ZMP Art of Fantasia

San Miguel de Allende The Art of Fantasía For All Guitars and Lutes Download Problems - click to see note The Art of Fantasía For All Guitars and Lutes: A Modern Guide to Counterpoint in the 16th Century Spanish Style Containing an Abridged Edition of the Arté de Tañer Fantasía (1565) of Fray Thomás de Sancta Maria Selected For Study on Fretted Instruments And A History of Intonation and Fret Setting By Jack Zelenka © 2024 Based on the Libro Llamado Arté de Tañer Fantasía of Thomás de Sancta Maria (1565)

Abstract I present a set of transcriptions of the fugues of Thomás de Sancta Maria, for application to the guitar or lute, accompanied by a translation of TSM's text. I precede the fugues with an extensive historical commentary in order to explain how TSM's tonal system is related to the historical fretting of the vihuela, a subject with a critical bearing on the authentic performance of "Spanish Musica Ficta," and which also opens a new window into the probable historical origin of the Church Modes. TSM did not notate his accidentals completely: I treat this historical fact as sensitively and as thoroughly as possible by tracing the history of accidentals in terms of the historical patterns of fretting the lute, so that the reader may make his or her own authentically informed choices about the "missing" inflection marks, working directly from my transcriptions, without the usual editorial bowdlerizations, but including a generous amount of historical information bearing on the "correct" interpretations. Book I, Overtones: I discuss the (well-known) possible origins of Pythagorean music in the musical bow. I present a selection of historical and theoretical evidence for an ancient non-diatonic, pre-Pythagorean musical system derived from consecutive steps of the harmonic overtone series, and I show how this system most certainly existed and persisted in medieval Muslim music theory in the form of the 40-division fret pattern of the tunbur-al-baghdadi described by Al-Farabi, which permits any number of overtone-series scales including several which are unequivocally attested in medieval sources contemporary with the use of the Church Modes. Book II, Tunings: I discuss Ernest G. McClain's theory of ancient diatonic tunings derived from the theory of the Music of the Spheres, and how astronomical and mathematical speculation led to the Pythagorean Tuning and to its symbolically encoded presence in the Christian Myth, in the mythic elements of the Kiss of Judas and the Trumpets of the Revelation. I then present the tunings of ancient Greece as reported by Claudius Ptolemy, Nicomachus of Gerasa, and Boethius, and closely examine the structural relationship between the Church Modes and the Greek Tonoi, which, as I show, is not particularly close. Book III, Frets: I note the political constraints on medieval Christian music theory resulting from the simultaneous rise of Islam and the Carolingian dynasty. I demonstrate the similarity of the Church Modes to a known set of 9th century (CE) Arabic lute fingering patterns, and I show that the Church Modes are the logical result of the application of this fingering pattern to the Greek Greater Perfect System as it was projected onto the fingerboard of the lute by Al-Kindi. I show that the Gamma-Ut and the Letters of Gregory can more logically be derived from Al-Kindi's and Al-Farabi's theories on ancient Greek music than from any known ancient Greek source, and that they appear in Christian music theory at the turn of the 11th century, in the works of Pseudo-Odo and Guido of Arezzo, immediately following the tenure of Pope Sylvester II, formerly known as Gerbert the Musician, who had studied Arabic theory in Spain before becoming Abbot of the Monastery of Rheims (an important locus of Benedictine music theory), and then Pope. Continuing with the development of fret patterns, I note that the 9th-century (CE) Pythagorean fret patterns of Al-Kindi are the same as the 16th-century fret patterns of Juan Bermudo. I then examine the impact of the medieval introduction into Arabic lute playing of both the 17-note-to-the-octave fret pattern of the Persian tunbur-al-khurusani and the 40-division fret pattern of the Persian tunbur-al-baghdadi. These two fret systems both offer Just-tuned tetrachords. I demonstrate that the scale tunings of a number of the 13th-century maqams are (a) derived from these fret patterns and (b) are identical to the C-Major and G-Major scales drawn from the Just monochords of Ramos de Pareja (1482) and Gioseffo Zarlino (1588). Book IV, Modes: I present the Church Modes as described and used by Thomás de Sancta Maria, and I discuss how his use of the modes differs both from academic medieval Pythagorean theory and from the more progressive (and better-known) proto-Baroque tonal theory of Zarlino. I show that in TSM's style, each of the eight Church Modes has a unique tonal signature resulting from its secondary cadences on the Psalm Tones, while in the 12-mode system of Glarean and Zarlino, these unique tone colors were eliminated through standardization of the cadences. Book V, Inflection: This volume is the most critical of the theoretical part of the work, and is a must read. (If you don't read Book V, you are just one of the lookie-loos, and your lack of serious interest is not my problem.) I discuss the pitfalls of "editorial accidentals" and that this is a distortion of the "original text." I present the opinions of various theorists both ancient and modern on the use of accidental inflections. I show