Review: Harmonic Experience, W. A. Mathieu

Reviews W. A. Mathieu. Harmonic Experience. Rochester, Vermont: Inner Traditions, 1997. Reviewed by Norman Carey The resurgence of interest over the past thirty years in spirituality and mysticism has brought in its wake a host of studies in music, as music claims an illustrious position in esoteric studies. The scholarly presses have, wittingly or not, eased access into the depths of musical arcana with new translations of ancient treatises with speculative components, including those of Ptolemy, Boethius, and Aristides Quintilianus. Other presses, such as Inner Traditions, Shambhala, Phanes Press, and Samuel Weiser, have swelled the tide with reprints of many other old sources (mainly neo-Platonic and Pythagorean treatises) and by presenting new authors. 1 These studies largely focus on the effect that music has upon the psyche and, correspondingly, on the musical (“harmonious”) nature of the cosmos. Studies involving the spiritual effect of music often prescribe a strict regimen of “pure” intervals, i.e., those derived from the Qrst several members of the overtone series. How to mold pure intervals into the ideal scale is still very much an ongoing quest. Indeed, many composers, performers, and theorists are passionately concerned with matters of tuning and temperament, as journals such as David Doty’s 1/1 and John Chalmers’s Xenharmonikon, as well as at least one very lively online discussion group attest.2 Aside from Chalmers and Doty, other champions of the Qeld include Easley Blackwood, Lou Harrison, Ben Johnston, Charles Lucy, Joel Mandelbaum, William Sethares, Ervin Wilson, and LaMonte For a sampling of what the Qeld offers, consult the works of its preeminent scholar, Joscelyn Godwin: Godwin 1986, 1989, 1995. 2Online Tuning Group: http://groups.yahoo.com/group/tuning 1

Young. Honored ancestors include Alain Daniélou, Ivor Darreg, Adriaan Fokker, Harry Partch, Nicola Vicentino, and Joseph Yasser.3 W. A. Mathieu—who has written about the role of music in a number of traditional contexts, including ethos, affect, and to some extent, cosmology—is a musician with a long and impressive vita. After a stint as an arranger for the Stan Kenton and Duke Ellington bands in the early 1960s, Mathieu has been composing works that bring together and honor an equally impressive array of genres and teachers, including SuQ music with Hazrat Inayat Khan, North Indian music with Pandit Pran Nath, African music with Hamza El Din, jazz with William Russo, and (in all likelihood) a host of musical idioms with composer and theorist Easley Blackwood. Mr. Mathieu has been on the faculties of the San Francisco Conservatory of Music and Mills College. Mathieu’s two previous books 4 have prepared the ground for the present study, Harmonic Experience, a large volume of 563 pages. The work is divided into four parts: “Harmonic Purity: Feeling The Numbers” (Chapters 1–18), “The Selective Use of Equal Temperament” (Chapters 19–26), “The Functional Commas of Equal-Tempered Tonal Harmony” (Chapters 27–34), and “Harmonic Practice: Analysis and Review of the Theory” (Chapters 35–44). The material in Parts Two through Four makes striking claims regarding equal temperament to be discussed presently. Here, it is only important to note that rather than relying upon the methods and results of cognitive science to support his claims, the author candidly admits that, above all, the work is a self-examination of his experiences as a singing and listening musician. Avowedly “subjective,” it is, in the end, less a general theory of harmony than it is an autobiography of harmonic experiences. Musical examples consist almost exclusively of the 3 The Huygens-Fokker Foundation has assembled a magniQcent Tuning Bibliography as an online resource: http://www.xs4all.nl/,huygensf/doc/bib. html 4Mathieu 1991, 1994.

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author’s own exercises and compositions. The harmonic theories presented here tacitly, and circularly, rely upon this repertoire of original works for their veriQcation. The few examples not of the author’s own composition are all European music, which is somewhat disappointing given the author’s obviously broader interests. (It would have been interesting to see how Mathieu analyzes nonWestern musics.5) Finally and perhaps most interestingly, with the use of his own form of Tonnetz, Mathieu not only reinvents much of neo-Riemannian theory, but also advances it with a signiQcant new perspective. ***** The “harmony” of the title is approached through the principle of “resonance.” It takes some effort to uncover exactly what the author means by this term. On page one, we read: “By resonance I mean those specially reinforcing combinations of tones that in their mutual resounding—their perfect in-tune-ness—evaporate the boundary between music and musician.” The glossary offers this: “resonance: the conventional deQnition is the reinforcement of tones by synchronous or near-related vibration; as used in this book, the term refers to sensible (that is, singable) combinations of tones related by low-prime ratios” (528). There seem to be three different deQnitions in all: one on page one, and two more in the glossary. The deQnition “used in this book” is in fact not the only one in play. At various points, resonance is said to accrue to all manner of harmonies, and we learn that the effects of resonance will make themselves felt even in equal temperament.6 Concatenating and extrapolating from the two glossary deQnitions, the idea seems to be this: when some intervals are sung, a 5Four measures of a single line taken from dictation given by Pandit Pran Nath on p. 494 are the only exception. 6Gary Don has recently investigated the music of Debussy from a similar perspective. Don’s study, inspired by theoretical work of Ben Johnston, concerns “a method whereby just intonation and equal tempered realizations of [passages in Debussy] can be heard side by side, providing a direct comparison of the different structures that result from just intonation” (Don, 2001, 73).

sensible phenomenon of reinforcement occurs. This phenomenon has a rather small bandwidth, in the midst of which stands an interval whose ratio is determined by small whole numbers. However, any interval that appears within the Qeld of tolerance is resonant to some extent. If this is correct, then resonance is a refashioning of a number of theories of consonance and dissonance, although it is important to mention that these terms are largely absent from this book. Resonance provides the foundation for harmony. To Mathieu, harmony is “not simply chord progressions but the relationships of all the notes in a piece both to the keynote and to each other” (1). Consulting the glossary again, we Qnd: “harmony: refers primarily, in this book, to events that can be quantiQed by ratio, as opposed to events that can be measured by interval.” The term “interval” for Mathieu always signiQes unquantiQed “melodic” distance. Harmony is two-fold: it is both “chord” as simultaneity and also (surface) “chord progression.” Harmony is the primordial musical experience, and rules over and regulates all others including melody, counterpoint, and rhythm. As a result, non-harmonic tones are vexatious to Mathieu. ***** The Qrst part (“Harmonic Purity: Feeling the Numbers”) stands well on its own as a teach-yourself text, whose main focus is learning how to hear and sing intervals in just intonation. Indian solfège syllables (sa, re, ga, ma, pa, dha, ni)7 are used in place of Guido’s do, re, mi. The range of instruction is breathtakingly vast. Readers begin by learning to sing unisons and octaves and, by sticking to the program, progress on to produce a plethora of commas. Along the way, Mathieu is there to extol, to challenge, to rail, to scold, to nurture, to amuse, to encourage, to exhort, to entertain, 7The second syllable, re, is taken from rishabha, and often transliterated ri. One also comes across re, but the pronunciation is the same. A more accurate transliteration is r. s.abha, where the dots under the r and s indicate the retroRex position of the tongue. The word indicates a bellowing, “like a bull.”

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to enlighten. Each topic is drawn in painstaking detail. The chapter that teaches the student to sing perfect Qfths concludes with instructions to open the vowel “with the steadiness of the sun at midday,” to drop the jaw, relax the tongue, and to stand straight (26). The very abundance of exercises, cajolings, and meanderings can be of great value. Students who Qnds themselves interested in the relationship of tuning and intonation to music making will feel a safe and friendly guide near to hand every step of the way. Mathieu proposes that in order to center the ear and voice in the resonances, a tonic-Qfth drone should be used. The drone takes on great signiQcance in the modal and tonal theories that follow. Central to Mathieu’s understanding of harmonic experience is the role of the tonic note whose gravitational pull is, if anything, more forceful here than in other tonal theories. The tonic is both origin and reference point of all harmony. This is a crucial point. The tonic is not only the “keynote” of a composition; it is also the “generating tone.” Whereas a keynote needs only to be perceived as referential in some respect, a generator must people its realm with its overtones. This double burden brings Mathieu directly to the central dilemma of harmonic dualism: Tonal systems entail relationships above and below the tonic, (“overtonal” and “reciprocal” are Mathieu’s terms), but like a run of Biblical “begats,” the overtones run asymmetrically, in one direction only. Where do the reciprocals come from? Propagation metaphors falter. If the tonic is also the generator, metaphysics must be summoned to explain the riddle of the subdominant: “When you sing F you create C. How can you create the creative principle? How does one go about giving birth to a musical god? That is the work of the Musical Mother [the syllable ma stands for the fourth degree of the scale] . . . You who dare to sing F in the C world become the embodiment of the creative and the sacred” (43). Similarly intricate machinery is necessary to explain other notes, such as the “reciprocal” major third below the tonic: In order to generate A , we momentarily pretended that it was the tonic, even though our larger context is C. We are not really in A . That is pre-

cisely the trick of perception implicit in reciprocal harmony: A generates the harmony, but C is still home—that is, A becomes the harmonic root, but C remains the tonic (48).

The reader will see that, while portentous, this explanation does not stand up to much scrutiny.8 The progenitors in just intonation are the primes. Each prime establishes its own line of harmonies extending in both overtonal and reciprocal directions, and is endowed with a distinct affect. Indeed, “Each prime number generates its own musical universe” (124). Much attention is given in this work to Qve-limit systems.9 There is a fair amount on seven-limit systems, but very little on systems with larger limits. Mathieu explains, “As the primes ascend father from unity, they become less functional as musical elements, less able to generate their musical worlds” (125). In Qve-limit systems, the primes three and Qve procreate other tones, and the octave is responsible for normalizing register. Example 1 shows a portion of the pitch space associated with Qvelimit just intonation. Mathieu provides a similar map with Qfths along the x-axis, and thirds on the y-axis, and points out that this kind of representation (in fact a Tonnetz 10) is standard in depictions of Qve-limit just intonation. Mathieu’s innovation is to tilt the plane a few degrees counterclockwise so that the points represent notes in staff notation. The student is encouraged to trace

8A comical rendering of a similar patrimony paradox is found in Joyce’s Ulysses: “He proves by algebra that Hamlet’s grandson is Shakespeare’s grandfather and that he himself is the ghost of his own father” (19). 9Extended just intonation tuning systems are described as p-limit systems, where p is a prime. The unqualiQed term “just intonation” will refer to Qve-limit just intonation. 10 Mathieu apparently believes that Alexander Ellis (in Helmholtz [1863] 1954) is the originator of the Tonnetz. While Ellis himself makes a similar claim, Cohn (1997) awards the palm to Euler in 1739, although it might be rightly claimed that the so-called lambda diagrams of antiquity (Archytas, Nicole of Oresme, etc.) depicting octaves and perfect twelfths in two dimensions are Tonnetze, rendering all proprietary claims moot.

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354 (or 358 )

Example 1. A portion of the Qve-limit just-intonation Tonnetz with pitch classes represented by pitches in the octave of C = 1. Each cell displays pitch-class name, ratio, and cents value. Subscripts on pitch-class names indicate syntonic commas; e.g., D-1 (10:9) is lower than D (9:8) by 80:81.

B22 (50:27) 1067¢

F 22 (25:18) 569¢

C 22 (25:24) 71¢

G 22 (25:16) 773¢

D 22 (75:64) 275¢

A 22 (225:128) 977¢

E 22 (675:512) 478¢

G21 (40:27) 680¢

D21 (10:9) 182¢

A21 (5:3) 884¢

E21 (5:4) 386¢

B21 (15:8) 1088¢

F 21 (45:32) 590¢

C 21 (135:128) 92¢

E (32:27) 294¢

B (16:9) 996¢

F (4:3) 498¢

C (1:1) 0¢

G (3:2) 702¢

D (9:8) 204¢

A (27:16) 906¢

C +1 (256:135) 1108¢

G +1 (64:45) 610¢

D +1 (16:15) 112¢

A +1 (8:5) 814¢

E +1 (6:5) 316¢

B +1 (9:5) 1018¢

F+1 (27:20) 520¢

A +2 (1024:675) 722¢

E +2 (256:225) 223¢

B +2 (128:75) 925¢

F +2 (32:25) 427¢

C +2 (48:25) 1129¢

G +2 (36:25) 631¢

D +2 (27:25) 133¢

3 32 (or 334 )

journeys through harmonic space upon this map, which will reinforce and deepen the aural understanding. Mathieu’s Tonnetze require a tonic, which is the pitch-class C for the most part in this book. The tonic is endowed with its own symbol, a sunburst. Due to their roles as generators, perfect Qfths and major thirds and their direct descendents have the most privileged status, and all other intervals are “secondary.” Mathieu’s derivation of the

minor third illustrates: E , the minor third up from C, is derived by generating G a 3:2 Qfth up from C, and then appending a 5:4 third downward. There is no direct path from C to E . Because the “overtonal” direction is strongly privileged here, the minor triad is not conceived as the simple inversion of the major: C is the tonic; G is an overtone of the tonic; E is formed reciprocally downward from G. There is some resemblance here between Mathieu’s

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explanation and Moritz Hauptmann’s “twin generator” idea of the minor chord. 11 Mathieu’s modal and tonal theories, introduced in this section, are a direct outgrowth of the concept of “dronality.” The glossary deQnes “dronal,” “dronality,” and “drone” without pinning down the central concept. It appears that the drone is called upon to act as a disambiguating agent in the realm of tones. The drone is the power of the tonic made immanent. The authoritarian dronal tonic will brook no insurrection, no usurpation. (The primary discussion about modulation does not begin until p. 306.) As Mathieu admits, “If a drone is sufQciently assertive—that is, loud—you can put anything above it, even a chain saw, and it will prevail as the tonic” (234). Its disciplining power is summoned out of what seems like uneasiness that without it, the tones will lose sight of their rightful ruler, form unauthorized allegiances among themselves, or worse, form none at all. “Unambiguous” harmonic progressions are, for Mathieu, those in which there is a direct relationship between the tonic and every note of every harmony. Dronality admits no second-order relationships. The drone insists on direct contact with each of its subordinates. Two examples illustrate the megalomaniacal nature of the drone. The Qrst is Mathieu’s analysis of a jazz cadence, a pair of parallel thirteenth chords from D down to C, shown in Example 2. Mathieu tells us that this formula is “typical to the point of being a cliché” (384). Half step cadences are certainly common in jazz. This variant has no particular prototypical status however, but rather seems arrived at by a careful process of stacking the deck. Like other jazz theorists, Mathieu assigns scales to chords, which is here quite easy to do, since both chords are heptatonic. While the progression can be analyzed within the context of tritone substitution, this explanation is not invoked. Nor does the smooth, all-half-step voice leading come into play. Instead, Mathieu insists upon a Qrm anchoring of all of the tones of both

Harrison (1994, 228–9) provides a good summary.

