Monday, July 9, 2012

The Best (and Worst) Recordings of Palestrina

Considering the undisputed significance of Palestrina in the history of music, and the uniformly high quality of his output, it is amazing that only a selection of his works is available on CD. For instance, a famous work that has never, not even once, been recorded on a commercially available CD is his Missa ad fugam, an early masterpiece in which two pairs of voices are composed throughout in canon at the fourth. Another unfortunate fact is that new CDs tend to feature the same works repeatedly. Due to the colorful myths associated with its creation, Palestrina's Missa Papae Marcelli receives a disproportionate amount of attention. This work is certainly of outstanding quality, but so are his hundred-and-three other settings of the Mass! However, encouraging signs indicate that the situation may change in the years to come. This is largely thanks not to Italian, but to British choirs.

If anyone ever doubted it, British choirs are best. Over the past thirty years, The Tallis Scholars, directed by Peter Phillips, have played a key role in setting the standards for performances of Palestrina's music. Their discography includes exquisite recordings of the Missa Assumpta est Maria, the Missa Sicut lilium inter spinas, and the Missa Benedicta es. There appears to be a world-wide consensus among music critics that the quality of these recordings remains unsurpassed. Yet there are several other British choirs and vocal ensembles whose Palestrina recordings from the 1970s to the present are of an exceptionally high standard: The Sixteen, Westminster Cathedral Choir, The Hilliard Ensemble, Oxford Camerata, Pro Cantione Antiqua, The Cardinall's Musick, Christ Church Cathedral Choir, and others. It may seem paradoxical that, in Italy, choirs are far less interested in exploring Palestrina's legacy. It is tempting to quote Giuseppe Verdi (see Conati, 1984, p. 153):

You [Germans] are fortunate in still being the sons of Bach! And we? We too, sons of Palestrina, used to have a great tradition, and our own! It has now become bastardized, and ruin threatens us! If only we could go back to the beginning?!
In fact, if one were to look for nominees for the worst Palestrina recording of all time, the first CD that comes to mind is an all-Italian production. I am thinking of a 3-SACD box set featuring the entirety of Palestrina's Missarum liber primus, recorded and released in 2003. The conductor, Roberto Gabbiani, seems to lack even the most rudimentary feeling for stylistic issues; and the sound of the choir, Coro Polifonico dell'Accademia Nazionale di Santa Cecilia, is amateurish to the point that any listener would feel insulted. Luckily, this is not the whole story. There is an old stereotype that Italian singers are more comfortable as soloists than as members of a big choir. When it comes to Palestrina, this stereotype is certainly accurate to some extent. Thus, examples can be found of small Italian ensembles universally praised for their fine interpretations of Renaissance music. The Naxos CDs featuring the Cappella Musicale di San Petronio di Bologna, directed by Sergio Vartolo, break away from the idiom grown out of the English choral tradition, but are highly worth listening to. So are the three Palestrina CDs released some fifteen years ago by Delitiae Musicae, directed by Marco Longhini. Nevertheless, the conclusion is clear that British choirs and vocal ensembles are bursting with so much creative diversity that when speaking of Palestrina, their Italian colleagues would have to go a long way to match the quality of their singing.