how changes in harmonic style from the late 15th century to the middle 16th century are reflected not only in the vihuela tablatures but in the fret patterns of the lute and vihuela. I compare a number of passages by TSM, in which the inflections are not marked, with parallel passages in the tablatures. I analyze the inflections in a Josquin duo intabulated by Miguel de Fuenllana. I show a number of mandatory inflection patterns which are taught by TSM in his text but which are very often not actually written in the staff notation, and then I show a number of other inflection patterns which are optional or discretionary. Book VI, Consonances: The theory of "Playing in Consonances" is mentioned by several of the vihuelists. TSM's material on this is comprehensive and authentic, the most accessible (to me) presentation of 16th-century modal harmony in four real parts that I have ever found and studied. (Granted that there is, of course similar material in other 16th-century treatises by other authors.) I have abridged it by removing many of those examples which I judged to be technically impossible on any lute, but many impossible difficulties remain, and the intelligent guitar or lute player may interpret these as best he or she might according to the instrument at hand. The study of TSM's progressions in four parts will certainly stretch the imagination as well as the fingers. Book VII, Cadences: TSM devotes a huge section to cadences. The purpose of the study of cadences is to be able to construct a cadence on any intended target tone incorporating the structural details required to introduce a new fugal entry before, during, or after the cadence. As a matter of either practical composition or improvisation, the skillful prolongation, evasion, and bridging of cadences is a high art. The cadence is one of TSM's three main techniques of composition, and is of critical importance to his theory of fugue. Book VIII, Counterpoint: I present a modified version of Fux's theory of Species Counterpoint, with comparisons between the theoretical systems of Fux and Jeppesen and the contrasting authentic stylistic evidence of the vihuela tablatures and of the teaching of TSM. Books IX - XII, Fugue: I present TSM's teaching on fugue in four voices, with a translation of his text and historical commentary. Most of this is a faithful translation into English of TSM's own text, but I have commented as I consider necessary for clarification of many details.
Overview of the Contents Thomás de Sancta Maria's *Libro Llamado Arte de Tañer Fantasía,* or "the Book Called the Art of Playing Fantasía" (1565), on which Books 6, 7, and 9 - 12 of the present work are based (while the other Books are commentary), is one of the great monuments of 16th-century Spanish music theory. It is one of the great early works on the theory of fugue, and it has the additional virtue of being technically accessible to players of the guitar and lute. Volume One, a "Musica Speculativa" following the classical models of Boethius and Zarlino, is a history of intonation. The vihuelists of 16th century Spain used a limited set of accidental inflections, only three sharps and two flats, derived from a fret pattern already played on the oud in the 9th century CE. In order to understand the origin of Spanish inflection practice, we will investigate the development of the musical languages of the Old World, focusing on that of ancient Greece, and then we will examine the projection of the Greek "Perfect Immutable System" onto the fingerboard of the oud in the 9th century CE, and compare the patterns of fingering and fretting used on the oud in the Middle East from the 9th through 13th centuries with those of 16th century Spain. The point of intersection between the classical Greek system, the oud, and the nascent church modes illuminates questions about the origin of the church modes which are not answerable by the traditional appeal to Greek theory alone. The tension between Just and Pythagorean fret patterns is shown to have a continuous history on the oud since the 9th century. Volume Two, a "Musica Practica," deals with modal counterpoint in four real parts. The pivotal Book Five, on the so-called musica ficta, sums up the research reported in Volume One with examples from the vihuela tablatures. Four-part harmony, much neglected in guitar and lute pedagogy, is addressed in Books Six and Seven with authentic material taken directly from TSM's *Arte,* largely avoiding references to "functional" harmony, which is inapplicable to this style. Book Eight is anachronistically devoted to the 18th-century practice of Species Counterpoint in the style of Fux, in order to place this useful study method in its correct perspective against authentic 16th-century practice, which it is purported to represent, but in fact does so only in a limited way, because it was invented in the 17th century and perfected in the 18th as a very stylized re-creation of a then-obsolete style of composing. Volume Three is devoted to Fugue itself. This immense body of material contains dozens of examples by TSM of the construction of fugal expositions in four parts. The study of this material will probably require several years, and should not be approached in a hurry. Of the earlier material in Volumes One and Two, it is essential to have read Book Five, the first book of Volume Two, on inflection and on the issues of the so-called musica ficta, before studying the material on fugue, in order to avoid naive errors in the inflections of cadences and fugal subjects.