11

Example 2. A jazz cadence (Mathieu’s Example 37.9)

chords to the C tonic. That is, the Qrst chord is to be understood as C phrygian, the second as C lydian. Note the effect of this explanation. What bubbles to the surface is something that routinely remains submerged: the C common tone. (That its dronal companion G also forms a common tone here can only add fuel to Mathieu’s Qre.) A linear analysis of the cadence would have the C in the Qrst chord acting as a dissonance needing to be resolved—to be resolved, indeed, into the B of the second chord. In Mathieu’s interpretation, the C has the same degree of structural importance in both chords. In other words, the cadence is not to be realized as a lydian mode on D followed by another on C, but by two different modes of C (384). In like fashion, Mathieu rails against hearing any non-tonic chord as giving rise to its own scale (359). The second example is one of the few that is not the author’s own music. Instead, Mozart is taken to task for spelling errors. This example splendidly demonstrates the skew that dronality applies to tonality. Example 3(a) reproduces Mathieu’s Example 15.5, taken from mm. 49–51 of the Qrst movement of the F Major Sonata for piano, K. 332. Example 3(b) (Mathieu’s 15.6) shows the author’s emendations to Mozart’s notation. A linear analysis of this passage would likely depict both the D and the F as ascending chromatic appoggiaturas, while only the F is susceptible to that interpretation in Example 3(b). 12 As a chromatic lower 12 I don’t think it succumbs to it, however. The fact that Mathieu leaves the F notation unaltered has more to do with the fact that F comes on the “overtonal” side of C—either up six Qfths, or up two Qfths and a third—than with any secondary relationship between G and F .

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Example 3. Rewriting Mozart K. 332, Qrst movement (a) Mozart’s original notation (Mathieu’s Example 15.5)

(b) Mathieu’s corrections (Mathieu’s Example 15.6)

(c) “Major/minor” seventh chord

neighbor, the D assumes a leading-tone quality, a perspective openly mocked by Mathieu: The passage obviously does not imply the key of E minor, so the D in Mozart’s spelling is not its diatonic major seventh . . . Nor is the D in the key of C. Or is it? Can you (honestly) hear a D over a C drone—that is, truly in the key of C—as a raised second without it either becoming a minor third in your head (in which case it is E ), or modulating to E Minor? I think the D in this harmonic context is simply a wrongness . . . a kind that appears increasingly as equal temperament becomes the European norm. (105–6)

While the D notation subordinates an appoggiatura to its resolution, the choice of E connotes an uneasy oscillation within the chordal third. Neither third accepts the subordinate position. The dissonance is entirely acoustic rather than syntactic.13 Mathieu’s explicit avowal of the identity of tonality (“truly in the key of C”) and dronality (“over a C drone”) is very telling, however the conceptual amalgamation comes at the expense of both idioms. It should be noted that when modulation is discussed later on, multilayered levels of tonal relationships are acknowledged. Example 4 reproduces Mathieu’s Example 38.28. We are told that being in a key is not always sharply deQned. There are degrees and shades of gray. In this passage, “the C is heard as the leading tone of the 10:9 re, giving that re Reeting credibility as a tonic.” This reading is subtler than, and inconsistent with, the Mozart analysis. Mathieu nicely revises the analogy of scale and ladder to include sliding rungs for notes altered by a chromatic half step (102). Perhaps the Mozart passage is best understood in terms of a D rung that has been slid up to be nearer to the E, than as an E rung that slides up and down while we are standing upon it. Mathieu makes an interesting claim in this context, namely, that Bach never falls into Mozart’s kind of notational error. In the given circumstances this is a claim that cannot be tested, because the use of an unsupported 2ˆ as a chromatically altered lower neighbor to 3ˆ is simply not in the Baroque language. The only way for Mathieu to prove his case here would be to present a passage in which Bach employs a notation such as the one in Example 3(b), eschewing that of 3(a). I cannot leave this passage without suggesting another reason for Mathieu’s E preference. Mathieu tells us that he Qrst came to harmonic experience through jazz, and only later discovered 13 That dissonance has anything other than an acoustic basis is never challenged in this book. Among many works that might modify this view are Tenney 1968 and Krumhansl 1990. Recently, William Sethares (1998) has demonstrated the intimate connection between timbre and the perception of consonance and dissonance.

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Example 4. Weak tonicization of D minor (Mathieu’s Example 38.28)

European art music. Example 3(c) shows a common jazz/funk chord, a “major/minor” seventh chord. In its context, this chord is quite stable, and easily carries tonic function. (Mathieu shows one with a dominant function on p. 355.) Neither of the thirds embellishes the other, and, in fact, the sonority suggests a “bent” blues third. The E is perfectly correct here. However, it would not be correct to propose the chord in Example 3(c) as an idiomatic harmonization for the Qrst measure of the Mozart melody. The modal system presented at the end of the Qrst part is unique, although its names are derived from the church modes and its process of organization is somewhat akin to the Indian melakartas. Mathieu’s modes involve a lower tetrachord beginning on C, and an upper one beginning on G. There are four step patterns allowed for the upper tetrachord: 2–2–1, 2–1–2, 1–3–1, 1–2–2, and eight for the lower: these same four, and four tritonal variants of these that add one to the last member of each: 2–2–2, 2–1–3, 1–3–2, 1–2–3. The resultant set of thirty-two modes includes all of the “white key” modes except locrian, both harmonic and melodic forms of the minor, and a remainder made up of those the process admits. Mathieu also proposes a “Magic Mode” that contains all 12 notes needed for the set of thirty-two. The absence of locrian is telling. The inRuence of dronality commands that, by construction, all modes must have a perfect Qfth above the Qnal. Quite reasonably we are told that locrian is a “latter-day theoretical construct” (234), and with respect to the usages of European modality, this is certainly true. Parts 2 through 4 recount the adventures of the modes and their harmonies as they are transformed by equal temperament.

Modality is given a modern triadic treatment, and harmonic progressions for Mathieu’s thirty-two modes, particularly for the more familiar types, are suggested. Part 2 is concerned with compositional techniques whereby all harmonic progressions can be mapped into a just-intonation prototype. Mathieu identiQes harmonic ambiguity as arising from two causes: the appearance of two versions of a single tone differing by a comma, and progressions that leap over Tonnetz adjacencies. Ambiguity is avoided to begin with by forbidding both of these. “Matchstick” harmony is the name given to the allowable “stepwise” progressions along the Tonnetz. 14 Ambiguity and its attendant commas are introduced gradually, leaving matchstick harmony to do the job of harmonic clariQcation. (As I discuss later, Mathieu is equivocal about ambiguity. It is “a dramatic—even dark—force in music” [349]. Part of his difQculty comes from presuming tonality to be inherently unambiguous.) There are three commas that come under consideration: the syntonic comma 81:80 (21.5¢), that represents the difference between Pythagorean ditone and just major third, the diaschisma, 2048:2025 (19.55¢) that represents the difference between an octave and the sum of a Pythagorean ditone, and two just major thirds, and the minor diesis, 128:125 (41¢), that represents the difference between an octave and three just major thirds. Mathieu apparently conRates the minor diesis and the major diesis, 648:625 (62.57¢) that is the difference between an octave and four minor thirds. He may have overlooked this larger comma because of the inferior status accorded to the minor third. In the beginning of Chapter 30, describing what neo-Riemannians call a “PR” cycle, the major diesis is achieved, but the references here are all to the

14 The Tonnetz reminds Mathieu of “the matchstick puzzles and games we played as kids” (158). One puts a match down, connecting two points. The match may be moved so that one end stays Qxed. For example, from C major one can get to G major, or E minor, or A minor, or F major, or F minor, or C minor.

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“Great Diesis,” Mathieu’s unfortunate name for the minor diesis.15 Mathieu does not consider the Pythagorean comma, 531441:524288 (23.46¢), to be of great practical signiQcance since there are few compositional contexts in which its presence is felt. The schisma, 32768:32805 (1.953¢), the difference between an octave and the sum of a just major third plus four Pythagorean whole tones, is never mentioned, but would be, at 2¢, cognitively irrelevant for Mathieu’s purposes. After presenting exercises that teach the student to sing the commas in just intonation, Mathieu goes on to track their effect in equal temperament. There are Qne insights in this part of the book, yet much of it remains exasperatingly elusive: The primary concern of this book is the behavior of twelve-tone equal temperament, and we raise a question central to it: Physiologically and psychologically, how can we accept a musical approximation for the real thing [i.e., just intonation]? Any answer to this question, at least at the present state of our knowledge, must be subjective, evanescent, and nonquantiQable. Even the terms of the question cannot be rigorously deQned. ScientiQc method cannot save us. We do, however, have ourselves, not only individually but also collectively. By examining deeply our own responses to musical phenomena, we can shed light on our musical behavior. (137–8)

Indeed, the scientiQc method cannot save us, but it might provide our inner examination with a structure that is intersubjective, not completely evanescent, and enumerable. We may even boldly and rigorously deQne our question. The problem with not wanting to say anything too precisely is that of not in the end saying anything at all.

15More evidence of this problem is found in Table 41.1 (473). Here the difference between four 6:5 minor thirds and an octave is equated incorrectly with one diaschisma plus one (minor) diesis. Curiously, Mathieu posits a “superdiesis” on p. 501. This is none other than the missing “major diesis,” 648:625. Here it is correctly equated with one syntonic comma plus one (minor) diesis, and then incorrectly equated with “four pure thirds plus four perfect Qfths.” “Plus” probably should have been “minus.”

Let us nonetheless try to understand what Mathieu is telling us about equal temperament. The conclusion at the end of the book is that in the simplest contexts, the sounds of equal temperament stand unambiguously for the resonances of just intonation. This unambiguous reference is equated with “tonality.” Then, “as ambiguity increases, tonality weakens, resulting Qnally in the emergence of the affective force inherent but hidden in the tuning: its symmetry and ultimate atonality” (508). The possibility of ambiguity being absent even at the beginning of this process is questionable; ambiguity is present ab ovo if melody and harmony are conjoined. Mathieu attempts to demonstrate how context can reveal the pure intervallic prototypes for harmonies sounding in equal temperament. Triads imply just intonation, and stacks of Qfths imply Pythagorean tuning. The syntonic (“Didymic”) comma is invoked by harmonizing E4 in two different ways: Qrst, using a C-major triad (E = 80), and then with a stack of four perfect Qfths from C2 through E4 (E = 81). Through a kind of homeopathic view of intonation, Mathieu would have us believe that even in equal temperament, the comma is still operant: “[In just intonation we] hear a small change in pitch as a large change in function. In equal temperament, the pitch difference is gone, yet the harmonic effect, washed out as it may be, is not washed away” (254).16 Any retention of this effect is further diluted by the fact that there are often multiple contexts for a single harmonic event. As Mathieu points out, the stack-of-Qfths chord producing E = 81 is often employed in jazz as a tonic-triad surrogate, and so clearly the E4 would need to be modeled after the just-intonation 5:4 major third as it sits atop the stack of 3:2 perfect Qfths. Which third is the clear prototype here? This would be a likely place to discuss meantone temperaments, but “meantone temperament” has a single entry in the 16 “Hearing” a harmonic effect in an interval that is acoustically identical to unison is reminiscent of the passage in Plato’s Republic (VII:531) in which the “teachers of harmony” put their ears close to the strings to see who can hear the smallest pyknon.

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index. The history of intonation presented here traces a more or less straight shot from Qve-limit just intonation directly into equal temperament. The reader would accordingly get the impression that the historical tuning for the church modes was Qve-limit just intonation, despite the clear evidence of medieval treatises (e.g., Dialogus in musica) explaining in great detail how to establish the monochord in Pythagorean tuning—three-limit just intonation, if you will.17 Mathieu is absolutely right in saying that learning to hear and sing intervals in just intonation is a fabulously enriching, even empowering musical experience. It opens a door from the Ratland of equal temperament into a multi-dimensional new world. It can be exhilarating to the point of vertigo. It can also give new respect for equal temperament through a deeper appreciation of what it so elegantly accomplishes. We acknowledge with greater insight all of the intonational conRicts it is able to quell and delight in its own alluring duodecimal symmetries. Furthermore, there are many circumstances in which it is possible to disambiguate the intervals that we hear in equal temperament; for example, we expect our students to spell their chords correctly, even when they are taking dictation from the piano. However, as earlier examples have shown, some enharmonic functions have become so fused in equal temperament that it is not possible to disambiguate the harmonies without removing some of the harmonic signiQcations. A many-to-one mapping is not reversible. For Mathieu then, just intonation is authentic harmonic experience, but equal temperament will allow, when conditions are right, a close replica. While this position is reasonable enough, there is no real acknowledgement of the snake in the garden in the story of tuning, the sinuous allure of melody unadorned. The slighting of melodic study in this book could be easily justiQed—this is a book about harmony, after all, and not melody. However, this masks a more serious issue—namely, that harmony and melody are not equal partners in the author’s view. Harmony commands and over-

shadows melody. Harmony can exist without melody, but not the other way around. This view is in direct conRict with the notion that melody is historically prior to harmony and, arguably, conceptually prior as well. Mathieu proposes a thought experiment by way of support of his position (390). He asks us to hear a cadence performed in Shepard tones (without calling them such). There is no melody to speak of, but the harmonic syntax would remain completely clear. Another hypothesis, tested and proven in fact by Roger Shepard, suggests that the inRuence of melody is so great, the ear would tend to create melodies out of the smallest potential intervals of every interval class.18 If asked to sing what was heard, some such derived melody would be the result. Thus, melody and harmony share equally in the cadential effect. Neither can be factored out. Melodic principles and harmonic ones generate different kinds of tonal spaces. Curt Sachs proposed “cyclic” and “divisive” principles of scale construction. 19 The cyclic principle is that of a generated set, while the divisive one uses arithmetic or harmonic means in order to subdivide the octave. Melodic contexts favor the cyclic principle, harmonic ones the divisive. The cyclic systems, such as Pythagorean tuning, offer both a manageably low number of step-interval types and a great range of potential tonics or modal “Qnals,” and they also easily adapt to the challenges of modulation. They may, however, be poorer in what Mathieu calls resonance. The divisive systems, such as just intonation, are more tonic speciQc, maximizing harmonic purity for the sake of the central tone and showing less regard for the remaining ones. If other tones are to be made into Qnals, intonational adjustments are generally required. The number of melodic step intervals tends to be higher in divisive tone-spaces. While enthusiasts of Qve-limit just intonation can delight in its subtle varieties of major and minor tone, Pythagorean tuning has at least equal pedigree, and no such differences. 18

17

Strunk 1965, 103–16.

19

Shephard 1964. Sachs 1948, 14 ff.

