MARTIN, Henry. 2010. "Seven Steps to Heaven" _ a Species Approach to Twentieth-century Analysis and Composition

Seven Steps to Heaven: A Species Approach to Twentieth-Century Analysis and Composition Author(s): Henry Martin Source: Perspectives of New Music, Vol. 38, No. 1 (Winter, 2000), pp. 129-168 Published by: Perspectives of New Music Stable URL: http://www.jstor.org/stable/833591 . Accessed: 06/04/2014 09:35 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp

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SEVEN STEPS TO HEAVEN:

A SPECIESAPPROACH TO TWENTIETH-CENTURY ANALYSISAND COMPOSITION

HENRYMARTIN

PROPOSE TO OUTLINE a system of species counterpoint applicable to twentieth-century modal music. In so doing, I hope to provide this repertory with the kind of broad-based analytical tools that have long been available for tonal music. It is well-known that traditional species counterpoint is useful both for analysis and as a step-by-step method for students of tonal composition. It is my hope that the twentieth-century update outlined here can function effectively in both roles as well. The first of two articles, this paper summarizes two- and three-part first species counterpoint as the basis of the method. The original motivation behind this species counterpoint approach was the intractability of the analysis of much twentieth-century repertory,

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particularlythe music of Hindemith, Shostakovich, Bart6k, and Copland. Such music is often difficult to analyze from either a tonal or atonal perspective. Whereas clearly tonal or clearly atonal music have theories that are fairly exact in their application, much twentieth-century practice, influenced by the modality explored in this paper, is hazier; the musical grammar can shift on a sliding scale from common-practice tonality to outright atonality. This can be true not only among pieces by different composers, but also within the same piece or even the same passage. Hence, we need a general way of approaching those "in-between" works-those passages that are clearly not tonal, but clearly not atonal either and do not specifically depend on the practice of one composer. The sliding scale of the "seven steps" of diatonic modality to be presented here provides one means of getting a broad handle on much of this literature. The presentation in this paper is theoretically focused, but I discuss several completed species counterpoint exercises in order better to show the method's advantages. A more pedagogically oriented presentation, based on material developed for use in class, is planned as well. I have found this material to be stimulating pedagogically-as step-by-step training for students of both composition and analysis, especially for those who have familiarity with traditional species counterpoint. Its greatest advantage is introducing students to compositional models that gradually become more and more dissonant until tonality has diffused into atonality. The method's efficiency is such that students are able to apply its principles immediately to their own work, whether it be composition or analysis. Students of composition, in working through twentieth-century species exercises, begin with models that approximate the conservative Hindemith or Shostakovich style. Later, by incorporating bimodal and bitonal two-part writing and more dissonant trichords, these students can experiment with the harmonic textures of Bartok or Stravinsky.At the limits of the theory, students write atonally, thinking in terms of atonal set-theoretical principles derived from experience with the prime trichords. In all cases, students learn the diatonic modes and the prime trichords thoroughly. As a result, they are subsequently able to work effectively with set-based atonal theories or jazz theories of modal design. Thus, students of jazz have also found it helpful in both composition and improvisation. For students of analysis, the method is equally productive. Again, they will learn the diatonic modes and the twelve prime trichords thoroughly. Much twentieth-century literature can be tackled with this method to