Recommended Listening
  • The Tallis Scholars Sing Palestrina [2-CD box set]. The Tallis Scholars, Peter Phillips (dir.), Gimell CDGIM 204.
  • Palestrina Masses, Missa Nigra sum. The Tallis Scholars, Peter Phillips (dir.), Gimell CDGIM 003.
  • Palestrina Masses, Missa Benedicta es. The Tallis Scholars, Peter Phillips (dir.), Gimell GIMSE 402.
  • Palestrina, Volume 1. The Sixteen, Harry Christophers (dir.), CORO COR 16091.
  • Palestrina, Missa Tu es Petrus. The Choir of Westminster Cathedral, Martin Baker (dir.), Hyperion CDA67785.
  • Palestrina, Canticum canticorum, Spiritual madrigals [2-CD box set]. The Hilliard Ensemble, EMI Records/Virgin Classics 7243 5 62239 2 9. (Originally issued in 1986.)
  • Palestrina, Missa Papae Marcelli, Missa Aeterna Christi Munera. Oxford Camerata, Jeremy Summerly (dir.), Naxos 8.550573
  • Palestrina, Missa de Beata Virgine I (1567). Soloists of the Cappella Musicale di San Petronio di Bologna, Sergio Vartolo (dir.), Naxos 8.553313
  • Palestrina, Missae ex Cipriano de Rore. Delitiae Musicae, Marco Longhini (dir.), Stradivarius Dulcimer STR 33423.
  • Palestrina, Missae ex Jacquet de Mantua, volume I. Delitiae Musicae, Marco Longhini (dir.), Stradivarius Dulcimer STR 33477.
  • Palestrina, Missae ex Jacquet de Mantua, volume II. Delitiae Musicae, Marco Longhini (dir.), Stradivarius Dulcimer STR 33478.
  • Palestrina, Choral Music (O Magnum Mysterium). Vienna Vocal Consort, Vijay Upadhyaya (dir.), Dorian Sono Luminus DOR-93255.

Bibliography
Conati, Marcello (Ed.). (1984). Encounters with Verdi (Richard Stokes, Trans.). Ithaca, New York: Cornell University Press. (Original work published in 1981).

Friday, July 6, 2012

The Fascination with Bach's Last Fugue

As a follow-up to my previous post on Thomas Daniel and his completion of Bach's last fugue, I would like to offer some thoughts on a doctoral dissertation by Indra Hughes (2006). Hughes, an early-music specialist living in New Zealand, completed his dissertation four years before the publication of Daniel's book, but is not mentioned by Daniel. Both authors share an interest in Bach's use of numbers and gematria. However, the conclusions reached by Hughes differ radically from those of Daniel.

The dissertation seeks to explore the idea that the unfinished state of Contrapunctus 14 is not to be explained as a result of Bach's sudden death. Rather, Bach's intention in the first place was to leave the final fugue of The Art of Fugue unfinished, and to provide a number of hidden hints as to how the performer might complete the fugue. In other words, according to this hypothesis, Contrapunctus 14 should be viewed as a type of exercise in composition! The basis for the hypothesis is the observation that Bach's fragment breaks off after 239 bars. The sum of the digits of this number is 14, a number of great significance to Bach. (If the value of each letter equals its position in the alphabet, the letters BACH can be combined by summation to yield the number 14.) Taking Gregory Butler's 1983 article as a starting point, Hughes argues that the number of missing bars is exactly 47. Markings at the end of the score are used as corroborative evidence for this inference. However, these considerations do not lead up to a full completion of the fugue. Instead, the reader is introduced to a schematic solution that involves a number of "building blocks."

The background material on gematria is well worth reading. However, a general impression is that Hughes's interpretations of the evidence are too speculative to warrant serious consideration. The idea that Bach intentionally refrained from completing the fugue is in fact a recycled version of the notion that, with this fragment, Bach wished to create a deliberate torso. As pointed out by Daniel, such a notion is anachronistic (see Daniel, 2010, p. 9, n. 4). A further weakness is that it is not clear from the dissertation why Bach would wait until the final forty-three bars of this long fugue to introduce the main theme of the cycle. Finally, it is understandable, yet disappointing, that Hughes declines to compose a completion of the fugue, declaring the task to be "outside the scope" of the dissertation.

Hughes's dissertation is available for free public access via the following page:

Bibliography
  • Butler, Gregory (1983). "Ordering Problems in J S Bach's 'Art of Fugue' Resolved," in: The Musical Quarterly, 69, pp. 44-61.
  • Daniel, Thomas (2010). Bachs unvollendete Quadrupelfuge aus "Die Kunst der Fuge." Studie und Vervollständigung. Cologne: Verlag Dohr.
  • Hughes, Indra (2006). "Accident or Design? New Theories on the Unfinished Contrapunctus 14 in J. S. Bach's The Art of Fugue BWV 1080." Doct. diss., University of Auckland.