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In Mathieu’s “dronal” circumstances, vertical relationships are all-powerful. But while much ancient and traditional music made use of drones, this is not a musical universal. There is, for example, no evidence that the Gregorian chant repertoire originated with an accompanying drone. Without the drone, purely melodic considerations take over. There is, then, a conRict between (at least) two “natural” intonational systems, one that rules the harmonic realm, one the melodic. In the mythic language of love, the vertical agape, connecting the human and divine, would be all harmonious were it not for a conRicting horizontal eros connecting beings of the same kind. Dionysius’s passionate aulos discords with the rational lyre of Apollo. The history of temperament, including equal temperament, tells of the mediation between these conRicting “natural” claims. That there is a difference between the intonational norms of harmony and melody is implicit in Mathieu’s presentation of his modal theory. After Qrst introducing the major and minor tones in Chapter 10, the step patterns of the primary modes are illustrated in Chapter 11 using step sizes of “1” and “1/2.” What has happened to 9:8 and 10:9? The maps depicting these modes clearly show that they must be understood in just intonation. Even for Mathieu, the melodic need for intervallic parsimony has transcended the harmonic need for purity. (The interval labeled “1/2” that connects leading tone to tonic is invariably 16:15 in this book. There is virtually no mention of the smaller, more melodically oriented Pythagorean half step, 256:243.) With the strong emphasis on resonance and verticality, embellishments and tones of Qguration have little chance to Rourish. The approach is in agreement with Schoenberg’s assertion that “non-harmonic tone” is a misnomer.20 This proposition is one that Schoenberg ultimately found difQcult to support— at least in 20 Schoenberg [1911] 1978. See in particular Chapter 17, “Non-Harmonic Tones,” pp. 309–44.

relation to tonal harmony—but Mathieu is willing to shore it up at the expense of considerably problematizing melodic composition. Perhaps, like many others, Mathieu believes that harmony can be taught, but melody cannot. When telling us how to Resh out a harmonically constructed skeleton, we are reassured that, “the tones seem to spontaneously generate melodies on their own” (38). Similarly, “in a way these melodies write themselves. If a harmonic progression is balanced, the melodies inside it are eager to be awakened” (170). This is not likely to be much consolation to beginners who cannot get their melodic kites airborne. There is very little information about chordal inversion in this book, but this, too, is consistent with the view of harmony presented here. What attention the subject does get is both sketchy and misleading. On p. 370, we are told that 63 stands for Qrst inversion and 3 stands for root position, but are not told why, nor that 63 may be abbreviated to 6, nor that root position is generally abbreviated with no Qgure at all. On the following page, jazz-based Qgures are introduced, and we are told that a 7 standing by itself always means to add a minor seventh above the bass. All of these are true in some context, but there is no single context in which they are all true. (Some pages later, we are informed that 65 means Qrst inversion of a seventh chord, and 42 means third inversion. The Qgures are never explained; nor is there ever a 43.) On the other hand, the cadential 64 chord, although always labeled “I64 ” is lucidly described as a double suspension whose content may be tonic, but whose context is clearly dominant. He is oddly ill at ease with the dominant seventh chord. He Qnds V with the seventh to be more “dramatic” but no more “compelling” than it is without. Monitoring his own inner responses to the chord, he reports, “When I hear it without thinking about it, and respond to it simply, there remains a mystery at the heart of it. I get it and I don’t get it. Maybe this mystery is the actual deQnition of tonality: the mystery of the center” (391).

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***** Mathieu has a fresh approach to many issues that have come under the rubric “neo-Riemannian” theory. Diatonic and chromatic sequences are examined very carefully throughout the second half of the book. On p. 157, there is a description of the Leittonwechselklang (not called such), connecting a “major triad to its mediant” or a “minor chord and its submediant.” The various “cycles” that have become the focus of Neo-Riemannian theory are all present without the now conventional nomenclature. At the beginning of Chapter 30, which deals with the minor diesis 128:125, the “PR” cycle is illustrated on p. 286. This cycle would eventually create the major diesis, 648:625; however, as mentioned earlier, the major diesis is not distinguished from the minor in this book. (His claim that “[the PR cycle] is not commonly heard harmony” is not supported by Neo-Riemannian studies, in which a number of examples from nineteenth-century compositions are cited.) The “LP” cycle is described on p. 348, here properly illustrating the minor diesis. The “RL” cycle, evoking the Pythagorean comma, is fully described on pp. 448–9, using an example that might have been suggested by the Scherzo of Beethoven’s Ninth Symphony.21 Whereas the cognitive claims about commas in equal temperament are perhaps questionable, Mathieu has some interesting things to say about commas with regard to their capacity to structure and delimit Tonnetze. He describes a method he calls “positional analysis” that tracks the harmonic path of a piece along the Tonnetz. He is especially concerned with topological issues that cast commas in the roles of delimiters. The gist of the method is to determine whether the excerpt in question is forced to employ an

enharmonicism.22 Even if one travels far out in one direction along the Tonnetz, if one returns by means of a continuous path back to the tonic (here is where the “matchstick” approach pays off ), there is no enharmonic legerdemain. He invents a kind of “shape note” system for the analysis: each Qfth-based horizontal of the Tonnetz has its own note shape. The approach, as one may expect, is completely non-mathematical, although the choice to formalize these procedures within the strictures of transformation theory is more a matter of style than it is of substance. Mathieu’s analysis of the rondeau Fumeaux fume par fumée (pp. 495–9), by the Ars Subtilior composer Solage is the most convincing analysis of the four he presents. Without much commentary, Mathieu demonstrates that, despite the extreme chromaticism, no comma shifts are employed and all enharmonic debts are paid. The work does not proceed, out and back, literally stepwise along the lattice. However, the analysis shows that the piece may be performed within a closed region of the Tonnetz without the need for topological “loops.”23 There is even a playful text/music relationship drawn out of his analytical method. While situating the piece within a triadic context is anachronistic, there is nothing about the analysis that relies upon the conventions of common practice-tonality. There would seem to be a great deal of repertoire that could yield to this method, including essentially the whole of the Renaissance, particularly the chromatic works of either the fourteenth or sixteenth centuries. Less successful is his positional analysis of the Qrst movement of the Beethoven Appassionata sonata (p. 506). Its fervently chord-by-chord approach arrives at the conclusion that, counting all comma crossings, the piece begins in F minor and ends in A minor.

21Measures 132–71. Again, the dearth of examples from the literature is unfortunate. Mathieu shows us that while the bass moves down by minor and major thirds alternately (with some upward sixths for registral normalization), each of the three upper voices travels in one of the three different octatonic scales. This elegant result is found also in Cohn 1991, 1992, 1997. See also Douthett & Steinbach 1998.

22Brian Hyer (1995, 106) describes Riemann’s sensitivity to the pathways along the Tonnetz for their role in determining intonation. 23In Hyer (1995, 119) the topological transformations of the Tonnetz are depicted as they are mapped from inQnitely extended just intonation into equal temperament.

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***** While clearly passionate about his topic and eager to spread the joy of his discoveries, Mathieu is often woefully vague in the deQnition of terms. Aside from examples already given, deQnitions of the terms “scale,” “mode,” and “key” are either misleading or simply uninformative. Like many autodidacts, Mathieu can be rather desultory in recounting the histories of his topic. Neither is he averse to casting a wide but tattered net of aspersions on predecessors. This is perhaps the most troubling aspect of the book. For example, we are told on p. 1 that “there exists no satisfactory general theory of harmony,” and “We have no comprehensive music theory today.” Later, Mathieu writes: “Over the centuries, classical music theory has developed a wide variety of misleading concepts” (319). Telling music-historical tales with little regard for precision, and having reached the Qfteenth century, Mathieu opines, “Remember that there was no unifying viable music theory at the time—certainly no practical one—that clariQed procedures. (There still isn’t, unless this is it.)” (135). So what is new? Mathieu claims that what “clariQes procedures” is deriving the laws of harmony from resonance or from the overtone series. While there may not be much information on the overtone series in standard college harmony texts, it would have been well to consider the contributions of some of his true predecessors in the Qeld of harmonic theory. Taking, for example, three well-known theorists with important things to say about harmony, Rameau, Riemann, and Schenker, we notice that none of them Qnd their way into this book, and yet all were at least as concerned as Mathieu to derive harmony from the sonorities of the overtone series in some way (nor are they unique in this respect). Rameau’s notion of the corps sonore, for example, closely mirrors Mathieu’s “resonance.” Like Riemann and Oettingen, Mathieu derives systems of sonorities in dualist terms and displays them in Tonnetze. There is even a lovely recasting of Hauptmann’s “having an overtone—being an overtone” solution to the undertone problem (42). Furthermore, Mathieu would agree with Hauptmann that perfect Qfths and major thirds are, along

with octaves, the only “directly intelligible intervals.” Finally, Mathieu reveals that “harmony is form.” Summing up the main contributions his harmonic theory makes, he writes: The theory . . . demonstrates how elemental harmonic principles are architectonic— that is, how their structure controls or directs other structures— and how this active, forming energy cuts both ways across the orders of magnitude . . . One begins to grasp . . . how the smallest elements and the largest formal shapes are mutually nourishing. (510)

A lofty vision, indeed; however, it would not have been remiss to acknowledge the powerful manifestation of this same vision in the work of Heinrich Schenker. Most of all, Mathieu criticizes European music theory (“classical theory” as he calls it) for not concerning itself with affect. “I could not Qnd—try as I might—the connection between classical theory and the palette of feeling that its music inspires” (2). The apparent assumption, that the feelings are caused by harmonies themselves, is carried by the force of revelation here, and alternatives to it barely merit mentioning. We are, he concludes, designed to respond to certain harmonies in certain ways: “The forces that govern the production of overtones govern our ears also, and our ears’ responses” (41). In short, “pure harmony is hard-wired” (141). Furthermore, the wiring takes the shape of “Qfth-by-third” Tonnetze: “The ease with which we comprehend the nested geography of music indicates that the harmonic lattice is not merely a metaphor for musical behavior, but corresponds to a spatial geography in the brain” (359). This is not a book with scholarly pretenses, and so an extensive citation of the work of others is not the point. To be sure, in the very Qnal section entitled, “Whose Theory Is It?” he graciously acknowledges a debt to his teachers, and is quick to confess that he has not “created anything new.” Nevertheless, before we get to this point, we have been told repeatedly that all harmonic theory up to but not necessarily including the present opus is unsatisfactory, misleading, and impractical.

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***** Perhaps Mathieu’s greatest unacknowledged debt is to Moritz Hauptmann. It is quite possible that Hauptmann is unknown to Mathieu, but he would nonetheless Qnd in Hauptmann an ancestor worthy of his esteem. Let me recapitulate some of the points of correspondence between the two theorists: in addition to the understanding of octaves, Qfths, and thirds as the only “directly intelligible intervals” and the solving of the “undertone” problem with the device of “having/being” an overtone, both employ a “twin generator” approach to the origin of the minor chord; both are concerned with the church modes as well as derivatives thereof in the context of just intonation; both are guided fundamentally by dualism and committed to its metaphysical underpinnings. Whereas the roots of Hauptmann’s thought are found in Hegel, Mathieu himself takes an occasional Hegelian turn: “We need to elevate the status of the equal-tempered comma from that of a pun, where a single thing stands for two incidentally related things, to that of a matchmaker, where complementary energies are conjoined and synthesized into a higher meaning” (347). There is no more exacting discipline than that of looking within and reporting accurately on one’s Qndings. Mathieu is brilliant in describing his own inner journey of harmonic discovery. He writes with a distinct voice, and his passion for his subject is profound and profoundly moving. It Qnally does not matter knowing how much of his tongue may have been in his cheek as he intones a “Hymn to the Great Diesis” (298). We intone along with him. Nor can one respond with anything other than fondness as he conjures up his alter ego, “Dr. Overtone.” The range of encomiums on the back cover from the likes of John Coltrane, Pete Seeger, and Ben Johnston attest to a life lived in great devotion to his subject, a profession in the truest sense. While problematic in the respects I have addressed, this book has much to offer to every musician who is beguiled and beckoned by the mystery at the center of the musical art.

LIST OF WORKS CITED Aristides Quintilianus. 1983. Aristides Quintilianus On Music In Three Books. Translation with introduction, commentary, and annotations by Thomas J. Mathiesen. New Haven: Yale University Press. Barker, Andrew. 1989. Greek Musical Writings II: Harmonic and Acoustic Theory. Cambridge: Cambridge University Press. Boethius, Anicius Manlius Severinus. 1989. Fundamentals of Music. Translated by Calvin Bower. New Haven: Yale University Press. Cohn, Richard. 1991. “Properties and Generability of Transpositionally Invariant Sets.” Journal of Music Theory 35: 1–32. ———. 1992. “Dramatization of Hypermetric ConRicts in the Scherzo of Beethoven’s Ninth Symphony.” 19th-Century Music 15.3: 22–40. ———. 1997. “Neo-Riemannian Operations, Parsimonious Trichords, and Their Tonnetz Representations.” Journal of Music Theory 41: 1–66. Daniélou, Alain. 1943. Music and the Power of Sound: The InGuence of Tuning and Interval on Consciousness. Revised edition of Introduction to the Study of Musical Scales. Rochester, Vermont: Inner Traditions. Douthett, Jack, and Peter Steinbach. 1998. “Parsimonious Graphs: A Study in Parsimony, Contextual Transformations, and Modes of Limited Transposition.” Journal of Music Theory 42: 241–63. Don, Gary. 2001. “Brilliant Colors Provocatively Mixed: Overtone Structures in the Music of Debussy.” Music Theory Spectrum 23: 61–73. Godwin, Joscelyn, ed. 1986. Music, Mysticism And Magic: A Sourcebook. New York: Arkana. ———. 1989. Cosmic Music: Musical Keys to the Interpretation of Reality. Essays by Martius Schneider, Rudolf Haase, and Hans Erhard Lauer. Introduction by Joscelyn Godwin. Translated by

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Marton Radkai and Joscelyn Godwin. Rochester, Vermont: Inner Traditions. Godwin, Joscelyn. 1995. Music and the Occult: French Musical Philosophies, 1750–1950. Rochester, N.Y.: University of Rochester Press. Harrison, Daniel. 1994. Harmonic Function In Chromatic Music: A Renewed Dualist Theory and an Account of its Precedents. Chicago: University of Chicago Press. Hauptmann, Moritz. [1853] 1991. The Nature Of Harmony And Metre. Translated and edited by W. E. Heathcote. New foreword by Siegmund Levarie. New York: Da Capo Press. Helmholtz, Hermann. [1863] 1954. On The Sensations of Tone. Translated by Alexander Ellis. New York: Dover. Hyer, Brian. 1995. “Reimag(in)ing Riemann.” Journal of Music Theory 39: 101–38. Krumhansl, Carol. 1990. Cognitive Foundations of Musical Pitch. New York: Oxford University Press. Mathiesen, Thomas. 1999. Apollo’s Lyre. Lincoln: University of Nebraska Press. Mathieu, W. A. 1991. The Listening Book: Discovering Your Own Music. Boston: Shambhala. ———. 1994. The Musical Life: ReGections On What It Is And How To Live It. Boston: Shambhala.

McClain, Ernest G. 1978. The Pythagorean Plato. York Beach, Maine: Nicolas-Hays. Sachs, Curt. 1948. Our Musical Heritage. Englewood Cliffs, N.J.: Prentice Hall. Schoenberg, Arnold. [1911] 1978. Theory Of Harmony. Translated by Roy E. Carter. Berkeley: University of California Press. Sethares, William. 1998. Tuning, Timbre, Spectrum, Scale. London: Springer. Shepard, R. N. 1964. “Circularity in Judgments of Relative Pitch.” Journal of the Acoustical Society of America 36: 2346–53. Strunk, W. Oliver. 1965. Source Readings In Music History: Antiquity and the Middle Ages. New York: W. W. Norton. Tenney, James. 1988. A History Of “Consonance” And “Dissonance.” New York: Excelsior. WEB BASED SOURCES:

Huygens-Fokker Foundation, Tuning Bibliography. URL: http:// www.xs4all.nl/~huygensf/doc/bib.html Tuning Group. URL: http://groups.yahoo.com/ group/tuning

2

1

Schenker’s early writings are collected in Federhofer 1990. See Schenker 1906.