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Seven Steps to Heaven

131

yield a "first-step"overview of the music. Of course, more particulartheories should be brought to bear on specific composers and pieces as becomes necessary, but much as functional Roman-numeral analysis is largely applied as a first-step reading of a tonal piece, the seven-steps method and the trichordaltheory has proven helpful for trying to unlock twentieth-century literaturethat reflects some tonal bias, i.e., music that traditional tonal theory might consider to have "wrong notes" and is unable to explain generally. There is a long history of the pedagogical applicationof species counterpoint. Its fame as a tool for teaching composition spreadthrough publication of what is probably the most well-known compositional treatise in Western history, the Gradus ad Parnassum of Johann Joseph Fux.1 While Fux did not originate pedagogical use of the species, he consolidated the work of his predecessors.Many counterpoint treatisesfollowed Fux's work,2 but the most thorough study of species counterpoint appeared in the twentieth century, Heinrich Schenker's extensive and definitive Counterpoint.3 In his Counterpoint, Schenker pioneered a species approach not intended as compositional pedagogy. Instead, Schenker showed that species counterpoint not only underlies tonal syntaxin general, but also provides a superb point of departure for the analysis of tonal free composition. It was originally Schenker's inspiration that suggested the seven-steps method as a useful tool for analysis;from that idea the compositionally oriented approachfollowed. This paper begins with a brief general discussion of tonality versus modality.An important aspect of the tonal-modal distinction depends on a revised concept of intervallic consonance, which is then developed. From the revised concept of consonance, the second part of the paperon two-part first-speciescounterpoint theory-follows. Its general idea is describedfirst, followed by examples of analysisand sample exercisesthat illustratethe varying levels of the "seven steps." In the third part of the paper, the three-part first-speciescounterpoint theory is summarized.First, the twelve prime trichordsare analyzed;then follows a demonstration of how musical analysisproceeds from an understanding of those sonorities. As with the two-part theory, sample exercises are provided to show the method in a pedagogical environment. The paper concludes with discussion of a fugal exposition of Hindemith in order to show how the two- and three-part theories can be united in the analysisof a twentieth-century work.

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TONALITY VERSUS MODALITY

The following practices, which can be called "cues," usually occur in music we call tonal. They are shown in roughly decreasing order of importance. Tonal Cues 1. principal pitch-class collections usually reducible to major or minor scales; 2. normative dependence of dissonant melodic intervals on consonant intervals prolonged at a higher structural level; 3. functional harmonic succession based on triads;in two-part writing, on consonances that may imply functional harmonic succession; 4. harmonic rhythm arising from functional harmonic succession; 5. presence of Stufen arising from hierarchical, nested prolongations that ultimately give rise to tonal center and key; 6. norms of melodic writing in which conjunct intervals predominate; 7. half, full, and deceptive cadences; 8. meter; 9. phrase and section groupings that project two-, four-, and eight-bar symmetries. In the twentieth-century repertory we are considering, these cues of tonal grammar vary in presence and degree of strength, often within the same piece or even the same passage. This variance contrasts with the repertory of common-practice tonality of the late eighteenth and early nineteenth centuries, in which all the cues tend to be present.4 This common-practice repertory is normatively "tonal." But because tonality varies according to the presence and strength of the cues, it is not always clearly defined: note that tonality first emergedfrom medieval and Renaissance modal practice; then, beginning in the nineteenth century, tonality divergedinto twentieth-century modal practice. From this perspective, it might be better to consider tonality a special case of the modality that has pervaded western music since the early middle ages. Thus, tonality is fluid-its strength or lack of strength a dynamic judgment based on the salience of the cues enumerated above. When a sufficient number of cues are lacking, these weakened, quasi-tonal grammars

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may often be conceptualized as modal, i.e., relating to the diatonic modes of the major (Ionian) scale. Much of the twentieth-century repertory under consideration here is modal, although modality (like tonality) varies depending on the weight of the tonal cues. "Conservative" modal music will feature the cues shown above with considerable presence. "Less conservative" music will contain fewer of the cues. When the cues are lacking entirely or almost entirely, the music will probably be heard as atonal. Of especial significance for the theory to follow are the first and second of the tonal cues. For now, we will take for granted the first cue, that the music under consideration be reducible to principal diatonic collections. The second cue is important because it is defined carefully in species counterpoint, which, though originally modal, also underlies common practice tonality. This second cue is also important, since the two- and three-part theory to follow is based on a revised concept of consonance that has proven very helpful for establishing a species environment reminiscent of Fux and Schenker. In order to motivate a suggested revision of consonance, let us examine the second cue in more detail. Traditional consonance and dissonance in species counterpoint can be summarized as in Example 1. Pitch classes:

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EXAMPLE 1: TRADITIONAL TWO-PART COUNTERPOINT

In Example 1, the pitch classes (pcs) of two voices in C major are represented, across and down.5 Their intervals are either consonant (C) or dissonant (D). For example, E-C is either a third or sixth (consonant-C), while G-D is either a perfect fourth (dissonant-D) or perfect fifth (consonant-C). Counting this way, we find that two-part species counterpoint contains a balanced twenty-seven potential consonances and twenty-two potential dissonances.

