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Playing in consonances: a Spanish Renaissance technique of chordal improvisation.

The practice of improvisation played a significant role among 16th-century Spanish instrumental performers and composers, as indicated by two major treatises of the period devoted to the codification of improvisational techniques - Diego Ortiz's Tratado de glosas (1553) and Tomas de Santa Maria's Arte de taner fantasia (1565).(1) Ortiz's well known treatise is a practical guide to three frequently used improvisational techniques: (1) extemporization on a previously composed vocal piece; (2) improvisation on a given cantus firmus (including such familiar ground basses as the romanesca, the passamezzo antico and the folia); and (3) free improvisation. To illustrate these procedures, Ortiz includes pieces he calls recercadas, for viol with harpsichord accompaniment. The main improvisational technique used by the viol is melodic elaboration and diminution of cadential formulas and intervals (glosado) according to an exhaustive catalogue of examples which he provides. In the case of renditions of pre-existing compositions, the keyboard player performs a reduction of the vocal parts while the viol improvises over it. For pieces on a cantus firmus or a ground bass, Ortiz indicates that the accompaniment should be performed 'in consonances' and also use 'some counterpoint appropriate to the recercada played by the viol'.(2) The accompaniment of free improvisation should be based on the same techniques - 'playing in consonances' and occasional imitation when appropriate.(3)

The chordal technique of improvisation known in Spain as 'playing in consonances' - to which Ortiz alludes only in passing - was indeed commonly used by composers and performers of the period. Miguel de Fuenllana, Luis Milan, Luis de Narvaez and Enriquez de Valderrabano include various references to 'playing in consonances' in their respective vihuela collections. Some of the compositions by these authors are even titled fantasia de consonancias.(4) In all these cases, the term consonancias is used as a synonym for the modern term 'chord', and the technique is thus applicable to any instrument with chordal capabilities.

Vihuela compositions based on chordal textures also reveal an improvisational origin. Fantasias 10 to 28 from Milan's El maestro, as well as his four tientos, alternate chordal passages with sections of fast idiomatic figuration. Milan explains that these pieces illustrate a type of music which consists of 'playing the vihuela in consonances mixed with redobles', and that 'the consonances are to be played slowly and the redobles quickly'.(5) Fuenllana and Mudarra each include eight tientos in their respective collections, all written 'in consonances'. A vihuela tiento was an improvised prelude with the function of establishing the mode before the performance of a composed work. 'He who wishes to play a transcription or fantasia in the first tone, or in any of the eight', Fuenllana states in his preface, 'making a beginning with one of these tientos, he can move into the tone without disturbing the ear. ... The composition of these tientos is of chords and nothing more ... [la compostura destos tientos es de consonancias y no mas]'.(6)

Spanish musicians in the Renaissance were thus thinking in terms of chords to describe some of the textures in their compositions.(7) However, as much as musicians may have been aware of the triad as a unified entity, the concept of triadic invertibility was not established until Johannes Lippius's Disputatio musica tertia (1610), and the equal status of triadic inversions, as well as the principles of functional progression, were not accepted until Rameau's Traite de l'harmonie (1722). How, then, did Renaissance musicians approach the composition or improvisation of chordal textures? A valuable clue to help us answer this question is provided by the second major Spanish treatise on improvisation, Santa Maria's Arte de rafter fantasia, in what seems to be the earliest published complete description of an improvisational and compositional technique based on the supremacy of a treble-bass duet filled in with vertical sonorities. Santa Maria's presentation of the technique of taner a consonancias ('playing in consonances'), one of the central focuses of the treatise, covers as many as 24 chapters laid out through 102 pages (part 2, chapters 6-30, ff.12r-63r). The basic compositional principle is the same as that which in the 17th century would result in the familiar thoroughbass technique: a bass line is added to an existing treble line, thus creating an outer-voice structural duet; the two inner voices are then added, taking into account the quality of the resulting vertical sonorities, which in turn are defined by the intervals counted from the bass upwards. The importance attributed by Santa Maria to 'playing in consonances' testifies to the significant role of the technique in the 16th century, and to the continuity in this sense between the Renaissance and the Baroque.(8)

