21M.302 | Spring 2005 | Undergraduate
Harmony and Counterpoint II


Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Sight-Singing Laboratory: 1 session / week, 1 hour / session

Keyboard Laboratory: 1 session / week, 1 hour / session

Course Description

In this subject, we explore the harmonic, melodic, and formal practices of western music, principally the so-called “Classical” idiom of central Europe, ca. 1750-1825. Topics include a quick review of material covered in 21M.301, chromatic harmony (viio7, bII6, and chords of the augmented sixth), and chromatic modulation; lecture study and discussion are complemented by work in the keyboard laboratory and sight-singing laboratory. All areas of study will be integrated in a semester-long project of composing a theme and two variations in Classical style.

Subject Components

Required Sight-Singing Laboratory


Vocal models underlie virtually all the contrapuntal bases of our classical music (yes, even in purely instrumental idioms); hence, practice in singing classical music is one of the most efficient ways for you to internalize the classical norms of voice-leading.

The lab meets each once a week for one hour. Please be sure to bring the following materials to the first lab meeting: the required texts: Various Composers. Five centuries of choral music for mixed voices. Vol. 1. New York, NY: G. Schirmer, 1963.: Ottman, Robert. Music for sight-singing. 6th ed. Upper Saddle River, NJ: Prentice Hall, 2003. ISBN: 9780131456709., music paper, a pencil, and a tuning fork.

Required Keyboard Laboratory


Even in our modern age of computer-assisted sound manipulation, the traditional musical keyboard still provides the most efficient way for an individual to perform or improvise contrapuntal polyphony in real time, and thus receive instantaneous aural feedback.

Keyboard lab consists of a weekly session with a private piano instructor, doing keyboard exercises based on this subject but tailored to your individual skills. You are requested to work in the lab for one hour each week, during which the instructor will work with you individually for about 15 minutes.

Daily Homework Assignments

Expect to complete one assignment for each class meeting. Each late assignment is penalized one letter grade for each calendar day it is late; no assignment will be accepted more than three days late. If you must miss a class meeting, leave your work in the bin by my office door by 2:00p the day it is due, or have a friend leave it there.


Nearly every week, I will give a timed quiz (typically of five minutes’ duration). These quizzes will measure your mastery of the most basic vocabulary (triads and seventh chords) as well as some of the more important syntactic concepts of harmony and voice-leading.

Analytic Reports

You will present two or three brief oral reports to the class, lasting about 10 minutes apiece, in which you summarize the important features of a Classical variation in relation to its theme. In particular, you will seek to abstract useful procedures for transforming a simple theme into a figurated variation, so that you can share them with the class for everyone’s benefit. On the day that you report, you must submit to me by noon a copy of your handout so that I can make copies for the class. (If you miss this deadline, then you are responsible to make multiple copies for the class.)


Two class sessions are reserved for midterm tests: one on voice-leading and diatonic harmony (i.e., material covered in 21M.301), and one on elementary chromatic harmony (viio7, bII6, and chords of the augmented sixth) and modulation. Each test will last one hour.

Final Project

Over the course of the semester, you will write an original theme and variations (at least four, but no more than six) in Classical style, most likely for piano (but possibly for a small instrumental group).

Weighting of the Components of Your Semester Grade

Lecture Preparation and Participation 10%
Sight-Singing Lab 10%
Piano Lab 10%
Daily Homework Assignments 15%
Weekly Quizzes 10%
Analytic Reports 10%
Test 1 (Voice-Leading and Diatonic Harmony - Lecture 8) 10%
Test 2 (Elementary Chromatic Harmony - Lecture 16) 10%
Final Project (Theme and Variations)
(Drafts = 5%; Final Set = 10%)

Failure to complete any one of these components will result in failure as your semester grade. The labs are graded by their respective instructors; I will grade all other components.

Music Manuscript Paper

European classical music notation is a (comparatively) efficient graphic medium for conveying musical information. Unfortunately, many manufacturers don’t know (or don’t care) about the principles of proper graphic organization, so that there is much soi-disant music paper on which it’s virtually impossible to produce proper, legible notation.

There are four absolute requirements for the music manuscript paper you use.

  1. Each page must be no smaller than letter-size, and no larger than 9"x12".
    Anything smaller is probably intended for the simple jottings of small children; anything larger is probably intended for professionals writing for large ensembles.
  2. Each page must contain at least ten staves, and no more than 16 (12 is usual).
    At this paper size, nine or fewer staves would be excessively large and/or excessively far apart. The larger the staff, the more effort is required to produce appropriately round noteheads, thick beams, straight barlines, etc.
  3. The space between staves must be greater than the width of a single staff.
    With less than a staff’s width between staves, there’s not enough room for notes that require ledger lines, flags and beams when multiple voices share a staff, or analytic symbols below the bass.
  4. In each staff, the lines must be of hairline thickness.
    Ideally, the staves are printed in gray or brown ink, for further contrast between the hairlines of the staff and the slightly thicker lines of stems, barlines, etc.

At this writing, the bookstore sells two products that are acceptable

  • Roaring Spring Paper Products, 12-stave music refills
  • Roaring Spring Paper Products, 12-stave music book

Music paper may be purchased online from various vendors.

Yes, obtaining such paper requires some extra initial effort on your part, but it will make your life (and, more critically, my life) easier over the course of the semester. Properly proportioned staves will make it easier for you to produce legible notation, and heavier paper will better sustain repeated erasure.

What About Free Music Paper on the Web?

Don’t go there. Some people have made files freely available for printing your own paper. So far, I haven’t seen any acceptable music paper available in this way. It typically fails to meet requirement no. 4 above (staff lines of hairline thickness), so music written on it falls short of ideal legibility. This problem is compounded if the paper is printed by inkjet. Laserprinting achieves better hairlines, but the toner doesn’t hold up under repeated erasure; this is also true of photocopied manuscript paper.

OK…now that you’ve obtained proper music paper.

There are two absolute requirements for your use of the paper.

  1. Always leave a blank staff between notated staff systems.
    If you use every staff on the page, the marks below each bass staff (including Roman numerals and bass figures) will collide with the marks above the treble staff of the next system. For the sake of legibility, you must leave at least one blank staff between systems. (If the staves are small and the bass staff includes many low notes, phrase or pedal markings, it may be desirable to leave two blank staves between systems.)
  2. Always use only one side of the paper.
    If you write on both sides of the paper, it will be inconvenient to compare parallel passages on opposite sides of the same leaf, and it will be that much more difficult for you to spot errors in the move from the end of one page to the beginning of the next.

Music Notation Software

Music notation software (e.g., Sibelius, Finale, GNU LilyPond) is typically capable of producing professional-quality output. The problem, though, is that such software often doesn’t produce proper output by default. If you use notation software, you are responsible to learn how to edit your files to produce proper output. I will deduct points for improper notation, and I will not accept “But this is what the software does!” as an excuse. (When in doubt, consult classical scores from publishers such as Breitkopf & Härtel, G. Henle, C.F. Peters, G. Schirmer, Schott, Universal).

Course Info
As Taught In
Spring 2005
Learning Resource Types
assignment Problem Sets
grading Exams
group_work Projects with Examples