Double Counterpoint Schemata in Partimento Practice

The Prinner is a galant voice-leading schema identified by Robert Gjerdingen, characterized by a treble line descending from scale degree 6 to 3 while the bass descends from 4 to 1. It is often termed the Prinner riposte due to its typical function as a response or continuation following preceding musical material. Rather than a single fixed pattern, the Prinner is better understood as a family of closely related schemata, including the Stabat Mater Prinner, the Circle-of-Fifths Prinner, the Modulating Prinner, and the Prinner Cadence. These variants are illustrated through examples from composers such as Mozart, Haydn, Beethoven, Pergolesi, J. C. Bach, Couperin, and others. Additional resources for study include Gjerdingen’s "Music in the Galant Style," William E. Caplin’s analysis in "What is a Cadence?" (2015), and Open Music Theory’s schema page. Specific YouTube examples demonstrate each variant, such as Mozart’s Clarinet Quintet for the Prinner Cadence and Marcello’s Oboe Concerto for the Circle-of-Fifths Prinner. The schema was not confined to Europe; it was imported to the New World and employed by composers in Mexico and Brazil, as documented in studies by Olga Sánchez-Kisielewska and Guilherme Aleixo da Silva Monteiro. These analyses confirm the Prinner’s presence in Hispanic and Brazilian sacred and instrumental music of the 18th and early 19th centuries, highlighting its transatlantic influence within the galant style.

The soprano solo "Amplius lava me" from Andrea Bernasconi’s surviving D-minor Miserere is analyzed as a dense application of galant schemata within 69 measures. At least thirteen distinct harmonic-melodic patterns are identified: Sol-Fa-Mi, Heartz, Converging Cadence, Fenaroli, Passo Indietro, Do-Re-Mi, Ponte, Lully, Fonte, Monte, Circle of Fifths Prinner, Morte, and Volta. The movement is in binary form, with a strong cadence in the relative major at the midpoint. Despite this structural symmetry, melodic parallelism between the two sections is minimal, limited only to the recurrence of the Fenaroli schema and the final cadences following it. The schemata function as compositional building blocks, providing structural and expressive material without relying on traditional melodic repetition. The Volta schema, identified by Nate Mitchell, is noted as a galant gesture of culmination. The analysis is supported by a timestamped schema script that maps the occurrence of these patterns throughout the performance. The work is presented as a sacred masterpiece from Mozart’s Munich context, with further study recommended through Christoph Riedo’s edition (Edition Kunzelmann) and an accompanying Academia.edu overview. The performance is by I Barocchisti under Diego Fasolis.

Schémas galants are harmonic formulas developed by Robert Gjerdingen that analyze recurring patterns in Baroque music, enabling musicians to improvise by understanding standard harmonic progressions like the German sixth, primary progression, and question-answer structures, which were historically learned through copying and practicing these formulas.

The instructor recommends Robert Gjerdingen's book 'Music in the Galant Style' as a Western music theory book that takes a similar approach to Arabic music. The book shows that in the 18th century, musicians like Mozart knew specific chord sequences (called schemas) that were built up and used as vocabulary for building songs. This demonstrates that the approach of learning musical vocabulary and expectations is universal across musical traditions.

Musical schemata (esquemas) are standardized harmonic patterns introduced by Robert Jingan in 'Music in the Galant Style' (2007) that serve as foundational formulas for both composition and improvisation in Baroque music. These patterns, which typically involve two or three voices, include specific bass movements (such as descending scales, fourths, fifths, and pedal points) combined with characteristic harmonic progressions like second-to-sixth resolutions, seventh-to-sixth movements, and cadential formulas. Key schemata include the lament bass (used for expressing sadness), the fa-bordón (parallel thirds and sixths), the Do-Re-Mi opening pattern, and various cadences (simple, compound, double, Neapolitan, and Meyer). Understanding these schemata enables musicians to create coherent, historically-informed improvisations by recognizing and applying these recurring harmonic structures.

Preluding and improvisation were essential practices from the Baroque through Romantic eras. Practical reasons included warming up hands in cold rooms and bridging between pieces in distant keys. Aesthetic reasons, as expressed by Franz Liszt, involved preparing the audience emotionally and spiritually before the main piece. Historical improvisation can be learned through specific sources: Czerny's 'Art of Improvisation' and 'Art of Preluding,' Clara Schumann's preludes for her pupils (which include passages, harmonies, and full cadences leading into pieces), and Hummel's 24 preludes. Clara Schumann's preludes demonstrate how to take a motive or rhythmic structure from a piece and create a prelude that leads directly into it.

