78048 - Elements of Harmony and Counterpoint

Course Unit Page

Academic Year 2022/2023

Learning outcomes

By the end of the course the student: develops faculties of intuition and intelligence of morphologies, relationships, and processes of tonality; knows how to create cognitive maps of what he/she is listening, or reading in the musical score and imagining; possesses an analytical, historical, stylistic knowledge of tonal phenomena in the evolution of Western musical thought.

Course contents

Bach's Partitas and Suites for solo instrument

An introduction to the harmonic style (including its historical antecedents) of one of the most important genres in Bach's instrumental music.

The possibilities of evolving students’ comprehension of harmony and poliphonic textures, increased by the study of this repertory.


(1) Chapters 1-6, 9, 16, 17, 20 of: W. Piston, Harmony, Norton, New York 1987 (fifth ed.).

(2) Chapters XI (pp. 113-126), XVI (165-172), XVIII (185-191), XX (210-225), XXI (226-239), XXII (240-256), XXIII (257-286) of: L. Ratner, Harmony. Structure and style, Mc Graw-Hill, New York 1962.

The notions available in this twofold integrated path, must then be reconsidered in the light of:

(3) M. Mastropasqua, Abbozzo di un nuovo sistema teorico-analitico dell'armonia tonale, in conformità alle consuetudini stilistiche di Bach (to be delivered at the beginning of the course).

Those who wish to practice further in four-part writing by means of harmonic schemes, can usefully take as models the progressions in the chapters IV to XV of: A. Schoenberg, Theory of Harmony, University of California Press, Berkeley-Los Angeles 1983.

(4) Compendio antologico di teoria musicale (to be delivered at the beginning of the course).

On the general aspects of Bach's works in object and the pieces chosen for the exam, students will autonomously find some brief references.

Teaching methods

The first half (approximately) of the course aims to understand, from the very beginning, the harmony and the four-parts writing compatible with Bach's Chorale style. Students who already know these topics, are recommended to assiduously attend the lessons of the second half of the course, more specifically dedicated to the analysis of the repertoire.

Assessment methods

The exam consists of a written test and an interview; the two parts will be assessed with one final mark.

1. Written test

Completion of a four-parts Chorale (in the Bach's style), without the Tenor and Alto voices (Bass and Treble given), assigned by the examining board on the exam day. The students’ work on the score shall also contain the symbolic indication (Roman numerals or functions) of each chord, to assess how candidates have understood and interpreted the harmonic succession implied in the given parts.

Maximum time allowed for the written test: 2 hours. Students may take the oral examination maximum on 3 exam dates following that of the written test - if passed.

2. Oral examination

(a) Assessment of basic skills in reading a musical text: intonation of a short tonal melody (in the two main clefs, in one of the 24 keys); aural recognition of intervals, chord types, principal cadences;

(b) knowledge on the topics included in the bibliography.


-Discussion of the analysis (harmony, syntax, form), previously realized by the student, of two pieces (not of the same kind - e.g., not two Gigues but an Allemanda and a Gigue) from two different harpsicord partitas (BWV 825-830), with exception of Allemanda BWV 825 and of Allemanda BWV 826;

-Extemporaneous analysis (same topics as above) of a brief extract, assigned to the student by the teacher , from Bach's Suites for violoncello solo (BWV 1oo7-1o12), or the English Suites (BWV 8o6-811) or the French Suites (BWV 812-817).

Very useful for harmonic interpretation of this last part:

Winold, Allen, Bach's cello suites: analyses and explorations, Indianapolis university press, Bloomington 2007, 2 volls. [in vol. 2, musical examples with harmonic ciphering)

The analyses will give emphasis to the interaction of vertical and linear aspects, the relationship between essential and unessential chordal elements, and between the harmonic regions touched in the piece; in the case of Clavier-Übung III, also in relation to the presence of the Chorale melody (the given cantus firmus) on which the piece is based, in its structural and tonal properties.

The scores for the exam must be free of any added notation.

It will be assessed as excellent the performance of those students achieving an organic vision of the course contents, penetrating analytically into technical details of the musical text and settling them in an organic frame of the compositional process and creating meaningful connections between this process and the perceptive and representational sphere as well as using a proper specific language. It will be assessed as discrete the performance of those students showing mostly not articulated synthesis and analysis capabilities, a correct but not always appropriate language, as well as a scholastic study of the discipline. It will be assessed as barely sufficient the performance of those students showing approximate skills in recognizing harmonic structures and relations and their meaning, or limited to a purely mnemonic, mechanical, conventional, notional cognition, or unfamiliarity with the standards of harmonic and contrapuntal analysis. It will be assessed as insufficient the performance of those students showing untrained representations of the musical text, lacking or non-existent sense of tonal orientation, gaps in the theoretical knowledge of the chords and in the relief of the energetic fluctuation inside their progressions; apparent inexperience in the intonation of even single intervals; faulty knowledge of the stylistic standards of the repertoire under examination and of the arguments of the bibliography.

Teaching tools

Students who wish to take this exam but, in a degree courses or of any sort, have already taken a similar exam (covering topics such as harmony, counterpoint, and so on), they shall contact the teacher.

Of course, to sit the examination, students are required to read music fluently, at least in the two main clefs. Those who wish to begin, may be helped by the following ideal path (the texts are not part of the exam bibliography). (1) Students are required to study "Grammatica della musica" (pp. 1083-1095) from the Enciclopedia della musica Garzanti (Torino 1996), or Otto Karolyi, La grammatica della musica. La teoria, le forme e gli strumenti musicali, a cura di G. Pestelli, Einaudi, Torino 1972. (2) Students are required to practice the intonation of intervals and of tonal melodies of any kind. (3) Students are required to make the exercises of intonation proposed in Paul Hindemith, Teoria musicale e solfeggio, Suvini Zerboni, Milano 1984.

Office hours

See the website of Mauro Mastropasqua