Thursday, July 5, 2012

Instrumental Accompaniment before 1600

It is not unusual to hear the claim that Palestrina is "boring." The term "Renaissance polyphony" all too often evokes the image of an unaccompanied choir or a group of three to six singers performing austere music with no instrumental accompaniment. Traditional notions of how to perform the music of Palestrina, Lasso, Victoria, and other sixteenth-century composers were, at least in part, shaped by Cecilianism, a nineteenth-century movement aimed at eliminating "secular" elements in religious music. Another contributing factor has been the erroneous view that the practice of thorough-bass accompaniment arose as a Baroque phenomenon, distinguishing the seventeenth century from the preceding period. (What was new, of course, was the notational practice of adding figures to a bass line; see Ashworth and O'Dette, 2007.) Over the past four decades, a desire to challenge the conventions has resulted in a growing number of innovative recordings. A recent example is a CD recorded by Ensemble Plus Ultra in 2008 to commemorate the 400th anniversary of the death of Tomás Luis de Victoria (1548-1611). The CD, part of a box set of ten CDs, includes a transcription of a six-part motet, "Vadam et circuibo," reduced to a single voice, with the remaining parts arranged for the organ. This highly ornamented version was published by Giovanni Battista Bovicelli in Venice in 1594, and certainly challenges the listener to think differently about the assumed uniformity of Renaissance polyphony (cf. Sherman, 1997, pp. 100-116). Alfred Einstein, writing in 1949, characterized Bovicelli's versions of this and other compositions as "monstrosities," and later scholars tended to agree (see Brown, 1976). However, it is only during the past two decades that early-music performers have begun to make recordings of these rather extreme pieces. They sound far less frightening than they look on paper. Hence, musicologists may have been too quick in judging music they had never actually heard.

The use of colorful instruments to double or replace vocal parts inevitably raises the question of historical plausibility. Evidence does indeed exist that, in Spain, Burgundy, Austria, Bavaria, and other places, combinations of voices and instruments were used in liturgical contexts. For instance, the richly decorated volumes containing Lasso's Penitential Psalms, illuminated by Hans Mielich (1516-1573), as well as other sources, make it possible to determine which instruments were available to the court in Munich. Gerhard Schmidt-Gaden and Holger Eichhorn relied heavily on this information when creating their idiosyncratic arrangements of the psalms, featured on two captivating CDs. For those interested in the subject, the below list of relevant recordings might provide a starting-off point.

Victoria, "Vadam et circuibo," opening (click to enlarge)

Suggested Listening

  • Tomás Luis de Victoria, Sacred Works [10-CD box set]. Ensemble Plus Ultra, Michael Noone (dir.), DGG Archiv 477 9747.
  • Lassus and Palestrina, Motetti, Madrigali e Canzoni diminuiti. La Fenice, Ricercar RIC 208.
  • Thomás Luis de Victoria, Et Jesum—Motets for Solo Voice. Carlos Mena (countertenor), Juan Carlos Rivera (lute and vihuela), Harmonia Mundi HMG 507042.
  • Orlando di Lasso, Prophetiae Sibyllarum, Christmas Motets. Weser-Renaissance, Manfred Cordes (dir.), cpo 777 468-2.
  • Alessandro Striggio, Mass in 40 Parts. I Fagiolini, Robert Hollingworth (dir.), Decca 478 2734.
  • Orlande de Lassus, Laudent Deum—Sacred Music. Choir of St John's College, Cambridge, His Majestys Sagbutts & Cornetts, Timothy Ravalde (organ), Andrew Nethsingha (dir.), Chaconne CHAN 0778.
  • Lassus, Hassler, Erbach, Festival Sacred Music of Bavaria, c1600. Westminster Cathedral Choir, His Majestys Sagbutts & Cornetts, James O'Donnell (dir.), Hyperion CDA66688.
  • Orlando di Lasso, Penitential Psalms [Nos. 1-3]. Tölzer Knabenchor, Musicalische Compagney Berlin, Gerhard Schmidt-Gaden (dir.), Capriccio CAP 67 018.
  • Orlando di Lasso, Penitential Psalms [Nos. 4-7]. Tölzer Knabenchor, Musicalische Compagney Berlin, Gerhard Schmidt-Gaden (dir.), Capriccio CAP 67 130.