There is little doubt regarding the connection between Santa Maria's expositions and actual performance practice. Santa Maria was himself a well known organist, at least within the realm of the Dominican order to which he belonged, and his treatise seems to have been widely used as a keyboard tutor.(9) Moreover, we should remember the likely personal and musical association between Santa Maria and Antonio de Cabezon, the blind court organist to both Charles V and Philip II and the leading organ composer of the period. The opening pages of the Arte inform us that 'the book has been examined and approved by His Majesty's eminent musician, Antonio de Cabezon, and by his brother, Juan de Cabezon', and in the ensuing prologue Santa Maria declares again that in the 16 years he took to write his treatise, he 'consulted with persons skilled and knowledgeable in the faculty [of improvising fantasia], especially with Antonio de Cabezon, His Majesty's eminent musician'. We should also note that while Santa Maria refers to 'playing in consonances' as an improvisational process, the connections between improvisational and compositional (that is, written) techniques in some instrumental genres are very close. Numerous examples of passages that fit Santa Maria's description of 'playing in consonances' can be found in Cabezon's compositions, some of which will be analysed later in this article. Moreover, the modal and compositional structures described by Santa Maria, and illustrated by his fantasias, are the same that underlie Cabezon's tientos. The Arte is thus not only a treatise on improvisation and keyboard performance practice, but also on Renaissance compositional techniques and musical structure.(10)

The technique of playing in consonances

Santa Maria states the compositional principle and the supremacy of the treble-bass pair early in part 2:

It has to be known that any consonance, whether given in three, four, or more voices, is understood and counted from the bass to the discant, which are the outer voices, because the middle parts, tenor and alto, are used only for the accompanying consonances and to fill the void between the outer parts.(11)

It should be noted that Santa Maria's purpose is pedagogical, and that his style of presentation is rational, comprehensive and highly organized. The Dominican virtually exhausts every possibility, and provides numerous examples for each new step in the method. It would seem that a performer who would have studied, practised and assimilated the chapters on 'playing in consonances' in a thorough and systematic way would indeed have become highly proficient in the art of chordal improvisation at the keyboard.

Santa Maria begins his technical exposition by introducing the concept of 'the differences of every consonance', referring to the possible ways in which a consonant interval between the outer voices can be divided into other consonant intervals by means of the inner voices. The differences of a consonance that he says sound best are those which 'do not have many octaves, but only one' (in other words, those in which only one note is doubled, and hence are made up of a complete triad), and those in which the octave does not involve the discant, but rather the bass and tenor or the bass and alto (that is, the bass should preferably be doubled).(12) Using these criteria, Santa Maria classifies the differences of each sonority by degrees. Differences of the first degree are to be used when possible, and only when one cannot use a certain degree should one move to the next. Ex.1 reproduces Santa Maria's table of the differences for the octave, the 10th, the 12th and the 13th, with their respective degrees listed below every sonority. Since first degrees are to be used the most, Santa Maria summarizes all of them at the end of his tables.(13)

In chapters 11 to 30 Santa Maria explains the next step in his method. All practical music, we learn, is made up of three movements: repeated notes, ascending motion and descending motion (unisonar, subir, y baxar). Upward and downward motion can be effected by steps or by leaps (subir y baxar de arreo o de salto). All of these movements refer to the treble line, and if one learns how to play in consonances with the remaining three voices on given trebles which follow these motions, then one should be able to deal in a similar manner with all practical music. To achieve this, Santa Maria sets out to study in detail all the possible ways in which treble lines can be harmonized when they ascend or descend by steps, when they repeat notes, and when they ascend or descend by leaps of 3rds, 4ths, 5ths, or octaves. The procedure used to harmonize given treble lines is as follows: first, Santa Maria establishes the consonances which the bass will define with the treble; then the two inner voices result from the application of the differences of the consonances. In other words, the treble-bass frame is established and then filled in with the 'best' possible sonorities, avoiding parallel perfect consonances.

The chapter devoted to the treble which ascends or descends by steps in minims, for instance, includes 53 musical illustrations, of which two are reproduced in ex.2. Both cases are completely made up of first-degree sonorities, all in root position in ex.2a, and with the repeating pattern root position/first inversion/root position in ex.2b.

