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Efficient Teaching: Species Counterpoint and Developing

Computer-Aided Instruction

Dr. Leon W. Couch III and Daniel GriffingConverse College Texas A&M Universityhttp://ProfCouch.us/ naxiel@neo.tamu.edu

INTRODUCTION TO SEDE

Today, many undergraduate theory textbooks incorporate rudimentary species counterpoint. Intended for mid- and large-sized classrooms, this pedagogy was designed for online delivery inorder to increase the efficiency of student learning while simultaneously decreasing instructor’stime input. Rather than relying solely on traditional master-student, trial-and-error models, thisapproach employs highly organized sequences of handouts, sample solutions, grading rubrics,and quizzes. With visual & aural computer-aided instruction (CAI) at initial stages, studentsprogress at their own pace and master required competencies with automated grading andfeedback. Student responses provide real-time data on the effectiveness of instruction. Becauseinstructors spend less time on routine drills, they devote more class time to artistic and stylisticissues, as well as demonstrating perceptual concepts. I.e., students more appreciate themethodical presentation and getting to the “musical part” of the topics more quickly.

DESCRIPTION OF SEDE

The Species Error-Detection Exercises (SEDE) teach students about two-voice speciescounterpoint. Although originally designed for first-year music-theory students, SEDE alsoworks well as a component of upper-division and graduate counterpoint courses.

The computer-aided instruction (CAI) through WebCT/Blackboard permits students to learnabout the rules, the visual appearance, the sound, and the musical effects of each species, beforethey proceed to the writing and analysis of counterpoint with an instructor. I.e., SEDE forms thefirst stage of instruction in counterpoint.

Students can learn the characteristics of species through error-detection exercises. And, thus,SEDE avoids instructors wasting valuable grading time teaching rules through multiplecomposition submissions, and it reduces the amount of class time devoted to basic rule learning. This approach thus frees instructors to concentrate on more creative work once the goals of

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SEDE are accomplished (the composition and/or analysis of counterpoints which requires moreflexible feedback from an instructor). With resubmissions permitted, the CAI allows students tolearn from their mistakes and provides automated feedback.

LEARNING GOALS OF SEDE

SEDE is designed to accomplish the following learning goals:1. Students can list the rules governing melody writing, species, and imitativecounterpoint.2. Students can compare and contrast rules between various species.3. Students recognize the visual appearance of each type of species.4. Students recognize the sound and musical effect of each species.5. Students identify good passages of counterpoints.6. Students identify errors with counterpoints.

TOPICS AND OVERALL DESIGN OF SEDE

SEDE contains seven units of two-voice counterpoint. Each unit contains three to four exercisesets comprised of five exercises.

SEDE teaches the following topics (units) in sixteenth-century vocal style: 1. Melody writing (“CF writing”). Contains one melodic line.2. First-species counterpoints. Contains a cantus firmus and a counterpoint.3. Second-species counterpoints. Contains a cantus firmus and a counterpoint.4. Third-species counterpoints. Contains a cantus firmus and a counterpoint.5. Fourth-species counterpoints. Contains a cantus firmus and a counterpoint.6. Fifth-species counterpoints. Contains a cantus firmus and a counterpoint.7. Imitative counterpoints. Contains two contrapuntal lines.

The first five units work independently and may be taken out of order. Instructors can choosespecific units and not proceed through all units. Likewise, instructors may elect to assign aportion or all of the exercise sets.

In each unit, beginning exercises concentrate on major rules and characteristics. As studentsgain knowledge and skill at error detection, exercises progress to secondary rules and morecomplicated musical situations.

THE MATERIALS OF SEDE

Each unit of SEDE contains introductory lecture notes, a grading rubric, a tutorial, and 15–20

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error-detection exercises.

The lecture notes on each unit provide a brief description of the goals and characteristics of eachspecies (two to three paragraphs).

The species tutorials for each unit show students (1) the stereotypical errors instructors find instudent compositions, (2) how to use the rubrics, and (3) what codes to enter into WebCT duringthe exercises. They are one-page long.

The grading rubrics for each unit list the rules for their respective topic. These provide thecodes students will use to take the WebCT CAI. These rules usually fit within a page.

The error-detection exercises for each unit are on WebCT. Students accomplish the learninggoals through this without instructor input required.

The SEDE materials also include installation instructions for teachers and a basic WebCTtutorial for students. Lastly, it contains a document summarizing the compositional conceptsunderlying each of the units.

