Theory History

The History of Music Theory: 1700 to 1850: An Outline.

Compiled by Daniel Robbins for PhD Qualifying Exam from tutorial sessions.

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Figured Bass

General concepts of the Figured Bass school:

A. Development of the Basso Continuo.
B. Rule of the octave.
C. Importance ofthe consonant triad: Heinichen's Trias Harmonica.
D. Inversion of chords: Rameau's clarification of Harmonic Inversion, Fundamental Bass, and Harmonic Generation.

Johann David Heinichen: Der Generalbass in der Komposition,1728.

A. Fundamental clavis and the intervallic arrangement of chords.
B. Classificaton of intervals.
C. Two systems of chordal classification.
D. Reform of key signature notation relevant to the modern major and minor system.

Johann Mattheson: Kleine Generalbass Schule, 1735.

A. The perfect harmonic triad.
B. Methods of chordal classification:

1. Consonant and dissonant chords distinguished according to interval.
2. Chords of most and least common usage.
3. Chords at the diminished, minor, major, and augmented second.

C. Rules of chordal resolutions.
D. Modal system.

Johann Philippe Kirnberger: Grundsatze des Generalbasses; Die wahren Grundsatze zum Gebrauch der Harmonie, (1773); Die Kunst des reinen Satzes in der Musik, (1774-79).

A. Chord origins not based on chordal generation.
B. Method of harmonizing the major scale according to rule of the octave principles.
C. Distinction of ascending leading-note (Rameau's major dissonance) from the descending leading-note (Rameau's minor dissonance).
D. The consonant triad.
E. The dissonant essential chord of the seventh.
F. Accidental (zufallige), non-essential dissonant combinations.
G. The passing seventh.
H. Chord of the augmented sixth.
I. Consonant and dissonant form of the six-four chord.

C.P.E. Bach: Essay on the True Art of Playing Keyboard Instruments, (1753, 1762).

A. The Triad as the perfect consonant chord.

1. Intervallic structure.
2. FIgured bass indication.
3. Distribution of chord tones.
4. Doublings.
5. Voice leading.

B. The diminished triad.

1. Intervallic structure.
2. Figured bass indication.
3. Distribution and doubling of chord tones.

C. THe augmented triad.

1. Intervallic structure.
2. Figured bass indication.
3. Doublings.
4. Resolution of the augmented fifth as a dissonance.

D. Chord of the second.

1. Intervallic stucture.
2. Resolution of the second as a dissonance.

a. Tied note.
b. Passing tone.

F.W. Marpurg: Systematische Einleitung in die musikalische Setzkunst nach den Lehrsatzen des Herrn Rameau, (1757).
Handbuch bei dem Generalbass und der Komposition, (1755-58).

A. Marpurg as a disciple of Ramesu.
B. The combined Rameau-Marpurg system.
C. Harmony as developed from the scale.
D. Harmonic significance of intervals.

Daniel Gottlieb Turk: Kurze Anweisung zum Generalbaßspielen, (1791, 1800).
Klavierschule (1789).

Klavierschule

1. Exceeds its precursors by C.P.E. Bach and Marpurg in its range and thoroughness.
2. The last textbook of the first generation of teaching manuals of keyboard instruments before the era of the hammerklavier.

Kurze Anweisung

1. One of the last textbooks in the declining tradition of thoroughbass.
2. Underwent a 5th edition through the efforts of J.F. Naue some 50 years after it first appeared and was used by Beethoven in 1808.

C. Unfinished Violinschule, (ca. 1799).

Georg Muffat: Regulae Concentuum Partiturae, (ca. 1699).

A. Outstanding for its large quantity of fully figured and realized examples.
B. Although Muffat has a concern for generally applicable rules, he does no lose sight of actual practice.

1. Sounding, mi agains fa is accep[table in certain circumstances.
2. Full harpsichord doubling not strictly according to the rules.

C. The common chord.

1. Intervallic structure.
2. Doubling.
3. Resolution of the third.

D. The prepared seventh.
E. The unprepared seventh.
F. The passing seventh.
G. The augmented sixth.

Jean-Philippe Rameau: Traite de L'Harmonie Reduite a ses Principes naturels, (1722).

A. Scenario.
B. Mathematical manipulation of thirds.
C. Intervals arising from the partial series in an order of decreasing perfection.

1. Octave provides for inversion of intervals and chords by serving as a central bounday.
2. Fifth is the basis for all harmony.

E. Inversion theory.

1. Primary consonance can never be regarded as the inversion of a secondary consonance.
2. The secondary depends on the primary for its definition.

F. Explanation of dissonance.

1. The difference between consecutive consonances.
2. Alteration of consonances chromatically.

G. Principles for defining a chord.

1. Chord may not exceed the range of an octave.
2. Fifth is the basis of all chords.
3. Either of the two thirds may determine the construction of the chord.

