Part I, Introduction, and the Acoustic Foundations of Music.

Looking at the seventeenth century in Europe, one is somewhat overwhelmed by the tendency for dramatic, often violent change. The century is bisected into two halves; Medieval (in which I include the Renaissance) on one side, and following 1648, the Modern Period. The shift was felt in nearly all aspects of society. In art, the renaissance gave way to the baroque, in science, astronomy led to physics and alchemy to chemistry, and in music, the modal and contrapuntal morphed into tonal harmony as we know it today. Rather than attempting to trace the development of many fields simultaneously, it is far more practical to focus on a single arena, in this case, the changes in music. The examination of music in the seventeenth century will serve as a microcosmic view of the character and scope of the changes occurring in Europe at large. Identification of the root changes in music will require the use of technical jargon, with which the reader may be unfamiliar. The level will be kept simple however, and explanations will be furnished. It is hoped that any specialists will forgive the abstractions, simplifications, generalizations, and ignoring of subtleties made in the name of clarity and simplicity.

Unfortunately, most accounts of seventeenth century music make a disclaimer, stating that it stands as a sort of hole in the history and repertoire. C.Hubert H.Parry, in the preface of his The Music of the Seventeenth Century, writes: "The seventeenth century is, musically, almost a blank, even to those who take more than the average interest in the Art;..." Parry's history, and the many of its ilk fail to organize a cohesive narrative, with any thesis or logical development. They instead give a piecemeal account of events, figures, and works of the period. Hodgepodge lists of facts are presented in a semi chaotic, non-patterned fashion, common to many studies of the period, musical or otherwise. The changes in music are limited in these histories to the transition from renaissance to baroque, from fluid vocal lines to trill heavy violin fireworks displays, from restraint and poise to larger than life flurries of emotion. These changes were of course dramatic and important, reflecting a great deal about society and culture. They can and should be, however be seen as expressions of a deeper change, medieval to modern, the transition from modal/contrapuntal polyphony to triadic tonal harmony. In this manner, a basic trend is revealed to have been at work, not only in the affective and aesthetic impact of music, but in the ideas which underpinned not only music, but western thought and society general. Grandiose? Indeed, but bear with me.

It is, to the credit of Parry however, admittedly difficult to pin down the 17th century in concrete terms. It eludes our attempts to assign a hallmark description in the manner of “Renaissance,” “Age of Enlightenment,” or “Industrial Revolution.” Terms like “Age of Absolutism,” and “Baroque,” refer only to specific facets of the period, and fail to sum it up. As a whole, change seems to be the century's salient feature. Major labels associated with the time, "The Scientific Revolution", and "The Reformation" attest to the powerful current of cultural upheaval to which the seventeenth century was privy. To capture the essence of the period, it must be viewed more as an age of transition than a distinct period onto itself. Seeing the 17th century as the adolescence between the rebirth that was the Renaissance, and the adulthood of the modern period says more than either “Age of Absolutism” or "Scientific Revolution". With this in mind, the seventeenth century will therefore be approached as the link between the medieval and modern, not simply 1600-1699.

With this view of the seventeenth century as an age of transition having been put forth, the nature of the transition must be addressed. The question which drives this exploration is essentially; 'what is the fundamental difference between medieval and modern?' To answer this, the starting and finishing points of the process of change must be viewed side by side. The starting point was the modal/contrapuntal system of the medieval/renaissance period, exemplified in the music of Palestrina, and the end result was the tonal system used today in pop, rock, jazz, rap, country, and any other style save modern and contemporary avant garde music, perfected by J.S. Bach in the early 18th century.

Medieval and Renaissance composition was based upon the idea intervals, or distances in pitch between notes. Certain notes were pleasing when played together, the intervals between these notes being known as “consonant.” Those intervals which were displeasing were “dissonant.” Consonant intervals were preferred, dissonant ones were to occur rarely, and be treated in a special manner. There was little worry over what the notes happened to be, so long as they were the desired distance from each other. Of course the distinction between consonance and dissonance has a factor of subjectivity, and has changed over time, but it is rooted in basic physics.

Pythagoras was the first to propose and explore the relation between natural law and musical perception. He preformed an experiment using a single string, which was stopped at varying distances, and plucked. When the string was stopped at exactly half its length, it produced the most consonant sound, the octave. The experiment was repeated with a division ratio of 3/2, which produced another, slightly less consonant sound, the perfect fifth. Pythagoras concluded from these results simpler ratios resulted in more pleasing sounds, and repeated his experiments for more complicated ratios of 5/3, 4/6, 5/9, etc, finding that consonance, or agreeableness to the ear diminished with each successively more complex ratio. The basic rule for composers of the medieval/renaissance era was to write two or more separate melodies to be played simultaneously, gaging and controlling the distance between the notes at any given point. The unattributed maxim of Renaissance music put it succinctly; The composer should start by writing the most beautiful melody he can conjure, then writing the second most beautiful melody he can to be played with the first, the same method being applied to each subsequent voice to be added. In this music, the harmony was conceived of as simply intervals, and was propelled by the the resolution of dissonant intervals to consonant ones.