We learn in the Arte that all the possible ways of ascending and descending must be mixed together for the sake of the necessary variety in the consonances. In order to teach the beginner how to effect these ascents and descents with diversity, Santa Maria provides eight pages of examples with 'the most gracious ways of ascending and descending eight degrees [ocho puntos] with variety, each closing with a cadence'.(14) These harmonizations of a treble covering an octave by steps are, in a way, precursors of the harmonizations of bass octave scales found in Baroque thoroughbass treatises, and known as 'rules of the octave'.(15) Before presenting the complete octaves, Santa Maria proposes harmonizations of ascending and descending three-note fragments. Then the complete octave is harmonized using different combinations of the previous fragments. Ex.3 shows the proposed ascending three-note fragments, harmonized with the following consonances: 8-10-10, 8-13-10, 10-13-10, 10-13-15 and 13-10-10, followed by three octave harmonizations, starting at the octave, 10th and 12th respectively. I have outlined the different segments which are combined in these examples, together with the consonances that constitute them. The three-note descending fragments proposed by the Castilian theorist are formed by the consonances 8-10-13, 10-10-8, 10-13-8 and 10-10-10 [ILLUSTRATION FOR EX.3E OMITTED]. A complete octave illustrates the harmonization of a three-note segment by 13-10-10 [ILLUSTRATION FOR EX.3F OMITTED]. Exx.3g and 3h reproduce two descending octaves harmonized with combinations of the fragments above.

Musical applications

Santa Maria mentions two applications of the technique of consonances. Within his presentation of the harmonization of repeated notes (unisonar), he includes a chapter with examples of fabordones in the eight modes.(16) The fabordones, or chordal harmonizations of the psalm tones, 'usually begin with repeated notes, and for this reason we include them here', he declares.(17) In the second place, passages in consonances can also be included, according to Santa Maria, in the course of a fantasia.(18)

The ultimate purpose of the Arte de taner fantasia, as stated in the title, is to provide and teach the technical and musical tools that will enable the student to master the art of improvising fantasia. These tools include keyboard technique and the art of glosa (ornamentation and diminution), the mensural system, modal polyphonic structure, the technique of 'playing in consonances', the rules of use and control of dissonance, the contrapuntal details of four-voice cadences, and, finally, the techniques of imitative counterpoint and their role in generating the formal structure of a fantasia. Santa Maria refers to the fantasia as a process, not as a finished product. Thus, he writes of 'playing fantasia' (taner fantasia), in the singular, rather than 'writing fantasias' in the plural. Formally, the fantasia is a piece divided into sections, each of which usually begins with a new subject in imitation, and ends with a cadence on one of the essential modal degrees (which, for Santa Maria, are the final and the 'mediant', or psalm-tone tenor, of each mode). As a matter of fact, the formal and tonal processes he describes are identical with those found in the Spanish organ tientos of the second half of the 16th century, particularly those by Antonio de Cabezon. The study of Cabezon's works fully confirms Santa Maria's prescriptions for playing in consonances. Six of the tientos by the blind organ master include prominent passages in consonances (Libro de cifra nueva, nos.1, 3, 7 and 11; Obras de musica, nos.3 and 9).(19) All his fabordones, some of his versets, and some of his sets of variations (diferencias) are also written in this style.

Passages in consonances in the tientos are normally used to close a piece or a major section. The bass is frequently played with diminutions (glosado), and other voices may also carry melodic elaboration of the sonorities. Ex.4a reproduces two phrases of the closing section of Obras 9. In the first phrase a treble 'descending by leaps of 3rd in minims' is harmonized with a bass in parallel 10ths (see Santa Maria, 'bajando terceras de salto a minimas con el bajo todo a decenas', f.57v), all elaborated by a sequential dialogue between treble and alto. In the second phrase, a bass with diminutions (bajo glosado) harmonizes the treble with the consonances 10-10-8/12-10/8-10/8-10.