H. Augmented and diminished chords not recognized because they do not contain a perfect fifth and two thrids.
I. The dominant seventh chord serves as a model for the treatment of dissonance.

1. Minor dissonance: dissonance between the root and seventh.
2. Major dissonance: dissonance between the major 3rd and the 7th.
3. The major third ascends.
4. The minor third ascends.

J. All chords derived from the perfect major triad and the dominant seventh by manipulating the different kinds of thirds.
K. Bass represents the lowest and heaviest sound but not necessarily the root of chords (that is fundamental bass).
L. Voice leading.

1. Bass should proceed by consonant intervals.
2. Upper parts should move diatonically and more quickly than the bass.

M. Cadences.

1. Perfect cadence: Five7-one.
2. Irregular cadence: bass ascends a fifth.
3. Broken cadence: Five7-six.
4. Interrupted cadence: Five7-Five7 of six.

N. Tonic note alone bearing the perfect chord serves as the basis of tonality.
O. The perfect cadence builds the major mode from a movement of tension to repose (from less perfect to perfect).
P. Notes contained within the octave according to an established proportion of tones and semitones (scale degrees).
Q. Same tonic note may bear two modes, distinguished as major or minor, depending on the type of third within the tonic chord.
R. Rule of the octave.
S. Chromaticism used as chains of dominant-seventh resolutions.
T. Harmony is the sole basis for music and produces the greatest effect on the listener (as opposed to Gasparini, who felt that melody was the sole basis).

Counterpoint

Johann Josef Fux: Gradus ad Parnassum, (1725).

A. The study of fugue as central to Fux's work.
B. THe church modes.

1. The diatonic system based on the mi/fa half-tone step.
2. Fux as a disciple of Palestrina.
3. the 16th Century polyphony as the ultimate standard of musical strictness and purity.
4. Construction and illustration of the modal system.

C. Imitation.

1. Definition.
2. Examples.

D. Fugue.

1. Fugue, as distinguished from imitation.
2. Entrances of the voices and thematic construction according to the nature of the modes.

Giambattista Martini: Essemplare o sia saggio fondamentale prattico di contrappunto fugato, (1774, 1775).

A. THe didactic method of Martini.
B. Two-part fugue.

1. Clarification of the definitions of duo and duet (differences).
2. Duo by Giacomo Antonio Perti.

C. Three-part fugue: Solfeggiamenti by Cristoforo Baresana.
D. Four-part fugue: Four-part Dixit for voices and instruments by Angelo Predieri.

Friedrich Wilhem Marpurg: Abhandlung von der Fuge, (1753, 1754).

A. Marpurg as an interpreter of Bach.
B. Imitation as distinguished from repetition and transposition.
C. Registers of voices.
D. Species of imitation.

1. Imitation at the unison: imitatio homophonia.
2. Imitation at the upper or lower second: imitatio in secundo superiori ossia inferiori.
3. Imitation at the upper or lower third: imitatio in hyperitono ossia in hypoditono.
4. Imitation at the upper or lower fourth: imitatio in hyperdiatessaron ossia in hypodiatessaron.
5. Imitation at the upper or lower fifth: imitatio in hyperdiapente ossia in hypodiapente.
6. Imitation at the upper or lower sixth: imitation in hexacordo superiori ossia inferiori.
7. Imitation at the upper or lower seventh: imitatio inheptacordo superiori ossia inferiori.
8. Imitation at the upper or lower octave: imitatio in hyperdiapason ossia in hypodiapason.

E. Types of harmonic motion.

1. Direct or similar: modus rectus.
2. Indirect or dissimilar: modus contrarius.
3. Oblique: modus obliquus.

F> Types of melodic motion.

1. Similar: imitatio aequalis motus.
2. Dissimilar or inverted: imitatio inaequalis motus.

a. Strict: al contrario riverso.
b. Free: al rovescio.

3. Retrograde: cancrizans.
4. Inverted retrograde: imitatio cancrizans in motu contrario.

G. Rhythmic proportions of imitation.

1. Augmentation: imitatio per augmentationem.
2. Diminution: imitatio per diminutionem.
3. Interrupted imitation: imitatio interrupta.
4. Imitation in contrary rhythm: imitatio per arsib et thesin.

H. Imitation in double counterpoint Iinvertible imitation): imitatio invertibilis.
I. General categories of imitation.

1. Periodic: imitatio periodica (incidental or formal).
2. Canonic: imitatio canonica.

J. Fugue: generla definition and number of voices.
K. Formal proportions of the fugue.

1. Opening statement: phonagogos.
2. The Answer: comes, vox consequens.
3. The exposition: repercussio.
4. Counterpart or counterpoints.
5. Episodes.

L. Types of fugue.

1. Regular: fuga propria

a. Strict: fuga obbligata
b. Free: fuga libera.