Heinrich Schenker’s major theoretical works are widely known today, thanks to a series of translations as well as a vast secondary literature and numerous textbooks. Because of this dissemination of his ideas, Schenker’s work is often perceived in purely theoretical terms. But viewing Schenker solely in relation to such concepts as structural levels results in a limited and distorted picture of this preeminent Qgure in twentieth-century music theory. Schenker began his professional career not as a theorist, but as a pianist, conductor, and composer. (His compositions were favorably regarded by Brahms and Busoni.) Between 1891 and 1901, Schenker was also active as an author of essays and reviews; his subsequent theoretical work developed in part from the desire to establish a more satisfactory basis for criticism of composition and performance.1 Harmonielehre demonstrates that he saw himself as an artist Qrst: when Schenker published it, the words “von einem Künstler” (by an artist) appeared in place of his own name on the title page.2 He remained an active practical musician and teacher throughout his life, giving private lessons in piano and theory. Schenker’s teaching methods went far beyond those of conventional piano and theory instruction. Some of his students have written about their lessons with him. One student, the conductor Hans Wolf, speaks of the interest Schenker took in all aspects of his musical life and recounts how Schenker quizzed him about the details of performances that he had heard. Writing of the close attention he received, he records Schenker as saying at the beginning of a theory lesson (consulting the detailed notes he kept on each student): “Last time I noticed that you didn’t completely un-

Reviewed by David Gagné and Hedi Siegel

Heinrich Schenker. The Art of Performance. Edited by Heribert Esser. Translated by Irene Schreier Scott. New York: Oxford University Press, 2000.

4

3

Wolf 1937, 176–77. From William Drabkin’s summary of von Cube’s letter to his father (10 January 1924). See Drabkin 1984–85, 184. 5Rothstein 1984, 21.

Schenker’s theoretical and analytical approach was developed chieRy to serve the performer—to impart an understanding of the

The subject of hand motions on the piano may seem an esoteric one to the non-pianist. It is surely far from the realm of what is generally considered music theory. Yet both Vom Vortrag and the Entwurf contain important sections on hand motions, Qngering, and other aspects of piano technique. Despite appearances to the contrary, there is no contradiction here: indeed, it is Qtting that Schenker, who saw his mission as the reuniting of theory and practice, and who often used the lowly piano lesson as the vehicle for his theoretical teaching, should have paid so much attention to such practical matters. 5

derstand this problem. I will explain it to you again.” He describes how Schenker, for whom “rule and masterwork were one and the same,” invariably illustrated theoretical rules with practical examples, which he always had at his Qngertips. 3 Another student, the theorist and composer Felix-Eberhard von Cube, is reported as praising “his teacher’s sense of humor, his patience, and above all his insistence that the piece his pupil is studying be learned thoroughly, down to the Qnest detail, so that all of the pianist’s resources contribute to a uniQed performance.”4 But these are second-hand reports. We are most fortunate that Oxford University Press has published Heribert Esser’s edition of The Art of Performance in a lucid translation by Irene Schreier Scott. This book is a Qrst-hand account of what Schenker taught: it permits us to eavesdrop on his lessons, so to speak, putting us in the position of one of his students. William Rothstein commented on the value of such piano instruction when discussing the as yet unpublished materials—Vom Vortrag (“On Performance”) and Entwurf einer “Lehre vom Vortrag” (“Sketch of a Theory of Performance”)—that he consulted at the Oswald Jonas Memorial Collection at the University of California in Riverside:

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7

6

See Schenker 1976, 44 ff., and Schenker 1984, 63 ff. Statements regarding its forthcoming publication abound in Schenker’s writings, e.g., in Beethovens neunte Sinfonie (Vienna: Universal Edition, 1912), quoted by Esser at the beginning of his introduction (xi). See Schenker 1992, 8.

true content of the music. Many of his analytic essays conclude with a section on performance, and his critical editions likewise contain practical performance advice. Two early works, Ein Beitrag zur Ornamentik (1904, revised 1908) and J. S. Bach, Chromatische Phantasie und Fuge: Kritische Ausgabe (1910), include discussions of such topics as tempo, dynamics, touch, and Qngering that are directly linked to his work on a separate performance study.6 Holding the book in one’s hand and looking at the author and title, one might think that it represents Heinrich Schenker’s completion of his long-promised monograph on performance.7 But in fact this slim book (fewer than 100 pages of text) is a compilation of drafts and fragments: it could have been published as an essay called something like “Schenker’s UnQnished Theory of Performance.” The editor and translator, however, made the decision to shape the material into a book that has the appearance of a Qnished work, and give it Schenker’s intended title, Die Kunst des Vortrags (The Art of Performance) even though they knew it could “never be the ‘book’ Schenker intended to write” (xii). We think they were right to do so, given the diverse and unQnished nature of the manuscripts, and they have accomplished their aim to create a practical work attractive to the performing musician. The material is too valuable to be treated as an archival study and thus be consulted mainly in libraries; it seems to demand application in the studio and the concert hall. The text of the book originated mainly in the two manuscripts found in the Jonas Collection. As mentioned above, the Qrst is a draft with the title Vom Vortrag, and consists of twelve chapters taken down from dictation by Jeanette Schenker in the summer of 1911; the second is a gathering of fragmentary notes mainly in

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8 These are Esser’s sources A and B; see his listing of source materials (xvii–xviii). 9Jonas 1962 discusses and quotes several important Vortrag passages. 10 The typescripts that emerged from this collaboration are listed by Esser as sources C and D (xviii). Copies that Esser made of some of the source material found their way into the Oster Collection of the New York Public Library, which also houses related material. 11 Jonas issued the following new editions: Schenker 1954 (a revision and translation of the 1906 edition), Schenker 1956 (a revision of the 1935 edition), Schenker 1969 (a revision of the 1910 edition), and Schenker 1971–72 (a revision of the 1913–20 editions).

Schenker’s hand, most dating from the late 1920s. 8 Soon after her husband’s death in 1935, Jeanette Schenker and Schenker’s student Oswald Jonas together organized the Vortrag materials found in Schenker’s Nachlass. Jonas was occupied with them for the rest of his life, transcribing, compiling, and annotating the manuscripts, as well as lecturing and writing about his Qndings. 9 In the 1950s he worked intensively with the editor of the present volume, Heribert Esser, and, in consultation with Ernst Oster, laid the foundation for the publication of the book which Schenker had hoped to publish himself.10 Thus, Esser, who was asked to take over the editorial work after Jonas’s death in 1978, has a long history of involvement with the Vortrag project. His collaboration with Jonas perhaps led him to edit the book very much in Jonas’s spirit. Jonas, without whose editorial efforts many of Schenker’s works would never have become widely available, edited with a free hand; his aim, understandable given the climate of his time, was to present Schenker’s writings in the best possible light. 11 Adopting a similar editorial policy, this time in the interest of practicality, Esser modiQed the structure of Schenker’s early text and liberally interpolated the later material contained in the sketches. Stating that he “felt the need of handling the material with a certain amount of freedom,” and that it “would have been extraordinarily pedantic to present the sources literally in every detail” (xx), he provides little or no correlation of the text passages with the original. One

12 Some of the original source material may be found in Rothstein 1984. Rothstein includes passages he translates from Vom Vortrag (the early text that Schenker dictated, Esser’s source A), and from the Entwurf einer “Lehre vom Vortrag,” a 38-page typescript prepared by Jonas from Schenker’s later fragmentary sketches (Esser’s source D). The German original (and its location in the sources) is given for each quoted passage. We are grateful to William Rothstein for making available to us his transcription and photocopies of the Vortrag material he consulted at the Jonas Collection. 13 This analogy is only approximate, of course, since new material is supplied in the completion of a musical work, whereas Esser reorganized Schenker’s text without adding to it. However, given the substantial nature of the revision, such a comparison is perhaps not misplaced.

cannot help wishing that a way had been found to provide fuller documentation—and even to include the original German text— without sacriQcing the orderliness and clarity that gives the book its wide appeal. For now, the scholar interested in tracing the text to its sources must consult the material in the Oster and Jonas Collections. 12 Characterized by its editor as the Qrst major publication to come out of Schenker’s Nachlass, this book is unique among Schenker’s writings, not only because of its focus on performance matters, but also because it represents a reconstruction of incomplete and fragmentary material. One is reminded of analogous projects in the realm of musical composition—the completion of works left unQnished at a composer’s death.13 With his free juxtaposition of material from various sources, Esser is in a sense emulating Schenker’s own procedures. The manuscripts Schenker created with his wife, now in the Oster and Jonas Collections, often show signs of having been literally cut and pasted together. Even Free Composition originated in this way: in the early 1920s, as Schenker set out to revise a version he had dictated around 1917, he started by rearranging the original chapters and inserting new ones. He eventually abandoned his efforts to create a composite text; the Qnal version of Der freie Satz is based mainly on a freshly dictated manuscript. But, in a few places, vestiges of the earlier versions can be detected.

14 Part of this passage, which is from the Entwurf, is quoted in Rothstein 1984, 25 and 28 (note 60). 15 See Esser’s introductory remarks (xv–xvi and xxi). 16 Summaries are given of these chapters, “On the Technique of the Piano in Particular” (Appendix A), and “On the Degeneracy of the Virtuoso” (Appendix B). We agree with the editor’s decision regarding the polemical latter chapter, which is now mainly of historical interest. The reason given for moving and curtailing the former chapter is enigmatic: “Its publication in full is planned in a different context” (81).

In the text of The Art of Performance it is the language of Schenker’s more mature theory that invites detection. Even in the chapters that seem to derive largely from the manuscript of 1911, one Qnds interpolations or additions drawn from the later material. These are recognizable from the use of such terms as “background” and “foreground,” familiar from Schenker’s writings beginning with the Tonwille essays of the 1920s. This sometimes results in a mixture of varying stages of Schenker’s thought. Yet it seems appropriate that the editor supplement the earlier text with later passages such as the following fragment, rich in poetic imagery: “Light and spirited renditions are made possible only by an overall view, by thinking ahead, thereby giving wings to the hand. The ear, too, like the eye, must offer us perspective. This ability comes from understanding the background” (73). 14 Despite the disparity of the source material, the incorporation of such passages enriches the text. A decision was made, however, to exclude examples that would require readers to be familiar with the mature theory presented in Free Composition. 15 The editor’s desire to create a practical rather than theoretical work is understandable; nevertheless the absence of this material is to be regretted. Surely, room could have been made for the examples in an appendix, as was done with the two chapters of Vom Vortrag (the 1911 manuscript) that were omitted from the main part of the book. 16 About half of the chapters, mainly those that include musical examples, seem to derive almost entirely from the later material. A representative illustration will demonstrate the difQculties posed by the notes Schenker hastily jotted down on scraps of

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17

From the Entwurf, page 21, under the heading “Klavier Hand”; part of this passage is quoted in Rothstein 1984, 21 and 27 (note 47). 18 At Qrst glance, the translation of “die Hand darf nicht lügen” as “the hand may not lie” is ambiguous; the German word “lügen” has none of the double meaning of the English “to lie.” Translating the phrase as “the hand may not tell a lie” might have removed the ambiguity. 19 See Rothstein 1984, 21 and 27 (note 47). 20 Esser, a conductor, is also a performing musician; thus both the editor and translator approached their work from a performer’s point of view.

The translation preserves Schenker’s vivid endowment of the player’s hand with the power of speech,18 found again in the chapter on Qngering: “Fingering also must be honest; the hand—like the mouth—must speak the truth; it must correspond to the voice-leading” (34).19 Irene Schreier Scott, the translator of Esser’s reconstruction of Schenker’s text, is a pianist and teacher.20 As Oswald Jonas’s step-

The hand may not lie; it must conform to the meaning of the voiceleading. It lies if in Example 3.5 [rendered here as Example 2] this is violated by playing a2–a1; the connection must be f 2 and c 2. (9)

In the book, this passage appears in the chapter entitled “The Technique of Playing the Piano”; it expands on Schenker’s statement that “the meaning of the phrase determines the position and motion of the hands” (8):

also [die] Hand darf nicht die Oktave a2–a1 spielen, muß verbinden vielmehr: [example] 17

Die Hand darf nicht lügen, sie muß dem Sinn der Stimmführung folgen. Sie lügt, wenn sie gegen die Stimmführung verstößt: Mozart, A dur Sonate, Thema [example]

paper. The small collection of illustrations from the manuscripts offered in the introductory pages of the book includes a sketch we reproduce in Example 1. A transcription of the Qrst musical illustration within the sketch is given in Example 2. Schenker’s barely legible and telegraphic notes, shown in Example 1, were transcribed and reconstructed by Jonas as follows:

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daughter and student, she literally grew up with Schenker’s approach to performance; her Qrst piano teacher was Moriz Violin, Schenker’s close lifelong friend. Her translation of the German text is generally accurate, elegant, and smooth. She provides quite literal translations for the terms Schenker coined, e.g., “piano singing” for Klaviersingen, “light-point” for Lichtstelle, and “painting gestures” for malende Bewegungen (8–9), although the German original could perhaps have been revealed in more instances, as is done for the term Luftpedal, rendered as “air pedal”

Example 2. Mozart, Sonata K. 331, Qrst movement, theme, bars 17–18 (The Art of Performance, Example 3.5, 10)

Example 1. Schenker’s manuscript sketch (The Art of Performance, from Plate 2, xxv)

21 There are some misprints in the bibliography (96): in lines 2–4, an article by Oswald Jonas is erroneously included under the heading “Works of Heinrich Schenker” (it is listed again, in the correct place, under “Related Works,” where, in the second line, “pp. 122–129” should read “pp. 127–129”); in the last line on the page, “vol. 7” should read “vol. 8.” For additional corrections, the comprehensive list of the book’s misprints (that incorporates an inventory of errata prepared by Yosef Goldenberg) is available on the smt web site; it is one of the book errata lists included in the Virtual Poster Session managed by Dave Headlam.

with the German term given in brackets (12). She understandably retains the German word Rahmenanschlag (literally “framing touch”), a term Schenker invented to characterize a kind of touch used to emphasize main notes that “frame” those of lesser importance (49–52). In addition to the question of source identiQcation discussed above, some minor aspects of documentation should be mentioned. While explanations and supplementary material supplied by the editor are mainly relegated to the notes at the back of the book, some commentary is included as part of the text or example captions. Referring to Schenker by name in the midst of his own words (33–4) can be jarring to the reader, even when this occurs within example captions, as in Example 8.16 (50) and Example 9.20 (63). These comments would have been better as notes, especially where reference is made to modern editions or Schenker’s other writings (note 3 to Chapter 9 is, in fact, used for just such a purpose). Another aspect of the example captions could impede the reader: where examples and text are placed on the same page, it is sometimes difQcult to distinguish the captions from the text, since they are both set in the same type size (see, for example, p. 36). There are also formatting problems in the bibliography, particularly in the “Related Works” list.21 Overall, however, the book is an outstanding achievement. Surmounting considerable difQculties, the editor and translator have created a coherent text that presents Schenker’s ideas about performance in a style and manner consistent with his other writ-

ings. Its content is organized according to various aspects of performance, especially on the piano, as in “The Technique of Playing the Piano” (Chapter 3), “Legato” (Chapter 5) “Staccato” (Chapter 6). Details of technique are presented in the context of a larger view of the composition and in light of the performer’s role as interpreter of the composer’s vision. The book begins with a chapter entitled “Musical Composition and Performance” that opens with this statement: “Basically, a composition does not require a performance in order to exist” (3). If a composition is performed, however, it must not be misrepresented; to this end Schenker characteristically requires the performer to have a thorough knowledge of the laws of composition. In addition, an understanding of the signiQcance of the notated score is held to be crucial; this is discussed in the second chapter, “Mode of Notation and Performance.” While Schenker afQrms that scores should preserve the composer’s original notation, he also states: “The author’s mode of notation does not indicate his directions for the performance but, in a far more profound sense, represents the effect he wishes to attain. These are two separate things” (5). Despite his belief that great composers are “as inspired in their notation as they were in the actual composing” (6), Schenker makes suggestions such as the following recommendation, found in the chapter on legato playing: “In some instances, it proves to be appropriate in a longer series of notes to hold some Qngers down longer than written” (22). Thus to discern the intention of a composer one must see beyond the palpable symbols of the notation. Schenker’s approach is both poetic and Rexible. In Chapter 8, “Dynamics,” we read: “Pianissimo under certain circumstances means nothing other than stillness—that particular kind of stillness which does not lose its character even if one or more voices Roat through space” (40). His discussion of Qngering (Chapter 7) is also highly evocative, as in the following comment: “The free mobility of the ‘soul’ of a work of art ever will demand total freedom of Qngering” (34). His sense of Rexibility is particularly evident in Chapter 9, “Tempo and Tempo ModiQcations”: “Repeated