The instructor demonstrates how to combine all the learned schemata into a complete improvisation. By playing the different patterns in sequence (from beginning to end), a complete musical piece can be created. The instructor shows how these simple patterns, when combined, create something that sounds sophisticated and effective. This demonstrates that complex-sounding music can be created using basic building blocks.

Historical improvisation is not creating music from nothing but building upon established foundations including theoretical bases (chord structures), practical bases (piano exercises), and rhythmic bases. The term 'historical' refers to the specific time period defining boundaries: Baroque (1600-1750), Classical (1750-1820), and early Romanticism. This music was originally composed for keyboard instruments like organ, harpsichord, and clavichord, adaptable for modern piano. Key rules include specific consonance and dissonance patterns where dissonances like the seventh interval rarely appear without preparation. The 7-6 sequence is fundamental, where a prepared seventh resolves to a sixth, creating characteristic musical phrases.

Baroque keyboard music (1600-1750), exemplified by composers like Bach and Scarlatti, is characterized by three key elements: (1) strong improvisational elements where performers created right-hand melodies from figured bass chord symbols, (2) counterpoint involving completely independent melodic lines in both hands that support each other harmonically rather than one hand accompanying the other, and (3) distinctive instrumentation using harpsichords or clavichords which produce harsher, more detached sounds compared to modern pianos, limiting the expression of subtle emotions that became possible later in the Classical era.

The penultimate bar of the early version of the Prelude in C major is very similar to a C-major Prelude by Johann Kaspar Ferdinand Fischer. Fischer's music was an important source of musical ideas and material for both Well-Tempered Clavier projects. Alfred Dürr's reconstruction of stage two shows the newly expanded version from 17 to 34 bars. The Prelude has doubled in length by transplanting bars 5 to 14 on the left-hand side in blue and moving them to the top of the second page, transposing them into the subdominant key (an upward transposition). Two new bridge bars (14 to 19) were composed, and on the second page bars 28 to 31 and the coda 32 to 34 were added. There is also a change at the beginning instead of one note, there are now two notes. Stage three consists of major additions and revisions which further hone the contrapuntal lines and increase the density of chromatic notes. At bar 11, Bach introduces a wonderful Neapolitan harmony with the note E-flat (significant for C major as the minor third). He does the same thing at the equivalent place (bar 26 on the second page). At bar 14, he rewrites the first of his previous transitions, now sounding smoother to F major with new notes (C-sharp to take us to D minor, B-flat again that Neapolitan relationship). At bar 22, he makes a fundamental change to the harmony, going to G major and ups the ante with C-sharp. The final version in Out Nichols' manuscript (1744) has revisions that fall into three categories. They refine the voice leading (bars 11 and 25). They fill in a lot of the semi-quaver patterns with additional demi-semiquavers. There is one single slur (bar 21) which groups together 5 demi-semiquavers or fourth demi-semiquavers at under semiquaver. This is the version familiar to most performers. There are further variants which only performers can add and judge, such as those highlighted in Andreas Schiff's 2018 performance. The variants include repeating the top note in bars 3-4 to hear the full seventh, preferring D-natural at the end of the sequence in bar 19 rather than D-flat, and adding a very short ornament appoggiatura in the much-discussed fissure bar.

Partimento provides a systematic approach to understanding musical structure through bass line development and upper voice reconstruction. The method teaches how structural melodies are created through the interaction between bass lines and upper voices, allowing musicians to reconstruct multiple bass lines from upper voice patterns. This bidirectional understanding enables flexible composition and improvisation. The Partimento method involves studying each pattern separately before combining them, with a recommended approach of studying one pattern per day or week to develop strong compositional abilities within one year.

Bach's Well-Tempered Clavier is considered the 'Old Testament of music' by musicologist Hans von Bülow, with Beethoven's sonatas representing the 'New Testament.' This collection contains an unfathomable diversity of styles, from strict counterpoint to five-voice writing, representing virtually every musical tradition of the period. It can be used as daily practice material by playing one prelude and fugue in a different key each day. Bach's two-part inventions are excellent for learning composition because they contain multiple compositional elements in a compact form, including imitation, modulation, the role of octaves, cadences, and ornamentation.

The Well-Tempered Clavier represents one of Bach's most significant contributions to Western music literature, comprising two volumes of 24 paired preludes and fugues spanning all 24 major and minor keys. Originally intended for musical youth desiring knowledge and advanced students, these works became foundational for pianists worldwide, earning the title 'old testament of pianists.' The analytical approach involves examining the subject (principal motive with pitch patterns and harmonic implications), answer (at a fifth interval), counter-subjects working contrapuntally, episodes with techniques like invertible counterpoint, stretto, augmentation, and diminution. Understanding overall design through sectional organization, harmonic progression, cadences, and cross-sectional relationships reveals the character, mood, articulation, dynamics, and realization of elements within each fugue.