The Rule of the Octave: Insanguine's Partimento Rules Explained

The Galant Schemata are standardized harmonic progressions developed between 1720-1770 during the transition from Baroque to Classical music, designed to simplify the elaborate ornamentation of the Baroque era; these schemata include specific patterns like The Meyer (I-V7c-V7b-I), The Jupiter (I-Vb-V7b-I), The Aprile (I-V7c-V7b-I), The Pastorella (I-V7-V7-I), The Sol-Fa-Mi (I-II-V7b-I), The Romanesca (I-Vb-VI-Ib), and The Prinner (IV-Ib-VIIb-V7-I), which provide effective solutions for harmonic writing by employing contrary motion between outer parts, avoiding consecutive fifths, and using inversions of dominant seventh chords to create satisfying harmonic resolutions.

This video demonstrates how Johann Adolf Hasse, at age 26, fully mastered galant schemata in his 1725 aria 'Quel candido armellino' from 'Marc'Antonio e Cleopatra', utilizing the Romanesca as an opening gambit, the Ponte, the Monte, the Circle-of-Fifths Prinner, and sequences built on stepwise ascending bass segments (5-6 and 7-6) within a da capo structure to express Cleopatra's courage and equanimity.

This video explores how Mozart employed galant schemata—conventional melodic and harmonic patterns—in the great quartet from his opera Idomeneo. Robert O. Gjerdingen’s analytical framework is used to reveal that nearly every measure of the quartet involves at least one such schema. Specific schemata are linked to characters: the Triadic Descent identifies Idamante; the Meyer and Indugio accompany Ilia’s entrance; the Passo Indietro marks Idomeneo’s arrival. The Morte schema, combining a chromatic descending bass with a rising treble line, dominates the quartet, initially expressing Idamante’s emotion but later extending to all characters, including Elettra’s cry for vengeance and Idomeneo’s lament “Nettun spietato.” Two dramatic tonal digressions into D flat and C flat major are interpreted as an elaboration of the Morte’s chromatic notes, framed by the conventional Overture schema, which helped audiences accept these harmonic extremes. Mozart adheres to binary form but subverts it in the seconda parte, introducing five previously unused schemata—Monte Romanesca, Long Comma, Aprile, Corelli Leapfrog, and Quiescenza—at measure 134, coinciding with the return to E flat major. The Monte Romanesca and Corelli Leapfrog, associated with sacred music, evoke a liturgical atmosphere, transforming the operatic conflict into a metaphysical confrontation. These innovations occur as the music regains tonal stability, enabling a climactic expansion of schematic variety and expressive depth.

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.

The Galant style, characterized by clearly articulated and arithmetically balanced phrases with symmetrical lengths and motivic-harmonic parallelism, is present in J.S. Bach's Six Cello Suites written before 1723, as evidenced by the prevalence of Galant schemata (such as the Fon schema with its four-stage structure) throughout the suite movements, contrasting with the Baroque style's long, unpunctuated phrases; this finding challenges the traditional view that Bach was exclusively a Baroque composer and demonstrates that Galant phrasing was already in use by the time he composed these works, supported by historical evidence from contemporaries like Vivaldi and Kurz who employed similar techniques.

The most popular practice among Renaissance instrumentalists was creating diminutions or divisions, which involved slowing the original vocal melody down considerably and filling all the space between notes with many notes of smaller value. These embellishments included florets, scalar passages, trills, turns, or combinations thereof. There are eight 16th-century vocal and instrumental sources that present several pages of diminutions on every interval from a second going all the way through an octave, including cadences.

Before going on with the canon, Josquin decorated the line with simple diminutions at the end of both phrases. Diminutions are melodic embellishments that add beauty and refinement to the melody. This technique was commonly used in 16th-century vocal music to enhance the expressiveness of the text.

The first category of historical improvisation involves adding ornaments and diminutions upon a given part or parts. The composer supplies the basic notes, and the performer adorns the music with graces and elaborated passages. Diminutions refer to note values that become smaller and faster. The earliest treatise on this subject is Sylvestro Ganassi's Fontegara from 1535. By the early 17th century, treatises by authors like dalla Casa, Bassano, Bovicelli, and the Rognoni brothers became prominent. Students learned to fill intervals with diminutions, enabling them to perform pieces according to accepted performance practice without deep counterpoint understanding.

In Renaissance music performance, diminutions (ornamentations) are improvised embellishments that performers add during instrumental silences, particularly when the bass line plays alone, creating a more elaborate and expressive musical texture while maintaining the underlying harmonic structure.

Diminutions occupy a middle ground between true composition and improvisation. They are compositions that are halfway between a real composition and a snapshot of what the musician created in that moment. The famous diminutions contain something demonstrative, perhaps more carefully composed than true improvisation, but they are still connected to the improvisational practice of the time. The concept of 'music that never ends' (musica che non finisce mai) is central to understanding historical music practice. The term 'durezze' (hardnesses) used to describe certain passages in historical music is not the best term. These passages are not intended as dissonances to express something, but rather are often within a discourse that aims at something else, such as creating a particularly beautiful, idiomatic, and effective line.