INTERFACE DESIGN OF SEDE

We desired a common platform that would be relatively simple to deploy. WebCT takescare of enrolling students into the course, providing secure access to students, tracking students,and producing statistics in addition to presenting problem sets, grading, and providing studentsfeedback. This allowed us to concentrate on designing the content and developing the CAIpedagogy, rather than on programming an interface.

WebCT produces statics on student accomplishment and the assessments. Instructors can trackthe amount of time and the number of attempts individuals and classes spend on particularexercises or quizzes. The success rates on particular questions and the distribution of responsescan be observed as a group to give instructors feedback on their instruction and/or SEDE itself.

The WebCT platform, however, is admittedly not perfect. WebCT offers very few batchprocesses for the many repetitive programming tasks that a designer needs to save time. Overthe internet, the web interface is somewhat clunky and slow. Programming WebCT to accept avariety of student responses that did not strictly observe our formatting conventions was timeconsuming and hard to discover from their materials. Likewise, it was initially difficult to findout how to incorporate audio along with musical scores. Lastly, flash animation and othertechnologies might have produced better looking and more interactive interfaces that may havepermitted annotation onto the musical score and tracking musical scores while audio is playing. But, in the end, the functionality of WebCT as a whole best fulfilled our needs.

We selected answer formats that would allow students to make and learn from common

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mistakes. Interval ID, for instance, uses fill-in-the-blank in lieu of multiple choice or otherconvenient formats, so that students refine their notation. They can make capitalization errors(“”M6” vs. “m6”) and produce bad labels (“M5” vs. “P5”). The intervals were organized intorows, generally one for each measure, to ease reading.

For error detection, we also used fill-in-the-blank. Multiple choice with so many rules wouldhave been unwieldy, and the citing of measure numbers, unduly complicated. In the end, weadopted a format with “[error code] [measure numbers]”, which usually prevents wrong scoringby the computer. Without measure numbers, WebCT occasionally credited students for wronganswers. The measure numbers required forecasting the variety of student responses, as someerrors such as a leap over a barline, might be considered to be within one, two, or a span ofmeasures. All exercises were given three or more answer blanks, and unused ones require theanswer “no error” so that students must enter responses and mentally claim an exercise has noerrors.

Because we desired to make SEDE a learning tool rather than purely an assessment tool, weallowed students to take each exercise set (“quiz”) up to three times with automated feedback. We also limited the time per attempt to three hours. These limitations prevent clueless studentsfrom spending excessive time on SEDE. The instructor could then help students and reset anattempt to allow the student to try additional times with more guidance.

Students incidentally found the technical WebCT term “quiz” problematic, as the term ledstudents to stress about grades above valuing learning through multiple attempts. By avoidingthe term “quiz” and emphasizing multiple attempts with the goal of learning, the second testingphase was better accepted by students.

TUTORIALS OF SEDE

Limited to one page, the SEDE tutorials demonstrate the major rules for each species and howgeneral errors such as parallel fifths can occur within particular species. (In second species, e.g.,the presence of a passing tone does not negate parallels.) Through them, students can familiarizethemselves with the use of rubrics within SEDE and can focus upon the major characteristics andcommon problems of a particular species. Without such tutorials, the first encounters with sucherrors would be within a tested environment.

RUBRIC DESIGN OF SEDE

Automated computer grading requires a discrete number of student responses. SEDE thusprovides rubrics for each unit with a list of all possible responses a student may choose. Eachrubric was distilled from the writings of Fux’s Gradus ad Parnassum, Jeppesen’s Counterpoint,and Salzer/Schachter’s Counterpoint in Composition into a single page of rules. We then

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categorized those rules by scope and importance in order to make the lists manageable forbeginning college students.

Each rubric organizes counterpoint rules into global rules and species-specific rules. Generalerrors, such as parallel octaves, occur within all species and therefore must appear on eachrubric. Species-specific errors, such as half-note neighbor-tones, occur within some but not allspecies and therefore must appear only when applicable. The global rules are further dividedinto important rules and less important rules, so that students can initially concentrate on themost important items and waste less time sifting through too much information. A melodictritone leap, for instance, is considered a more important error than an upwards leap of a third tothe leading tone.

As a culmination of species-counterpoint studies, fifth-species and imitative counterpointemploy select rules from earlier species in addition to a few new rules specific to the new unit’srespective techniques. In this way, students can observe the few new rules for each unit whileseeing what is common to earlier studies.

