A New History of the Humanities: The Search for Principles and Patterns from Antiquity to the Present (Part II)
Musicology
The oldest science is music with the central question in harmony theory being whether the constant intervals (harmonies where separate notes dissolve in each other) are based on an underlying system. Pythagoras (c.570-495 BC) believed they were and made the consonances coincide with the first four whole numbers (1, 2, 3, 4), the sum of which is equal to ten. The Greeks generalized this view to the world – the harmonia mundi – where it can be described using simple mathematical proportions like music. The Music of the Spheres saw the relative distances between the seven planets correspond to the ratios of the musical intervals: Sun, Moon, Venus, Mercury, Mars, Jupiter, and Saturn. Pythagoras added music to astronomy, geometry, arithmetic and later the sophists included it in grammar, logic, and rhetoric.
However, there were problems with the Pythagorean system, such as the third and sixth intervals. The third interval was consonant but in the Pythagorean system they corresponded to a more complex ratio (64/81) than the dissonant second (8/9). The system also did not explain why the simple ratio 8/9 (the second) sounded dissonant while the 3/4 (the fourth) sounded consonant. Aristoxenus (c.375-c.335 BC), the first musicologist of antiquity, contended that it was better to sing and play what sounded good rather than be governed by mathematical proportions: empirical findings were to take precedent over theoretical considerations. He still retained the formal principles to the study of music, unlike his opponents the “harmonists” who did not want to apply any formal principles, but ultimately believed that empiricism had the final word.
Aristoxenus also studied melody and established axioms and theorems to govern it. These twenty-five “natural melodic laws” regulated the Greek musical tradition. Unfortunately, the oldest surviving Greek melodies were composed approximately two hundred years after Aristoxenus. Nevertheless, Martianus Capella’s (c. 410-2) Nupitae Philologiae et Merurii adopted the Aritoxenus’ perspective on harmony and defined early musicological knowledge in medieval Europe, along with Boethius’ (480-524) De institutione musica, which espoused a Pythagorean view.
Unlike the other artes like grammar, logic, and rhetoric, music underwent as a substantial change from Rome to medieval Europe with the emergence of the Gregorian chant. The monk Hucbald (c. 840-930) wrote the first work in European music theory, De harmonica instiutione, where he guided singers through the theory of music on the basis of well-known hymns to make them aware of the distances between different tones and the harmonic way in which the tone system was ordered. He also improved the existing musical notation for Gregorian chants by including indications of the exact pitch. Guido d’Arezzo (991-1033) later established staff notation that replaced neumatic notation, with his Micrologus being the second-most-widely distributed work on music after the writing of Boethius.
Whereas these works were concerned with musical notation of the Gregorian chant, the Musica enchiriadis appeared at the end of the ninth century that tried to establish a system of rules for polyphonic composition. But the rules were so complex that there was a shift from rules to examples in its description and therefore it did not yield a musical theory. The development in notation continued so that when the Ars Nova appeared in 1318 rule-based organum composition had ended. This freer way of composing reflected a growing awareness about the concept of musical style, which Johannes de Muris (1290-1351) endorsed and Jacques de Liège (c. 1260-1330) opposed.
Nicole Oresme (1323-82) discovered the overtone (the sound with a frequency that is higher than that of the fundamental tone as sensed by the ear). Oresme contended that overtones played a major role in the concept of timbre (sound quality). Some overtones were harmonic (e.g., a lute and an organ playing exactly the same note), which meant their frequencies were whole number multiples of the fundamental tone, while others were not. This was the first breakthrough in harmony theory since Pythagoras but this finding was not taken further until the seventeenth century by Marin Mersenne (1588-1648).
Whereas Latin texts defined European musicology, Greek texts shaped the Islamic world. Al-Kindi (c.801-73) was one of the first persons to apply mathematical Greek music theory to the Arabic twenty-four parts tone system. al-Farabi (c.872-c.950) provided a schematic classification of rhythms and melodies, using the example-based description principle in his Kitab al-musiqa al-kabir. al-Isfahani (897-967) gave an overview of Arabic singing and poetry in the eighth and ninth centuries with descriptions of associated rhythmic cycles and melodic modes. Another important musicologist was Safi al-Din (1252-1334) who developed the seventeen-tone scale. However, Arabic musicology was unknown to Europe and vice versa.
