Guest Post: Jack on Guitar Counterpoint

Today, a special guest post from an old friend who has done a great deal of research into how the 16th century vihuelistas managed counterpoint:

Bryan has asked me to write a guest post summarizing my research into counterpoint on the guitar. This has been difficult to condense to a short essay because of its extensive ramifications into further areas of research: the histories of the lute, of counterpoint instruction, and of intonation, fretting and tuning. Here I address only my central discovery of an authentic 16th century method of fugue for the vihuela.

 I have been a commercial musician for 50 years, but in my teens, before learning the more lucrative skill of jazz harmony, I studied Jeppesen’s Counterpoint  [Knud Jeppesen, Counterpoint: The Polyphonic Vocal Style of the Sixteenth Century (in Danish, Copenhagen 1931, in English NY 1939, reprint Dover 1992)]. Over a period of 40 years I composed many species counterpoint exercises and a few studies in imitation, but Jeppesen’s method does not address fugue. Not to denigrate the valuable practice of species counterpoint, I only state that it raises some issues when applied to the guitar; this we will save for another essay. However, I ask: of what use is “counterpoint” without Fugue? Is not Fugue the real goal of counterpoint study? Species counterpoint, after all, is only a form of glorified four-part harmony.

Ten years ago I studied Fux’s teaching on fugue from his 1725 Gradus Ad Parnassum. [English trans. by Alfred Mann in The Study of Fugue (Rutgers Univ. Press 1958, reprint Dover 1987), pp 75-123.] To my disappointment I found his method not practical for the guitar. Fux assumes more independence of the voices and more florid motion than is possible on the fingerboard. But in 2013 I had my first nine-string guitar built, with fanned frets and a range from F#1 to F6. I wished to review the history of fugue, to see if I might find another approach, and this instrument proved useful in studying keyboard music. 

In 2018, several years into my fugue research project, I read and transcribed Fray Thomás de Sancta Maria’s 1565 Libro Llamado Arte de Tañer Fantasía, obtained online. The title page states that it is “for harp, keyboard or vihuela”, but in fact it is written for a keyboard with a range from C2 to A5, a range which my nine-string guitar accomodates fairly well, not perfectly. A plucked-string instrument designed specifically for the study of TSM’s work might be an eleven-course A-lute A4-E4-B3-G3-D3-A2, with five unfretted basses G2-F2-E2-D2-C2, basses which would correspond exactly to the short octave (lacking accidentals) on TSM’s keyboard. But I do fairly well with my own instrument. 

Though often exceeding the practical range of a six-course instrument, TSM’s affinity with the style of the vihuelists is such that much of his music does fit comfortably on the fingerboard with little modification. TSM’s model fantasía in the Dorian authentic mode [Thomás de Sancta Maria, Libro Llamado Arte de Tañer Fantasía (Valladolid 1565), Book I, f67v] opens with a point of imitation very similar to the point that Mudarra used for the very first fantasía in his Tres Libros en Cifra of 1546.

Note that both Mudarra’s and TSM’s soprano lines cover completely the upper Dorian authentic range D4 -D5, and both tenor lines cover the lower Dorian authentic range D3-D4. Mudarra’s alto and bass occupy only their respective modal pentachords D-A, thus not declaring themselves as either authentic or plagal, while TSM’s alto covers the partial plagal range A3-G4, and his bass occupies only the lower register of the lower plagal range, A2-E3. 

Example 1: Mudarra’s Dorian authentic point: 

Click to enlarge

Example 2: TSM’s Dorian authentic point: 

The Arte provides a guitar-friendly method of fugue (not to say that it is technically easy by any means) in a style similar to that of the vihuelistas, although with consistently denser voice leading. In a nutshell, the technique is (see examples) to play a closely linked subject-answer combination in the soprano and alto (or any other voice pair), followed by a cadence; before, during, or after the cadence, the bass and tenor (or other two voices) enter with the same point of imitation an octave lower ( or higher), and after this entrance, the first two voices may drop out, as in Mudarra’s fugue, or may play minimalist accompaniments as shown by TSM. All four voices play seldom at once except during the cadences, and all that is required to maintain the four-part contrapuntal texture is that each voice should be heard to state the subject or answer in its appropriate range – hence a necessary emphasis on the modal ranges. 

