Dance Music in the High Renaissance

Chordal Advances Applied: Later Dance Music

Social dancing has been part of human activity from the earliest times. Social dancing furnished its practitioner with the opportunity to have amiable interactions with other members of his social group, meet potential mates and to advertise to them desirable physical traits as stamina and strength, and to benefit from the exercise inherent in a healthful diversion.

The first Western European dance music that comes to use in recorded, that is, written form is actually quite recent, dating form the the estampie. A larger body of recorded music, the basse danse, comes to use from the late fifteenth century.

Basse danse derives its name from its steps. Here the dancer kept his feet close tot he ground, avoiding high steps. Its music comes to use in collections of melodies. The melodies were played as the lowest voice in the musical texture. Second and third musicians who played higher-pitched instruments then improvised over the basse danse melody.

Basse danse choreography reflected the character of the melodies. The melodies tended to have considerable length, the ones from Italy running for over a hundred modern measures without repetition. Hence the choreography for any single basse danse had to be learned, practiced frequently, and then matched, on the spot, to the music. To make matters more complex, the dancer had to memorize a significant number of choreographies since he could not determine which basse danses or the order in which the musicians would play them.

By the last decade of the fifteenth century, several important musical developments made the life of the social dancer easier. An important development was the emergence of the basse danse commun, a variant in which the number of measures in each musical phrase was reduced to even numbers usually falling between eight and twelve. Furthermore, dance-step patterns emerged that were universal to the number of measure in the musical phrase.

A second development was the emergence, in the first decade of the sixteenth of new dances and music to accompany them. The music reflected the new dances, and the older longer forms of the basse danse were abandoned in favor of shorter sectional forms.

A preference for eight, ten, and twelve-measure musical periods or sections were evident as early as the first large-scale printed collections of dance music in the 1520s and 1530s. The eight-measure period has remained the musical standard in Western music to this day and is found in music as diverse as the Classic symphony and the American rock 'n' roll tune.

<>Last, construction of the music over the bass danse melody was supplanted by structures built on chord progressions and the bass frameworks. The advances in basse danse choreography, including standardized steps and stanza limited stanza lengths (i.e. eight measures), remained as important features regardless of construction and were also carried into newly-emerging dances.

The music forms of the new dances were constructed in sections, each of which was repeated immediately. There was no set number of sections. A dance could contain as few as two sections or as many as five or more. Hence a typical form might be AA' BB' CC'. Each letter represents a different period of music, and the prime mark on the second letter of each pair indicates that the musicians emblished the melody upon repetition. The most typical way to ornament the melody was to connect the principal melody notes with fast runs most typically called passaggi.

The Favored Dances of the High Renaissance

By the 1570s, three dances, the pavan, the galliard, and the allemande, had been established as the most important. The pavan, a slow and serious dance in duple meter (4/4), became a serious vehicle for art music. The galliard was a moderate-tempo dance in triple meter (3/4) and was the most popular of sixteenth-century dances. The allemande, the relative newcomer, was a moderate-tempo dance in duple meter (4/4). The passamezzo, one of the bass frameworks, also survived, especially in Italy. In dances of the second half of the sixteenth century, a bass framework could underpin an entire dance composition, a section of a dance composition, or not be used at all.

The pavan and galliard, under the names pavana and salterello, appeared by the first decade of the sixteenth century. The allemande, which means "German," first appeared around 1540. The allemande had a formal quality. It survived into the seventeenth and eighteenth-century dance suite. Its stately nature lent it to use as processional music and, more importantly, in the dance suite, it became the movement in which the composer sought to make art music. The allemande ultimately evolved into the first movement of the Classic era sonata allegro.

The new dances were important for social reasons, but they were also critical in the development of a functional system of chords. The composers of dance music were largely lutenists. They were among the first to understand chords and apply them as the underpinnings of their compostitions (see "bass frameworks" in the previous lectures).