File history: The last update was 06-02-2025. The file name includes the most recent date. This replaces the previous files of 12-26-2024, 01-26-2025, 03-05-2025, 03-31-2025 and 4-16-2025 - I have corrected only typographical errors and minor infelicities. Please delete any files with earlier dates, and take this one. There will be none with later dates, unless I should issue a clearly identified revised second edition, which I do not plan to do. The errata are listed below. PDF Display: The PDF will be correctly displayed if the PDF reader is set to center the first page and make the second page a left-hand page, and the third a right-hand page. My Waterfox browser calls this an "even spread." The page numbers and marginal notes will then be shown in the outside margins of a two-page spread as though you were reading it as a printed book, and for this you will need a full-sized computer screen. There are no separate page numbers for the Front Matter, so that the page numbers of the PDF correspond to those of the TOC. The PDF is set up to print on either US Letter or A4 paper, and may be spiral bound in the center margin. I encourage serious readers to make their own print copies. Download Problems on small devices: Now that the work has been widely distributed and downloaded, it has been brought to my attention by a number of readers and would-be readers that the PDF is too big to be loaded by cell phones or I-pads. It is 1018 pages and 700 MB. I will, sometime, perhaps, post the three volumes separately, and some of the individual books or essays, but you will have to wait. If you can't download it on your device, well, you are out of luck! Perhaps you should reconsider your relationship with technology. In truth, because I am very old myself, and accustomed to still working with 1990's technology, I never had any idea of formatting it to be read on such a small screen, and I believe this to be impossible, futile, and even, perhaps, ridiculous. I rejected Kindle as a vehicle for precisely the reason that it has a very bad reputation for not reproducing graphics well, and I can hardly expect that anyone will make much sense out of it on a cell-phone screen. My model for the page layout, much of which is in two-pages spreads with hundreds of marginal notes in 9-point type, was taken from classic works as far back as the incunabula, and from elegant modern works published by Oxford University Press in hard-back, such as Gjerdingen's Music in the Galant Style, and my treasured volume of Guido by Dolores Pesce, and my inherited library of music theory from W. W. Norton, beautiful and precious works which have served this project well. Those are serious works of music theory, many of which I purchased myself and paid good money for. I have also downloaded and printed out quite a number of doctoral dissertations which number in the hundreds of pages, and while I acknowledge that many people would not and will not go to such lengths as I have for the sake of their own continuing education, I must emphasize that this work IS for the serious reader, and that I don't too much care about the non-serious readers. I don't see that Dolores Pesce or Robert O. Gderdingen do either; although their work may be pirated in PDF, it so happens that I myself bought their works, which are printed in beautiful hard-back. Please note that I am NOT charging for this PDF, and that it is your responsibility to step up to the plate if you are serious about the study of Counterpoint, punto. I believe that my work rates such a format (however badly I may have abused it by shoe-horning in extra material so that some pages have no margin left) and that to bowderlize it by trying to reduce it to palm-size would be to seriously diminish its readability. Now, this is my opinion. I do apologize to those scholars who no longer possess large-format screens, or who are unwilling to spend the money to print the work, but really, the work is intended to be read on a music stand with instrument in hand by those who are seriously interested in studying the fugues of Thomás de Sancta Maria, and the extensive historical background which is given in the first Five Books is intended for those readers, and not for the casual amusement of non-serious lookie-loos who will never play the fugues anyway. So, dear reader, if you cannot download the book on your device, then please find a PC or Mac with a large screen and a wide-band internet connection, or even better, have it printed in three volumes and spiral bound, and don't complain to me about your unwillingness to own the appropriate technology. If I had chosen to sell it as a hardback, it would be unaffordable to thos young musicians who might benefit from it the most; I have met you halfway, now it lies with you, dear reader, to either demonstrate your sincerity, or just go away and amuse yourself somewhere else, along with all of the so-called "classical" guitarists who can't read the Grand Staff. *Errata* There are some errata; here are four of which I am currently aware, and I will almost undoubtedly find others since the apparently spontaneous generation of typographical errors is the eternal bane of self-published authors. I have not corrected these few listed here, because I do not want to continue to generate different file versions now that the work has been widely distributed. (1) My inline reference to Josephus on page 21 should have been to the "Letter of Aristeas" which gave the number 72 for the translators of the Alexandrian Septuagint