Music 15100
Harmony and
Voice-Leading I
Lawrence Zbikowski
University of Chicago
Department of Music
Autumn Quarter 2008
MWF, 10:30—11:20
Goodspeed Hall 402
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Music 15100
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This course begins the three-quarter sequence of harmony and voice-leading courses for students who have some background in music and who are familiar with musical notation. The course will focus on things necessary for an adequate comprehension of tonal music. These include a review of music fundamentals (including chord structure and rhythm), an introduction to two-part counterpoint, an overview of tonal syntax, and an initial consideration of the four-part harmonization of melodies and basses. The course is accompanied by two skills sections: one focuses on the piano keyboard, the other on aural skills. Course assistants:
Week 1 (9/29—10/3)We began class on 9/29 with an introduction to the goals and scope of the class, and a short practical demonstration on the relationships between basic two-part counterpoint and harmonic compositions effected by turning a bit of counterpoint into Tamino’s aria from the Finale of Act I of Mozart's The Magic Flute. On Wednesday, diagnostic tests in theory and aural skills. Diagnostics tests in aural skills and theory were administered on 10/1. Not a huge amount of fun, but extremely helpful to the instructional staff (me). Instruction in music theory began in earnest on 10/3 with a review of scale structure, key signatures, and conventions for identifying steps (including carated numbers for scale steps and traditional names such as tonic and dominant). I then turned to the notion of a musical interval, which I characterized as a relationship between two notes, and distinguished two basic realtionships for the intervals between pitches: direction (“ascending”/“descending”) and temporal arrangment (the interval between simultaneous notes being calledharmonic, and between successive notes being called melodic).I also reviewed basic classifications of musical intervals, including numerical size (basically, counting lines and spaces) and quality (major, minor, and perfect, reckoned in terms of the constituent whole steps and half steps of the interval). Finally, I noted a simple tool for figuring out interval quality: given two pitches (say, an A with an F above), counting lines and spaces will tell you it’s a sixth, but it can be a bit tedious counting whole and half steps to figure out if it’s major or minor (or something else). So imagine the key signature for the lower note (A), which would be three sharps (F#, C#, and G#). If the upper note of the interval fits into this key signature, the interval in question is major or perfect; if the upper note doesn’t fit into the key signature (which is the case with F), it’s either minor or (in the case of perfect intervals) diminished or augmented. In this case, the interval from A up to F is a minor sixth. (It bears mention that matters don’t stop there, since increasing the size of a major interval creates an augmented interval, and decreasing the size of a minor interval creates a diminished interval, but that’s for another day . . . ).
Week 2 (10/6—10/10)The topic for class on 10/6 was counterpoint, but we approached it from an oblique angle, and through the last couple minutes of the Finale of Mozart’s Symphony in C K. 551, popularly known as the “Jupiter” and composed in 1788. We explored the effect of the music (variously characterized by members of the class as “triumphant” and “victorious,” but also “nostalgic” and “reaching out”) and the way Mozart accomplished this effect. One source is the contrapuntal writing he uses—in German-speaking countries the nickname of the symphony is “die Symphonie mit der Schlussfuge” (“the symphony with the fugue finale”)—which allows him to build up an incredibly dense musical structure that both contributes to the climax of his ending and makes reference back to the preceding music. We then turned to the opening Kyrie of Giovanni Pierluigi da Palestrina’s “Pope Marcellus Mass,” from around 1556. Here the effects were very different, suggesting holy reaches and soothing efforts. Palestrina’s means of achieving these ends—as one might suspect, quite different from those of Mozart—nonetheless also relied on counterpoint, but here to guide the combination of his six different voices to create an ethereal and yet substantive musical texture. And it was the school provided by this counterpoint—both in terms of its continuing influence on church music, and the model it offered to later generations of composers—that is articulated, in its humblest but also most robust form, by species counterpoint. We then reviewed basic types of species counterpoint, its classification of musical intervals (unisons, thirds, fifths, sixths, and octaves as consonant, and seconds, fourths, sevenths, and any augmented or diminished interval as dissonant), and some of the basic rules for beginning and ending a counterpoint exercise. Some of this was illustrated by a counterpoint exercise that I contributed, which gave us some sense of how these rules were implemented, and the musical results thereby obtained. More on this, and musical intervals, on Wednesday. Our consideration of first-species counterpoint continued on 10/8, beginning with the four types of motion possible between two voices in this style: parallel motion, it’s cousin similar motion, their opposite contrary motion, and finally oblique motion. I also reviewed the harmonic intervals that are not permitted in first-species style as well as the melodic intervals that are disallowed: sevenths, and any augmented or diminished interval (with the understanding that sixths should be used quite carefully). To get a sense of what counterpoint was about, we sang through three examples of first-species counterpoint from the homework for Friday, which gave us a better idea of what these exercises are about but left scant time to consider some of the niceties of voice-leading and melodic writing. The latter first: as a general rule, after any melodic leap larger than a third (that is, fourths and larger intervals) great melodic fluency is obtained if one steps opposite the leap. Indeed, one could make that a rule. With regard to voice-leading, J. J. Fux, in his Gradus ad Parnassum of 1725, gives four fundamental rules:
