Music 30A

Theory, Literature, and Musicianship I
Basic Harmony and Counterpoint
UC Santa Cruz, Fall Quarter 2012 

30A Section 01 (class# 21405)

Ben Carson | contact (click to email, or roll-over to see address. I’m also available sometimes via IM. If you’re patient.)

Office: Music Center 148

Meetings: Music Center 131 on Mondays, Wednesdays, and Fridays 9:30 to 10:40 AM

Enrollment requirements: Excellence in Music 14, or proficiency demonstrated in placement exam & permission of instructor

Office hours: Mondays 11:00a - 12:20p, and Fridays 12:30-1:30 pm, or by appointment. 

Phone:  9-5581 (I do not check voicemail frequently!)  

Adjunct instructor for Rhythm Workshops: George Marsh
Aural Skills Teaching Assistants: Jay ArmsTobin ChodosJessica Loranger 

MSI Tutor: Jennifer Lependorf

Course Catalogue Description for Music 30ABC:   


  1. Develop advanced skills in reading and writing Western music notation.
  2. Improve musicianship, through exercises in singing and keyboard playing.
  3. Learn to analyze and compose traditional tonal harmonic progressions.
  4. Learn fluency with pulse, rhythm, and meter.
  5. Learn to analyze and compose simple two-voice contrapuntal textures.
  6. Comprehend basic musical materials in the 18th-century tonal style, including rhythm, meter, intervals, chords, and scales.

Required Texts: 


*Kostka and Payne. Tonal Harmony. 6th Edition (New York: McGraw Hill). Available Thursday, October 4.

*Robert Ottman and Nancy Rogers. Music for Sight Singing. 8th Edition (Upper Saddle River, NJ: Prentice Hall, 2006). Available Thursday, October 4.


*Charles Burkhardt. Anthology for Musical Analysis. 6th Edition (New York: Cengage).

J. S. Bach. 371 Harmonized Chorlales & 69 Chorale Melodies. (Milwaukee: Hal Leonard Publishing Group, 1941).

*top priorities this quarter.

Miscellaneous Aspects of the course: 
1.              Being there:   Regardless of any reason for absence, students are responsible for completing whatever work they have missed when they are gone.  Please let me know about absences that result from health conditions, family emergencies, or major transportation accidents, and so on.  However, in any case of absence, be sure to check with a classmate for information about what was discussed on that day, and get a clear sense of all new assignments. If you can’t get that information from a classmate, please contact me via email. More than five unexcused absences from class and lab combined, or three unexcused absences from lab, will result in a grade of NP. See “Course Credit and Grading” (below) for more details. 

2.             Performance anxiety:  In class, we’ll work on your skills and your knowledge in a direct and conversational way.  But I’m never interested in getting you to prove anything on the spot.   You will find that if you can’t get the answer right away, I’ll take lead the conversation differently so the class will work on it together.  I hope you’ll find I’m pretty good at diffusing any public sense of student deficiency. 
3.             Deadlines:  Please complete your homework in clear hand-written  notation, with a pencil, and get them in on time!  Late assignments will be accepted but they will not receive full credit and I cannot guarantee that I will give them thorough comments.  This can be a problem because I expect to see improvement from one assignment to the next, so one late assignment can affect your later grades if you don’t take the initiative to get my informal comments on your progress, and keep the “conversation” going. 
4.             Communication:  I respond to most email, IM, and text-messaging within 12 hours or so, to answer important questions about course material, the assignments and so on.  I love getting emails with questions about music and the actual content of the course.  I also want to hear from you if you’re having any trouble getting the concepts, getting the homework in, or getting to class.  But please limit the use of email for excuses about already-past absences of unfinished assignments – there’s no hurry to give me that information so it’s better to focus on your work and think about what you need to do for the next class. 
Course Credit and Grading: 

Theory Lecture Participation = 5%
Theory Homework = 25%
Theory Mid-term = 10%
Theory Final = 15%
Aural Skills Quizzes (approximately 10) = 15%
Musicianship Lab* (graded separately by your TAs) = 30%

*A grade of 50% or less in the musicianship final exam will result in a credit of zero percent under this heading.  Your percentage for the aural skills portion of the grade (combining attendance, the quizzes, and the final) must also exceed 70%, in order for you to qualify for Music 30B.

More about grading: 
Grades are an evaluation of your accomplishments, not your intentions, your sincerity, or my sense of your potential. That might make some grades seem cold or harsh, but to me, it’s the only way to handle grading respectfully. I don’t want to judge your character—if I tried to do that, it would take all the fun out of the everyday challenge of learning about music. (And it puts me in a judge’s chair I don’t want to be in.) I hope you’ll be comforted to know that a C- doesn’t mean I’m annoyed at you, and an A+ doesn’t mean I’m your newest fan. It’s not personal.