The lute was one of only a handful of instruments that could play chords. The other instruments were the keyboard (harpsichord, organ) and the harp. Keyboard composers did not participate in the creation of dance music on a significant scale until the end of the sixteenth century. The harp of the day was severely limited in the notes that it could play.

As noted, in the sixteenth and seventeenth centuries, the lute became the most important musical instrument. Skill at playing was developed by members of the educated class, and the aristocratic households always retained at least one professional lutenist. The lutenist did not provide music for dancing, but background music. The music used in dancing was also used for listening, and here the lutenist fulfilled the role taken in modern times by the CD player. The dance music repertory was augmented by the chanson and fantasia, both forms cultivated as part of the "correct" Humanist education.

Girl playing the lute

Humanist Poetic Forms: the Sonnet

Humanist Poetic Forms: the Sonnet

Chansons of the fourteenth and early fifteenth centuries utilized three poetic forms, the formes fixes. The sonnet breaks with the repeated text and music lines found in formes fixes stanza schemes. The single stanza of the sonnet, itself in turn divided into shorter sections, contains the entire thought or message. In the musical setting of the madrigal, no music is repeated, and the composer fashions music that best expresses the emotion or thought of
each line of text. The music of the madrigal, then, is through composed.

Two sonnet forms dominated the sixteenth century, both in poetry and in the madrigal. They were differentiated by form, language, and geography. The first, of course, was the Petarchan sonnet. It was written in the Italian vernacular and was used in the madrigal primarily in Italy. Petrarch's sonnets are in iambic pentameter (see rhythmic modes) and consist of a single stanza of fourteen lines. Iambic pentameter is an ancient poetic meter that places the syllabic accents in the pattern of weak-strong. The lines of the stanza are in turn divided into two groups of eight and six lines. The first group is called an octet or octave; the second, a sestet. Smaller line groups sometimes occur. Four-line units are called quatrains, and two-line units are called couplets. The rhyme scheme of the octet of the Petrarchan sonnet is usually abbaabba. Variants include abbacddc and abababab. The rhyme scheme of the sestet may also be one of several variants including xyzxyz or xyxyxy. The following sonnet, written by Petrarch, follows the rhyme scheme abbacddc xyxyzz. The final rhymed couplet of the sestet is a variant that was carried into English language sonnets.

Octet:

As oftentimes a foolish butterfly,

Used to the light, in the hot weather will

Fly into people's eyes his joy to fill,

Whence comes that others weep and he will die,

Like this I turn toward the fatal rills

Of the eyes from which comes a ray so bright

That Love tears reason's fetters in despite,

And who discerns is conquered by who wills.

Sestet:

And I see well how great is their disdain,

I know that this will mean true death to me,

My valor being lesser than my pain;

But Love dazzles my sight so pleasantly,

That I mourn others' wrongs and not my breath,

And my blind soul consents to its own death.

A second form, developed first by Henry Howard, Earl of Surrey (1517-1547), is today called the English or Shakespearean sonnet. Its language and geography are self-evident. It follows the form of three quatrains and a couplet, and features rhyme schemes such as abab cdcd efef gg. Sheakespeare's Sonnet VIII follows as an example of the genre. The lute, the principal instrument of the sixteenth century, makes the music Shakespeare describes in the sonnet. The first quatrain addresses the most powerful contradiction of hearing music.

Sonnet VIII

First quatrain:

Music to hear, why hear'st thou music sadly?

Sweets with sweets war not, joy delights in joy.

Why lovest thou that which thou receivest not gladly,

Or else receivest with pleasure thine annoy?

Second quatrain:

If the true concord of well tunes sounds,

By unions married, do offend thine ear,

They do but sweetly chide thee, who confounds

In singleness the parts that thou shouldst hear.