The Obras include four fabordones for each mode, all written in consonances, and in accordance with Santa Maria's prescriptions for the harmonization of repeated notes (f.31r). The first of each group is a fabordon llano, or unornamented fabordon, the second presents a glosado in the treble, the 3rd in the bass, and the 4th in both of the inner voices. Ex.4b reproduces the opening of the fourth fabordon in mode 1, with glosado in the inner voices, and with my indication of consonances and their possible grouping. Among Cabezon's ten sets of variations (nine from the Obras and one from the Libro), eight are based on the principle of consonancias: the three sets on Guardame las vacas, the three sets on the Pavana italiana (including the Pavana con su glosa from the Libro), and the sets on the Gallarda milanesa and La dama le demanda. Ex.4c reproduces the theme of the Diferencias sobre la vacas.(20) The basic frame of this piece is provided by the romanesca bass (f-c-d-A/f-c-B[flat]-A-D) and the Spanish popular tune Guardame las vacas in the treble (f'-e'-d'-c[sharp]'). The harmonization of the treble is an application of the criteria expounded by Santa Maria to harmonize lines descending by steps, according to the basic pattern 8-10/8-10//8-10/10-10-8, indicated by circles below the staff. (Compare this with Santa Maria's harmonization of descending treble lines in ex.3.) Between these consonances, repeated notes are harmonized with the consonances 8-12-10, 8-13-12-13 and 10-12 respectively. The passage is elaborated with glosas in the tenor and bass.

The technique of playing in consonances is thus, in the first place, a method to improvise in chordal style and to accompany given treble lines with a bass-supported homophonic texture. In the second place, the presence of numerous passages in consonances in the works of Cabezon and other organ composers of the period, as well as in the tientos and fantasias for vihuela by Fuenllana, Narvaez and Valderrabano, provides ample evidence that 'playing in consonances' was also a compositional technique. And finally, we should not overlook the significance and implications of the technique as a theoretical formulation.

Evaluation of Santa Maria's harmonic theory

The harmonic system expounded by Santa Maria is based on the following criteria: the outer-voice duet has structural priority; the added inner voices fill in the outer-voice consonance with one of several possible consonant arrangements; these arrangements are classified by their intervallic content as reckoned from the bass. The concern of the theorist lies in the quality of the resulting sonorities - driven by the melodic motion of the treble - and not in the progression of the bass. The elements examined to determine the quality of a sonority are the note which is doubled (the bass is preferred) and the fullness of the sonority (complete 'triads' are preferred, although the term is not mentioned in the Arte). Finally, we should note that Santa Maria's classification of sonorities also shows his preference for root-position triads, and within these, for sonorities with larger intervals at the bottom (although neither of these two categories is explicitly mentioned).

The significance of such an approach to harmony will be apparent if we compare it with some 17th-century harmonic formulations. But before we do so, we should remember that while in the 16th century some treatises started to acknowledge the role of the bass as a foundation for the sonorities above it, most theorists continued the tradition of considering the tenor as the main structural voice in the polyphonic texture.(21) In the old dyadic technique of polyphonic composition, the treble-tenor duet had structural priority, while the alto and bass were added later in their subordinate harmonic role. The tenor was, indeed, the first voice to be composed or the voice that bore the borrowed tune. In contrast, the harmonically conceived music of the Baroque presupposed a free and independent bass that could act as the foundation for the triadic sonorities above it.

While Renaissance theorists usually stressed counterpoint as the main compositional technique, Benito Rivera has demonstrated that, beginning in the late 15th century, treatises reveal the triadic orientation of polyphonic composition in their treatment of counterpoint. Rivera's main arguments are that the relaxation of the rules of counterpoint regarding intervallic progressions which can be noticed in this period is meant to accommodate and enhance triadic sonorities, that the emancipation of the bass from the formerly controlling structure of the discant-tenor duet brought with it a more triadic orientation, and that all of this was reflected by the concern of theorists in the 16th century to account for intervallic inversion and the formation of triads by mediation.

The theory of functional harmony and the equal status of triadic inversions were not clearly formulated until Rameau's Traite. The long intermediate period (from the late 15th to the early 17th centuries) should not be simply seen as a transitional epoch between the dyadic and the functional-harmonic approaches, but rather as a period in which composers and theorists took into consideration the vertical component of music, albeit from a totally different perspective than that of Rameau. This is precisely the perspective expounded in the Arte de taner fantasia. Speculative harmony in the 17th century relied largely on the science of numerical proportions, and the concepts of triad (trias harmonica) and triadic inversion, unknown to Santa Maria, were generally acknowledged after their unequivocal presentation by Lippius. Otherwise, the common practical approach to vertical composition was based, until well into the 18th century, on the same concepts found in the Arte.

