquet: e molti altri eccellentissimi dottissimi et espertissimi Musici Compositori, tanto vivi quanto morti (i cui nomi si lasciano qui per brevita, et non per sminuire la lor fama) i quali non hanno voluto usare, gli alzamenti et abbassamenti delle intonationi predette, ne meno osservare la predetta malconsiderata legge ò regola, nelle lor compositioni, considerando che tutti i canti composti di questa maniera che sarebbon del primo: o secondo: o terzo: o quarto tuono: lasciando il lor proprio procedere e la lor natural sede, e determinata fine, accennano di voler esser del quinto: o sesto: o settimo: o ottavo tuono.

"These modern composers [compositori novelli] also scorn and castigate, with those convictions of theirs, all skilful works composed by the very excellent, very perfect and very experienced musicians, from whom they received the light, and without whose examples they would not have known how to form a consonance, such as are: Josquin Desprez, Jean Mouton, Divitis, Mathurin Forestier, Brumel, Richafort, Guascogne, Fevin, Carpentras, Costanzo Festa, Consilium, Andreas da Silva, Morales, Adrian Willart, Jacquet, and many other very excellent, very learned and very experienced musicians [and] composers, living as well as dead (whose names we shall omit here for brevity's sake, and not to lower their reputation), who did not want to use the raising and lowering of the said pitches, nor [did they want] to observe the said ill-founded law or rule in their compositions, considering that all songs composed in that manner, and which would be of the first, second, third or fourth mode, leaving their proper progression and their natural seat and established end, would seem to allege to be of the fifth, sixth, seventh or eighth mode."

[Rome, Biblioteca Vallicelliana, MS R 56, fol. 408r/408v; quoted by ARLETTAZ, Vincent: «'La malconsiderata legge.' La pureté modale selon Ghiselin Danckerts (XVIe siècle)», in: Revue Musicale de Suisse Romande 64/1, mars 2011, p. 20-47; see p. 36-37 (with French translation).]

It should also be noted that Danckerts and Coclico are the only two Flemish theorists of some importance in the entire sixteenth century. As we have seen, almost no Germanic authority of that time has approached the principle of attraction; and now we see that both Flemish authors explicitly resist the same doctrine, a very striking coincidence indeed.
 

Other countries

The treatises of other countries are less problematic. Spanish authors (Tovar, Bermudo, Santa Maria...) confirm the attraction principle, both in its melodic and harmonic formulations, improving on Gaffurius if necessary (Bermudo). They also attest the existence of implied accidentals (more particularly Tovar and Bermudo).

[See -MARTINEZ DE BIZCARGUI, Gonçalo, Arte de canto llano y contrapunto y canto de organo con proportiones y modos brevemente compuesta, Saragossa, 1508, cap. 22. Ed. A. Seay, Colorado College Music Press, Critical Texts 8, Colorado Springs, 1979, p. 25-26.
-TOVAR, Francisco, Libro de musica practica, Barcelona, Johan Rosebach, 1510, lib. III, cap. 6-7.
-BERMUDO, Juan, Comiença el libro llamado declaracion de instrumentos musicales..., Osuna, 1555, fol. 67r-v, 81v-82r, 87v ff.
-SANTA MARIA, Tomás de, Libro llamado Arte de tañer Fantasia, assi para Tecla como para Vihuela, y todo instrumento..., Valladolid, 1565 (facsimile: Geneva, Minkoff Reprint, 1973); I, fol. 63v, 74v, 76r.]
 

As for the French treatises, they are less numerous, and less informative on the whole. The one written by Nicolaus Wollick (a native of Lorraine, a region in Eastern France with a Germanic dialect) is very close to the German tradition. Moreover, its most instructive passages are the work of Wollick's master in Cologne, the German Melchior Schanppecher; they do not introduce the attraction principle, but merely repeat Gaffurius' weakened formulation (as Ornithoparchus' Micrologus does as well). By contrast, Guillaume Guerson (about 1500) and Loys Bourgeois (1550) are seen to put forward rather explicit melodic formulations; but they both require chromatic inflections to be written down.

[See -WOLLICK, Nicolaus, Enchiridion musices, Paris, F. Regnault, 1512 (facsimile: Geneva, Minkoff, 1972), book 6, chap. 5, sig. l.ii. (see also chap. 3, 2 pages before l.i.).
-GUERSON, Guillaume, Utilissime musicales regule [...], Paris, Marnef-Regnault, 1513, sig. C.ii.r.
-BOURGEOIS, Loys, Le droict chemin de musique, Genève, [Jean Gérard], 1550, chap. 2.]
 

Two more treatises should be mentionned here, the former by Michel de Menehou (1558), the latter by Jean Yssandon (1582). But they do not present anything special for our inquiry (in spite of its late date, Yssandon's treatise only restates Gaffurius' weakened formulation, without amending it).
 

Summary

In the theoretical literature, the attraction principle appears towards the end of the thirteenth century. In spite of some resistance in fourteenth-century England (Pseudo-Tunstede), it develops significantly during the fourteenth and fifteenth centuries. But in the late years of the fifteenth century, it loses much of its strength, to the point of being suspended, so to speak, by Gaffurius (weakened harmonic formulation).
   From that time up to the mid-sixteenth century, it is virtually absent from the Germanic treatises (Glarean, Ornithoparchus, Sebald Haydn...), and even rejected by the few known Flemish authorities (Coclico, Danckerts).
   The recovery movement commences in the 1530s in Italy. Gaffurius' weakened formulation is then progressively criticized and amended by Lanfranco (1533), Vanneo (1533) and Dentice (1553). At the very same time, part of the Italian theorists come out against implied accidentals (Aaron, 1529, Vicentino, 1555), but others still hold to the traditional view (Vanneo, 1533, Zarlino, 1558).

As one cannot fail to recognize, such an evolution is absolutely consistent with the observations of our first section, regarding specified accidentals in the vocal sources. More particularly, the reappearance of sharps in Italy (from the 1530s) clearly corroborates the new conceptions put forward by the theorists.
 

Continued: (III) The instrumental tablatures >>>