Further east in India, Bharata Muni (c. first-century BC) described the underlying system of rules for music where its oldest musical tradition was linked to the ritual memorization of the Vedas. This system specified the principles of scale (shadja), consonance, and emotion in Muni’s Natya Shastra. Later in the thirteenth-century, Sarngadeva’s (1175-1247) Sangita Ratnakara appeared that was the definitive text for Hindustani and Carnatic music. A system of rules was devised based on the relative tone (sruti), the music sound of a single tone (swara), the mode or melodic formula (raga) and the rhythmic cycle (tala), with the rhythmic cycles subdivided into specific rhythmic ratios.
In China the Book of Rites, which was attributed to Confucius and in which a chapter was devoted to musical practice, is the first analysis of music in China. The relationship between music and reality was based on the pentatonic Zhou scale (named after the Zhou dynasty, 1046-771 BC). The next important musicological work was the the Huainanzi (a compendium of Taoist, Confucianist, and Legalist teachings), which was edited by Liu An (179-122 BC). This work analyzed the Chinese twelve-tone temperament with approximations accurate to six figures and two decimals.
During the Tang Dynasty (618-907) Chinese opera was born and musical history was part of court chronicles, although there was no attempt to understand underlying musical principles or patterns until Cai Yuanding’s (1135-1198) Lülü xinshui. In this work he described how the tones in the traditional circle of fifths contradicted the widespread cosmological interpretation of the twelve standard tones. The twelve tones should be equidistance, cyclical, and form complete octaves. However, as Cai demonstrated, this interpretation was incorrect if scales were transposed, producing higher or lower tones. Thus, the cosmological concept of cyclicity, which played a key role in Chinese historiography, was refuted on purely musicological grounds. Although his proposal of using an extra six notes was not adopted, Cai’s work showed that mathematical harmony theory was studied during the Song Dynasty (960-1279).
In the medieval period there were no new principles in musicology but new patterns were discovered. The mathematical proportion principle (which defines constant interval) was used in the Arabic, Indian, Chinese, and European musicology. European musicology lagged behind these other civilizations but it did produce innovations by employing existing principles–the mathematical proportion principle of Pythagorean music theory and the procedural system of rules–that resulted into two new patterns. The first was a procedural system of rules for pieces of music (Musica enchiriadis) and the second was the concept of musical style as a shared set of rules.
A renewed interest in the laws of harmony led European humanists to see consonances as based on an underlying system. But this search for a theoretical foundation for the ratios between consonances within the empirical-Aristoxenian approach failed in the fifteenth and sixteenth centuries. By the seventeenth-century, musical practice came to the aid of theory by the increasing acceptance of previously perceived dissonant intervals in music compositions. Yet from Galileo Galilei (1564-1642) to Leonhard Euler (1707-83) Europeans tried to devise either an empirical or theoretical explanation of the “pleasantness” of consonances with all of them sharing the insight that consonance was no longer linked to abstract ratios of numbers but to the physical category of vibration frequency where the ratio remained the same. While they failed to find an underlying law, they did discover that the distinction between consonances and dissonances was not clear (which in turns rebuts the Pythagorean theory of cosmic harmony) and empiricism was to be valued over theory.
Other important developments in European music was Jean-Philippe Rameau’s (1683-1764) analysis of chords using harmonic progression (sequence of chords) and Gallus Dressler’s (1533-80/9) system of musical grammar. Although Dressler’s system was soon outdated, he set forth study in the rules of musical grammar with declarative rules replacing rules of procedure: the boundaries or constraints within which polyphonic composition could occur (e.g., Johann Joseph Fux [1660-1741]; Johann Mattheson [1681-1764]). The history of music also emerged with Giovanni Battista Martini (1706-84), Martin Gerbert (1720-93), and Charles Burney (1726-1814) playing key roles in the history of musical instruments (organology).
While little agreement or advancement about musical theory or history transpired in Europe, musical theory and history continued in China with Zhu Zaiyu’s (1536-1611) Yuelü quanshu providing a historical account of musical theory. In India several treatises appeared, like Raga-Vibodha (1609) and Sangit-Sudha (c.1650), which described how features, like mode, could be expanded into complex variations. However, it was not clear whether the system of rules was intended to be descriptive or prescriptive. Dimitrie Cantemir (1673-1723) wrote a treatise of Turkish music, Kitab-i ilm al-musiki ala vech al-hurufat, where he developed a specific script, the ebced notation, to represent Turkish instrumental music and thereby preserved hundreds of seventeenth-century pieces of Ottoman music for posterity.