Lippius recommends the harmonization of an outer-voice structure using root-position triads exclusively - only occasionally should first or second inversions be used. The triads should always be complete, the root should be doubled most of the time - sometimes the 5th, rarely the 3rd - and larger intervals should be placed at the bottom of the sonority.(23) Pietro Cerone borrows Santa Maria's presentation of the 'differences of the consonances' almost literally and without acknowledgement. He also summarizes Santa Maria's technique of 'playing in consonances', referring to it as 'accompaniment of the treble' (acompanamiento del tiple) when it repeats notes, or when it ascends or descends by steps, by leaps of 3rd, 4th, or 5th.(24) Marin Mersenne also establishes the primacy of the treble-bass pair, and lists all the possible ways in which octaves and 10ths can be filled in with two inner voices, in charts similar to Santa Maria's 'differences of the consonances'. Considering the frequent references to Cerone which can be found in Mersenne's Harmonie universelle, the influence of Santa Maria's classification of sonorities on Mersenne seems likely.(25) As late as 1702 Andreas Werckmeister classifies all possible arrangements of a C major triad in four voices following the criteria of triad position (root position is best), doubling (the root should be doubled), disposition of the voices (closed positions are better than open positions) and fullness of sound (triads should be complete).(26)

The prevailing approach to chordal composition in the 17th century can be found in thoroughbass treatises, and these rely frequently on the same principles outlined in the Arte. In chapter 14 of Li primi albori musicali (Bologna, 1672), Lorenzo Penna discusses the accompaniment of a solo melody. Penna's examples provide the melody and the bass, leaving the chords to be supplied by the performer, according to the rules stated in the treatise's first chapter. The first rule is: 'the harmony is to be replete with consonances, namely the Prime, Third, Fifth, or Sixth, Octave, and their compounds'.(27)

Matthew Locke's directions for chordal composition are all based on intervals counted from the bass. Locke considers first the bass motion (by steps, or by leaps of any interval), then lists the possible intervals between the bass and the discant with each particular bass motion, and finally instructs the performer to fill in the structure with consonances unless the figures indicate otherwise.(28) The same approach is found in Gasparini's L'armonico pratico al cimbalo (Venice, 1708). Gasparini starts from the motion of the bass (by step, or by leap of different intervals,), and determines what intervallic arrangements can be used to harmonize each particular motion.(29) Some of Gasparini's other major concerns are dissonances and cadences (all discussed according to their vertical intervallic content), and diminutions. Gasparini's examples for the latter are made up of a melody and a bass, and he instructs the performer to play the bass 'and consonances' with the left hand, while the right hand plays the embellished melody.(30)

The basic difference between the approach to vertical composition in figured-bass treatises and in the Arte is that the former always start from the bass, while Santa Maria starts from the treble and then adds the bass. This difference of stress between the treble and the bass is also apparent in their harmonizations of octave segments. Santa Maria harmonizes treble octave segments, while the later 'rules of the octave' refer to the harmonization of a bass octave. Otherwise, the elements, procedures and criteria presented in the Arte are virtually the same as those used in 17th- and early 18th-century harmonic formulations. And in all cases the main concern lies in the intervallic content and connection of the vertical sonorities, rather than the linear progression of the bass. The Arte thus contains an early exposition of a theory of harmony that would be in effect for almost two centuries, and which would provide musicians of the Renaissance and Baroque periods with the means for understanding and rationalizing their practice of vertical composition and improvisation.

1 Diego Ortiz, Tratado de glosas sobre clausulas y otros generos de puntos en la musica de violones (Rome, 1553), ed. M. Schneider (Kassel, 1936); Tomas de Santa Maria, Libro llamado arte de taner fantasia (Valladolid, 1565), trans. A. Howell and W. Hultberg as The art of playing the fantasia by Fray Thomas de Sancta Maria (Pittsburgh, PA, 1991).