As I noted in class, we can reduce this to only one rule: one cannot proceed by parallel or similar motion into a perfect consonance. Although it might seem incredible, I also provided a quick list of the modes used in species counterpoint, which we could catalog as follows:
Knowledge of the different modes is particularly important for writing the clausula formalis with which each exercise must end, and which is covered in greater detail on pages 15-17 of Hyer’s A Manual for Species Counterpoint. We proceeded in a minor mode—or, more properly, through a variety of minor modes—on 10/10, beginning with the fiddle tune “Crossing over to Ireland.” After I played the tune on mandolin we explored its structure by extracting its constituent pitch classes and arranging them from lowest to highest. This yielded a D major scale, but that was construct that ill reflected the melancholy character of this little tune. So we then rearranged the notes to create an E Dorian scale, a construct that did a somewhat better job of reflecting salient aspects of the tune. My point in doing this exercise was to reinforce the notion of a scale as an abstraction from the music: scales are certainly useful constructs, but they hardly represent the raw stuff of musical expression, for such expression requires not only a foregrounding of intervals and musical motives but also the arrangement of such materials through the temporal framework provided by rhythmic structures. That said, I provided a quick tour through the three canonical forms of the minor scale: natural minor, harmonic minor (with the seventh step raised), and melodic minor (with steps six and seven raised in ascent, and lowered in descent). I then suggested that natural minor was a music-theoretical fiction, not the least because without the leading tone the pitch centricity typical of tonality was lost. I then tried to illustrate this point with a Venezuelan waltz in E minor by Antonio Lauro, which I played on guitar. This composition not only showed a more realistic view of the role of scales in actual musical works (typically as passages from one place to another), but also the ways leading tones (both global—that is, pertaining to a given pitch center—and local) operated.
Week 3 (10/13—10/17)We returned to minor scales on 10/13, and covered the relationship between relative keys (such as A major and F-sharp minor, which share the same key signature but have different tonics) and parallel keys (such as A major and A minor, which share the same tonic but have different key signatures). I also re-emphasized the importance of the leading tone in minor keys, which is one thing that prevents music that’s in minor from flopping over into the relative major (both because the leading tone contributes to tonal focus, and is a note foreign to the relative major). I also offered a couple of strategies for determining intervals. The first focused on knowing a familiar (and important) interval, and then using it as a basis for figuring out slightly less familiar intervals. For example, perfect fifths provide a handy point of reference which can be used to figure out minor and major sixths, something especially useful when dealing with descending intervals. Another handy interval is the perfect octave, useful for getting to major and minor sevenths. The second strategy built off a knowledge of interval inversion. For instance, if one is asked to write a minor seventh below a given note (say, C), one could first think of a major second above the C (that is, D) and then transpose it down an octave to create the required note. In the latter portion of class we embarked on a small-group exercise which gave everyone a chance to take a pass through identifying intervals similar to those that appear on the last page of the homework that’s due Wednesday. Counterpoint was our main focus on 10/15, although I spent a bit of time reviewing a few aspects of more recondite intervals like the augmented sixth (which, incidentally, would invert to a diminished third). Most of our time was spent with two counterpoint exercises that I provided. We sang through them (emphasizing once again the that this is a vocal style), and then discussed several of their features, as well as problems that can arise when writing counterpoint. I emphasized melodic fluency (realized through strategies such as making as much use of stepwise motion as possible and balancing each leap with a step in the opposite direction) and melodic variety (helped by avoiding repeating one or two notes and striving for a melodic range of around a sixth). Both of these desiderata are intended to be in the service of writing a directed melodic line which, when all is said and done, is one of the main goals of counterpoint exercises. I began class on 10/17 with a brief exercise in which I clapped out a rhythm and then had the class clap it back to me (a simple version of call and response). The rhythm was just a bit tricky—the durational pattern was 2+2+1+2+2+2+1—but is commonly known among Africanists as the “standard pattern,” owing to its ubiquity in various African musics. (For a discussion, I recommend Kofi Agawu’s “Structural Analysis or Cultural Analysis? Competing Perspectives on the Standard Pattern of West African Rhythm,” the Journal of the American Musicological Society 59/1 (Spring 2006), pp. 1-46.) Once the class had the pattern down fairly well I answered them with variations, and then connected this entire activity with the latter portion of the homework due on Monday (which is concerned with completing tiny rhythmic compositions that adhere to a basic period-form structure). The latter portion of class was taken up with a group exercise focused on species counterpoint, which made use of the strategy of figuring out all the possible notes that can be written against a given note of the c.f., and then tracing a path through these possibilities to create a counterpoint. This yielded a number of successful solutions, which we then put up on the board and discussed before once again being defeated by time.