The nature and description of each rule must be carefully planned and written, such that all rulesare orthogonal. Orthogonal rules ensure that any given error can only be described by one rule. For this reason, for instance, the traditional distinction between direct motion and parallel motionof perfect intervals was conflated into one rule. The rare instances of intractable intersectionsare carefully explained within the automated feedback, because such situations confuse andquickly frustrate students. Musical exceptions are generally reserved for automatic feedback(described later in this paper).

All rules need to be easily understood (“musically” intuitive) by beginners without beingoversimplified. Most rules are limited to a short sentence and lists of exceptions kept to aminimum. (A cited exception to requisite stepwise dissonances in third species, for instance, isthe nota cambiata.) Even more important, the language of each rule has been tweaked as a resultof testing in order to make statements brief, unambiguous, and somewhat self-explanatory. Anexplanation of each rule in the rubrics is avoided, as it would defeat these goals of clarity andimmediate comprehension. Verbose explanation is best left to a textbook or classroompresentation.

Although we careful designed rules to be orthogonal and immediately comprehensible,classroom testing of the SEDE was crucial. Even after two years of testing, studentsoccasionally found musical instances in which the scope of two rules overlapped (notorthogonal) or seemingly intuitive but inaccurate descriptions led to misunderstandings.

Incidentally, students reported that the rubrics were often more useful than standard assignedreadings, and that the rubrics helped them comprehend verbose discussions such as in Salzer &Schachter more readily. I.e., it formed a sort of “outline” for each topic.

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The design of rubrics was the most challenging and problematic aspect of SEDE. When welldone, the rubrics more easily generated the exercises and predictable responses from students.

EXERCISE DESIGN OF SEDE

SEDE exercises encourage students to learn the visual, aural, and theoretical nature of eachspecies. Thus, each exercise contains a musical score, an audio file, interval ID, and answerblanks.

The creation of the visual component of the exercises for a single unit followed this process:1. Develop the rubric by condensing rules from Fux and Jeppesen.2. Collect the major and minor cantus firmi from Fux and Jeppesen.3. Write an upper and lower exercise against each cantus firmus.4. Introduce errors from the rubric to the exercises.5. Transcribe exercises into Finale using the WebCT template we developed. 6. Create an exercise key by labeling all errors and intervals.7. Use image-editing software to screenshot Finale and the exercises.8. Crop exercises and export as *.gif in our naming convention.

The creation of the aural component of the exercises for a single unit followed this process:1. Export Finale file containing all exercises into a MIDI file.2. Splice MIDI file into separate pieces, one for each exercise.3. Generate *.wav files via a software sampler controlled by the MIDI file.4. Convert *.wav file into an *.mp3 in our naming convention.

Already discussed, the rubrics embody the theoretical component of the exercises; and,presumably, in-class instruction and supplementary reading from standard texts would bolsterthis knowledge. I.e., this teaching resource is intended to accompany instruction.

THE EXERCISES OF SEDE

Each exercise set has an interval-identification (ID) “quiz” and an error-detection (ED) “quiz”with five exercises. After completing an ID quiz with a 70% or higher score, students proceed toan ED quiz with the same species exercises. Students were permitted three hours on threeattempts per quiz. (Students usually invested less than an hour per quiz in a total of twoattempts.)

SEDE practices the fundamental skill of Interval ID (ID), because most theoretical observationsin species counterpoint depend upon careful study of intervals. The ID exercises are presentedvisually and aurally, and students must identify each interval between the two given voices. For

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beginning theory students, this initially proved to be quite time consuming; but, students quicklygain the requisite skill with the musical goals in mind (rather than seeing interval exercises astedious exercises as a goal unto themselves in most theory workbooks). More important, the IDquizzes emphasize the vertical as well as the horizontal nature of counterpoint. Because cantusfirmi are notated in alto clef, students develop some facility at moveable-C clefs. (The relativesimplicity of the musical excerpts prevents this aspect from being a major stumbling block or asource of frustration.) The interval ID quizzes are most appropriate for first-semester theorystudents, and WebCT can easily be programmed to omit them for more advanced students.

The Error-Detection (ED) quizzes in each unit increase progressively in difficulty. Here, theexercises contain the score, audio, and correctly labeled vertical intervals. Students identifyerrors and enter the code(s) from the rubric with the location of the error (the measurenumber(s)). Early exercise sets contain common and species-specific errors, while laterexercises focus on minor and obscure errors. Normally, each ED contains between zero andthree errors, so that exercises can demonstrate both good as well as bad contrapuntal writing. (Furthermore, excessive numbers of errors overwhelm students and does not bolster learning.) Students proceeding through SEDE gave good feedback about rubrics as well as the exercisedesign. And, in subsequent trials, I have been able to increase the efficiency and quality oflearning merely by making directions and rubrics clearer—these are generally the source ofproblems.