2 Ortiz, Tratado de glosas, P.55.

3 Ortiz, Tratado de glosas, p.51.

4 See Miguel de Fuenllana, Orphenica lyra, ed. C. Jacobs (Oxford, 1978), pp.lxxviii, xcii, xciii, xcv, and fantasia 49, P.951; Luis Milan, El maestro, ed. C. Jacobs (University Park, PA, 1971), pp.298, 300, 311, 312; Luis de Narvaez, Los seys libros del delphin, ed. E. Pujol, Monumentos de la Musica Espanola, iii (Barcelona, 1945), fantasia 5, p.10; and Enriquez de Valderrabano, Libro de musica de vihuela, intitulado Silva de sirenas, ed. E. Pujol, Monumentos de la Musica Espanola, xxii, xxiii (Barcelona, 1965), i, p.22, and fantasia 30, ii, p.29. J. Griffiths, 'La "Fantasia que contra-haze la harpa" de Alonso Mudarra; estudio historico-analitico', Revista de musicologia, ix (1986), pp.29-40, argues that Mudarra's well known fantasia, written in the style of the 15th-century harpist Ludovico and based on the harmonic frame of the folia, seems to suggest an old practice of instrumental improvisation on such harmonic-melodic patterns as the romanesca, the passamezzo and the folia.

5 Milan, El maestro, pp.298, 311, 312.

6 Fuenllana, Orphenica lyra, p.xcv. See also L. Jambou, Les origines du tiento (Paris, 1982), pp.27-8, 93-7, 133-6. Some terminological clarification is necessary at this point: while the early vihuela tientos were chordal, improvisational preludes, the later tientos by Cabezon and other organ composers, as well as the organ fantasias by Santa Maria and those for vihuela by Fuenllana are imitative pieces akin to the Italian ricercar.

7 The vertical, triadic orientation of Renaissance music was certainly not an exclusive characteristic of either Spanish or instrumental repertories. Let it suffice to mention such well known examples as the Italian frottola and early madrigal or the Spanish villancico, with their tendency to homophonic, homorhythmic textures, and, among compositions traditionally considered contrapuntal, passages in the motets of Josquin and Willaert. The chordal approach to instrumental composition is also especially evident in the toccatas by Merulo and Diruta, the variations by Spanish vihuela and organ composers, and lute songs of Dowland and other English composers.

8 While Santa Maria's chapters on keyboard performance practice have received considerable attention, the only detailed descriptions of the technique of 'playing in consonances' can be found in S. Rubio, 'Las consonancias (acordes) en el Arte de taner fantasia de Fray Tomas de Santa Maria', Revista de musicologia, iv (1980), pp.5-40; and M. Roig-Francoli, 'Bass emancipation in sixteenth-century instrumental music: the Libro llamado arte de taner fantasia by Tomas de Santa Maria', Indiana theory review, ix (1988), pp.77-98. Other scholars, however, have pointed out the significance of the technique. J. Ward, The vihuela de mano and its music (PhD diss., New York U., 1953), p.283, states that 'Santa Maria's recognition of the consonancia as a chord to be reckoned from the bass, both in his writing and in the illustrative musical examples, is far more clearly expressed than similar ideas tentatively voiced in other 16th-century treatises'. A similar remark can be found in R. Murphy, Fantasia and ricercare in the sixteenth century (PhD diss., Yale U., 1954), p.46. A precise summary of the treatise's part 2 is provided in M. Schneider, Die Anfange des Basso continuo und seiner Bezifferung (Leipzig, 1918/R Westmead, 1971), pp.30-46. Schneider notices that Santa Maria's approach is based on the same principles that would later become the foundation for thoroughbass playing, stresses Santa Maria's use of vertical sonorities and of a soprano-bass structure filled in by inner voices, and outlines the technique of 'playing in consonances'. Similarly, attention is called to Santa Maria's discant-bass structures in C. Dahlhaus, Untersuchungen uber die Entstehung der harmonischen Tonalitat (Kassel, 1968), p.89. See also M. Roig-Francoli, 'En torno a la figura y la obra de Tomas de Santa Maria: aclaraciones, evaluaciones y relacion con la musica de Cabezon', Revista de musicologia, xv (1992), pp.55-85. The following are studies that focus on Santa Maria's chapters on keyboard technique and performance practice: E. Harich-Schneider, 'Zum Klavichordspiels bei Tomas de Santa Maria', Archiv fur Musikforschung, ii (1937), pp.243-5; E. Harich-Schneider, Die Kunst des Cembalospiels (Kassel, 1939), passim; E. Harich-Schneider, The harpsichord (Kassel, 1954), pp.20, 32; Ward, 'The vihuela de mano and its music', pp.64ff; C. Jacobs, La interpretacion de la musica espanola del siglo XVI para intrumentos de teclado (Madrid, 1959), passim; H. Lange, 'A tutor by Santa Maria', Dolmetsch Foundation bulletin, xiv (1968), pp.5-6; D. Poulton, 'How to play with good style by Thomas de Sancta Maria', Lute Society journal, xii (1970), pp.23-30; and Spain, 1550-1830, ed. C. Johnson, Historical Organ Techniques and Repertoire, i (n.p., 1994). A paraphrase of Santa Maria's complete treatise can be found in W. Hultberg, Sancta Maria's Libro llamado arte de taner fantasia: a critical evaluation (PhD diss., U. of Southern California, 1964).