Third quatrain:

Mark how one string, sweet husband to another,

Strikes each in each by mutual ordering;

Resembling sire and child and happy mother,

Who, all in one, one pleasing note do sing;

Rhymed couplet:

Whose speechless song, being many, seeming one,

Sings this to thee: "Thou single wilt prove none."

As Vesta was Descending

First quatrain:

As Vesta was from Latmos hill descending
She spied a maiden queen the same ascending,
Attended on by all the shepherds swain,
To whom Diana's darlings came running down again.

Second quatrain:
First two by two, then three by three together,
Leaving their goddess all alone, hasted hither,
And mingling with the shepherds of her train,
With mirthful tunes her presence entertain.

Rhymed couplet:
Then sang the shepherds and nymphs of Diana,
Long live fair Oriana!

Madrigal: the Marriage of Musical Textures

A New Art Form, the Madrigal

The motet of the early sixteenth century still used the cantus firmus technique, but was informed by Josquin's pervasive imitation rather than the poetic form of the stanza of the text. The Franco-Flemish chanson, although it did not use canti firmi but instead substituted newly composed melodic ideas, likewise was structured by pervasive imitation techniques rather than poetic form. In sharp contrast, the frottola, and it derivatives the Parisian chanson and dance music, unfolded in simple strophes sung in a trebled-dominated texture. Instead of the sophisticated imitative polyphonic texture pioneered by Josquin, the musical texture consisted of a soprano melody supported underneath by block chords.

From the point of view of the newly emerging madrigal, however, neither genre wholly suited. The imitative motet texture was too restrictive in expressing the sonnet and its music too rigid and technical to be highly expressive. The frottola texture, while giving the composer free rein in constructing expressive melody, was not sophisticated or interesting enough for art music. Composers drew upon both textures to express the emotive content of the sonnet, switching rapidly from one to another as the text demanded. Imitative expositions no longer shared thematic material. Instead, when imitation was used, each subject was newly composed to express the textual idea. The subjects were not derived from a cantus firmus and no two subjects within a madrigal were related to each other. Once an imitative expostion ceased to serve expressive ends, it immediately gave way to sections of chordal or frottola texture.

Important Madrigal Composers

Early experiments in the first third of the century made apparent that madrigal poetry required a marriage of the two musical textures. In the early part of the sixteenth century, northerners held the important musical posts in Italy. Northern composers working in Italy such as Adrian Willaert (c1490-1562) attempted to assimilate the madrigal, but the music frequently resembled the motet, with polyphonic musical textures that were too busy and heavy to properly treat the poetry. Other northerners such as Franco-Flemish composer Jacques Arcadelt (c1505-c1568) fared better. His madrigals featured square rhythms and homophonic texture that linked them to the frottola. The musical line did not always, however, follow the poetic line, and a pause point in the melody would sometimes occur before the line of text was stated completely.

Italian composers such as Cipriano de Rore (1516-1565) expanded the expressive character of the madrigal in the second generation. The music began to feature a combination of textures, often in alternation in the music, borrowed and reworked from the imitative style of the motet and the chordal motion of the frottola. Imitative procedures were retained, but the concept of a cantus firmus, a pre-existent melody from another often, liturgical source, was wholly abandoned. Instead, melodies were fashioned that expressed the meaning of the text. The melodies could change their contour, rhythmic values, tempo, and even keys to suit the expressive needs of the text. Madrigal melodies often introduced extensive application of chromaticism, that is, the usage of sharps and flats.

To expressive end, composers often took dramatic musical license, called tone or word painting, to create or reinforce pictorial elements of the words. A line "from the highest spire" might be supported by a melody that leaps downward from a high note or the description in the text of a babbling brook might be sung to a running line. The graphic musical representations are also called "madrigalisms." Despite expressive advances and sometimes excesses, the madrigal may be regarded as a hybrid of the two important genres of the period, the motet and the frottola, and their highly individual textures, which composers manipulated in alternation to expressive ends.