Bibliography
  • Ashworth, Jack; O'Dette, Paul (2007). "Proto-Continuo," in: Jeffery Kite-Powell (Ed.), A Performer's Guide to Renaissance Music, 2nd edn. Bloomington, Indiana: Indiana University Press, pp. 225-237.
  • Brown, Howard Mayer (1976). Embellishing 16th-century Music. Oxford and New York: Oxford University Press.
  • Einstein, Alfred (1949). The Italian Madrigal, 3 vols. Princeton, New Jersey: Princeton University Press, vol. 2, pp. 840-842.
  • Sherman, Bernard D. (1997). Inside Early Music: Conversations with Performers. Oxford and New York: Oxford University Press.

Wednesday, June 27, 2012

Froberger's "Art of Fugue"

Johann Jacob Froberger, Complete Capriccios [CD]. Bob van Asperen (organ), rec. June 2002 and May 2010, St. Ludgeri, Norden, Netherlands. AEOLUS AE-10701 [79'30].

In 2000, the renowned early-music scholar and performer Bob van Asperen embarked on a complete series of Froberger's keyboard music, performed exclusively on historic instruments. The seventh and final volume, released in 2010, features a total of eighteen capriccios, including a capriccio discovered as late as in 2006. In this context, the term capriccio designates a fugal genre that includes unified wholes as well as pieces in several sections with successive variations of the opening theme being developed separately. In the latter case, the themes are subject to a multistage metamorphosis. The opening themes are typically of a lively character, involving leaps and striking rhythms. In the liner notes, van Asperen writes that, with these masterpieces, Froberger rose to his greatest heights as a composer of contrapuntal music. Indeed, when listening to this recording, it is impossible not to be impressed by the exceptional quality of Froberger's capriccios. Stylistically "progressive" techniques allow Froberger to reveal new and unsuspected depths. This is music that paved the way for Bach's fugues.

Bach's name also comes to mind for another reason. In a group of four non-autograph manuscripts, works based on the same theme are ordered in pairs. For instance, Capriccio No. 9 is preceded by Fantasia No. 4 (which appears on the fifth CD of van Asperen's Froberger series). These monothematic structures point forward to The Art of Fugue, in which the fugues and canons are all based on a single theme. Van Asperen notes that, in The Art of Fugue, "the contrapuntal possibilities of one and the same theme were treated in several fugues, whereby at the same time, like as in Froberger's capriccios, thematic transformations play an important role."

Van Asperen is naturally not the first performer to have recorded Froberger's capriccios, but this SACD release is certainly an essential addition. With 46 stops, the three-manual Arp Schnitger organ of the Ludgerikirche, Norden, offers a rich palette of contrasting colors and sonorities. This gem of an organ, finished in 1687, is ideal for Froberger's music; and the sound is brilliantly recorded. The textural clarity achieved on this recording is indispensable in these contrapuntally conceived pieces. The extensive liner notes written by the performer are a fine bonus to listeners interested in the registration and other aspects of the interpretation. The performance is invigorating, and van Asperen holds the listener from beginning to end. Discipline and erudition blend seamlessly with joyful virtuosity, elevating the recording into a class of its own. Van Asperen's razor-sharp articulation of each phrase feels as natural as a breath of fresh air, and is precisely what the style requires. Van Asperen employs a variety of registrations, but the use of bright mixtures is never excessive. Quiet textures allow him to demonstrate the effect of the tremulant. In this respect, Capriccio No. 16 features a section of particular beauty. In short, van Asperen's meticulous playing more than renders justice to Froberger's music by bringing out its tremendous inventiveness and sophistication. The listener is left with the question of whether this music has ever been played better.