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The balance between consonance and dissonance is described as "potential" for an important reason. Composers determine the levels of consonance versus dissonance in each specific work within the context of its general system. This can be seen in traditional species counterpoint itself: a second-species example might feature a large number of dissonances on the upbeats or avoid them entirely. The same principle is true of twentieth-century writing: the method to be developed here provides a measurable potential for consonance and dissonance, but the actual ratio of consonance to dissonance in a composition varies according to the piece. In traditional species counterpoint, any dissonant interval must be treated precisely; it must function as (1) a passing tone (almost always between two consonances), (2) a suspension (properly prepared as a consonance and resolving downward by step to a consonance), or (3) a neighbor tone or adjacency (between two consonances). The passing tones and suspensions may be considered as prototypes for, respectively, the rhythmicallyweak dissonances and the rhythmically strong. Thus, the wide variety of dissonances permissible in two-part writing more generally-appoggiaturas, anticipations, escape tones, incomplete neighbors, and so on6-are based on either the "off beat" dissonance (the passing tone) or the "on beat" dissonance (the suspension), as developed in species counterpoint. Using traditional species counterpoint as a model, we can also argue that dissonances are dependenton consonances. First, as suggested above, there is the simple definition of the dissonance, as in the key rule of the second species: any dissonance must occur on the upbeat of the (2/2) bar and resolve stepwise (in the same direction) to a downbeat consonance. Similarly, a dissonant suspension must be prepared as a consonance on the upbeat of the previous bar and be resolved downward by step to a consonance. The definitions both hinge on the presence of consonances that give meaning and impart function to the nonchord tones; that is, the conceptually prior consonances give the dissonances a raison d'etre. A second illustration of the dependence of dissonances on consonances follows from the above and involves structural levels. Virtually without exception, a more background structural level must absorb and convincingly account for the dissonances of the more foreground level. For example, a dissonant passing tone prolongs the third created between the initial tone of the passing motion and its goal tone. The suspension creates a temporal displacement whereby motion to the resolution is delayed through the dissonance of the downbeat; that dissonance would be subsumed and the temporal shift "corrected" at a higher background level.

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Seven Steps to Heaven

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Thus, dissonances are nearly always shown as more foreground elaborations of the consonances they depend upon.7 Yet much two-part twentieth-century writing does not always project dissonant intervals as functionally dependent on consonances. Two illustrations follow. "Fugue 3" of Shostakovich's Twenty-fourPreludes and Fugues, op. 87 (Example 2) begins by projecting a modal environment in its very opening gesture, which outlines the dissonant major seventh from G4 to F#5. After the wedge-like convergence of the compound melody in measure 2, the major seventh is further emphasized by the C5-B5 leap in measure 3. Hence, while the pitches from G Ionian are used exclusively in the subject (satisfying cue 1), these standing, unresolved dissonances alert us that the syntax is not classicallytonal (cue 2 unsatisfied). At the entrance of the answer in measure 5, the counterpoint proceeds momentarily in classical fashion. The C#s atop the run in the alto (measure 5) can be heard as prepared by the F#5-E5-D5 eighth notes in the soprano; further, note the conventional 4-3 suspension at measure 6. Yet, in measure 7 the leap of G4-F 5 in the alto brings us back to a nontraditional orientation: both the G4 and F#5 are consonant with the D6 of the soprano, but the harmony is vague: is it a G major seventh? Or is there a change of harmony: D major to G major to D major-all in the span of the first half of measure 7? It seems preferable to infer a D Ionian mode through the passage rather than seek specific functional usages. Once the less harmonically specific D Ionian is conceded, then the sequence of dissonances in measures 7-9 becomes more easily comprehensible: while the E5-A5 fourth at beat 5 of measure 7 can be understood as a passing sonority, the sequences of fourths and sevenths in measures 8-9 are not treated as functionally dependent on any consonant intervals. The same E5-A5 fourth at beat 3 of measure 8, for example, proceeds to the B4-A5 seventh. Then follow the parallelfourths Ds-G5 to C#5-F#5 from measures 8-9. Since the fourths and sevenths in measures 7-9 of Example 2 are not functionally dependent on more consonant intervals (as passing sonorities, suspensions, or other nonchord tones), it seems preferable to group them as stand-alone intervals. These usages, in which intervals that are dissonant in tonal practice do not seem to have foreground consonances to depend on, are labeled M. Charlie Parker's"Ah-Leu-Cha" (Example 3) also shows fourths, major seconds, and minor sevenths as functionally independent. In measure 1, the consecutive seconds followed by a fourth cannot be explained as deriving from some prior conception of consonance.8 In measure 5, the third and fourth beats parallel measure 1, with three consecutive functionally independent intervals: note that the M2-M2-P4 interval succession in measure 1 is answered in measure 5 with P4-M2-M2 (the major