Luca Marenzio (1533-99) defined the "classic" madrigal. His efforts took the madrigal to its highest state of development. His music utilized the full arsenal of devices of the madrigal, yet his settings reflected both a finely honed sensitivity to the meaning of the text and sense of restraint and balance. His music was transmitted to England in the Musica Transalpina (1588), the book of Italian madrigals that planted the seeds of the genre among native English composers. Of all Italian madrigal composers, Marenzio exerted the greatest influence upon the English madrigalists, and his sense of balance and expression echoed in the madrigals of the English school. Thomas Weelkes and Thomas Morely were among the most prominent madrigal composers in England.

Renaissance Term List

Late Medieval and Early Renaissance
Isorhythm-review by listening and score analysis the isorhythmic works from the Ars nova
Means by which Machaut unified the non-syllabic movements of Messe de notre dame
English polyphony including imitative forms
Italian imitative forms caccia and madrigal
French chausse
Characterisitics of English music as compared to continental music
General history of England and France (King and Burgundy) in the first half of 15th century
faburden and fauxbourdon (differences and similarities and who used each)
John Dunstable
Giles Binchois
Guillaume Dufay
formes fixes
International song style (impact of Ars subtilior and Johannes Cicconia)
Franco-Flemish composers (importance and impact)
Antoine Busnois
Johannes Ockhegham

Mid-Renaissance Vocal
Pervasive imitation and impact upon form and composition methods
Josquin Despres (or Des Prez or Desprez)
motet
Franco-Flemish chanson and spin-off, the fantasia
Methods of Mass composition (i.e. parody, cantus firmus, etc.)
canti carnascialeschi
frottola
Marco Cara
Villancico
Juan del Encina
Cancioniero de Palacio and contemporary MSS (MSS=manuscripts)
Parisian chanson
Claudin de Sermissy
Lutheran chorale

Late Renaissance Vocal Music in Italy and Spain
Adrian Willaert
Council of Trent
Giovanni de Palestrina
Tomas Luis de Victoria

Dance Music in the very late 15th and entire 16th Centuries
basse danse and basse danse commun (texture, form, and composition method)
Early new dances-pavana and saltarello
Characteristics of late favorities-pavan (also pavana or pavane), galliard, and almain (also allemande)
bass frameworks and significance-you should know progressions for folia and passamezzi (antico and moderno)
Significance of Canconiero de Palacio and contemporary Italian MSS
variation form
passaggi, diferencias, glosas, diminutions
English Lute and Virginals School (especially John Dowland and William Byrd)
lute ayre and its derivative settings

English Renaissance Sacred Vocal Music
Reasons for Anglican Church
Service and types
Anthem and types
William Byrd

Rise of Music Printing
Ottoviano Petrucci
Pierre Attaingnant

Italian Madrigal in 16th Century
Sonnet form
Petrarch
Pietro Bembo
"Bemb-isms"
Adrian Willaert
Jacques Arcadelt
Cipriano de Rore
Luca de Marenzio
Carlo Gesuado
Musica transalpina
Thomas Morley
Thomas Weelkes

You should describe the styles of each composer in the list and note his contribution. Perhaps more critical is the polarity established between pervasive imitation and homophony during this time span. The single most significant point of looking at all this material and listening to all this music is that you understand and establish geneologies, tracing each thread through all the subsequent related genres. to do this, make two columns, one marked "pervasive imitation" and the other "homophonic." List each genre according to type.

Toward a New Genre: Opera

New Modes of Thinking

By the 1580s, theoretical advances in music and the madrigal's apparent shortcomings in expressing emotions caused music thinkers and practical musicians alike to seek new directions. Although the madrigal continued in England into the early seventeenth century, it began to loose its vitality and import in Italy.

As noted. the madrigal was a hybrid form, a combination of highly-regulated imitative techniques and frottola texture. Despite the beauty and sophistication of the genre, the rules imposed upon the music in the imitative sections effectively prevented the construction of natural melodic lines, creating instead music that seemed plagued by artifice. Madrigalisms such as tone painting, so revolutionary and exciting at inception, became targets of mockery.