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Schenker frequently compares the piano to the orchestra (especially the strings) and to the voice. He describes the use of the pedal by saying: “Since the piano cannot provide all sustaining voices as the orchestra can, pedal gives it the possibility of compensating for these missing parts. The damper pedal unshackles the overtones, whose radiance substitutes for the orchestra’s sustaining voices” (10). He describes ways in which the hand can create a type of “pedal” that produces orchestral effects: “hand pedal,” a way of holding keys down to create a sustained, Frenchhorn-like sound, and “air pedal,” the use of an extremely short touch to produce an effect analogous to the fading out of breath or bow strokes. He pays particular attention to the left hand, noting, for example: “When the bass moves in octaves, the result often is a certain orchestral interaction of registers, as if the lower note were played by the basses and the higher one by the cellos” (14). While the book focuses on many practical aspects of technique, it also emphasizes Schenker’s conviction that a performance is not a mechanical playing of notes, but comes from within the performer and the work. One of the drafted chapters

The identity of legato technique in violin, voice, and piano can be observed in a particular type of legato. This consists of individual notes within a group that receive pressure separately, notwithstanding a strictly observed legato. The violinist can Qnger individual notes while continuing to draw his bow in undulating motions without compromising the legato. The singer, similarly, is able to emphasize individual notes within one single breath. The same effect can be attained by the pianist if he plays legato as described previously with strictly held keys, simultaneously moving the arm and hand in an elastic, swaying motion in order to play the following key from a higher point than he would otherwise. Perhaps a different image describes this technique more suitably: it is as if the arm were striding back and forth in the keys, which serve as its Qrm ground. (24–5)

notes demand hurrying on to the next downbeat . . . Neighboring notes, chromatics, diminutions of the lowest order want expressive treatment; without pushing ahead—holding back, this would be impossible” (54–5). The following comments on legato playing are characteristic of his expressive yet precise way of writing:

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Drabkin, William. 1984–85. “Felix-Eberhard von Cube and the North-German Tradition of Schenkerism.” Proceedings of the Royal Musical Association 111: 180–207. Federhofer, Hellmut. 1990. Heinrich Schenker als Essayist und Kritiker. Hildesheim: Olms. Jonas, Oswald. 1962. “Die Kunst des Vortrages nach Heinrich Schenker.” Musikerzeihung 15: 127–9.

LIST OF WORKS CITED

summarized as an appendix, “On the Degeneracy of the Virtuoso,” compares the pursuit of virtuosity for its own sake with the playing of composers such as Handel, Bach, C. P. E. Bach, Mozart, Beethoven, Mendelssohn, and Brahms, who were brilliant improvisers and who performed a work as an integrated whole. Technique, expression, and understanding should be fused; we read in Chapter 12, “On Practicing”: “Technical difQculties in a work of art can be equated with the difQculties fate brings in life—but they must be generated by the synthesis” (77). Keeping the entirety of a work in view is essential. Schenker observes: “The requirement that a composition’s form not be exposed too nakedly frequently demands considerably quicker playing where the seam occurs . . . Played in this way, the separate sections are pulled together, whereas without such a tempo deviation they would fall apart needlessly, compromising the texture of the form” (55–7). Yet ultimately he places the focus not on the composition or its performance alone but rather “on the listener, who at all times is the object and measure of the effect” (54). We have quoted generously from the book in order to convey the Ravor of its language and the nature of its content in relation to Schenker’s theoretical writings. Despite its brevity, The Art of Performance contains an extraordinary profusion of ideas that are expressed in highly original terms—ideas that can potentially have a wide audience in the musical community. They are of such quality as to deserve that audience.

Rothstein, William. 1984. “Heinrich Schenker as an Interpreter of Beethoven’s Piano Sonatas.” 19th-Century Music 8: 3–28. Schenker, Heinrich. 1906. Neue musikalische Theorien und Phantasien, Vol. I: Harmonielehre. Stuttgart: Cotta. Reprint edition, with a foreword by Rudolf Frisius, Vienna: Universal Edition, 1978. ———. 1954. Harmony. Edited by Oswald Jonas. Translated by Elisabeth Mann Borgese. Chicago: University of Chicago Press. Reprint edition, Cambridge, Mass: mit Press, 1973. ———. 1956. Der freie Satz. Revised edition. Edited by Oswald Jonas. Vienna: Universal Edition. ———. 1969. J. S. Bach, Chromatische Phantasie und Fuge: Kritische Ausgabe. Revised edition. Edited by Oswald Jonas. Vienna: Universal Edition.

———. 1971–72. Beethoven, Die letzten Sonaten: Erlaüterungsausgabe, of Op. 101, 109, 110, 111. Revised editions. Edited by Oswald Jonas. Vienna: Universal Edition. ———. 1976. “A Contribution to the Study of Ornamentation.” Translated by Hedi Siegel. In The Music Forum 4: 1–139. ———. 1984. J. S. Bach’s Chromatic Fantasy and Fugue: Critical Edition with Commentary. Translated and edited by Hedi Siegel. New York, Longman. ———. 1992. Beethoven’s Ninth Symphony. Translated and edited by John Rothgeb. New Haven: Yale University Press. Wolf, Hans. 1937. “Schenkers Persönlichkeit im Unterricht.” Der Dreiklang 7 (October): 176–84.

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1 Examples of visual representations of music are in Cogan 1984, Clendinning 1995, Bernard 1999, Brackett 2000, and Hisama 2001.

Understanding Charles Seeger, Pioneer in American Musicology contributes new perspectives on the wide-ranging intellectual enterprises of polymath Charles Seeger. Many of Seeger’s ideas from the 1930s through the 1970s resonate with music theorists’ present-day concerns—for example, his forward-looking insistence on studying music in its contexts; his advocacy for expansion of the repertoire studied by scholars to include American music, world music, folk music, and orally transmitted music; and his bridging of philosophical concerns with musical ones. Further, his invention in the 1950s of the melograph, an electronic tool for transcribing a performance or recording, anticipates work in music theory published several decades later that examines sound through its visual representation. 1 This collection of eight essays by theorists, musicologists, and ethnomusicologists celebrates the variety and evolution of Seeger’s thought while sounding common themes that emerged in his writings over a span of some sixty years. As noted by the book’s co-editors, Bell Yung and Helen Rees, Seeger published approximately eighty musicological papers on topics as varied as contemporary composition, the European art-music tradition, the melograph, folk music, music of the Americas, applied musicology, music education, and the philosophy of music. On p. 6, they identify six themes in Seeger’s writings: (1) the deQnition of music and musicology, (2) the relationship between language and music, (3) language as the lens through which music is understood, (4) theories of value, (5) the social responsibility of musicians and musicologists, and (6) the social contexts of music.

Reviewed by Ellie M. Hisama

Understanding Charles Seeger, Pioneer in American Musicology. Edited by Bell Yung and Helen Rees. Urbana: University of Illinois Press, 1999.

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2See Nicholls 1990, Tick 1990, and Straus 1995. Burkett 2001 also explores the relationship between Seeger’s theories and Crawford’s music. Slottow 2001 discusses Seeger’s theories in relation to compositions by Carl Ruggles. 3Other analyses of this movement can be found in Straus 1995, 158–72, Hisama 1995, and Hisama 2001, 12–34.

Yung & Rees’s organization of these diverse yet interconnected essays is exemplary. One essay Rows to the next, gracefully picking up a theme or idea. As a companion volume to Taylor Greer’s recent book on Seeger’s philosophy of music (Greer 1998), Understanding Charles Seeger offers theorists a number of significant and novel avenues of exploration. In “The Dynamics of Dissonance in Seeger’s Treatise and Crawford’s Quartet,” Greer does a superb job of writing lucidly about the intricate web of Seeger’s ideas presented in his landmark treatise “Tradition and Experiment in (the New) Music” (Seeger 1994). Seeger’s legendary prose often requires the reader to mine the text multiple times for the idea, and Greer’s long engagement with Seeger’s writing (Greer 1994 and 1998) makes him the ideal guide to this theoretical work. Greer skillfully navigates the waters of Seeger’s treatise, setting his sights upon a single piece to illustrate the analytical application of Seeger’s ideas, the third movement of Crawford’s String Quartet 1931. Greer is not the Qrst scholar to apply Seeger’s ideas to Crawford’s music—as he notes, David Nicholls, Joseph Straus, and Judith Tick have also done so—but Greer’s reading of this quartet movement through the lens of Seeger’s work in “Tradition and Experiment” is still original and revealing.2 Greer’s explication of Seeger’s six functions of musical experience that are divided into two groups, tone (encompassing pitch/dynamics/timbre) and rhythm (encompassing proportion/accent/tempo), and his application of Seeger’s ideas about dynamics and accent to Crawford’s quartet movement whose underlying plan the composer herself identiQed as “heterophony of dynamics—a sort of counterpoint of crescendi and diminuendi” (Crawford [1948] 1997, 357) is absorbing. 3 One especially interesting feature of the piece that Greer

examines is the pattern of dynamic peaks in mm. 13–18 (played by the viola, second violin, and cello on beats 1, 2, and 3), which occurs a total of six times, and the completion of the pattern in m. 19 by the Qrst violin on beat 4. Although Greer notes that he hopes his “brief discussion of the quartet [he discusses 19 of the movement’s 99 measures] serves as an initial step to help stimulate other, more detailed analyses of the relationship between philosophical theory and compositional method” (24), I would have liked for him to continue; his discussion of the opening bars made me to want to discover how he hears the subsequent passages, particularly the striking climax and subsequent descent that contribute to the movement’s structural fascination and dramatic power. Greer’s discussion might also have contemplated the relation of Seeger’s ideas to Crawford’s own observation in her brief analysis of this piece that “the melodic line grows out of this continuous increase and decrease; it is given, one tone at a time, to different instruments, and each new melodic tone is brought in at the high point of a crescendo,” as well as her accompanying sketch of a portion of this composite melodic line (Crawford Seeger [1948] 1997, 358). One aspect of Greer’s discussion of the quartet warrants further discussion. His statements that “there is an overall balance of musical functions [in Crawford’s quartet movement] whereby a constant Rux in one function is counterbalanced by less activity among the others” (23) and “these observations . . . suggest that the sense of balance exhibited in Crawford’s quartet can be interpreted as a musical realization of . . . Seeger’s philosophical theory of mediation” (23) seem at odds with his conclusion, in which he writes: “It seems rather ironic that the one composer who had the beneQt of studying closely Seeger’s theories about the ideal of balance, Ruth Crawford, wrote several works that were distinguished by the imbalance among functions” (24, emphasis added); the endnote to this sentence then mentions the quartet’s third movement as well as Crawford’s Piano Study in Mixed Accents. It is unfortunate that the reproduction of the Qrst page of the Presser score, given in Figure 1.3, is of poor quality in this otherwise well-produced book (22). Still, these minor 4 Numerous recordings and books chronicle the musical contributions of three of Seeger’s children, Peggy Seeger, Mike Seeger, and Pete Seeger. A sampler includes Mike Seeger 1964 and 1998, Peggy Seeger 1998a and 1998b, and Pete Seeger 1993 and 1998.

points detract minimally from an effective fusing of theory and analysis. In “The American Composer in the 1930s: The Social Thought of Seeger and Chávez,” Leonora Saavedra explores Seeger’s and Carlos Chávez’s attempts to reconcile their leftist politics with their interest in modernist music. Saavedra’s decision to place Chávez alongside Seeger, both of whom were struggling to understand the social relevance of modernist music during the 1920s and 1930s, makes for an interesting pairing. In Saavedra’s words: “In the course of trying to examine the links between art and society, Seeger and Chávez came to understand music as a social product with a social function rather than as the suprasocial creation of an individual mind” (53). Initially opposed to folk music, which in 1934 he labeled “conventional, easy going, subservient” (Seeger 1934), Seeger came to champion the traditional music of the working class: “Plainly, if we are to compose for more than an inQnitesimal fraction of the American people, we must write in an idiom not too remote from the one most of them possess—their own musical vernacular.” (Seeger [1939] 1994, 387). One wonders what Seeger would have thought of postmodernism; would he have embraced postmodern music because it allows a composer to reach a broad audience through repackaged vernacular styles? Or would he have sided with its critics who regard postmodern pastiche and stylistic juxtaposition as lacking in value and content, and therefore devoid of any political meaning and efQcacy? Saavedra’s essay reminds contemporary readers of the social responsibilities of composers and scholars as well as the potential impact of their work on society, issues that were central to Seeger and evident in the directions his research, teaching, and children would take.4

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6

5

I discuss this development in Hisama 2000. Examples of analytical work that explores new repertories include Clarke 1999 and Burns 2000.