After the initial testing of the SEDE materials, I added automated feedback (AF) to the CAI, inorder to increase learning efficiency and reduce instructor time answering student questions. This feedback points out common mistakes, guides frustrated students, answers potentialquestions, and discusses any further musical observations in exercises. (These observationsoccur more often in later species where musical judgements become more subjective). Commonmistakes include missed and incorrectly identified items. At the beginning, some students didnot follow directions or formatting, such as forgetting to submit “no error” in blanks, and neededto be reminded to observe these requirements.

In the first exercises of each unit, the automatic feedback provides beginners significantand detailed help: the number of errors in an exercise, the approximate location of the errors,and the nature of the error (where to find them in the rubric). Students also needed to bereminded how to calculate intervals when voices crossed. In subsequent exercise sets, theamount of feedback reduces as students’ skills increase. In the second exercise sets, forinstance, the automated feedback merely comments upon common wrong answers and rarelyhints about the location and nature of the right answers. The feedback for third exercises sets islimited to consistently confusing items or ambiguous circumstances.

The automated feedback for fourth exercise sets only address musical exceptions. Theseoccur more often in third species, fifth species, and imitative counterpoint, where musicalitymore often justifies exceptions. Example musical exceptions include musical lines with aneffective climax but two literal two high points, rare items such as the nota cambiata over abarline, and so forth. In these situations, more variance in student responses is permitted:

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Students receive credit for either recognizing exceptions or marking them as literal errors. (Thisprevents frustration.) In either case, the automatic feedback throughly explains these situationsfound in real music. Some instructors may understandably elect to not introduce these ideas intheir first-year courses.

The most challenging aspect of exercise design was composing counterpoints with no more thanthree errors; that is, without introducing unintended errors. One error generally results in a hostof additional errors. Also creating good melodic lines with clearly contrasting, audible errorswas difficult. Despite the attention given to the exercises, I discovered several that literallycontained more errors than desired (up to seven). Most were musically inconsequential butliterally wrong according to the rubric. In some cases, these musically exceptional passages arenow explained in automated feedback, if very few students found these “errors. In other caseswhere students found them more often, the exercise provides more blanks for students to list allthe potential errors. (At some point, such exercises should be rewritten.) The cross-relatedtritone, error 21, was easily created and hardly noticed by students today. For this error,exercises state in the directions to enter the error code when applicable.

RESULTS AND SUMMARY OF SEDE

Students and their counterpoint composition confirmed that SEDE effectively achieved itslearning goals with a minimum of instructor time input. This anecdotal evidence can besupported from the data generated by WebCT over the past two years and from course examsgiven over a six-year period.

The main stumbling blocks involve (1) students learning to access WebCT through the computerresources of their particular institution, (2) students initially learning to using the WebCTinterface, and (3) students learning to enter error codes from rubrics in the correct format. If aninstructor spends a little time upfront to head off these problems, the instruction goes smoothlywith much less student frustration and significant time savings for the instructor for this initialeffort.

The SEDE materials were tested in two institutions with two different student populations andapproaches.

TESTS 1 & 2. I tested SEDE as a component of counterpoint instruction in freshman theorycourses at Texas A&M University (2005–2006) and at Converse College (2006–2007). For eachunit, the following procedure was followed:

1. The instructor gave an introductory lecture during one class period.2. Students then learned the rubrics through a SEDE exercise set that evening. 3. Students composed a counterpoint and received instructor feedback. 4. We repeated steps #2 & 3 until the class covered all problem sets of each unit. E.g., infirst species, students did four sets of ID and ED; and they produced four counterpoints.

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(1) The instructor explained how to use WebCT and SEDE briefly. After this overview, thebrief lecture introduced the species, concentrating on compositional approaches rather thanlearning rules or analysis. (Rules are left to SEDE.)

(2) On the first sets of ED, students usually spent thirty minutes to an hour on the firstsubmission. These first attempts were the most time consuming for students, as they werebecoming familiar with WebCT, SEDE, and the basic species rules. After reading automatedfeedback, students normally completed a second and/or third resubmission within a matter ofminutes (8–15 minutes). This increased grades and, more important, comprehension. Students were also provided paper copies of all the materials, including problem sets.

(3) Students composed their first species counterpoints on paper, employing the basic ruleslearned from SEDE. They reported that the initial counterpoints took less time to completeand certainly the quality increased in comparison to an approach with more time-consumingin-class instruction (without SEDE).