Two developments, a philosophical shift in thought based on Greek drama and a new concept of musical texture, led to the creation of the opera and recitative and effected developments that would resonate in all the other genres except the fugue in the period to follow.

The Florentine Camerata: New Concepts of Melody

The Florentine Camerata (fl. 1573-92) was a loose group of intellectuals based at the home of Count Giovanni Bardi in Florence. As noted in the text, the group included Vincenzo Galilei, father of the astronomer and a significant music theorist in his own right. The central figure, however, was Girolamo Mei. Mei was a humanist who immersed himself in the newly discovered and newly translated ancient manuscripts made available as part of the flowering of humanist scholarship. In particular, Mei read in Greek every available ancient treatise about music.

Dissatisfied with the shortcomings of the madrigal, he sought in Greek knowledge other musical means to express human emotion. His studies led him, as evident in his letters around 1577, to a startling conclusion: Greek drama was powerful because it was sung throughout. To Mei, effective melody should reflect the natural inflection of speech. For example, excited happiness is externalized in speech by a rise in pitch and an increase of speed. In anger, the voice drops and speech slows.

Monody and Recitative

The application of Mei's concepts regarding melody could not be applied, however, without the concurrent development of new concepts of musical texture. The singer Giulio Caccini (c1550-1618), along with singer Jacopo Peri (1561-1633), poet Ottavio Rinuccini (1562-1621) and others, experimented with grafting Mei's new ideas of melody to contemporary musical texture in little pastoral scenes produced at the royal apartments of Bardi and confederate members of the nobility.

Caccini's Le nuove musiche, likely composed in the 1590s but not printed until 1602, was the first music collection to feature a new musical texture, monody. The term derives from the Greek monos, alone, and aieden, to sing. The chordal textures promoted in the frottola and nascent bass frameworks served as the starting point. In monody, the soprano and the bass lines, the voices most clearly audible, became the most important and highly developed and the inner voices were reduced to filler chords.

In their early experiments, Peri and Caccini sought to reconcile the emotive power of speech with tradition concepts of melody. The result was a style of singing, called stile recitativo or recitative, which was essentially part song and part speech. The music was conceived for a solo singer and hence featured no imitative writing, contained no strophic or repeated sections of music as in dance, and no regular or repeated harmonic plan.

Instead, the music was through composed and roamed, free of the strictures of the learned style, through whatever harmonies and key areas as the composer thought best to express the emotion of the text. The rhythms were also extremely flexible to reflect speech. Note the similarity to the procedures and character of early Christian centonization. Similarities are also shared with the recitation of epic poems (chanson de geste) during the Middle Ages.

Peri's opera Euridice, mounted in 1600, is the first opera to survive in its entirety and the first to contain true recitative. It was sung by a few singers and accompanied by a few lutes, hidden from view by a screen, in a private apartment. The story is derived from the mythological tale of Orpheus and Euridice.

In the myth, a snake fatally bites Euridice. Orpheus charms the gods with his music upon the lyre and they allow him to retrieve his beloved from the underworld, provided neither look back as they ascend. Orpheus loses Euridice not only once, but twice. In a precedent that set the tone for the vast majority of later operas, the story focuses upon love and loss. Caccini also set the myth as an opera. The term "opera" is the plural of opus, or "work." Hence "pera" is the list of musical works to be performed and the musical equivalent of word "menu."

A few years later, in 1607, Claudio Monteverdi (1567-1643) also set the myth as an opera, Orfeo. Monteverdi is a difficult figure to address in music history because he was at once a master of the older madrigal style and the newer style of monody. Caught up in a debate about the merits of monody, he coined two terms which have remained both accurate and in circulation. Stile antico referred to music governed by the tenets of the learned style, or pervasive imitation. Stile moderno referred to monody and recitative.