Robert R. Grimes develops the topic of Seeger’s desire to effect positive social change in his essay “Form, Content, and Value: Seeger and Criticism to 1940.” Grimes pinpoints Seeger’s watershed article “Systematic and Historical Orientations in Musicology” (1939) as an important turning point in Seeger’s scholarly development. What Seeger meant by “value” is, as Grimes rightly notes, “not always clearly evident … in the context of music” (64). Grimes does an admirable job of sorting out Seeger’s ideas on value in the 1930s by closely examining his writings, both scholarly and journalistic, during this period: “For Seeger in his early writings value is the dynamic form of content; it is the act of valuing. Content, a more static term, is the link between internal and external, between the purely, intrinsically musical and the social function of music” (79–80). Like Greer, Grimes locates inRuences on Seeger’s thoughts in philosophy (Greer identiQes Bergson, Russell, Perry, and Goethe as signiQcant to Seeger, while Grimes discusses the impact of Georgii Plekhanov in addition to Perry). Grimes’s argument for Seeger’s attraction to Plekhanov’s work and his contention that Seeger was drawn to Plekhanov’s ability to connect art, society, and economic forces are convincing, as is his conclusion that Seeger’s concept of value was an evolving one (79). Grimes’s statement that “[Seeger] had found that music is something more than the luxury of an elite class” (80) is rich with implications for music theory’s potential directions in the new millennium. While professional analytic studies still concentrate on Western European art music, the tides are certainly shifting. Conference program committees, publishers, and search committees are showing increased interest in music outside of the canon.5 As the categories of music we consider worthy of theoretical scrutiny continue to change, we are also Qnding new applications for traditionally accepted tools and developing new tools for unex-

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7Recent analyses of popular music and world music appear in Middleton 1990, Moore 1993, Tagg 2000, Temperley 2000, and Tenzer 2000.

plored repertories.6 Music theorists interested in considering how one would analyze a repertory whose structural complexity would not be revealed by, for example, Schenkerian analysis, would do well to revisit Seeger’s article “Versions and Variants of the Tunes of ‘Barbara Allen’ ” (Seeger [1966] 1977). The thoroughness of Seeger’s analysis of a traditional tune dispels preconceived notions about the ability of American roots music to bear close study. Co-editor Helen Rees points out in her excellent essay “ ‘Temporary Bypaths?’ Seeger and Folk Music Research” that “Seeger’s discovery of American folksong contributed actively, materially, and discernibly to some of the most sophisticated and inRuential theoretical concerns of his later years” (85). The second half of Rees’s article is particularly relevant to music theorists. In it, Rees explores three interrelated sets of questions crucial to any analytical enterprise: Qrst, what constitutes the music to be studied? That is, what determines the identity of a piece when pitches, rhythm, or other musical parameters may vary performance to performance, as in the performance of works transmitted through the oral tradition? Ethnomusicologists, of course, deal with these questions routinely, but such issues force music theorists who are trained to analyze from a Qxed score notated in the Western art tradition to rethink the very foundations of their analytical projects. Second, what is the relationship between the oral and written traditions, and how should we treat music for which there is no score? Seeger’s musings on these questions some three decades ago are still relevant today as music theorists chart the waters of analyzing non-notated music drawn from popular music, vernacular music, and world music traditions. 7 Third, how does an analyst acknowledge and negotiate the shortcomings of Western notation in transcribing music? What does transcription represent? Although Seeger’s work provides no easy answers to these interlocking questions, his deliberations provide the foundation for a contemporary rethinking of these issues.

9Crawford’s published transcription of “Choose You a Seat ‘n’ Set Down” appears in Lomax & Lomax 2000.

8The correct title of the treatise is The Music of American Folk Song (singular), not The Music of American Folk Songs (plural).

Tick might also have drawn a link between Crawford’s metaphor of transcription as a skeleton, which Crawford uses in her treatise (“. . . it is only the extent to which [city or town

On the one hand, let us agree, melody may be conceived . . . as a succession of separate sounds, on the other, as a single continuum of sound—as a chain or as a stream. For the present, I am inclined to set . . . 1/10 of a second as fair margins of accuracy for general musicological use. (116; Seeger [1958] 1977, 169)

She then presents a strikingly similar passage in Seeger’s “Prescriptive and Descriptive Music Writing,” initially published in 1958.

A tune is a stream of sound whose variations in pitch and in time can be represented on paper as a curving line. Figure 5 represents within a margin of error of approximately .1 second, metrical irregularities observed in the original singing. (116; Crawford Seeger 2001, 9–10)

people] are, or become familiar with the idiomatic variations of American folk singing that they can expect to put approximately the right kind of Gesh, blood, and nerve Fbre back on this skeleton notation” [118]) and Seeger’s discussion in 1951 of whether transcriptions in three regional folksong collections “purport to be a hypothetical or logical skeletonizing of the tunes.” (Seeger 1951, 523). In order to illustrate the analytical complexities encountered by the transcriber of folksongs, Tick’s essay provides a brilliant example in Crawford’s work on the tune “Choose You a Seat ‘n’ Set Down” as well as additional evidence of Crawford’s inRuence on Seeger’s ideas published in “Versions and Variants on the Tunes of ‘Barbara Allen.’ ”9 As Tick sagely notes, although Seeger could have acknowledged publicly the importance of Crawford’s contribution to the scholarship on folk music, perhaps he did not do so because of “the entitlement of a certain kind of intellect and a certain kind of love” (123). In “Seeger’s Unitary Field Theory Reconsidered,” Lawrence M. Zbikowski picks up the topic discussed by Grimes and Rees of Seeger’s interest in the linguistic study of music. He chooses to tackle Seeger’s thorny work on the relationship between speech and music Qrst by examining Gilles Fauconnier’s theory of mental spaces and later discussing what Zbikowski calls “a properly musical concept,” which he concludes to be “a cognitive structure that can be speciFed for what we call music, leaving both ‘we’ and ‘music’ undeQned” (143). Zbikowski’s decision not to clarify the identities of the investigator and the music to which his idea might be applied is regrettable, as is the fact that the reference given in the endnote that might elucidate the discussion is to an unpublished paper (147 n. 8). The reader is thus left to puzzle over a murky deQnition. Also disappointing is the lack of explanation in the opening paragraph as to what the author precisely means by “sound images” (“sound images are part of the central business of

Ruth Crawford’s dismissal as merely a composition student of her teacher Charles Seeger will always best be exempliQed for me in a comment made in 1989 by a retired musicology professor who, upon seeing a graduate student with Crawford’s Diaphonic Suite No. 1, exclaimed: “Those were just solutions to exercises Charlie gave her!” Judith Tick’s quietly revolutionary essay, “Ruth Crawford, Charles Seeger, and ‘The Music of American Folk Songs’” encourages us to rethink the received idea that Seeger’s ideas were embodied in Crawford’s work. Tick powerfully argues that Seeger’s writings on folk songs have antecedents in a littleknown treatise by Crawford that she completed in 1940 entitled “The Music of American Folk Song,” published for the Qrst time in 2001 (Crawford Seeger 2001). 8 Tick provides example after example, both in the body of the essay and in an appendix to it, that Seeger’s ideas resonate with Crawford’s earlier work. For example, Tick quotes Crawford on transcription:

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(1) Seeger’s insistence that analysis of the internal workings of a piece of music is an incomplete project: “The inner, technical operations of the art of music cannot adequately be studied without consideration of the outer relations of music and the culture of which it is a part.” (158; Seeger 1940, 318) (2) His criticism (as early as 1940) of the “great man” paradigm in music scholarship and his promotion of the study of the musical vernacular of “the common man,” or folk music, which he considered a “socially molded thing, with a deep-set cultural function expressing not so much the varieties of individual experience as the norms of social experience.” (159; Seeger 1940, 321) (3) His proposal that European art music is as socially molded as vernacular traditions, and that it should not be regarded as the norm against which non-European musics should be measured. (160–62; Seeger 1941)

what we call music,” 130) and the absence of discussion about the detailed table in Seeger’s “Toward a Unitary Field Theory for Musicology.” These gaps are lamentable because Zbikowski offers a number of intriguing observations worth pursuing—for example, his revelation that “The basic notion of a properly musical concept is inRuenced by my own experience: I can remember having ideas and thoughts about music well before I discovered any way of describing them to others” (141). One hopes that Zbikowski’s important ideas will be further developed in future Seeger scholarship. Like Zbikowski, Nimrod Baranovitch considers Seeger’s ideas over a span of several decades. His contribution, “Anthropology and Music: Seeger’s Writings from 1933 to 1953,” adroitly demonstrates that Seeger anticipated foundational ideas and methodological issues in ethnomusicology well before the Qeld was ofQcially established. Four of Seeger’s insights presented in Baranovitch’s essay are particularly useful to music theorists who are interested in taking the Qeld in new directions:

146

Yung convincingly argues for Seeger’s attraction to general concepts in physics of the early part of the century, such as particle-wave duality and the theory of relativity, while also showing that the details of Seeger’s six-dimensional model of musical space-time are neither clearly deQned nor consistent (179). The depth of Seeger’s knowledge of physics remains little researched compared to work by scholars on Seeger’s interest in diverse Qelds within the humanities and social sciences, and Yung makes a strong case for the importance of further research about the interconnections between physics and musicology in Seeger’s theories. We should be grateful to Yung not only for his efforts to understand Seeger through a new portal, but also, in collaboration with Helen Rees, for this stimulating collection. Understanding Charles Seeger does not attempt comprehensive coverage of Seeger’s plethora of interests and endeavors—an

Musical space refers to pitch, dynamics, and timbre, while musical time refers to tempo, movement, and duration. In combining space and time into a hyphenated word, he is clearly borrowing the concept from the space-time of the special theory of relativity, implying that musical spacetime consists of six dimensions, but that these six dimensions are inherently related to each other and must be treated as such, just as the four dimensions in physical space-time are. (179)

Baranovitch’s traversal of these key texts that explore music as culture provides theorists with a useful reminder of the contemporary value of Seeger’s writings from the 1940s. The Qnal essay, a meditation on the relationship between physics and musicology in Seeger’s work, is penned by co-editor Bell Yung, who is well positioned to investigate such a connection, having received advanced training in both physics and music. “From Modern Physics to Modern Musicology: Seeger and Beyond” provides an important step toward a fuller understanding of the foundations of Seeger’s music theories. For example, Yung explores Seeger’s interest in “musical space-time” as follows:

(4) His challenge to the assumption that “the best music is written music.” (161; Seeger 1941, 18)

Bernard, Jonathan W. 1999. “Ligeti’s Restoration of Interval and its SigniQcance for His Later Works.” Music Theory Spectrum 21: 1–21. Brackett, David. 2000. Interpreting Popular Music. Berkeley: University of California Press. Burkett, Lyn Ellen Thornblad. 2001. Tensile Involvement: Counterpoint and Compositional Pedagogy in the Work of Seeger, Hindemith, and Krenek. Ph.D. dissertation, Indiana University.

LIST OF WORKS CITED

impossible task, to be sure. Instead of faulting such an impressive book for not addressing in more depth topics such as Seeger’s own compositions, the impact of Seeger on his children’s musicmaking and political beliefs, and the implications of his work for music education, we should take Yung & Rees’s collection as a Qrm reminder of the lasting signiQcance of Seeger’s work and as an invitation to pick up where the book leaves off. Seeger’s revolutionary ideas are many, including his call to expand the number and varieties repertories studied, to adapt ideas from disciplines outside of music to projects in theory and analysis, and to embed musical analysis within its social, historical, and political contexts instead of retreating to what Arnold Whittall has called “the safe shores of technical analysis” (Whittall 2001). As Seeger observed nearly thirty years ago, “The drive to internationalize the world economically, politically, intellectually—that is, as one cultural whole—is in full swing. Music is an integral factor in the process” (Seeger [1972] 1994, 434). In the twenty-Qrst century, it becomes increasingly necessary for music theory as a profession to Qnd its place within a larger social and disciplinary fabric while retaining its integrity as a Qeld that considers musical structure and meaning as its primary goals. Developing theories that consider music in its global as well as local contexts would be one way to ensure our survival as a profession and as a discipline in a rapidly changing world.

Burns, Lori. 2000. “Analytic Methodologies for Rock Music: Harmonic and Voice-Leading Strategies in Tori Amos’s ‘Crucify’.” In Expression in Pop-Rock Music: A Collection of Critical and Analytical Essays. Edited by Walter Everett. New York: Garland, 213–46. Clarke, Eric F. 1999. “Subject-Position and the SpeciQcation of Invariants in Music by Frank Zappa and P. J. Harvey.” Music Analysis 18: 347–74. Clendinning, Jane Piper. 1995. “Structural Factors in the Microcanonic Compositions of György Ligeti.” In Concert Music, Rock, and Jazz Since 1945: Essays and Analytical Studies. Edited by Elizabeth West Marvin and Richard Hermann. Rochester: University of Rochester Press, 229–56. Cogan, Robert. 1984. New Images of Musical Sound. Cambridge: Harvard University Press. Crawford Seeger, Ruth. [1940] 2001. The Music of American Folk Song. Edited by Larry Polansky. Rochester: University of Rochester Press. ———. [1948] 1997. “Analysis of the Third Movement of the String Quartet 1931.” In Judith Tick, Ruth Crawford Seeger: A Composer’s Search for American Music. New York: Oxford University Press, 357–60. Greer, Taylor A. 1994. “Critical Remarks about Tradition and Experiment in (the New) Music.” In Studies in Musicology II: 1929–1979. Edited by Ann M. Pescatello. Berkeley: University of California Press, 27–42. ———. 1998. A Question of Balance: Charles Seeger’s Philosophy of Music. Berkeley: University of California Press. Hisama, Ellie M. 1995. “The Question of Climax in Ruth Crawford’s String Quartet, mvt. 3.” In Concert Music, Rock, and Jazz Since 1945: Essays and Analytical Studies. Edited by Elizabeth West Marvin and Richard Hermann. Rochester: University of Rochester Press, 285–312. ———. 2000. “Life Outside the Canon? A Walk on the Wild Side.” Music Theory Online 6 (August). http://smt.ucsb.edu/ mto/issues/mto.00.6.3/toc.6.3.html.

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———. 2001. Gendering Musical Modernism: The Music of Ruth Crawford, Marion Bauer, and Miriam Gideon. Cambridge: Cambridge University Press. Lomax, John A., and Alan Lomax, coll. and comp. [1941] 2000. Our Singing County: Folk Songs and Ballads. Edited by Ruth Crawford Seeger. Mineola, N.Y.: Dover. Middleton, Richard. 1990. Studying Popular Music. Milton Keynes: Open University Press. Moore, Allan F. 1993. Rock, the Primary Text: Developing a Musicology of Rock. Buckingham: Open University Press. Nicholls, David. 1990. American Experimental Music, 1890–1940. Cambridge: Cambridge University Press. Seeger, Charles [Sands, Carl]. 1934. “Thirteen Songs from Eight Countries Included in Book Put Out by Music Bureau Internat’l,” The Daily Worker (1 February): 5. ———. [1939] 1994. “Grass Roots for American Composers,” Modern Music 16:143–9. Reprinted in Studies in Musicology II, 1929–1979. Edited by Ann M. Pescatello. Berkeley: University of California Press, 383–8. ———. 1939. “Systematic and Historical Orientations in Musicology.” Acta Musicologica 11: 121–8. ———. 1940. “Folk Music as a Source of History.” In The Cultural Approach to History. Edited by Carolyn F. Ware. New York: Columbia University Press. ———. 1941. “Inter-American Relations in the Field of Music.” Music Educators Journal 27: 17–18, 64–5. ———. 1951. Review of Alton C. Morris’s Folksongs of Florida, William A. Owens’s Texas Folksongs, and Byron Arnold’s Folksongs of Alabama, in Notes 8: 523. ———. [1958] 1977. “Prescriptive and Descriptive Music Writing.” Musical Quarterly 44: 184–95. Reprinted in Studies in Musicology, 1935–1975. Berkeley: University of California Press, 168–81. ———. [1966] 1977. “Versions and Variants of ‘Barbara Allen’ in the Archive of American Folk Song in the Library of Congress.” Selected Reports [University of California at Los

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Angeles, Institute of Ethnomusicology] 1: 120–67. Reprinted as “Versions and Variants of the Tunes of ‘Barbara Allen’ ” in Studies in Musicology, 1935–1975. Berkeley: University of California Press, 273–320. ———. [1972] 1994. “World Musics in American Schools: A Challenge to be Met.” Music Educators Journal 58 (October): 107–11. Reprinted in Studies in Musicology II, 1929–1979. Edited by Ann M. Pescatello. Berkeley: University of California Press, 427–34. ———. 1994. “Tradition and Experiment in (the New) Music.” In Studies in Musicology II: 1929–1979. Edited by Ann M. Pescatello. Berkeley: University of California Press, 49–266. Seeger, Mike. 1964. Old-Time String Band Songbook. Edited by Mike Seeger and John Cohen. New York: Music Sales Corporation. ———. 1998. Southern Banjo Sounds. Smithsonian Folkways 40107. Seeger, Peggy. 1998a. The Peggy Seeger Songbook, Warts and All: Forty Years of Songmaking. Edited by Irene Scott. New York: Oak Publications. ———. 1998b. Period Pieces. Tradition TCD 1078. Seeger, Pete. 1993. Where Have All the Flowers Gone: A Singer’s Stories, Songs, Seeds, Robberies. Bethlehem, Penn.: Sing Out. ———. 1998. If I Had a Hammer: Songs of Hope & Struggle. Smithsonian Folkways SF CD 40096. Slottow, Stephen P. 2001. A Vast Simplicity: Pitch Organization in the Music of Carl Ruggles. Ph.D. dissertation, City University of New York. Straus, Joseph N. 1995. The Music of Ruth Crawford Seeger. Cambridge: Cambridge University Press. Tagg, Philip. 2000. “Analysing Popular Music: Theory, Method, and Practice.” In Reading Pop: Approaches to Textual Analysis in Popular Music. Edited by Richard Middleton. Oxford: Oxford University Press, 71–103. Temperley, David. 2000. “Meter and Grouping in African Music: A View from Music Theory.” Ethnomusicology 44: 65–96.