whereas Josephus's number was 70, and there is a missing footnote on that item. (2) On page 224 regarding Ptolemy's tunings, I wrote "The neatness of his tunings may have had more to do with constructing a beautiful theory than with practical music." This I should have footnoted to Tolsa Domenec's dissertation, Claudius Ptolemy and Self-Promotion; I believe his phrase was "a tidy theory." However, I will have to wade through Dr. Tolsa's work again to find it, and this is difficult because his PDF is encrypted so as to be readable but not searchable. (This was a wise move to protect against the corruption of his material by AI.) (3) On page 261 (and following) I referred to Al-Farabi as "9th century," but he was in fact active in the first half of the 10th century. (4) On page 858, Example 12.018, there are three voice leading arrows which were not grouped with the staff notation and which, because I moved the staff notation but not the arrows, are now not correctly aligned with the notes which they were intended to connect. If you, dear reader, should discover what you believe to be errors of fact in my work (which I must admit is quite possible), then I do beg you to bring those to my attention in a reasoned way, with the appropriate references. I would be very interested to read such criticisms, and I will post them here with my responses. Email: publisher@"thisdomain".com (put the real domain in there from the header in your browser). Please no ad hominem attacks, but my homonyms are fair game. Author's Comments: In order to compose this, my life's work, it has been necessary for me to study aspects of logic, history, mathematics, and astronomy. A person without a basic understanding of these fields is likely to have a difficult time understanding the present work, although there is nothing very advanced in any of it, because these are fundamental to the knowledge base of our time. I composed this work, The Art of Fantasía For All Guitars and Lutes, as my own study guide to the fugal instruction of Thomás de Sancta Maria, and, having completed the book, I am now in the process of studying it myself! I read about TSM's *Libro Llamado Arte de Tañer Fantasía* many years ago, but I could find no English translation. By 2016 my Spanish had improved to the point that I could read TSM in the original, and I did so. I have also studied TSM's great contemporary, Fray Juan Bermudo, and I have referred to Bermudo throughout, because he is the greatest source of technical information on 16th-century vihuela fretting and tuning, an important secondary issue which is related directly to the musical style of the vihuelists and of TSM. Other works on fugue generally require a keyboard, and deal mainly with the later Baroque style of fugue; the present work is unique both in addressing specifically the 16th-century Spanish style, and in presenting a method adaptable to the technique of our instruments: specifically the guitar, vihuela and lute. As I see it now, the way to learn to improvise fugal fantasía using this book is the long and hard way: learn to play every fugue in the book, and study and understand its technical details as described by TSM. Some creative adaptation is certainly required, no matter how many courses on your instrument. Then practice (Book Seven) composing cadences which are directed to any desired cadence tone. Then, choose fugues which are in the same mode, and practice composing connecting links between them as shown in Books Eleven and Twelve. A point to notice is that Marpurg, in the 18th century, listed 24 possible orders of entry, the permutations of the four voices SATB, TBSA, etc, and that TSM uses only a half dozen of these, and so, one of the reasonable ways to develop TSM's material is to re-compose each of his examples in the 23 remaining variations of the order of entries. Another point to notice is that for the sake of economy, TSM uses many very short points of imitation, as short as three half notes. Any of these very short subjects could be expanded into long fugal expositions; the critical technical device is the melodic shape of the first few notes and how it is introduced in relation to the cadence. I am far from having mastered these techniques myself, and merely claim that TSM's work appears to have finally led me personally to having at least some hope of understanding fugue after a few more years of study. I have put very few such instructions of my own into the present work, and most of the actual instruction in fugue is a direct translation of TSM's own text. The introductory Volume I contains a lot of arithmetic, beginning with an introduction to tuning theory. This will probably chase a lot of readers away - who me? do arithmetic? (you ask). Well, sorry for the bad news, but if you can't even do arithmetic you may find the study of fugue to be also difficult, and TSM uses a lot of numbers for intervals - interestingly, from the unison to the 27th, the same limit as found in the Timaeus. Most of our ancient authors assumed a knowledge of arithmetic: even Guido of Arezzo, whose theory was "simplified" for the education of children, included a monochord in every work. For an entry into musical arithmetic, Guido's monochords are in fact an excellent place to start, as they are the simplest and easiest monochords of our tradition. To study Boethius, one of the great foundation texts of Western music, absolutely requires the study of arithmetic, and Boethius himself assumed that the reader would have read his De