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seconds expanded as ninths). The consecutive perfect fourths of measure 4 are paralleled by the concluding perfect fourth in measure 8 (as an eleventh). The two parallel events (measure 1 to measure 5 and measure 4 to measure 8) further exemplify the independence of these intervals, help unify the passage, and show a balance in construction that argues against the haphazard. Again, these independent dissonances are labeled M. Examples such as the Shostakovich and the Parker suggest that in modal music, perfect fourths, and minor sevenths/major seconds (interval class [ic] 2s) could be thought of as "virtually"consonant. Given the resonance of history, where the traditional consonances (ics 0, 3, 4, and perfect fifths) are strongly established, it also would seem that any functional independence of perfect fourths and ic 2s would have to take into account traditional tonal practice, which lingers tellingly in cultural memory and is supported (at least to some extent) acoustically. I propose that these perfect fourths and ic 2 intervals be called modal consonances:they are not "as consonant" as ics 0, 3, 4, and perfect fifths, but neither are they treated as dependent on tonal consonances at the foreground. Some theorists might suggest it simpler to abandon the dissonanceconsonance principle entirely in twentieth-century two-part writing. An argument can be made that in many similar contexts, the remaining intervals (ics 1 and 6) are also treated as independent, i.e., as consonant. But a graduated approach with the modal consonance as intermediary between tonal consonance and dissonance seems preferable, since the degree of tonal projection varies widely from piece to piece. Some pieces, such as the Shostakovich and Parker excerpts, are tonal except for their atypical (relative to traditional practice) use of fourths and ic 2s. Other pieces, as will be demonstrated below, vary more dramaticallyfrom tonal norms. The modal consonance, in fact, seems better suited as a (fairly consonant) independent interval in those pieces "closer" to the tonal benchmark. As practice veers closer to nontonal usages, the modal consonance loses its particularity.Again, this will be evident in examples to follow.

TWO-PARTFIRST-SPECIESCOUNTERPOINT

As based on the practices of the Shostakovich and Parker examples, a consonance-dissonance grid that includes modal consonances is given in Example 4. Intervals are categorized as tonal consonances (T), modal consonances (M), or dissonances (D). The model shown in Example 4 is called "ic 0" (or "Type A") modal counterpoint for reasons that will be explained shortly. The only disso-

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Seven Steps to Heaven

Pitchclasses:

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(Uppervoice) C D E

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EXAMPLE 4: IC 0 DIATONIC MODAL COUNTERPOINT (TYPE A)

nances are major sevenths, minor seconds, diminished fifths, and tritones-that is ics 1 and 6. In writing two-part first species counterpoint, only tonal and modal consonances are permissible. The interaction of tonal and modal consonances may be examined further in Example 5, which shows a first-species realization in F Lydian. The cantus firmus (C. F.) in the bass projects intervals that emphasize the lydian quality-a prominent tritone between the F3 in measure 1 versus the B3 in measure 3, for example. Most of the motion of the C. F. is stepwise, but after leaps of a fifth (measures 1-2) and a fourth (measures 4-5), the melody returns by step in the opposite direction.9 1

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EXAMPLE 5: F LYDIAN

The two-part first-species model can help us better understand other passages of free composition. Example 6 shows measures 43-53 of the second movement of Aaron Copland's Piano Sonata. While we can conceive of the parts as both being in B Ionian, the ending of the lower part on G#, the repeated bass motions of D#3 to G#3, the third created by G#3 with the upper B (measures 2 and 6), together with the modal

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