If you are ever uncertain about why I’ve given any particular evaluation, please come to me with questions about it. I’ll be happy that you want to understand the assignment, or the concepts, in greater detail. It helps this course a great deal if you try to build a conversation around my written feedback about your work. 


2:1 Writing in the 18th-century Style

Basic principles of 2:1 Counterpoint in the 18th-c style 

Before composing 18th-century style counterpoints in 2:1 relationships to accompanying lines, two concepts must be understood. Both are discussed in detail in Kent Kennan’s reading from the prior week.

(1) Non-chord tones (NCTs)—any notes that deviate from the essential, and usually consonant, intervals formed between the bass and the treble in a composition. We call them non-chord tones or non-harmonic tones because they are not part of the chord or implied harmony in which essential intervals participate. See Kent Kennan’s p 40-43 for a full description of the possibilities. (Most NCTs are dissonant, but resolutions from a 6th to 5th above the bass can qualify as NCT->CT resolutions.)

(2) Essential Intervals—the harmonic intervals that define the relationship between a bass line and an additional line above it. These intervals are usually consonant and they form part of a chord that’s clearly implied as part of a progression.

1. Chords and NCTs: 2:1 writing 

a. 3 possibilities:

i. Thesis CT -> Arsis NCT. A chord occurs plainly on the strong beat, and on the weak beat, a non-chord tone connects to the next strong beat.

ii. Thesis CT -> Arsis CT. Usually both CTs are consonant against the bass, so they are often a skip of a third. Note: 

iii. Thesis NCT -> Arsis CT. This possibility creates “accented NCTs,” especially accented passing tones, neighbor tones, and appogiaturas. (This is a very good thing; the presence of the NCT on the strong beat increases our attention to the resolution and can intensify harmony and motion.

b. In all of the above possibilities, non-chord tones are resolved by step, except in the case of escape tones. NOTE: Appogiaturas and escape tones involve three notes: the outer two notes are both chord tones, and are not the same tone. The escape tone (E) is a step away from the first note; an appogiatura (App) is a step away from the second note. (Usually the step and the leap on either side of an App or E are in opposite directions.)

c. Suspensions:

 i. All suspensions consist of a consonant preparation note (P), a dissonant NCT (Sus or S), and a step-wise resolution (R).

ii. In 2:1 counterpoint, P occurs on a weak beat (arsis), S on the following strong beat (thesis), and R on the following arsis.

iii. In more complex rhythmic situations (with triplets, 16ths, etc.) the preparation may not be shorter than the NCT. 

2. Step-Skip rules

     a. Avoid “step-skipping” (moving by step, and then immediately by skip in the same direction), such that the skip lands on a thesis. This has the effect of “halting” the melody or disorienting us to the meter.

     b. When step-skipping in the same direction to land on arsis, compensate the skip, with a step in the opposite direction. This has the effect of being awesome.

3. Interval Succession:

a. Build your counterpoint on a structure of imperfect consonances (ICs). 3rds and 6ths guiding the relationship between bass and treble. This does not mean that ICs always fall in metrically strong positions, but PCs (5ths & 8ves) on strong beats should be avoided, and dissonances (2nds, 4ths, 7ths, and tritones) on strong beats should generally resolve immediately to ICs. It’s often useful to start out writing a counterpoint as an interesting (non-repetitive) series of ICs, which you then connect with other intervals via passing and ornamental gestures.

b. PCs 

i. - do not write parallel 5ths or 8ves from arsis to thesis or from thesis to thesis. Exceptions are possible when one interval (especially a 5th) is a non-essential interval. (Kennan p 48.)

ii. - a 5th followed by an octave, or an 8ve followed by a 5th, should also be avoided, except when the succession is part of a standard cadence. (5^ in the bass and 2^ in the soprano forms a fifth; both notes can move to 1^, forming an 8ve, if this gesture is cadential. But other movements from PC to PC are not acceptable.)