9 In his Historia eclesiastica y flores de Santos de Espana, part 2, chap. 14 (Cuenca, 1594), the Dominican chronicler Juan de Marieta refers to Santa Maria's excellence as an organist: 'Fray Tomas de Santa Maria, of the province of Castile, was a great musician, both as a singer and performer. He did not want to hide his talents, but instead wrote for coming generations a treatise in the vernacular, divided in two books, on the art of organ performance, which is widely used by many musicians. He died in 1570.' (This and all translations from original Spanish sources in the present article are mine.) The treatise, however, is not only addressed to keyboard players. The title of the Arte de taner fantasia is followed by the subtitle Assi para tecla como para vihuela, y todo instrumento en que se pudiere rafter a tres, y a quatro vozes, y a mas ('for keyboard, vihuela, or any instrument that can be played in three, four, or more parts'). Thus, the only condition is that it be a polyphonic instrument. Despite this title statement, Santa Maria's examples are clearly for keyboard, and he devotes only two pages to the vihuela. Moreover, he does not refer to the organ throughout the treatise, but rather to the monocordio (clavichord).

10 For a study of the musical relationships between the two authors, see M. Roig-Francoli, Compositional theory and practice in mid-sixteenth-century Spanish instrumental music: the Arte de taner fantasia by Tomas de Santa Maria and the music of Antonio de Cabezon (PhD diss., Indiana U., 1990); and M. Roig-Francoli, 'Modal paradigms in mid-sixteenth-century Spanish instrumental composition: theory and practice in Antonio de Cabezon and Tomas de Santa Maria', Journal of music theory, xxx iii (1994), pp.247-89. The personal relationship between the two musicians has never been established as a historical fact beyond Santa Maria's statements in the opening pages of the treatise. In his Antologia de organistas clasicos (1914), L. Villalba proposed, with no documentary evidence, that Santa Maria resided at the monastery of San Pablo in Valladolid. This supposition has ever since been reported as a fact in all the biographical references to Santa Maria. Since Cabezon spent years in two palaces located in the same square as the monastery of San Pablo (the palaces of the Pimentel family and of Francisco de los Cobos, both residences of the itinerant Spanish court), Santa Maria's tenure at San Pablo would certainly be historically convenient. While it is a possibility, it is not a historical fact. For a critical biography of the theorist, see P. Aizpurua, 'Fray Tomas de Santa Maria', Retablo de artistas (Caleruega, Burgos, 1987), pp.255-7.

11 Santa Maria, Arte de taner fantasia, ii, f.13v. The modal supremacy of the treble over the other voices has already been established earlier in the treatise, when he recommends that the treble (and not the tenor) be examined in order to determine the mode of a composition, because the treble 'rules all the other voices' (ff.61r, 70r). I am grateful to John Griffiths for pointing out that Luis Milan was the earliest author to refer to the treble as the voice that determines the mode of a composition (Milan, El maestro, pp.14, 25-6). Such practice departs from the established theoretical convention in Renaissance treatises, according to which the tenor is the ruling voice in polyphonic modality (see n.21 below).

12 Santa Maria, Arte de taner fantasia, f.15r.

13 Santa Maria, Arte de taner fantasia, f.19r.

14 Santa Maria, Arte de taner fantasia, ff.35r-39v.

15 The term 'rule of the octave' (regle de l'octave) was first coined by F. Campion in his Traite d'accompagnement et de composition selon la regle des octaves de musique (Paris, 1716), to refer to the practice of pedagogical chordal harmonizations of diatonic bass scales which can be traced back to the early 17th century. The 'rule' became a standard device in 18th-century pedagogies of thoroughbass and improvisation. See T. Christensen, 'The regle de l'octave in thorough-bass theory and practice', Acta musicologica, lxiv (1992), pp.91-117.