The use of the hexachords and/or of the plagal and authentic ranges as controlling limits on the voice leading keeps the composition mostly within the Gamut and on the fingerboard (to a point, with some necessary transpositions and minor edits, and given that TSM demonstrates the complete sonic range of his keyboard and that these limits are not carved in stone). These voice leading control techniques, originating in the improvised vocal counterpoint of the 15th century, I discovered separately from reading Guilielmus Monachus, [Eulmee Park, De Preceptis Artis Musicae of Guilielmus Monachus, A New Edition, Translation and Commentary, PhD diss., Ohio State Univ. 1993, pp 57-60], Ramos de Pareja, [Luanne Eris Fose, The Musica Practica of Bartolomeo Ramos de Pareia: A Critical Translation and Commentary, PhD diss., Univ. of North Texas 1992, pp 369-370] and Zarlino [Gioseffo Zarlino, On the Modes, Part IV of Le Istitutioni harmoniche, translated by Vered Cohen (Yale Univ. Press 1983), ch 31 p 92 ff]. An analysis of TSM’s fugues with these techniques in mind shows a very tightly disciplined counterpoint, with each voice confined either (a) to the modal pentachord, (b) to a given hexachord or (c) to a given plagal or authentic range (a nominal octave sometimes extended to ten notes). The bass line is the voice most likely to use a mixed plagal and authentic range of three registers, but in fact this is fairly rare. 

Neither Jeppesen nor Fux considered the distinction between plagal and authentic modes to be important, because their methods suppose a less limited Gamut than we have on the guitar. Note that the medieval Gamut is perfectly expressed by the tuning and fretting of the six-course G-lute: Gamma-Ut is the lowest string, the three lowest basses are the roots of the three lowest hexachords, and ee-la, the highest note of the Guidonian Gamut, occurs on the 9th fret of the high G string. (The question of pitch standards is among the ramifications of this study.) It is important to state here my opinion that in order to understand modal counterpoint in a way that is idiomatic for the guitar – as well as to composed in an authentic 16th-century style – the modal ranges must be taken seriously as voice leading guides.

The mapping of the modal ranges onto the fingerboard of the modern guitar in the “original” keys leaves the low E string almost unused, and places the soprano ranges high on the fingerboard. There is a strong argument for transposing the entire modal system down a fourth for use on the guitar, moving the four modal finals D-E-F-G down to A-B-C-D, with a key signature of one sharp, which is probably close to the working pitch of the 16th century vihuela. This would be a good basis for species counterpoint exercises using the full array of modal ranges SATB while taking best advantage of the guitar’s more idiomatic positions. Since I have an extended range instrument, I have been able to systematically transpose most of TSM’s fugal examples (as well as my own species counterpoint exercises) through the circle of fifths. I find this to be much more effective, for learning the chord progressions and contrapuntal devices as fingerboard shapes and to get them into my ears, than to memorize them in one key only. Also, the most idiomatic transposition for each example is revealed by trying all the keys. It is not necessary to write out the transpositions. This practice shows that many of TSM’s examples will work best on the modern 6-string guitar transposed down a minor seventh with two sharps added. 

The practice of transposition within the Gamut reveals another interesting fact: that the traditional standard transposition of the entire set of modes up a fourth with a key signature of one flat is useful because when there are four voices, it permits the reversal of the positional assignments of the alternating plagal and authentic modes to the voices. In the untransposed modes, the Bass naturally is assigned the plagal range, the Tenor the authentic, the Alto the plagal and the Soprano the authentic. 

When transposed to one flat, in order to stay within the Gamut – and on the fingerboard! - the Bass naturally takes the authentic range such as Dorian G2-G3, and the other three voices are similarly reversed and stacked above the bass in alternating ranges. 