Tenzer, Michael. 2000. Gamelan Gong Kebyar: The Art of Twentieth-century Balinese Music. Chicago: University of Chicago Press. Tick, Judith. 1990. “Dissonant Counterpoint Revisited: The First Movement of Ruth Crawford’s String Quartet.” In A Celebration of American Music: Words and Music in Honor of

H. Wiley Hitchcock. Edited by Richard Crawford, R. Allen Lott, and Carol J. Oja. Ann Arbor: University of Michigan Press, 405–22. Whittall, Arnold. 2001. “Revoicing Expression: Postmodern Classicism.” Lecture presented at University of London (15 March).

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Conventional Wisdom grew out of McClary’s Bloch Lectures at the University of California at Berkeley in 1993—its publication postponed until 2000 because of professional circumstances. The delayed appearance of these essays changes rather signiQcantly their impact on the musicological community since many of the issues raised and approaches introduced have been discussed and debated in various contexts over the last eight years. Read in 2001, Conventional Wisdom seems less like a call to change—as it might have in 1993—and more like a conQrmation of issues that have enlivened music studies within the last decade. McClary has several simultaneous goals in this book: demonstration of (1) the kinds of roles that formal conventions play in a broad spectrum of historical styles and musical traditions, (2) how changes in the compositional uses of formal conventions respond to historical changes, and (3) how musical sound participates in processes of social signiQcation. ConQrming one of the long-standing strengths of McClary’s work, Conventional Wisdom takes musical sound as its focus and afQrms that music is not absent from processes of social meaning but participates directly in the articulation of cultural systems of value. While I understand this focus as a fundamental value, I also recognize that the particular ways that McClary engages musical sound have been controversial. Often, controversy hinges on issues of whether musical sound participates directly in our daily lives or whether it operates at a more general level of abstract or universal meaning. McClary argues Qrmly against a notion of the purely musical, the “music itself,” and for an understanding of the “power of music . . . to shape the ways we experience our bodies, emotions, subjectivities, desires, and social relations” (7). Here I want to demonstrate how, as a consequence of an ahistoricized

Reviewed by Judy Lochhead

Susan McClary. Conventional Wisdom: The Content of Musical Form. Berkeley: University of California Press, 2000.

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interpretative approach, McClary ends up relying on a notion very close to the “music itself ” to make claims about music as social construct. The Qve chapters of Conventional Wisdom survey the use of several formal conventions in Western music. Chapter 1, titled “Turtles All the Way Down (on the ‘Purely Musical’),” considers an aria from the oratorio La Susanna (1681) by Alessandro Stradella and a 1959 gospel performance of the hymn “Near the Cross” by the Swan Silvertones. Chapter 2, “Thinking Blues,” focuses on blues from Bessie Smith (her 1928 performance of “Thinking Blues”), Robert Johnson (his 1936 performance of “Cross Road Blues”), and Cream (their live Filmore performance of Johnson’s song issued on Wheels of Fire in 1976). The third chapter, “What Was Tonality?,” investigates a da capo aria from Scarlatti’s opera Griselda (1721), a movement of Vivaldi’s op. 3, no. 8, concerto (1715), and the courante from J. S. Bach’s Dmajor Partita for keyboard. Chapter 4, “The Refuge of Counterconvention,” considers Beethoven’s op. 132 string quartet (composed 1825), and Chapter 5, “Reveling in the Rubble: The Postmodern Condition,” discusses Glassworks (1982) by Philip Glass, Spillane (1986) by John Zorn, “Kiss” (1986) by the Artist Formerly Known As Prince, “Still Thrives This Love” (1992) by k.d. lang, and “Nighttrain” (1991) by Public Enemy. Rather than sampling the kinds of claims McClary makes about how and what kinds of cultural meanings music produces, I will focus here on the underlying argument of the third chapter since it applies to much of the book. As suggested by its title, “What Was Tonality?,” this chapter considers how “tonality,” as a musical practice emerging in the eighteenth century, conQrms Enlightenment ideals. The three works by Scarlatti, Vivaldi, and Bach are analyzed with respect to their articulation of a “tonal background . . . [which] proceeds through a series of arrivals, beginning in the tonic key, moving through a few other keys, and returning Qnally home to the tonic” (66). And this tonal background is interrogated for the way that it “works to produce a particular

construction of the self” (70). For example, in Scarlatti’s Griselda, the title character is able “to pull her conRicting emotions under one tonal trajectory, thus displaying the centered subjectivity—the belief in the unshakability of that inner core—which is still one of our favorite myths” (79). McClary’s analysis correlates differing motivic Qgures with the range of affects that depict Griselda’s varying emotional states during her aria “Figlio! Tiranno!” Her account of the tonal progress of the aria tells a somewhat different story, since it is the continuity of a single “tonal trajectory” that enacts the sense of a centered subjectivity. The sense of “self” depicted here is twofold: on one hand, there is the eighteenthcentury subject that gave rise to the paradigm of tonality as embodying Enlightenment values of “progress, rationality, intelligibility, quests after goals, and the illusion of self-contained autonomy,” and on the other hand, there is the contemporary subject who in “still embrac[ing] these ideals” hears tonality as “natural” (68). There is an assumption here that what eighteenthcentury listeners heard is identical to what contemporary listeners hear. The chapter then takes as a central assumption that what tonality was is identical to what it is. This assumption could be argued in principle on the basis of historical and contemporary accounts of musical experience or of how music was understood to work. McClary does not offer such evidence, however, but bases her argument instead on an analytic interpretation that borrows many of its concepts from nineteenthand twentieth-century notions of tonality. For instance, about Scarlatti’s aria McClary writes: tonality “possesses . . . a hierarchy of relationships that drew all moments of the composition together into a single goal-oriented network” (73). And later in the chapter one reads: “Vivaldi sets out with remarkable clarity the background tonal progression that had started life as a linear cadence pattern but that now stretches out to grant coherence to a full ninety-three measures” (83). It is worth noting in this regard that a concept of “tonality” per se did not exist in the eighteenth century. The initial articulation of that concept is cred1While the term “tonality” did not originate with Fétis, he was the Qrst to frame the concept in ways consistent with its contemporary understanding.

ited to François-Joseph Fétis, its fullest discussion occurring in the 1844 Traité complet de théorie et de la pratique de l’harmonie. 1 Concepts of function, hierarchically related key areas, and longrange coherence were not theorized until later in the nineteenth and into the twentieth centuries. One might argue that “the music” operated for eighteenth-century musicians and audiences in ways identical to those implied by late twentieth-century notions of tonality, but this would be a universalizing argument that runs counter to what I take as the spirit of McClary’s project. The issue hinges on the status of analytical observations and the types of historical and experiential claims that are founded on them. Since analytical observation is necessarily contingent upon concepts about musical sound, and since conceptual understanding is contingent on historical context, then the extent to which analytical observation about music and subjects of the past is grounded in historical context will affect the status of analytical observation. Thus, in order to address the question of “What was Tonality?,” one has to ask, For whom does such a concept apply? Such a prior question will necessarily lead to an investigation of the socially-constructed cognitive constraints of the concept. Inasmuch as I am in sympathy with McClary’s effort to demonstrate how musical sound participates in a wide variety of socially-constructed behaviors, I want to make explicit here how the universalizing of concepts about music can overthrow the spirit of the project. This is how I read the underlying procedures in Conventional Wisdom. McClary offers analytical interpretations of speciQc works that demonstrate how musical effects and structures both reRect and enforce socially-constructed behaviors, arguing that musical sound is subject to the contingencies of ethnicity, gender, class, and history. She uses analytic concepts in ways that are not, however, sensitive to the historical contingency of those concepts,

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2A very short list of authors who articulate a postmodern philosophical perspective include Roland Barthes, Jacques Derrida, Michel Foucault, Frederic Jameson, Maurice Merleau-Ponty, and Richard Rorty. On the speciQc issues of the contingency of experience, see Joan Scott, “The Evidence of Experience,” Critical Inquiry 17 (1991): 773–97.

while making claims about historical subjects. Such an ahistorical use of the terminology has the effect of universalizing those concepts. If we understand concepts about music as not simply reRective of but also constructive of experience in accord with what in very general terms I will call “postmodern philosophies,” then the claims made about such phenomena as tonality must be carefully qualiQed.2 But if we understand concepts as “applied to” an unchanging experience, then we must judge these concepts as tools which reveal a thing that is prior to its conceptual understanding. McClary’s universalizing music-theoretical concepts implies the latter—that there is a “music itself ” which is prior to the social constructions of language, a position that is clearly not in keeping with the spirit of her project, which disallows a retreat into “the purely musical.” While the analyses of Conventional Wisdom employ theoretical tools and make claims about musical experience that are not sensitive to historical contingencies within the Western tradition of music making, McClary seems to be aware at some level of the conceptual power of theoretical language. In the very Qrst pages of the book she writes: “The measuring sticks of Schenker graphs or the kabbalistic methods of set-based analysis strive to pull apparently unruly music back inside the horizons of the rational, the orderly, and (implicitly) the metaphysical. Why, I have always wondered, do we not label the procedures such theories trace likewise as conventions? And why do we neglect to talk about why these procedures matter so very much to us? . . . In this book, I want to claim that this split between conventions and the ‘purely music’ is itself socially and historically contingent” (3). Despite this stated concern for the “conventionality” of music-theoretical concepts currently in use, McClary’s descriptions of “tonal” procedures owe much to them: such phrases as “tonal background”

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and “tonal coherence” were not part of the conceptual landscape for eighteenth-century theorists. Rather than building upon eighteenth-century conceptual understanding in order to understand what musical experience might have been, McClary discounts it: “The fact that music theorists of the time did not by and large write about music in these terms should hardly surprise us: verbal accounts of ‘structures of feeling’ often appear only long after the fact, if at all” (65). In discounting contemporary evidence for the project of understanding “what tonality was,” McClary contradicts one of the fundamental observations of a postmodern philosophical perspective: the contingency of conceptual understanding and experience. Concepts such as tonality, cadence, dominant and tonic, harmonic hierarchy, and coherence do not transparently reveal music. While McClary’s project of linking musical sound to social behaviors is necessary and perhaps even urgent, the analytical base on which it rests needs careful consideration. To conclude, I will simply suggest here that a more considered and creative approach to analysis through channels of speculative theory might better serve the project of linking musical sound to social behaviors. All the chapters of Conventional Wisdom utilize universal notions of tonal conventions as a basis for depicting narratives of subjectivity. Such narratives are typically told through key relations, yet such relations are not foregrounded in musical experience. Rather, the immediacies of experience are such phenomena as texture, timbre, rhythm, and phrasing. One might assume that such aspects of musical sound might more readily be understood as doing the “cultural work” that interests McClary. While her analyses often refer to such features, they are not considered the signiQcant events that receive detailed analytical attention. For instance, in listening recently to a performance of Elisabeth-Claude Jacquet de la Guerre’s suite in D minor for clavecin (1707), I was struck by how the ornamental Qligree emerged as the structure of the pieces. I was not hearing the “improvised surface” as the icing on the tonally coherent cake. Rather, the animated surface was the source of playful design that

was anchored by cadential progressions serving as temporal markers. Structure in this usage is that which assumes the central focus of musical design, that which makes the piece hold together. Since the musicological community does not have sophisticated tools for taking account of how the textural effects of ornamentation operate, any analytical account would have to theorize this aspect of musical design in order to demonstrate the kinds of social behaviors it reRects and engenders. The absence of an appropriate analytical apparatus in Conventional Wisdom is also noticeable in McClary’s accounts of several of the pieces in the last chapter on postmodern musics. One is aware of McClary’s struggling to evoke the sounds of the pieces by, for instance, John Zorn and Public Enemy. But in the end, the reader does not have a clear sense of how the sounds of these musics accomplish their particular types of musical communication.

Conventional Wisdom offers many ideas about how music studies might proceed within the new paradigms of the late twentiethcentury intellectual traditions. Yet it does not offer a new vision of what kinds of descriptive languages about music the profession should be using to articulate these new approaches. One is reminded of Boulez’s criticism of Schoenberg: his predecessor’s innovations in pitch were not matched by complementary innovations in phraseology and form, a failure which blunted the overall effect of the purported revolution in music. As McClary works through her project of linking musical sound to social behaviors, we have every reason to expect that she will reQne her analytical tools and more adequately historicize her accounts of subjectivity and the nature of musical experience.

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1

Rameau 1722; Bach 1753–62. 2Soler 1762.

The major French and German music-theoretical treatises of the eighteenth century have long been available in facsimiles, modern editions, or translations. Some, such as Jean-Philippe Rameau’s Traité de l’harmonie and Carl Philipp Emanuel Bach’s Versuch über die wahre Art das Clavier zu spielen, have been sufQciently familiar and widely distributed in both their own time and ours to have had a profound impact on both music theory and musical practice.1 The same cannot be said of writings from elsewhere in Europe, including the Iberian peninsula, whose musical culture throughout the Baroque remains a domain of specialists. Of Spanish and Portuguese theoretical writings only the Llave de modulación of Antonio Soler is at all well known, thanks in part to a facsimile published over thirty years ago.2 Harpsichordists and organists may have at least passing acquaintance with the music of such major Qgures as Soler or Juan Bautista José Cabanilles (1644 –1712), but the instrumental and vocal repertory of eighteenth-century Spain and Portugal remains virtually unknown, and it is fair to say that most professional theorists and historians, if they think at all about eighteenth-century music in these countries, have only a vague sense of it as stylistically conservative and derivative. A new edition and translation of a major treatise from late-Baroque Spain therefore provides an opportunity for broadening modern awareness of Iberian musical culture in the eighteenth century. For a variety of reasons, however, this ambitiously

Reviewed by David Schulenberg

José de Torres’s Treatise of 1736: General Rules for Accompanying on the Organ, Harpsichord, and the Harp, By Knowing Only How to Sing the Part, or a Bass in Canto Qgurado. An annotated bitextual edition by Paul Murphy. Publications of the Early Music Institute. Bloomington: Indiana University Press, 2000.