Week 4 (10/20—10/24)We opened class on 10/20 with the chorale “Was frag’ ich nach der Welt” (“What care I for the world!”) as harmonized by J.S. Bach. We sang through the soprano and bass parts, and I noted the predominantly harmonic character of the music (although one inflected by a strong sense of counterpoint among the voices). This led, quite naturally, to a consideration of the triad, which I characterized as an abstraction roughly equivalent to that of the scale. That is, triad is to chord as scale is to melody. The triad thus serves as a compact representation of a chord. Conceived of in this way, it is well to distinguish between different elements of the triad. When presented in its privileged form as stacked thirds, the lowest note is called the root, the note above it the third, and the note above that the fifth. The respective notes then carry these names no matter how they are shuffled, which occurs when the notes of a triad a rearranged into either the first inversion (with the third the lowest note of the assemblage) or second inversion (with the fifth lowest). Talk of inversions led to a brief consideration of figured bass, a compact means of representing the notes to be found above a given bass note and a topic that we will give more attention to as the term progresses. Bach’s setting of “Was frag’ ich nach der Welt” was again our point of departure on 10/22, but this time we ventured forth in four (more or less) melodious parts. This led to a consideration of how triads can be used for the analysis of actual music (again, as a way to abstract information from a musical surface for the purposes of evaluation and comparison), and to a quick tally of triads in major keys (something discussed in greater depth in the textbook). We concluded with a brief small-group exercise extracting triads from four-part chords, which offered a bit of preparation for the homework assignment due Friday. First-species counterpoint was our point of departure on 10/24, specifically in the form of student exercises that demonstrated many of the laudable characteristics toward which we all aim. I put three up on the board and discussed some of their features, which provided occasion for a general review of the rules and guidelines for melodic writing. I then rather switched gears and took up the topic of seventh chords, which I characterized in straightforward (if ultimately simplistic) terms as a consequence of stacking yet another third atop the triads proper to a major scale. The immediate result was four types of seventh chords (which I give here according to their common name and the dual-appellation method that identifies the quality of the triad + seventh): the major seventh (major-major), the dominant seventh (major-minor), the minor seventh (minor-minor), and the half-diminished seventh (diminished-minor). To this I added a fifth, the fully-diminished seventh (diminished-diminished) whose natural home is harmonic minor, but whose origins and nature we’ll explore at a later point.
Week 5 (10/27—10/31)We returned to Bach on 10/27, first through the opening Sinfonia from his cantata “Wir müssen durch viel Trübsal in das Reich Gottes eingehen” (“We must through much tribulation enter into the kingdom of God”; BWV 146), and then by singing, in four parts, the chorale “Was frag’ ich nach der Welt.” The latter was occasion, in the first instance, for considering the role of such chorales within Bach’s cantata: in the case of the source cantata for “Was frag’ ich,” that work begins with a movement structured around the chorale melody, and ends with the chorale through which we sang. In the second instance, “Was frag’ ich” provided an illustration of the role of counterpoint in harmonic writing: Bach’s bass and soprano are almost perfect first-species counterpoint, the only exceptions being some of the passing dissonances he writes and his occasional use of a dissonance, such as the tritone, more typical of harmonic writing. And in the third instance, the chorale (specifically, a harmony at the end of the third measure) returned us to the topic of seventh chords, and in particular seventh chords in inversion. I rehearsed the three different inversions of seventh chords, noted their typical figured-bass designations, and then turned the class loose on a small group exercise that went over these various points. The bulk of class on 10/29 was devoted to a review of topics to be covered on Friday’s test. Toward the end of our meeting, however, I introduced the notion of equal divisions of the octave, a topic raised by possible enharmonic spellings of augmented triads. Thus the G# of a C augmented triad (C–E–G#) could be respelled as an Ab, yielding an Ab augmented triad (Ab–C–E). This is a consequence of an equal-tempered view of the chromatic scale (according to which G# and Ab are functionally equivalent), which renders major thirds such as E–G# functionally equivalent to diminished fourths like E–Ab. The ultimate result is that the augmented triad can be thought of as dividing the chromatic scale into three equal sections (each spelled as either a major third or diminished fourth, and all four half-steps in span). In a