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.

In the 18th century, keyboard musicians developed improvisational skills through partimento education, a comprehensive system where students learned to participate in musical construction by understanding consonants, dissonances, and voice-leading rules, rather than treating improvisation as a separate skill from standard musicianship. This approach, taught through systematic exercises like the rule of the octave and cadences, allowed musicians to compose, accompany, and conduct simultaneously, creating a unified musical understanding that modern music education no longer provides.

This segment examines the historical prevalence and contemporary loss of keyboard improvisation skills. Many 20th-century virtuosos like Hofmann and Rubinstein improvised during concerts, sometimes modulating between pieces or creating spontaneous variations when forgetting passages. These improvisations went unnoticed by unfamiliar audiences. The speaker advocates for classical improvisation competitions similar to jazz and pop traditions. Professional musicians, despite working for audiences, need creative freedom beyond written scores. Contemporary performers like Montero incorporate improvisations, demonstrating ongoing relevance. The speaker admits late-starting improvisation limits their own abilities, emphasizing that early exposure to these traditions develops natural fluency.

Partimento, the Italian system of figured bass improvisation, provides the essential harmonic vocabulary and procedural framework for keyboard artists to improvise fugues, as it teaches musicians to recognize and execute typical harmonic progressions, invertible counterpoint combinations, and thematic relationships that form the structural DNA of fugue writing, enabling them to create authentic historical fugue improvisations by understanding the underlying musical logic rather than memorizing specific pieces.

This video features a live clavichord improvisation performance by musician Eduardo Antonello, demonstrating real-time musical creativity on a historical keyboard instrument without post-production editing or effects.

Comparative pedagogy is a scientific discipline that identifies, analyzes, and explains similarities and differences in educational systems across countries, regions, or time periods, with its theoretical foundations developed by key authors including Jules Ferry (who proposed comparing educational establishments using anatomical methods), Michel Sadler (who emphasized the practical value of studying foreign educational systems), Hans (who focused on correlating theory with practice and analyzing factors like national character, geography, economy, and religion), and others who contributed to understanding how educational systems function within their social, cultural, and political contexts.

This segment examines Mazalevsky's pioneering work in comparative pedagogy and educational historiography. Mazalevsky conducted extensive comparative studies of European educational systems, visiting Germany, Switzerland, France, Belgium, and England, studying German pedagogy, psychology, and physiology, and examining educational institutions including kindergartens, secondary schools, vocational training programs, and teacher preparation colleges. He published systematic analyses of European educational practices in Russian journals, making him the first Russian scholar to introduce foreign pedagogical ideas domestically. His two-volume 'Outline of the History of Education and Teaching from Ancient Times to Our Day' became the first substantial historical-pedagogical work by a Russian scholar, establishing methodologies for studying educational evolution. Mazalevsky also made significant contributions to children's literature, composing the famous poem 'Pozhaluyte v shkolu' (Come to School), which became widely used in Russian primary education. He founded the Society for the Defense of the Russian Language, opposing the unchecked adoption of foreign loanwords. His work demonstrates how comparative analysis and historical research can inform educational practice and policy.

Critical pedagogy is primarily associated with Paulo Freire, who serves as the main reference in Latin America, alongside significant contributions from Henry Giroux and Peter McLaren. Freire's seminal work 'Letters to Those Who Dare to Teach' guides educators in adopting a critical pedagogy stance. The core foundation of critical pedagogy rests on emancipation and transformation, distinguishing it from traditional education that passively imposes knowledge. Comparative pedagogy relates to critical pedagogy by recognizing educational system shortcomings and seeking improvements through cross-system examination. This approach represents an alternative path that complements traditional education rather than rejecting it outright.

This section provides a comparative analysis between the 'teacher-mediator' concept from the New School movement and historical-critical pedagogy. The presentation explains that in historical-critical pedagogy, knowledge itself mediates, with the teacher providing access to scientific, artistic, and philosophical knowledge and facilitating its transposition for child appropriation. In contrast, the New School often positions the teacher merely as a companion who waits for child interest (e.g., when a butterfly enters the room). The section addresses special education considerations, noting that teaching children with disabilities follows similar principles as typical children using guided activities with concrete materials, though additional considerations are needed for different disability types. The presentation also critiques the Brazilian National Curriculum Base (BNCC) for diluting content for early childhood education, requiring teachers to recover essential content for children to master before entering elementary school.

Historical-Critical Pedagogy (Pedagogia Histórico-Crítica) is a theoretical presupposition of the Curriculum in Movement. This pedagogy, developed by Demerval Saviani, is part of a progressive, critical, and reflective educational perspective. It is based on the problematization of social reality, where students' initial practices are identified, problematized, and then modified through a process of instrumentalization. The goal is to enable students to transform society, culminating in a 'catarse' or turning point that leads to final social practice.