The end point, tonal harmony, is based not on the interval, but on the triad. A triad is a cohesive unit of three notes, built by selecting a note and placing two others on top of it, one a third above the root, and another a perfect fifth above the root. The triad is based in the harmonic series, the acoustic phenomena in which Pythagoras' work and human musical perception are based. A brief explanation of the harmonic series is thus required in order to adequately illustrate the fundamental difference the contrapuntal and tonal systems of music.

Every note is comprised of a fundamental tone, the main note which we name and recognize, C for example. This is the strongest vibration, but by no means the only one. Every vibrating body is segmented into smaller sympathetic vibrations, in the ratios verified by Pythagoras. The body's vibration is divided first at the halfway point, producing a secondary vibration which is half the wavelength and twice the frequency of the fundamental, producing an overtone an octave above, in our case, another, higher C. The next ratio prescribed by Pythagoras also occurs, the string vibrating in sections a third of the main length, producing a Perfect fifth. The perfect fifth is hence the interval with the second strongest relation to the fundamental, after the octave. It is also the second most consonant interval. The note a fifth higher in our case, with a fundamental of C, would be G. This note shares a strong relation with the fundamental, or tonic, and is strongly implied by the 2nd overtone. The attraction these two tones share is the basis of composition today, and has been since the end of the 17th century. This still isn't a triad however, it only has two notes. The third note of the triad comes not from the next overtone in the series, which is yet another C, but from the fourth overtone. In this case, C being the fundamental, the fourth overtone is an E. The triad comes then, from the first four overtones of the harmonic series. The notes of a triad thus share a relationship far more powerful and fundamental than the distances between them.

(Any guitar or string player will recognize the overtones by means of harmonics,the location of which are dictated by the harmonic series ratios, the notes produced being those of the harmonic series. ie, the 12th fret has the strongest harmonic, being 1/2 the string length, thence producing an octave interval above the open string notes. Every fret being a half step, 12 half steps make an octave, each step being 1/12 of the total octave.)

Wonderfully analogous to the changes in music were the changes in science. The humanism of the renaissance had led to an idea that the world was interesting in its own right, more than something which simply had to be endured on the path to paradise. The idea that the world should be examined had set off a flurry of investigation into the nature of, well, nature, producing an impressive catalog of phenomena and facts. The main process of the scientific revolution was not the acquisition and cataloging of new facts, as stated, this had been going on throughout the renaissance. Rather, the fundamental issue was the move from disparate lists of individual elements, facts and phenomena to ascertaining the basic similarities and underlying principles of these various facets of the natural world. The myriad of facts and figures were slowly being unified within theoretical frameworks and natural laws. The move from individual intervals to a unified theory of harmony based on the triad was mirrored in science, itself moving from the specific to the general. Newton would later in the century, opt not to catalog individual phenomena, but rather pursue the similarities of those phenomena, unifying falling bodies and celestial patterns both, with his universal laws of motion. Newton also displayed this new approach in his work on optics, demonstarting that white light was itself comprised of all the colors of the spectrum, and all colors were white light being reflected and absorbed in different proportions by different objects depending on their physical properties.

Copernicus, Galileo and Newton are well known as the founders of modern science, and its practice of looking for underlying causes of empirical observations. Less well known of course are the theorists and composers who put forth the principles of triadic tonal harmony. The names Zarlino and Lippius fail to register in the minds of most of us, yet they were as important to the development of music as Copernicus and Newton were to science. The advancement of musical theory can be said to have been in the same vein as the scientific revolution, both concerned with discovering the basic natures of their subjects, deriving general laws from catalogs of facts. Lippius attested to this spirit of inquiry when he said:

“Music is a mathematical science… involving the artful and prudent composition of a harmonic cantilena in order especially to move man moderately to the glory of God”.

Lippius, a German theologian and music theorist, saw music in the same way that Newton saw the natural world, as more than a fragmented jumble of intervals and falling bodies, but a set of basic laws governing the behavior of objects according to basic principles. Lippius was one of the first to articulate the meaning and use of the triad in his 'Synopsis Musicae Novae', in the first years of the Seventeenth century. Lippius observed that in the repertoire, triads frequently occurred when multiple voices were consonant with each other. These triads were however, still the by product of separate voices moving around each other. His proposal was that composers use the triad intentionally, each chord being treated as one entity instead of the configuration of three or more separate voices. The refinement of his ideas was unfortunately left to others. Lippius died young, in 1612, at the age of 27. Music, lacking as it does much of the objective basis of science, did not change immediately. It is never a matter of a theorist developing a new idea and composers immediately adopting it. There must be a pragmatic reason for composers to adopt the new techniques. [Francis Bacon would have been pleased, his notion, expressed in his Novum Organum that general laws could only be discerned when research and observation had produced enough data to draw general conclusions from. Bacon stated that one must gather;

“particulars, rising by a gradual and unbroken ascent, so that it arrives at the most general axioms last of all.”

Lippius had in effect, done just this, deriving chord based harmony by observing the works of composers, and proposing that the triad, not the interval was the basic unit of harmony. Further, the new idea had to be validated by practice, just as any scientific theory must jibe with experimental data.

The new theory of music had in it the kernel of Bacon's method, denying the long standing tradition of beginning from axiom, and deducing from there.

GoTo: Music and Europe in the 17th Century, Birth of the Seconda Prattica.

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