The dominance of music theory ended in the nineteenth-century when the historical approach was given central position. In 1885 Guido Adler (1855-1941) distinguished systematic and historical musicology: the former concerned with laws applicable within different trends in music while the latter looked for regularities in the history of music. In systematic musicology, Hermann von Helmholtz (1821-94) explained degrees of dissonance on the intensity of the beats in harmonic tones, from which he deduced whether two tones were in phase. Other factors were discovered to play a role in the perception of consonance and dissonance, such as acoustics, musical culture, and the critical bandwidth of a person’s audio capacity. Finally, there were other achievements in systematic musicology: the hierarchical analysis of music (music split into smaller parts, such as phases or segments); the concepts of the motif, relative pitch, and harmonic triads; and the continuing search for an underlying structure or grammar for music, including atonal.
Besides searching for patterns in musical compositions, musicologists also have searched for regularities and laws in music history. The classification of musical styles and periods was the result of this quest (e.g., baroque, classical). Like other disciplines in the humanities, musicology also had been influenced by structuralism, critical theory, deconstructivism, and new cultural history. The goal of this new musicology was to the creation of a new view (and criticism) of music rather than to increase knowledge about music. Once the example of an exact humanistic discipline, musicology now has become a vague discipline that rejects pattern-seeking for questions about race, class, gender, and power.
Art Theory
The oldest surviving art history is Pliny the Elder’s (23-79 AD) Naturalis historia which described the attempt to portray the world realistically as possible (illusionism). He rejected that good art can be spelled out in rules (the anomaly principle) but did believed that basic principles existed from which artists drew for their art: the canon and the mathematical proportion principles based on Pythagoras’ whole number ratios. The importance of mathematical proportions also was applied in architecture, with concepts like symmetry, beauty, firmness, and commodity being essential as explicated in Marcus Vitruvius’ (c. 80/70-15 BC) De architectura.
In India the Sadanga, written according to tradition in the first century BC, described the principles of painting as knowledge of appearances; correct observation, measure, and structure; action, feeling, form; grace; similitude; and the use of brush and color. The Vishnudharmottara (c. 400 AD) contained similar rules for artists to follow. Chinese art also specified six principles. Xie He’s (c. fifth-century AD) Gu huapin lu had similar principles found in the Sadanga and probably was inspired by it. Later Chinese painting was categorized as historiography became an affair of the state, with Zhang Yanyuan’s (c.815-77) Lidai minghua ji tracing the history, development, and classification of Chinese painting.
In medieval Europe, there were two Christian art theories: Pope Gregory’s (reign 590-604) “art as instruction” and the Byzantine mystic Pseudo-Dionysius’ (c. fifth and sixth-centuries AD) “art as anagogy.” For Gregory, art was to instruct the illiterate about the truth of the Bible, while for Dionysius art was to lead people to contemplate God. By the time of the Renaissance, art theory underwent a transformation with Leon Battista Alberti’s (1404-72) De pictura showing how to reproduce a three-dimension object on a two-dimensional surface: the linear perspective. Alberti’s theory of perspective in turn inspired Leonardo da Vinci (1452-1519) to search for an underlying law of perspective that was empirical rather than mathematical, at which he ultimately failed. Alberti’s De re aedificatoria also influenced European architecture with its principles of number, proportion, and distribution.
Art theory was also altered by art historiography, with Giorgio Vasari’s (1511-74) Le Vite de’ più eccellenti pittori, scultori, ed architettori that consisted of a collection of biographies of artists arranged in chronological order from the thirteenth century to Vasari’s own time. Vasari saw patterns of progress, beauty, persuasiveness, and the expression of abstract ideas. Johann Joachim Winckelmann’s (1717-68) Geschichte der Kunst des Altertums considered the classical period in Greek art to be the most perfect, while Alexander Baumgarten’s (1714-62) Aesthetica and Edmund Burke’s (1730-97) A Philosophical Enquiry into the Origins of our Ideas of the Sublime and Beautiful created the new discipline of philosophical aesthetics.
By the modern period, one of the most acute question was the relationship between art theory and cultural history. Franz Kugler (1808-58) adopted Hegel’s philosophy and divided art into pre-Greek, classical, romantic (medieval), and modern in his Handbuch der Kunstgeschichte. Another concern was stylistic analysis, first undertaken by Giovanni Morelli (1816-91) who found the depiction of painterly details remained constant during an artist’s career. Heinrich Wölfflin (1864-1945) developed an analytical method in which all the separate of parts of a work were examined, their relationships to one another, and the use of light and color. Erwin Panofsky (1892-1968) established iconology as an independent art-historical method that looked at the symbolic meaning in art. The most recent developments in art theory are computational image analysis and the new art history, which like the new musicology, is concerned about race, class, gender, and power.