Arithmetica before his De Musica, as he states at the beginning. Volume III of this book, the main course, is a study of 16th-century-style fugue, to be played on (theoretically) any guitar or lute (but eight courses would be useful). Volume II is a study of fingerboard harmony in the 16th-century Spanish style. The material in these two latter volumes is mostly taken directly from the Libro Llamado Arté de Tañer Fantasía of the Spanish Dominican monk Thomás de Sancta Maria, published in Valladolid in 1565. That original work took TSM sixteen years to write and six more years to publish, putting its inception about 1543, before the publication of Mudarra's Tres Libros in 1546. It was written for the keyboard (although TSM says that it is equally applicable to the vihuela, which is true except for the issues of range, since it would require an 8-course vihuela to completely realize) and was composed in typical 16th-century staff notation in which the four voices are written on separate staves without strict vertical alignment. I tried hard to read these non-aligned scores but I decided that it would be faster to transcribe them, which took me about six months in 2018. I have made my own completely new transcriptions into "modern" grand staff, working from an online scan of the original print, and I have checked them for accuracy over the last several years by playing them many times myself and double checking all questionable passages. It does happen that there are mistakes in TSM's own print; I have made corrections with explanatory notes. I have not referred to the transcriptions done by previous researchers. There are at least two other sets of transcriptions which have been done in recent decades besides mine, but my transcriptions are my own, brand new, and (almost!) error-free. It is impossible to claim 100% accuracy in transcribing such a vast work, but I have gradually eliminated my original errors to the point where I am 99% confident in sharing my transcriptions with other musicians. If you should find any errors, please let me know, of course. I will be happy to re-investigate and discuss any passage which any reader would like to question: this would be time well spent. The several years that I have spent writing Volume One - the last to be finished - has given me time to proofread my transcriptions, and I am reasonably confident of their accuracy. No Editorial Accidentals Here! Read Book V ! Completely contrary to the usual modern practice, I have NOT added "editorial" inflections. I have reproduced only TSM's own sharps and flats exactly as he gave them, which are incomplete, in accord with standard 16th-century practice, and according to a standard by which the reader of the staff notation was supposed to know when it was necessary, possible, or desirable to inflect a note sharp or flat, without being prompted by an accidental sign, famously called a mark "for donkeys" by Tinctoris in the late 15th century. TSM often marks a sharp or flat only once for a particular harmonic device, the first time that he presents it. He does so as a didactic concession, and then he expects the reader to remember the inflection the next time he or she encounters the same device. For an editor to begin to enthusiastically add editorial inflections is to shortly find himself or herself in deep and murky water: there are many mandatory inflections at the cadences which are unmarked but uncontroversial as to their realization, but there are also many optional inflections, such as the occasional augmented sixth chord cadence, and passing inflections in the passage work, which offer the reader the opportunity to make creative decisions based on personal taste just as did the vihuelistas. It is evident from the tablatures that there is a good deal of possible flexibility in the choice of inflections in some cases, while in other cases there are consistent rules which should be followed by the informed musician. Instead of pablum, I offer information - and I have given it exhaustively, particularly in Book V, with a thorough theoretical preparation in Books I through IV - so that the reader may make his or her own choices about the inflection of TSM's music. The chromatic inflection of 16th century music is an art requiring study: I offer that opportunity, rather than spoon-feeding the reader my own specific interpretations of the details of inflection as is done in typical modern editions for the uninformed. As Vincenzo Galilei admonished his readers, don't offer the "silly excuse" that you are just reading what's on the page! *It is necessary to study the issues of inflection;* this work is for the serious student of TSM's *Arte,* and it doesn't make a lot of concessions to the casual reader or to the lookie-loos. If you jump into playing the fugues without reading the text - with particular attention to my Book V - you will miss this necessary information. There are on You-Tube quite a number of embarrassing performances of TSM's fugues, on lutes and keyboards, in which it is evident that the performer has NOT studied TSM's text, and has no fricking idea how to inflect a cadence in the 16th-century style. I sincerely hope that no one will use my transcriptions to produce such naive recordings. More Overview: Volume One begins with an introduction to tuning theory, and I write at some length about the history of the European tonal system, and the relationship of the fret patterns used by Luis Milan et alia, to that history. There is a lot of very interesting