(4) On subsequent sets, students would spend twenty to forty minutes total on each SEDEset, including resubmissions. With subsequent sets, the number and obscurity of additionalrules increased. Occasionally students were frustrated by finding some miscellaneous errorswithout the generous hints provided for first sets. As previously mentioned, students wrotecounterpoints and received written instructor feedback.

Results of Tests 1 &2: Grading time was reduced dramatically, because students knew howtheir counterpoints should look and how to identify errors themselves. (In fact, studentsadmitted they often knew beforehand what errors were in their submissions!) Written feedbackon their composed counterpoints also required less instructor time, because I could cite the rubricwith its shared vocabulary and delimited number of points. The classes composed good speciescounterpoints with only two to three days spent on any given species; and, class time wasdevoted more to musical issues and composition than to basic rule learning. Overall, studentsalso admitted that SEDE helped them gain knowledge and skill at counterpoint. Furthermore,their interval identification was much, much faster and accurate than that in other sections notemploying the CAI.

Students seemed to learn the rubrics and the error-detection skills after three exercise sets (a totalof 15 exercises per species). Although the fourth set is required to cover all the rules listed in therubrics, testing suggests additional problems are gratuitous in terms of student learning. Furthermore, the exceptions and picky details of fourth sets sometimes seemed better reservedfor more advanced counterpoint courses. I.e., the fourth exercises are provided for the sake ofcompleteness and for more advanced courses.

The exercise sets cover numerous errors, but students normally make a few stereotypical errorsin their own species compositions, such as non-stepwise dissonances and parallel octaves in thirdspecies. And, thus, more exercises devoted to a smaller set of common errors might bewarranted.

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The CAI incidentally can also be compared to a paper-only beta version at Texas A&M during2004–2005. The first run with CAI was somewhat rocky, as many kinks with WebCT and therubrics were worked out that year as rubrics and exercises were being written. Studentspreferred hand grading, as it tended to yield higher a “human touch” and thus higher grades. (Their opinions and preferences were informally surveyed in class and privately in office hoursand email.) Despite student preferences, course exams over species and counterpoint-composition indicate that CAI was slightly superior, probably because of the immediate anduncompromising nature of CAI feedback. The preference for humans above computersfurthermore requires more human resources than most schools can allocate to large sections, andsuch instruction would steal too much time from traditional harmony instruction.

II. TEST 3. I also tested SEDE as a self tutorial in a graduate/upper-division counterpointsurvey at Converse College (2006-2007). Here, students learned eighteenth-centurycounterpoint in class from Benjamin’s The Craft of Counterpoint but learned about theappearance, sound, and rules of 16 -c counterpoint on their own solely with SEDE. They wereth

not required to compose any species counterpoints, nor were their species skills tested beyondSEDE.

The procedure for each unit here was as follows:1. In a few minutes, I briefly pointed out the main conceptual features of the species andoutlined how to use WebCT and SEDE.2. I required them to do only the first exercises sets of each unit without doing intervalID. The time input on these units was the same as the freshmen in the first tests. Students were also provided paper copies of all the materials.3. They were invited to do further problem sets, but only a few did so.

Results of Test 3: Students stated that SEDE helped them gain familiarity with and appreciationof species and sixteenth-century counterpoint. The slower students occasionally got confusedbetween species, with so little reinforcement though the CAI. As expected, they felt less adept atwriting counterpoint, which was neither taught nor tested. They seemed to be able to converseabout species counterpoint and seemed more insightful about two-voice excerpts in theeighteenth-century studies, making many good connections between the two styles on their own. They routinely expressed a desire to learn species techniques prior to doing eighteenth-centurystyle. And, they expressed a preference for human instruction if class time had permitted.

SUMMARY

Developing SEDE demanded much more time from the project designers than expected,requiring over 200 hours of work and over a year of testing in the classroom before any CAIcould be considered. Revising rubrics and fixing programming required approximately twoyears. And, tweaking automated feedback through two years of testing required even more timeand could use further development.

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Yet, SEDE is already successful at achieving its goals: efficient learning of two-voice speciescounterpoint while concentrating instructor’s limited time on feedback to more creative aspectsof the subject. With very little class time devoted to the topic of species counterpoint, studentsdemonstrated a good command of the rules, layout, sound, and error-detection of species andimitative two-voice counterpoint.

While at the CMS 2007 International Conference, you can try SEDE athttp://webct.converse.edu with the username “demo_student” and password “password”. Havefun!!!