In Zarlino’s practice, the Tenor is said to determine the mode. In TSM’s practice the Soprano is said to determine the mode: this displays the change to from a vocal to an instrumental idiom. The available transpositions and reversals of the modal ranges allow one to place the soprano in either an authentic or plagal range, and to then arrange the other voices idiomatically below, either in the most convenient hexachords, or in the appropriate alternating modal octave-ranges. Zarlino’s and TSM’s procedures are slightly different, because TSM often appears to rely more on the more traditional hexachord method rather than defining the ranges as alternately plagal and authentic as Zarlino does. When TSM composes an untransposed plagal soprano, he often merely compresses the ranges of the lower voices without reversing them. Both methods are valid and useful for considering voice leading on the guitar. 

The following examples show (Ex. 3) the original modal ranges of the Tenor (authentic) and Bass (plagal), with their octave duplicates in the Alto and Soprano ranges, as proposed by Zarlino; (Ex. 4) the transposition of the system to one flat, with the reversal of the ranges, and (Ex. 5) a transposition down by a fourth for use on the modern guitar.

Example 3: the “Original” Modal Ranges: in each case, the bass has the plagal range, the tenor the authentic, the alto the plagal, and the soprano the authentic. 

Example 4: The modal ranges transposed to one flat; the bass is in the authentic range, and the other voices are similarly reversed. 

Example 5: The modal ranges transposed for use on the modern guitar. The bass is in the plagal range, but lacks a transposed Gamma-Ut, which would be on D2. But Luis Milan did not use the Gamma-Ut, and we can do without it. (To offer the reader a glimpse into another ramification, it is my hypothesis that Milan used the A-tuning because it was a Hispano-Arabic projection of the Greek tonal system onto the vihuela without Gamma-Ut, while the G-tuning using the Gamma-Ut was Italian.)

The opinion of the later authors, that the plagal and authentic ranges may be disregarded, is counterproductive when applied to the guitar. There are clear technical reasons for making the distinction. But there is another dimension: the plagal and authentic modes were considered to have different affects, and different sets of cosmological associations. These distinctions are so subtle, even fantastical, as to be meaningless nowadays. But we are foreigners to this music. Do you understand the affects of ragas without explanation? No – not until you have lived in the culture for a number of years. Similarly, the modal affects as they were explained, for instance, by Ramos de Pareja in 1482, are foreign concepts to us over 500 years later. As this is one of the ramifications mentioned above, I save a lengthier explanation for another essay, along with the subjects of ancient fretting patterns, intonation and so on. However, even a brief consideration of the subject of modal affect yields a certain conclusion: modal counterpoint as taught by Jeppesen and other modern methods is undergraduate pablum designed for beginning composition students who will go on quickly to other studies, most certainly designed to avoid completely all metaphysical aspects of ancient modal practice, which are so completely contrary to modern materialist philosophy. The first step on this road to ruin was the invention by Glarean, elaborated by Zarlino, of the twelve-mode system, which utterly lacked any historical foundation (ostensibly found in ancient Greek theory, but considerably strained), appears to have been a very pale imitation of the much more colorful Arabic-Persian set of 12 maqams, and displaced or watered down the modal affects of the old medieval eight-mode system. The eight-mode system as used by the Spaniards in the middle 16th century was a unique expression of the modal system because of its hgh incidence of difficult-to-analyse chromaticism, variable expressions of the characteristics of the modes, and not least because of its retention of medieval modal metaphysics. The combined political pressures of the reconquista, the Inquisition and the Counter-Reformation, together with the ongoing suppression of all things Muslim, did not permit the adoption of the progressive 12-mode system in Spain until Salinas’s treatise of 1577 [Francisco de Salinas, De musica libri septem, Mathias Gastius, Salamanca, 1577, 1592], after the era of the vihuelists, and even so, we still find the eight modes mentioned briefly by Gaspar Sanz in 1674 [Instrucción de música sobre la guitarra española (Zaragoza, 1674)], although in the altered form of the 17th century.