One contribution is certain: Monteverdi saved opera. Peri and Caccini's operas suffered from the very element that made them progressive, recitative. The early operas contained too many extended sections of recitative. To the literate, the marriage of music and poetic text represented a valid entertainment. To those with poorer educational circumstances or who did not understand the language, recitative could present a true listening challenge.

Monteverdi's musical treatment in Orfeo did not diminish recitative, but he was careful to offer relief in the form interpolations of music in other styles. Strophic, monodic arias with dance rhythms and orchestral pieces were placed strategically to relieve the recitative and to frame scenes. His large-scale planning was careful that the each section of music related in a tonally coherent way to the preceding and following ones. Even his recitatives featured formal harmonic plans instead of wildly freewheeling. In addition, Monteverdi used a relatively large orchestra. Although he included no pieces in which all the instruments played together, he used different smaller combinations to create color and additional relief.

By mid-century, the recitative portions had been significantly diminished in size and consequence. Public audiences grew less interested in the emotional impact of the recitative and more interested in the beauty of the aria, the competition of singers talents, the ever-increasing flamboyance of stage scenery and costumes, and the general entertainment value of a night at the opera. Recitative was reduced to transitional material. It still featured melody that imitated speech and was dense in textual material, but it assumed the role of giving the information necessary to move the story along, set the scene, or prime the next aria. By mid century, opera became a series of pretty arias with short recitatives inserted between them.

The art and music of the Baroque era can be described as one of contrasts. The contrasts do not seem as clearly defined as in later periods, but during the period from the late sixteenth century until the end of the the seventeen century, artists and musicians strove to infuse their work with emotion.

For the musician, embracing affect was limited somewhat by the lack of plasticity of form. The technical capabilities of the instruments of the time also imposed constraints. For example, contrasts in dynamics (loudness and softness) could be attained only by suddenly paring down the number of musicians playing.

New Ways to Notate Monody

Figured Bass, Thoroughbass, and Continuo

A new, shorthand notation evolved to indicate the chords, now reduced in function to filling in the texture between the important outside voices. The notation system was called figured bass or thoroughbass. The bass line was written in musical score but the notes of the chord were not. Instead, numbers were written below the bass note indicating the specific notes to be added by the lutenist or harpsichordist, and the player could place them where he pleased. In the Baroque period, then, the chord player did not read a completely written part, but learned to improvise them at sight from a notated bass notes and numbers!

i>Continuo or basso continuo actually refers to the musical texture of the accompaniment. Here one must have both a chordal instrument playing the chords indicate by the figured bass and a bass instrument playing the notated line. The bass instrument was usually a violincello of a bassoon. The title "Sonata for Two Violins and Continuo" tells the reader that he will hear two violins, a harpsichord or lute playing chords, and a cello playing the bass melody.

The texture of two soprano instruments and basso continuo also illustrates the "trio sonata" texture pioneered by Arcangelo Corelli in the late seventeenth century. Note that the trio sonata texture requires four players, and the term shows clearly the diminution of overall importance of the chord fill. The figured bass notation did not remain long the exclusive property of opera. The monodic texture was quickly adopted for all genres of Baroque music except imitative fugues and motets, and suites written for solo lute or harpsichord.

Score for two soprano instruments, a bass instrument and a figured bass part for keyboard or lute.

Astronomy and the Church: the Scientific Revolution and a New Concept of God

Strides in astronomy helped to revolutionize man's concept of the universe, his concept of God, and validated once and for all the empirical approach advocated by the humanists. One central scientific issue of the sixteenth century was the ordering of the solar system. The view purported by Ptolemy in his Almagest (150 A.D.) and revered as both Church and scientific doctrine described a universe in which the sun, moon, and planets revolved around the earth. Concentric crystalline spheres that surrounded the earth supported the celestial bodies. The planets moved as the spheres rotated. Beyond the spheres lay the realm of God and the angels. Aristotelian physics justified Ptolemy's universe, and the construct stood unchallenged until the sixteenth century.