16 Santa Maria, Arte de taner fantasia, ff.42r-48r.

17 Santa Maria, Arte de taner fantasia, f.42v.

18 Santa Maria, Arte de taner fantasia, f.78v.

19 H. Angles, La musica en la corte de Carlos V, con la transcripcion del 'Libro de cifra nueva para tecla, harpa y vihuela' de Luys Venegas de Henestrosa, Monumentos de la Musica Espanola, ii (Barcelona, 1944); A. de Cabezon, Obras de musica para tecla, arpa y vihuela, Monumentos de la Musica Espanola, xxvii, xxviii, xxix (Barcelona, 1966).

20 Cabezon, Obras de musica, xxix, p.79.

21 Examples of treatises which acknowledge the structural role of the bass are Simon de Quercu, Opusculum musices (Landshut, 1516), in which vertical consonances are counted from the bass upwards, or Johannes Singer, Ein kurtzer Ausszug der Music (Nuremberg, 1531), which gives priority to the tenor-bass duet instead of the customary discant-tenor. See B. Rivera, 'Harmonic theory in musical treatises of the late fifteenth and early sixteenth centuries', Music theory spectrum, i (1979), pp.85-8. The tenor, on the other hand, is mentioned as the main structural voice in such treatises as Johannes Tinctoris, Liber de natura et proprietate tonorum, trans. A. Seay (Colorado Springs, CO, 1976), p.25; Pietro Aaron, Trattato della natura e cognitione di tutti gli tuoni di canto figurato (Venice, 1525), ch. 2., f.A2v; Adrianus Coclico, Compendium musices (Nuremberg, 1552), ch. 8, f.D1v; Heinrich Glarean, Dodechacordon, trans. C. Miller, Musicological Studies and Documents, vi (n.p., 1965), ii, p.247; and Gioseffo Zarlino, On the modes, trans. V. Cohen (New Haven, CT, 1983), p.92.

22 Rivera, 'Harmonic theory in musical treatises of the late fifteenth and early sixteenth centuries', p.81. The triadic component of 16th-century music, however, does not necessarily imply an orientation towards functional-harmonic organization. Even though such authors as Edward Lowinsky and Don Randel have seen the origin of functional harmony in what they label as 'V-I' cadences by 15th-century Burgundian composers, this does not justify the wholesale and anachronistic application to Renaissance music of analytical tools and systems appropriate to later styles. See E. Lowinsky, Tonality and atonality in sixteenth-century music (Berkeley, CA, 1961), and D. Randel, 'Emerging triadic tonality in the fifteenth century', Musical quarterly, lvii (1971), pp.73-86. For an example of anachronistic analytical criteria which seek justification precisely in Renaissance triadic textures, see D. Stern, 'Schenkerian theory and the analysis of Renaissance music', Schenker studies, ed. H. Siegel (Cambridge, 1990), pp.49-59. The same applies to 17th-century music; triadic progressions do not necessarily behave according to the tenets of functional tonality, as is clearly shown in B. Rivera, 'The seventeenth-century theory of triadic generation and invertibility and its application in contemporaneous rules of composition', Music theory spectrum, vi (1984), pp.63-78. See also T. Christensen, 'The Spanish Baroque guitar and seventeenth-century triadic theory', Journal of music theory, xxxvi (1992), pp.1-42.

23 Rivera, 'Harmonic theory in musical treatises of the late fifteenth and early sixteenth centuries', pp.65, 72.

24 Pietro Cerone, El melopeo y maestro (Naples, 1613), pp.730-37, 829-32.

25 Marin Mersenne, Harmonie universelle (Paris, 1636), pp.95, 207.

26 Andreas Werckmeister, Harmonologia musica (Frankfurt/Leipzig, 1702), p.5.

27 F. T. Arnold, The art of accompaniment from a thorough-bass (London, 1931), pp.135, 148.

28 Matthew Locke, Melothesia (London, 1673), p.7.

29 Francesco Gasparini, L'armonico pratico al cimbalo (Venice, 1708).

30 Gasparini, L'armonico pratico al cimbalo, pp.98-104.

Miguel Roig-Francoli is Assistant Professor of Music Theory and Music History at the School of Music, Northern Illinois University. He has published articles on Spanish Renaissance music and 20th-century analysis.
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