material to be found in the study of ancient monochords and fret patterns, in particular in the comparison of the maqams and the church modes as they appear on the fingerboard of the lute. Perhaps you have not noticed that the Church Modes fall in two precise parallel patterns on the fingerboard: the plagal modes on A-B-C-D on the A-string of the vihuela, and the authentic modes on D-E-F-G on the D-string - as though they grew there. As I will show, it is clearly a myth that the church modes were derived from the Greek tonoi: they must have arrived in Europe well before the Crusades (around the year 800 CE) on the fingerboard of the oud, on which they fit neatly and idiomatically just as they do on the modern guitar, while the Greek tonoi (as I will show by fret diagrams) do not fit anywhere near as neatly onto the fingerboard or into historical fret patterns on the lute. In the 9th-century Psalter of Lothair, King David is portrayed playing a lute: this shows the lute's presence in Europe several centuries earlier than is usually recognized. But the medieval Benedictine monks who wrote our early "music theory" could not possibly admit this because of the theological constraints under which they were required to work, and they invented the cockamamie derivation from the seven tonoi of Boethius which has gone into the history books along with the absurd Greek tribal names so beloved of the amateur musicians of our time. To correct this long-standing historical misunderstanding about the origin of the Church Modes, which now appears obvious, was part of my motivation in writing Volume One. The history of fret patterns is -- I believe that I can say this categorically -- the key to understanding the issues of the so-called musica ficta, that is, the idiomatic 16th-century use of sharps and flats by TSM and by the vihuelistas. TSM's fugues in general require an eight-course instrument for a complete realization, and certainly the vast majority of readers will be playing six-course instruments, which is like viewing the scores through a limiting lens which can only view a part of the range. Committed six-string players will no doubt work with this limitation creatively, and are encouraged to do so. Players of instruments with seven, eight, or more courses will find ample scope for the full use of their instruments. A thorough study of this work along with a study of the vihuela tablatures will reveal how the vihuelistas used these techniques on 4, 5 and 6 courses. A cadence on a 15th is standard on the six-course instrument, but a cadence at the 22nd requires eight courses. Six course players will have a lot of pruning to do to fit these fugues on their instruments. Certainly it can be done and I don't discourage anyone. For comparison at the opposite end of the spectrum, I recommend playing Mudarra's fantasías for the four-course guitar, in which the counterpoint is necessarily very compact. Perhaps the most appropriate instrument on which to study these fugues would be an A-lute tuned (top down) A4-E4-B3-G3-D3-A2, with five open bass strings tuned G2-F2-E2-D2-C2 which are the diatonic notes of the "short octave" on TSM's keyboard. My own solution is a nine-course fanned-fret guitar, string lengths 600-720 mm, tuned A4-E4-B3-G3-D3-A2-E2-B1-F#1. Your choice is your own. This is the only existing work on fugue for the guitar and lute. I myself have at times despaired of ever mastering it, but I am encouraged by the results of my more recent studies, for which I have more time now that I have finished composing this darned book, which has taken all of my spare time for the last eight years. After memorizing a certain number of TSM's fugues, I have begun to see the connecting links between the elements of TSM's vast database, and I understand that if one were to memorize all of the fugues in the book, that most of them display inter-connecting links which make it possible to string the individual fugues which are in similar modes together in any order according to the whim of the moment, and this is indeed the improvisation of fantasía. But in the short term it is not possible, in my opinion, to improvise completely new fugal expositions: these must be composed, practiced and memorized ahead of time to be ready for use. The amazing ability to improvise a fugue in so many voices on a brand-new theme, reported of J. S. Bach, was clearly dependent on his own possession of a vast mental database similar to that composed by TSM. Our first task is not to improvise, but to study the database. The improvisatory aspect lies in being able to frame any cadence grammatically in order to allow the entrance of a new theme, and this is done by choosing from a repertory of memorized components. TSM's treatment of cadences is every bit as extensive as his treatment of fugal themes, and this is one of the great strengths of his work when compared with many later writers on fugue. He describes them, relentlessly and repetitively, in the terms of a technical language resembling that of figured bass. To the modern harmonist this language appears archaic, simplistic and tautological, but once one analyzes these structures in terms of fingering patterns, they turn out to be an accurate technical description of essential composition details. Zarlino treats the subject flippantly: "Even peasants know how to inflect cadences," he says, and declines to elaborate. Fux gives the relationship between fugal subject and cadence no more than three pages. TSM has the real gold, and here it is.