similiar fashion, the fully-diminished seventh chord divides the octave into four equal sections (each spelled as either a minor third or augmented second, and all three half steps in span), and the whole-tone scale into six equal sections (each spelled as either a major second or diminished third, and all two half steps in span). Our meeting of 10/31 was occupied with Test #1. EXAM 1, Friday, 10/31. Review materials are now available for the exam. Week 6 (11/3—11/7)We began the post-exam (but pre-election) era that began on 11/3 with a listening exercise focused around Heitor Villa-Lobos’s “Mazurka-Chôro" from his Suite Populaire Bresilenne. Our focus was on the things that make for form in the work—that is, the various compositional strategies Villa-Lobos uses to keep his listener oriented as the music flows forward in time. We discovered various repeating sections (in a minor, C major, and A major), and an overall form that could be symbolized ABACA–Coda. I emphasized that each of these sections was set off by a cadence, which clearly indicated the end of one section and, in most cases, set the stage for the beginning of the next. In the latter portion of class I gave definitions for four types of cadence: the perfect authentic cadence (or PAC), the authentic cadence (or AC), the deceptive cadence, and the plagal cadence, and provided brief four-part examples for each. There being any number of questions about cadences from the previous class, I spent the first portion of our first post-election meeting on 11/5 reviewing cadence formulae in various keys. (Well, not so various, but various enough.) I then moved on to our second new topic, second-species counterpoint, using an example in Mixolydian mode provided by the estimable J.J. Fux (from his 1725 Gradus ad Parnassum). Other than the (almost) constant succession of half notes in the counterpoint, the main innovation was the introduction of dissonance which, in all cases, is permitted only on the second main beat of the measure (that is, the second half note) as part of a stepwise passing motion. Class on 11/7 was taught by Michael LaCroix, who spent time with the third movement of Haydn’s piano sonata no. 32 in c# minor (part of the assignment due today) and provided additional examples of second-species counterpoint.
Week 7 (11/10—11/14)Continuation of work with second-species counterpoint; resolution of tritones; use of V7 chords in cadences. Assignment 8. Matters took, at least for a brief moment, a biblical and tonal turn on 11/10 as we considered the opening of one of Johann Kuhnau’s (1660-1722) Biblical Sonatas, an example drawn from the first page of Unit 6 of our text. My emphasis was on the role of tonic and dominant in the thirty-odd measures to which we listened (and whose harmony consisted of nothing else), and the cadences through which Kuhnau articulated the form of this bit of music. The second cadence was, as might be expected, a perfect authentic cadence, but the cadence at the end of the first section was what the text calls a semicadence, and what I will probably more often call a half cadence. The second portion of class was occupied with the first example from the second chapter of Brian Hyer’s A Manual for Species Counterpoint. We noted the constituent gestures of this second-species exercise, prominent skips that served to articulate these gestures, and the role of passing dissonances in giving shape to the whole. We also explored briefly the way a sense of strong beats is enacted through the coincidence of notes of the c.f. and counterpoint (with the weak beats represented by the notes of the counterpoint that do not coincide with the notes of the c.f.). Finally, I cleared up what I meant by a consonant skip, which was simply a skip within the measure from one consonant note to another.
Week 8 (11/17—11/21)Continuation of work with second-species counterpoint; inversions of dominant seventh chords. Assignments 9 & 10.
Week 9 (11/24—11/26)Harmonization of a bass or a melody line; resolution of inverted seventh chords. Assignment 11. No class on the Friday after Thanksgiving (University holiday).
Week 10 (12/1—12/3)Continued work with harmonizing bass and melodies; further work on second-species counterpoint. Assignment 12.
FINAL EXAM: Friday, 12/12, 10:30—12:30. This exam will be cumulative.
Policies:Late assignments are not accepted for grade. GradesGrades will be determined on the basis of the two exams [40%] (Exam 1: 15%; Final Exam: 25%), homework assignments [40%], and performance in skills sections [20%]. (Note that the percentages given are approximate.)
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Text:The text for the course is the third edition of Harmony and Voice Leading by Edward Aldwell and Carl Schachter, which is available at the Seminary Co-op Bookstore, 5757 South University Avenue, and will be used throughout the year (that is, in Music 15200 and 15300, as well as Music 15100). Additional resources
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Copyright © 2008 Lawrence M. Zbikowski For inquiries about this page, or suggestions, contact Lawrence Zbikowski, Department of Music, University of Chicago. |