Andreas Cellarius (c1596-1665), "Location of Earth with Celestial Circles" (1661)

The Astronomers

Difficulties with Ptolemy's system had been recognized for a considerable time before Copernicus (1473-1543) published his De Revolutionibus Orbitum Coelestium (1543). His assessment of contemporary astronomy did not differ from that of Ptolemy except for a single point: if the sun were the center around which the planets orbited, the mathematical problems and inconsistencies present in the Ptolemic system were essentially resolved. An important tenet of humanism that Copernicus stressed and that later became a basic component of scientific method was that no process, in his case mathematics, could be applied without empirical data and observation.

Tycho Brahe (1546-1601), a scientific amateur, was able to furnish the next evidence for a sun-centered universe. He did not agree wholly with the Copernican view, but his objections gave Copernicus's ideas wider circulation. His contribution was in a form that Copernicus advocated, the collection of empirical data. Although he was not able derive mathematically verifiable theories of the order of the universe, Brahe's naked-eye observations of the celestial motion were the most accurate and comprehensive tables to be generated in centuries.

Andreas Cellarius (c1596-1665), "Brahe's Planisphere" (1661)

<>Johannes Kepler (1571-1630) inherited Brahe's data. Kepler embraced Copernicus's idea of a solar centered, but his reasoning actually derived from the Neoplatonist honoring of the sun. Brahe's observations did not support the concept of circular orbits, put forth first by Ptolemy and retained in the theories of Copernicus. In On the Motion of Mars (1609), Kepler used Copernicus's model and Brahe's motion tables to correctly identify that planetary orbits were elliptical, though he could not mathematically justify his conclusion.

Galileo Galilei (1564-1642), the son of Florentine Camerata member Vincenzo Galilei, increased the body of empirical data by the use of a new device, the telescope. He discovered stars where none had been known to exist, spots on the sun, craters on the moon, and moons orbiting Jupiter. His revelations did not prove the Copernican view, but they did disprove that of Ptolemy. Furthermore, the discovery that the universe was vast beyond comprehension unnerved many contemporary scientists and churchmen. His book Dialogues on the Two Chief Systems of the World (1632) earned him the wrath of the Catholic Church, and he was forced to recant his findings.

Andreas Cellarius (c1596-1665), "Northern Stellar
Hemisphere of Antiquity" (1661

<>Like Copernicus, Galileo believed that the universe was explainable in mathematical terms and behaved with mathematical regularity. His belief extended far beyond astronomy, however, and one of his crowning achievements was the concept that not only did celestial bodies conform in behavior to mathematical principles, but also that every aspect of nature was regulated by the same mathematical laws.

Sir Isaac Newton (1642-1727) resolved the thorny problems of planetary motion presented by the Copernicans, in particular that of elliptical orbits. In addition, he established a basis for physics that remained viable until the twentieth century. Newton drew upon earlier studies, especially that of Galileo. He agreed with Galileo's assertion that inertia encompassed both bodies in motion and at rest. Newton reasoned that all bodies in the universe moved by attraction to one another, and that gravity caused elliptical rather than circular orbits.

Newton believed in empirical study. No mathematical function could describe a phenomenon that could not be observed. With Newton's contributions came a view of a universe of mathematical law and regularity. Because older divinities and superstitions no longer sufficed to explain the universe and nature, a new concept of God began to emerge. Because the universe was rational and lawful, so must be its creator. Moreover, man was part of the creation, and a new concept of man as a rational being gave hope that he could improve his condition free of traditions and superstitions of the past. The rise of science did not seem incompatible with religion but, for some, science dispelled much of the mystery and the ethereal quality of spirituality. The new God was colder and further removed from man than the one of earlier times.