Thematic transformations in Froberger's Capriccio No. 10 (click to enlarge)

Thursday, June 21, 2012

Bernard Shaw and Counterpoint

Bernard Shaw's (1856-1950) writings on music, including his judgments of Bach, Mozart, Wagner, and other composers, are still eminently worth reading for their lively and humorous take on music history. "Whether or not you agree with Shaw, no one can fail to be challenged and stimulated by judgments expressed in a prose that is itself a feast of art and intellect, wit and humanity," as Louis Crompton (1978, p. xxiv) puts it. Shaw is also an excellent source on the role of music in late nineteenth-century British society. A text published in the Magazine of Music in November 1885 reveals that Shaw held strong views on the subject of contrapuntal music. He begins by suggesting that the fugue, as a musical form, has long lost its vitality: "To the average Briton the fugue is still an acute phase of a disease of dulness which occasionally breaks out in drawing rooms, and is known there as classical music." Shaw lends his moral support to music students who feel that life is not long enough for an exhaustive course in conterpoint. The argument seems to be that music students should no longer be required to write fugues. As for the great composers, he claims that Beethoven and Cherubini did themselves no favor by resorting to fugal technique. Beethoven "brutalized the fugue as completely as he humanized the sonata."

Shaw is anxious to point out that his critical attitude does not extend to music written before 1750. To the contrary, he declares that "Sebastian Bach could express in a fugue or canon all the emotions that have ever been worthily expressed in music." But he believes that, after Bach's death, the march of time has outdated the imitative forms: "The history of fugue as employed by the great composers during the last hunded and thirty-five years, is one of corruption, decline, and extinction."

After following Shaw through this maze of bewildering opinions, one can only wonder what might have prompted him to write the text. The reader is left with the feeling that the real reasons for his crusade against fugues are not being divulged. In searching for some clues to this question, it may be helpful to observe what qualities are attributed to Wagner's music. Shaw saw himself as a Wagnerite, and took a great deal of trouble to study Wagner's methods of composition. Wagner is indeed mentioned in the text: "Wagner wove musical tissues of extraordinary complication; but the device of imitation had no place in his method." It is surprising that, at this point, Shaw fails to mention Die Meistersinger, as the second act of this drama is, in fact, concluded by what can only be described as fugue-like music. However, as Shaw would have pointed out, Wagner, in Die Meistersinger, did not use counterpoint for its own sake. Wagner's point is to create an atmosphere of irony and absurdity. Mary A. Cicora (2000, p. 158) writes:

The music does not sincerely mean what it is saying ... For example, at the end of the second act, there is a fugue, with Beckmesser's serenade providing the "cantus firmus" of this fugue. This creates the blatant paradox of the chaos that is presently reigning in the streets of Nuremberg being portrayed with a fugue, one of the strictest forms of musical order. This fugue is thus paradoxical, somehow self-contradictory.
Writing "ironic" music is, of course, an entirely different matter than resorting to old-fashioned forms for their own sake. Against this background the suspicion arises that Shaw's views on counterpoint might have been rooted in his deep admiration for Wagner. For Shaw, fugal music written by modern composers seems to have evoked the image of Beckmesser, the hopeless pedant.

The days are gone when a music lover must despise the more conservative composers of the nineteenth century in order to appreciate Wagner. For this reason, Shaw's views on this particular subject may seem hopelessly out-of-date. However, as Crompton said, Shaw's prose remains "a feast of art and intellect, wit and humanity." His fine sense of humour is in itself a valid reason for reading his musical musings today.