2. Irregular: fuga impropria.

M. Simple and multiple fugues.
N. Fugues distinguished according to the type of imitation.

1. By the interval of the answer.
2. By melodic motion of the answer.
3. By change of note values of the answer.

a. Fugues by augmentation.
b. Fugues by diminution.

4. Fugues by imitation in contrary rhythm.
5. Fugues with interrupted imitation.
6. Fugues combining all the mentioned devices: fuga mixta.

O. Ordinary and extraordinary fugues.
P. Types of fugue according to the note progressions within the theme.

1. Stepwise motion: fuga composita.
2. Motion by skip: fuga incomposita.
3. Ascending note direction: fuga authentica.
4. Descending note direction: fuga plagalis.

Johann Mattheson: Der volkommene Kapellmeister, (1739).

A. Basic approach aimed at both the professional and amateur.

1. Diagram for the construction of the tonal answer.
2. Conciliato modorum.
3. Ratio between frequency of entrances and the basic tempo of the composition.
4. Duple meter yielding to a certain element of seriousness.

B. Themata.
C. Moduli.
D. Loci topici: locus natationis.

1. Time value of the notes.
2. The interchange or exchange of notes: evolutio.
3. Repetition: clausula synonyma; answer: Wiederschlag / repercussio.
4. Canonic imitation.

Ornamentation

General concepts of the Ornamentation school of music theorists.

A. Later Baroque ornamentation, harmonic as well as melodic: long appoggiaturas give rise to harmonic discrepancies when ornament is sounded with the original note.
B. Vocal ornamentation in later Baroque music.

1. Ornamentation mainly empoyed in declamatory sections.
2. In simple strophic songs and all songs built around repeat structures, gradually increased ornamentation builds interest.
3. Dr. Burney: History of Music (summary of ornamentation).

C. Instrumental ornamentation in later Baroque music.

1. Slow movements require ornamentation for enrichment and diversification; quick movements, if at all, for additional virtuosity.
2. C.P.E. Bach: Essay treatment of ornamentation.
3. Burney.

D. Concerted ornamentation in chamber and orchestral music.

1. Joachim Quantz: Essay (flute playing).

a. In a trio sonata, little ornamentation is used, and the second part must not be ornamentally overshadowed by the first part.
b. In a trio, both parts must sound the same embellishment at the same time.
c. In a quartet there is even less opportunity for overly florid ornamentation.
d. There is more freedom in a concerto for ornamentation, especially in the Adagio.

E.National differences in embellishments.

1. Quantz:

a. Pieces composed in the French style encompass composed appoggiaturas and trills, leaving little opportunity for improvised embellishment.
b. The simpler music of the Italian School leaves greater room for spontaneous ornamentation.

2. General comments concerning late Baroque ornamentation: Tosi. Opinioni.

a. Keep embellishments idiomatic to the instrumentation
b. Seek simple and natural solutions for all ornamentation.

F. Jean-Henri D'Anglebert

1. Harpsichord music represents the French school between Chambonniere's two Livres de clavecin in the early 1670's and the publications of the first decade of the 18th century.
2. Major contribution to the evolution of French keyboard ornamentation.
3. His table of ornaments is the most complete in the French classical repertory and contains many new signs that later became common to Baroque music in general.

G. Giuseppe Tartini

l. Pre-Classical style as setting for ornamentation.

a. Growing upper voice supremacy.
b. Increasing harmonic support function of bass lines.
c. Gradual shift from motivic interest to the complete phrase.
d. Frequent echo effects.
e. Elaborate cadential formulae.

2. Il Trattato, (1754).

a. Attempt to reconcile empirical observation with classical harmonics and the laws of physics and geometry.
b. Difference tone (terzo suono).
c. Melody.
d. Cadence types.
e. Dissonance.
f. Scale structure.
g. Harmonization.

Francois-Joseph Fetis: bringing the tradition into the 19th century.

A. Through his writings he tried to develop the concept that art does not progress, it simply changes.
B. Biographie universelle des musiciens, (1835-44) contains a large amount of information about his contemporaries.
C. Equisse de l"Histoire de l'harmonie consideree comm art et comme science systematique, (1840) shows the historical sequence of musical events as the development of a musical language.
D. Philosophie generale de la musique (unfinished).
E. Concerts Historiques: important concerts at which Fetis gave commentaries on performance practices and ornamentation.
F. Numerous studies that remain unfinished.

1. Edition of early theoretical writings.
2. Anthology of organ music.
3. Historical anthology of piano music.
4. Collection of vocal music from all countries.

G. Methode des methodes de chant: inventory of didactic 18th and 19th century Italian, French, and German works from which he extracted material for the training of singers and for the categorization of vocal embellishments.
H. Methode des methodes de piano: utilizes performance practice and examples of keyboard ornamentation from Bach, Scarlatti, Clementi, Hummel, Beethoven, and Liszt in an attempt to revitalize virtuosity.

Other theorists: Vogler, Sechter, and Czerny have some peripheral roles in the development of keyboard performance practice.