iii. - avoid approaching PCs by similar motion, except at cadences (called “direct” or “hidden” 5ths & 8ves)

iv. - avoid PCs on strong beats, except at cadences

v. - avoid approaching PCs by leaps in both voices

4. Harmonic movement and clarity

a. Avoid V-IV; maintain harmonic movement that keeps the variety of chords on a trajectory to the dominant, increasing the resolution

b. 6/4 chords are unstable, due to the P4 above the bass, and they must have a passing, arpeggiating, or neighbor-note role. DO use them in these ways:

i. in a bass arpeggiation: when the bass part moves through all the notes of the triad of the harmony it supports, it will obviously assume the 5th of that triad at one or more points, resulting in a 6/4 chord. It works because usually one of the other bass notes is the “real” bass for that part of the harmonic progression.

ii. in a pedal progression: when a root-position triad is proceeded and/or followed by simultaneous upper neighbor tones to both the 3rd and the 5th of the chord. It works because although the upper neighbors form a 6/4, they function as ornaments to the 5/3.

iii. in a cadential 6/4 construction (K6/4): this is a variant on the pedal progression, with the 5/3 chord functioning as cadential V. It’s worth a special mention because the 6/4 upper neighbor notes can be passing notes, appogiaturas, or suspensions, or a combination of two NCT types. (Most of those alternatives are not so elegant when they fall outside this cadential formula.

iv. in a passing progression: When bass notes a third apart are bridged by a passing tone, and the outer pair are part of the same harmony, the bridging note often forms a 6/4 chord with other notes that work well as passing tones. It works because, like examples i-iii, the chord is a collection of ornaments between two stronger chords.


c. Avoid repeating the bass note in a counterpoint, either from arsis->thesis, or from thesis->thesis. (in other words, from one thesis to the next, the bass should be in some kind of motion.) Common exceptions: when the bass voice forms a suspension or anticipation, or at the beginnings of pieces, where the tonic chord is being established for the first time.

d. Avoid implying a suspension (by tying a note from weak to strong) where there is no suspension (see 1c above)


3:1 and 4:1 writing with 2 parts.

First, let’s review. We’ve had a lot of guidelines and rules so far about melody and counterpoint in the baroque style. But there are ways to summarize them quickly:

I. Counterpoints form at least one “essential interval” with every cantus firmus note. Essential intervals need not occur on the thesis. Most essential intervals in 2-part writing imply a triad. Inessential intervals—usually dissonances, but not always—must behave like one of several formulae for non-chord tones.  

[ —- > This is covered in rule 1 (a, b, & c) of the post above: ”2:1 writing in the 18th-c style”]

II. Step-skip rules: steps followed by skips in the same direction often create a swooping or stalling motion that feels unbalanced. Two rules are designed to fix that problem. (1) Avoid stepping to weak and then skipping to strong in the same direction. (2) Compensate all step-skips. 

 [ —- > See rule 2 (a & b) of the 2:1 writing rules.]

III. Interval succession: 

i. Do not write || PCs (parallel perfect consonances). [See Rule 3b:i for a complete description.]

ii. Write in such a way that, except at the beginning and at cadences, imperfect consonances occur regularly, and leave perfect consonances “mobilized” and “transient.” [See Rule 3a.]

(This means not “exposing” the stability of PCs by writing them successively [Rule 3b:ii], or approached by leaps in both voices [3b:v], approaching them similar motion [Rule 3b:iii], or landing on them at strong beats [3b:iv].


Now, as we add more than one note between the “theses” of the cantus firmus (the given line against which you are writing a new line), we have just a few more rules to keep in mind.

Crucial Rules

1. Hidden parallel 5ths and 8ves

- Take care not to lose track of perfect consonances, now that there are more notes. Any 5th or 8ve formed on weak or strong subdivisions of a given beat or beat, followed by the same interval on the following thesis, forms problems with parallelism.

2. Dangling dissonance

- Do not write a dissonant note at the end of a stepwise run of notes, unless it properly resolves by step, as an NCT. Escape tones are difficult, and inadvisable as “dangling dissonances.”

3. Harmonic clarity

- Is always important in this style. To proof-read against “harmonic ambiguity,” consider that whenever perfect consonances are involved, there should also be a full triad involved.

Some other issues to look out for

1. UNITY—Try to avoid using too many different “shapes” in a single phrase. Repeating the same shape without any deviation would be overdoing it, but try to “reduce re-use and recycle” 1 or 2 patterns, varying and contrasting occasionally.

2. Movement is the goal. Avoid patterns that involve repetition within a single group of 3 or 4, especially repetition across from weak to strong.

3. When writing arpgeggiations (Kennan calls them “broken chords” on p 64), take care not to produce parellel 5ths or octaves that would result if the chords were collapsed onto a single point in time. For example, a series of triads, played from the 5th to the 3rd to the root in each case, sounds just as awkward as a succession of parallel fifths produced between simultaneous notes.