Shaw was not alone in handling the subject of fugues with humour. Ebenezer Prout (1835-1909), a British late nineteenth-century Bach scholar, wrote forty-eight amusing lines (which can be downloaded here) to go with the fugue themes in The Well-Tempered Clavier (see Vincent, 1911). The subject of Fugue No. 20 in Book 1 is set to a line that apparently seeks to create a cosy atmosphere for Bach's music: "On a bank of mud in the river Nile, upon a summer morning, a little hippopotamus was eating bread and jam." In contrast, the words for Fugue No. 22 in Book 2 speak of a "horrid" fugue! It is an interesting paradox that Prout's lyrics for the fugue themes in Bach's Well-Tempered Clavier seem to have outlived Prout's many and thorough textbooks on harmony, counterpoint, and composition. 

WTC, Book 1, Fugue No. 20 (click to enlarge)

WTC, Book 2, Fugue No. 22 (click to enlarge)
 
Bibliography
  • Cicora, Mary A. (2000). Modern Myths and Wagnerian Deconstructions: Hermeneutic Approaches to Wagner's Music-Dramas. Westport, Connecticut: Greenwood Press.
  • Crompton, Louis (1978). Introduction to Bernard Shaw, The Great Composers: Reviews and Bombardments (Louis Crompton, Ed.). Berkeley and Los Angeles: University of California Press.
  • Vincent, Charles (Ed.). (1911). The Forty-Eight Fugues for the Wohltemperirte [sic] Klavier (Vols. 1-2). London: Vincent Music Co. Ltd.

Sunday, June 17, 2012

A Canonic Treasury

Konrad Ruhland, Musikalische Rätsel. Quaerite et invenietis (Suchet und ihr werdet finden). Passau: Verlag Karl Stutz, 2009. Co-authored with Leopold Fendt and Johannes Geiger. Pp. 237. ISBN 978-3-88849-140-5.

Practice in solving puzzle canons, according to Peter Schubert (2008, p. 152), "is fundamental to Renaissance musical thinking, because it entails visualizing ways to combine melodies, imagining music that is not written down." The vogue for constructing, solving, and singing puzzle canons did by no means end with the Renaissance, but continued well into the late Baroque era and even into more recent times, a fact demonstrated in a relatively new book by Konrad Ruhland (1932-2010). Musikalische Rätsel is an anthology of canons written approximately between 1450 and 1770, with an emphasis on the sixteenth and seventeenth centuries. Many famous names, such as Guillaume Dufay and Hans Leo Hassler, are represented, as well as others less well known.

Ruhland is remembered as a pioneer, in Germany, of the early music revival. His numerous recordings, featuring Capella Antiqua München, include rarely heard settings of the Mass by such diverse composers as Machault and Josquin, as well as Renaissance love songs and Gregorian chants. In this anthology, published shortly before his untimely death, Ruhland conveys to the reader his life-long passion for collecting puzzle canons of various kinds. The first highlight of this passion was when, as a pupil, he came across the legendary canon "Sumer is icumen in," one of the earliest known examples of English polyphonic music. His curiosity was further excited by Palestrina's Missa ad fugam in perpetuo canone. In an anthology published by Fritz Jöde, Ruhland for the first time encountered esoteric and complex puzzle canons, written by Adam Gumpelzhaimer and Michael Praetorius. This prompted him to study Gumpelzhaimer's Compendium Musicae (Augsburg, 1595), which, according to Ruhland, might easily have provided enough material for a second book on puzzle canons.

Musikalische Rätsel does not primarily address an academic audience. As stated in the preface, the book is an attempt to inspire the readers to perform the canons compiled in it, because, according to Ruhland, music becomes music only when it becomes sound (p. 15). The book features not only facsimiles of printed and handwritten puzzle canons, but also modern transcriptions intended to facilitate performance. This makes it a comprehensive and helpful collection of canons, likely to be of interest to a wide audience, including singers and scholars. In choral settings, canons are sometimes used as warm-up exercises to relieve tension, for which reason the book may appeal to choral directors. With few exceptions, the canons are set to Latin texts. Hence, knowledge of German is not required in order to enjoy the book.