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3References are to the pagination at the bottoms of the pages, not the page numbers in the running heads, which are repeated on the Spanish and English sides of each opening.

planned volume is unlikely to alter prevalent conceptions of lateBaroque Spanish music and musical thought. José de Torres y Martínez Bravo was a composer and maestro de capilla at the royal chapel in Madrid from 1718 until his death in 1738. He is known as well for his publishing house, La Imprenta de M ◊ sica, founded at Madrid in 1700, through which he issued a number of theoretical works including the present treatise. The work comprises four parts, or tratados, whose subjects are: (1) musical fundamentals: notes, intervals, and modal scales; (2) progressions of consonant chords; (3) passing tones in the bass, suspensions, and transpositions; and (4) realization in the Italian style. Torres Qrst published tratados 1–3 in 1702; his second edition of 1736 not only added the fourth section but also recast the examples in typeset keyboard notation—a Qrst for Spanish music printers according to Murphy (xi). The present volume offers on facing pages the text of the 1736 edition and a new English translation. The Spanish (Castillian) text is newly set, with the original examples interspersed in facsimile; transcriptions in modern notation appear within the English text. In a brief introduction, Murphy places the treatise in its music-theoretical context, describing it as “the Qrst work in Spain to deal speciQcally and completely with thoroughbass accompaniment at the keyboard” (xi).3 More precisely, Torres’s chief concern is the correct writing or playing of three simple contrapuntal parts above a bass line, Qgured or unQgured. Practical matters of style and performance are largely ignored except in the closing chapters of tratado 3 (which provide examples of liturgical verses with Qgured bass) and in tratado 4. In both, Torres acknowledges borrowing material from Francesco Gasparini’s L’armonico pratico al cimbalo, which gives a more thorough introduction to the types of arpeggiation and the irregular

5

4

Gasparini 1708. Penna 1672. 6On German sources for this simpliQed division of the whole tone and its practical ramiQcations, see Oleskiewicz 2000, 205–8. 7Murphy equates the two intervals (280 n. 11). In fact, the ditonic comma, deQned as the interval between a major third (5:4) and a ditone (two major whole steps, or 81:64), corresponds to the ratio 81:80. Eighteen of the latter yield an interval (81 18:8018) imperceptibly larger than a major third.

dissonances, especially acciaccaturas, employed in Italian continuo playing of the time.4 Elsewhere, too, Torres relies on older writers, including a number of Spanish authors (identiQed by Murphy) and, above all, Lorenzo Penna, whom he cites frequently as an authority.5 The opening section on musical fundamentals offers few surprises, although it is notable for its adherence to the ninefold division of the whole tone, a feature also of contemporary German theory. Thus the chromatic (incantable) half step—the “unsingable” half step in Murphy’s translation—comprises four commas, the diatonic (cantable) Qve. This yields, for example, a G that is audibly lower than its enharmonic equivalent A , such as would occur in any of a number of keyboard temperaments that Torres might have used.6 Because Torres does not discuss temperament, the exact size of these intervals is undeQned, but if the intention was to create pure major thirds (e.g., E–G ) then Torres’s comma would differ by a minuscule amount from the traditional ditonic or Pythagorean comma.7 If not an original thinker, Torres was certainly an organized one. The most notable feature of his treatise may be the systematic manner in which it sets forth the types of voice leading most frequently encountered in early eighteenth-century music. Torres’s focus was presumably the old-fashioned Spanish vocal polyphony of which he himself was an important composer; his few works available in modern editions reveal a capable command of imitative liturgical counterpoint in the stile antico, in four to eight parts. Many of Torres’s examples would have seemed stylish at

8At that point Torres stops, declaring that motion through the sixth is the same as motion through the third (84).

the time of the Qrst edition; for instance, the illustrations of glosas (divisions or passing notes) in the bass are reminiscent of what one Qnds in Corelli’s trio sonatas (especially those of op. 1, 1681). But both the musical illustrations and the fundamental theoretical orientation as revealed in tratado 1, which is still grounded in liturgical practice and the church modes, might by 1736 have begun to seem old-fashioned in France, Italy, Germany, or Britain. The same is true of Torres’s scholastic literary style, untouched by Enlightenment wit or rationalism. Nevertheless, the progressions which Torres illustrates recur routinely as foreground voice leading in the music of Corelli, Handel, J. S. Bach, and other younger contemporaries. Tratado 2 describes the progressions of consonant chords—what would now be termed root-position and Qrst-inversion triads—that can take place over bass lines moving respectively in minor or chromatic half steps, major or diatonic half steps, whole steps, and so on, up to the diminished fourth and augmented Qfth.8 Tratado 3 presents various types of passing motion in the bass as well as the most common suspensions with similar rigor. In its emphasis on actual progressions, Torres’s volume differs from what are now the more familiar French and German treatises of the eighteenth century, which are organized according to chords—that is, individual classes of verticality as deQned by their Qgured-bass signatures (e.g., 54 , 73 , etc.). Indeed, Torres discusses the Qgures themselves only as an afterthought, after the presentation of the various progressions (164– 6). His strict contrapuntal orientation is also evident in his avoidance of the types of liberties which, in the French style of Qgured bass realization, led to the routine use of the petite sixte—that is, a 63 -chord with an added fourth—on the second degree of the scale. Rameau understood this chord—which incorporates an unprepared dissonant fourth—as the equivalent of what we would call a second-inversion dominant

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9Murphy asserts that “this treatise . . . considers chord inversion and voiceleading in the realization of the bass” but does not specify what passage he has in mind (xi).

seventh; contrary to Murphy, I Qnd no evidence of the principle of chord inversion in Torres’s treatise.9 Torres’s examples are accompanied by detailed descriptions or “rules”—the reglas of the title. But these amount to little more than note-by-note accounts of what is manifest in the illustrations. The book’s greatest value, particularly for students, probably lies in the examples themselves, which are sufQciently numerous and well designed to constitute a systematic exposition of the most common four-part progressions in late-Baroque music. Most examples are presented Qrst as bass lines with numerical Qguration, then in fully realized form on two staves. Practicing these illustrations at the keyboard would lead to familiarity with each progression in turn— which seems to have been their primary purpose. The book will prove less useful for practice in reading actual Qgured basses, however, since the initial presentation of each example uses not the sketchy Qguring of real continuo parts but a sort of tablature reminiscent of older Spanish keyboard notational systems: every note of the upper voices is indicated by numbers, speciQc registers being indicated through a system of letter abbreviations. The examples go well beyond the simple illustrations of typical chords that one Qnds in contemporary French and Italian Qgured-bass treatises, including Book 4 of Rameau’s Traité. Moreover, by offering variations of each basic progression in different keys within continuous passages of music, Torres provides a clearer sense of how each progression occurs in context than do German writers, such as Bach. To be sure, the latter reveals a more sophisticated sense of the possibilities of voice leading, especially in dissonant and chromatic progressions. Torres never goes beyond the conventional; even tratado 4, which includes numerous illustrations of extravagante chords, such as Neapolitan and full diminished-seventh harmonies, offers little that was out of the ordinary in contemporary Italian practice.

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10

For example, Banchieri 1609.

The book’s utility is diminished by the sketchy background information provided, as well as inaccuracies in the transcription of the examples, infelicities in translation, and remarkably poor editing and production. Although conscientious in the discussion of selected problems of translation, Murphy directs readers to unpublished dissertations (including his own) for substantive information about the author’s life and music; consideration of how the present work relates to Torres’s compositions would have been especially welcome here. Other important questions, such as the sources of the liturgical melodies in tratado 3, which more closely resemble seventeenth-century Italian recitative than chant, are left unasked. I would have liked to know how these examples relate to the long tradition of accompanied liturgical chant, documented in earlier Italian keyboard treatises that Torres probably knew.10 Some commentary on the instruments available to Torres (and their tuning and temperament) would also have been appropriate. Despite the mention of three instruments in the title, the account of musical fundamentals in tratado 1 assumes use of an organ with a so-called short octave (lacking C , E , F , and G in the lowest octave). The harp enjoyed widespread use in Baroque Spain, but Torres says nothing whatever about it or how his musical examples might have been adapted to it. The organ is distinguished from the harpsichord only in tratado 4, whose examples of arpeggiated accompaniment are intended chieRy for the latter instrument. The parallel Spanish and English texts, both containing illustrative material, posed production challenges that were not met with complete success. For instance, on page 174 the second musical example in the English text is repeated in place of the third example; the examples for the Spanish text on pages 259 and 263 are exchanged. More troubling is the astounding number of proofreading errors; for example, throughout the book, the word “method” appears more often than not as “mehtod,” and in tratado

1 the endnotes are misnumbered, starting on page 20. Even the book’s manufacturing is wanting; in my copy many of the pages were incompletely cut. More substantive problems attend the English version, which is literal to the point of obscurity, often reading like the unedited output of an electronic translation program. Problems begin with the title, which in the original Castillian reads Reglas generales de acompañar, en órgano, clavicordio, y harpa, con sólo saber cantar la parte, o un bajo en canto Fgurado. As Murphy explains (xviii), the last two words refer not to Qgured bass (as one might think) but to “Qgural music,” that is, polyphony. In the puzzling phrase “Sing the Part, or a Bass,” Murphy suggests plausibly that “the part” (la parte) is the bass (un bajo), that is, a Qgured or unQgured bass line; the two nouns are in apposition. But then in modern English the comma after “Part” should have been supplemented by a second one after the word “Bass.” Perhaps, too, the word cantar (to sing) should be understood metaphorically, yielding an idiomatic rendering of the title as “Rules for Accompanying on Organ, Harpsichord, Or Harp From Only the Bass Part of a Polyphonic Composition.” This makes it clear that the purpose of the book was to teach organists to accompany choral music without a score; evidently, there as yet existed no simpler terminology with which Torres could describe continuo playing for his Spanish-speaking readers. Although I was unable to check the reliability of the Spanish text against the original editions, it seems sound, and the English translation rarely contains outright errors. Murphy asserts that Torres refers to both perfect and augmented fourths as mayor (282 n. 18), but this reRects a misreading of the chapter heading “Del salto de cuarta hacia abajo, o quinta hacia arriba, así mayores como menores.” Murphy gives this as “On the leap downward, or the Qfth upward, both perfect and diminished” (76, 268), but it might be better rendered as “Leaps of a fourth downward or a Qfth upward, including augmented and diminished intervals.” Elsewhere, it is clear that Torres uses mayor only for augmented fourths and minor for diminished Qfths. 11

Contrary to what is stated in the introduction (xxi).

Unfortunately, the types of problems evident in the rendering of the title continue throughout the English translation, which consequently can be understood only by someone already familiar with the subject and with eighteenth-century musical terminology. Sometimes a reliance on cognates leads to unidiomatic translations—“the studious” for estudioso, student (50), “cantor” for cantor, singer (123)—or to non-words such as “unisonically” (50). Especies falsas, meaning “dissonances,” appears throughout as “false intervals”; voces and cuerdes, translated literally as “voices” and “strings,” respectively, more often seem intended metaphorically, as “notes.” Metrical and rhythmic terms present a particular problem; although Murphy acknowledges the importance of mensural thinking in Torres’s understanding of rhythm (ix), he nevertheless updates Torres’s terminology, offering, for example, “the measure’s downbeat or upbeat” for dar o alzar del compás (96). I would have preferred “thesis and arsis of the tactus,” using rhythmic nomenclature consistent with Torres’s archaic notation, which includes old-fashioned irregular barring and survivals of mensural notation such as coloration and proportions. Murphy updates the latter as well, frequently halving the values of examples in triple time.11 Numerous wrong notes further mar the examples, sometimes obscuring the points they are meant to illustrate. Thus on page 240 the 7 7 second of two 54 chords is realized instead as a 64 —in modern terms, 2 2 eliminating the dominant-seventh chord (over a tonic pedal) which the example was supposed to show. On page 182 the examples under the headings “Chord 1 . . . Chord 2” and “Chord 3 . . . Chord 4” have been exchanged, and a sharp has been added to a G in the bass, resulting in a diminished third and a cross relation— highly uncharacteristic dissonances for Torres! In such cases, comparison with the original notation on the facing pages will reveal the errors, but sometimes the original is clearly erroneous; only occasionally does Murphy offer corrections. Errors seem particularly common in tratado 4, suggesting that the aging Torres

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did not carefully oversee production of the concluding pages of his work; a glaring instance occurs on page 250, where all of the Qgures 5 and 7 are errors for 5-6 and 7-6, respectively. As disturbing as the outright errors is the faulty notation of the transcriptions, which wherever possible group the noteheads of the three upper parts—set on one staff for the right hand—onto single stems. This obscures the contrapuntal character of the voice leading, and further damage occurs when the stems of passing notes go in the wrong direction, as is often the case. To be sure, the original is often equally at fault, entirely omitting stems from the middle (alto) voice in most sonorities. This, however, is a common feature in typeset keyboard music of the period, for reasons logically analogous to those which today create difQculties for music-setting software in contrapuntal keyboard textures. It is ironic that, although Murphy duly notes the signiQcance of the high-tech printing process that Torres adopted in the 1736 edition, by the end of the century music publishers were returning to engraving as the best method for printing graphically complex keyboard notation. Despite its many shortcomings, this edition will prove valuable to serious students of Spanish Baroque music and eighteenth-century theory. It demonstrates that the strict, fourpart contrapuntal style of Qgured bass realization best known today from German sources, such as Bach’s Versuch, was also typical of what Torres calls “the rigorous Spanish style” (212). The extraordinary achievements that this style could produce in the seventeenth century are evident in the contrapuntal keyboard works of Cabanilles and other Iberian organist-composers. Future work might relate Torres’s teaching of this style to his vocal compositions and those of other eighteenth-century Iberian musicians.

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Bach, Carl Philipp Emanuel. 1752–63. Versuch über die wahre Art das Clavier zu spielen. 2 vols. Berlin. Facsimile, with Nachwort by Lothar Hoffmann-Erbrecht and supplement containing additions from the edition of 1787–97. Leipzig: VEB Breitkopf und Härtel, 1981. Translated by William J. Mitchell as Essay on the True Art of Playing Keyboard Instruments. New York, Norton, 1949. Banchieri, Adriano. 1609. Conclusioni nel suono dell’organo. Bologna. Facsimile. New York : Broude Brothers, 1975. Partial translation by Lee R. Garrett as Conclusions for Playing the Organ. Colorado Springs: Colorado College Music Press, 1982. Gasparini, Francesco. 1708. L’armonico pratico al cimbalo. Venice. Translated by Frank S. Stillings as The Practical Harmonist at the Harpsichord. New Haven: Yale University Press, 1963. Oleskiewicz, Mary. 2000. “The Flutes of Quantz: Their Construction and Performing Practice.” Galpin Society Journal 53: 201–20. Penna, Lorenzo. 1672. Li primi albori musicali. Bologna. Facsimile of the fourth edition (Bologna, 1684). Bologna: Forni, 1969. Rameau, Jean-Phillipe. 1722. Traité de l’harmonie réduite à ses principes naturels. Paris. Facsimile. New York, Broude, 1965. Edited by Erwin R. Jacobi in The Complete Theoretical Writings of Jean-Philippe Rameau, vol. 1. American Institute of Musicology, 1967. Translated by Philip Gossett as Treatise on Harmony. New York: Dover, 1971. Soler, Antonio. 1762. Llave de la modulación. Madrid. Facsimile. New York: Broude, 1967.

LIST OF WORKS CITED

Review: Harmonic Experience, W. A. Mathieu

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