Bibliography
Schubert, Peter (2008). Modal Counterpoint, Renaissance Style, 2nd edn. New York and Oxford: Oxford University Press.

Friday, June 15, 2012

A Recent Completion of Bach's Last Fugue

Thomas Daniel, Bachs unvollendete Quadrupelfuge aus "Die Kunst der Fuge." Studie und Vervollständigung. Cologne: Verlag Dohr, 2010. Pp. 140. ISBN 978-3-936655-83-4.

Thomas Daniel, Professor at the Cologne University of Music, is well-known for his textbooks on Renaissance polyphony and on the Bach chorale style. Daniel's latest book examines the three subjects of the final (unfinished) fugue in Bach's The Art of Fugue, BWV 1080, and whether and to what extent these subjects can be used in counterpoint against the main subject of the cycle. As Bach's fugue fragment fails to exploit the main subject, it has long been a matter of debate whether the fugue actually belongs to the cycle. Daniel advances the claim that, because the main subject melts very well with the three subjects of the fugue fragment, there can be no doubt that Bach's unfinished fugue is the beginning of a quadruple fugue that most certainly belongs to The Art of Fugue. He argues that by introducing the BACH theme (built around the notes B-flat, A, C, and B-natural), Bach symbolically put his personal seal on the fugue. According to Daniel, this is an indication that the quadruple fugue was intended to be the concluding movement of The Art of the Fugue. The book features the full score of Daniel's own completion, which adds no less than 133 bars to Bach's fragment.

The book consists of an introduction, seven chapters, and an epilogue with some reflections on Bach's idiom. First, Daniel persuasively argues that, contrary to the view of Gustav Leonhardt and many others, the compatibility between the main subject of The Art of Fugue and the three subjects of the unfinished fugue is not a coincidence. After a lengthy discussion of the four subjects and their possible combinations, Daniel turns to the topic of the structural layout of the fugue, concluding that what Bach is aiming at in the fragment is a quadruple fugue in which the four subjects are introduced separately; that is, in which there is one regular exposition for each subject. According to this scheme, the second, third, and fourth expositions are separated by sections in which the subjects already introduced are used in counterpoint against each other. The fugue was to be concluded by a section in which all four subjects were combined. Daniel then goes on to discuss the relevance of number symbolism. The incorporation of the Golden Section is one of many intriguing aspects addressed by Daniel, who believes that in bar 230 the melodic movement reaches a climax, and that the fugue was to consist of exactly 372 bars.

A very important part of the book (pp. 75-93) starts with formulating twelve criteria that any completion of Bach's fugue must satisfy. He then uses these criteria as the basis for judging the adequacy of eight different attempts at completing the fugue. The composers whose efforts are evaluated include, among others, Karl Herrmann Pillney (1896-1980), Yngve Jan Trede (1933-2010), and Zoltán Göncz (b. 1958). Daniel notes that Pillney's completion is more consistent with Beethoven's idiom than with that of the late Baroque period. And it does not help that Wilhelm Furtwängler, the great conductor, is supposed to have endorsed this completion. (Might it have been precisely because of the Beethoven-like features that Furtwängler reacted approvingly?) But there are worse examples. For instance, the completion published by Göncz in 2006 is shown to be riddled with glaring errors in counterpoint (see pp. 40-42; 83-84). Style-copying is not a trivial task! In contrast, the solution presented by Trede in 1996 holds up reasonably well under closer scrutiny. Daniel rounds off by discussing his own completion of the fugue.

The book is undoubtedly a significant contribution to the field, as it sets a new standard of rigour for those presuming to write on this thorny subject. The emphasis on the stylistic and idiomatic features of Bach's music is to be welcomed. One can only hope that this meritorious effort will soon be followed by a CD recording of Daniel's completion, preferably as part of a recording that includes the whole of The Art of Fugue. A complete recording would enable the listener to understand better how well the epic proportions of the quadruple fugue fit into the entire context.