Rameau’s Harmony

Rameau’s importance to the development of opera notwithstanding, his claim to fame lies in his music theory. Rameau’s harmonic innovations, and especially his development of a fundamental bass, form the basis of modern theories of tonality. Rameau’s 1722 Treatise on Harmony (https://en.wikipedia.org/wiki/Traité_de_l%27harmonie_réduite_à_ses_principes_naturels) more or less governed musical composition until Debussy more or less threw it out the window over 150 years later.

The Treatise is divided into four parts: Book 1 (the relationship between harmonic ratios and proportions); Book 2 (the nature and properties of chords); Book 3 (Principles of composition); Book 4 (Principles of Accompaniment). Rameau’s revolutionary text proposed a comprehensive system that covered all aspects of composition: Rameau describes how keys or tonalities are developed and why certain harmonic progressions work, while others do not. His basic terminology for describing fundamental principles of music—chord inversion, tonic, dominant—are still used today. Here is a great article that describes the math and science behind Rameau’s Treatise in greater detail: https://www.reddit.com/r/classicalmusic/comments/31v6nz/til_jeanphilippe_rameaus_treatise_on_harmony_1722/

In his Treatise, Rameau sought to establish, much as Pythagoras had done at the dawn of Western music, that the rules of harmony were derived from nature.  Using mathematical proofs, Rameau presents an analysis of overtones by pitch, finding that the natural harmony of any individual note is a major triad: the octave; the fifth; and the third.  Rameau subsequently broke down these triads into smaller intervals, major and minor thirds.  A chord is either major or minor, diminished or augmented.  In Rameau’s view, the quality of a chord is determined by the relationship of the thirds that are used to construct it.  Those rock songs that are based on three chords?  That’s Rameau all over again.

And yet that’s arguably not even Rameau’s greatest contribution to the development of Western Music. That would be his groundbreaking argument that the figured bass is the prime generator of harmony and harmonic progression, an innovation that pushed music forward in a way not seen since Monteverdi’s Seconda Practica. Rameau’s view, that harmony is produced through functional chord progression grounded by the bass line, endured; the German School’s emphasis on harmony through counterpoint did not. Rameau’s harmony is the foundational rock upon which Western music was ultimately built. For those seeking a more in-depth analysis of Rameau’s music theory, this is a great starting point: https://symposium.music.org/index.php/24/item/1970-composition-before-rameau-harmony-figured-bass-and-style-in-the-baroque.

We close with three instrumental works: one of Rameau’s “concerts”, best described as a harpsichord concerto, followed by one of the more recognizable of his works for harpsichord (the pieces de clavecin are often cited as one of the high points of Baroque composition), before ending with his Le Dauphine for solo harpsichord. 

Jean-Philippe Rameau: Six concerts transcrits en sextuor, I. Premier concert, Le Coulicam:

Jean-Philippe Rameau: Pieces de clavecin, Suite in E Minor, No. 8, Tambourin:

Jean-Philippe Rameau: Le Dauphine: (with some bonus material for Gert.  Le Dauphine is the first piece).

Why so much harpsichord? Partially because Gert requested it. But also because of the wonderful quote about Rameau, who loved the harpsichord above all others: “His heart and soul were in his harpsichord; once he had shut its lid, there was no one home.”

Rameau’s controversial compositions notwithstanding, he died in great popular esteem—200 musicians performed at his funeral to a crowd of over 1000.  At the close of his funeral, the harpsichord lid was shut and the great man laid to rest.

Baroque Music IX: Jean-Philippe Rameau (1683-1764)

Of that generation of composers who were born in the decade between 1675 and 1685, there is a good argument to be made that Jean-Philippe Rameau had the greatest influence.  Not Bach.  Not Handel.  Not Vivaldi.  In fact, the term “baroque” was derived from a pejorative comment made about Rameau’s Hippolyte et Aricie: Jean-Baptiste Rousseau dismissed Rameau as a “distiller[] of baroque chords of which so many idiots are enamoured.”  Other critics complained that Rameau’s “misshaped composition lacked coherent melody, was overly dissonant and changed key and metre too much.” 

Rameau was savagely attacked during his lifetime by traditionalists who braced at his harmonic innovations.  And yet Rameau held on to his exalted position as court composer, much to the dismay of the so-called “Lullyists” who championed the cause and aesthetics of his predecessor.  Perhaps it is hard to hear today what caused passions to run so hot in Paris during the 1750s—but it is fair to say that Rameau’s opera subverted Lully’s conception of French opera completely—driving the entire composition through harmonic progression and changing overnight what French society deemed to have been unchangeable.  To find a parallel to the storm of controversy created by Rameau’s Hippolyte, we need to look to 20th century Paris and the premiere of Stravinsky’s The Rite of Spring.  And that guy drank with The Rolling Stones.

So let’s listen to this revolutionary work.  In the Act IV conclusion to his controversial Hippolyte, we see opera take on a bigger, grander sound—perhaps even more so than Handel ever composed.  The discordant tones that so enraged the Lullyists back in the day are clearly discernable, even if their shock value has diminished over the centuries. 

Jean-Philippe Rameau, Hippolyte et Aricie, Act IV conclusion:

For my money, Rameau’s best opera is Les Indes Galantes, which I doubt will ever be performed again given the subject matter.  Rameau is often derided for lack of melody.  This selection puts that debate to rest.  

Jean-Philippe Rameau, Les Indes Galantes, Tendre Amour:

Rameau is the first true modern opera composer, laying down the maxim that has guided the art form to this day: “I conceal art with art,” he said, signaling his intent to unite all of the arts (music, fine art, architecture, decorative arts, dance, poetry, etc.) in opera itself.  Rameau was the originator; Wagner was its realization a century later. 

Personal note:  As some may know, my other passion lies in antitrust law and economic theory.  It is therefore unsurprising that Rameau is a personal favorite of mine, not only because of his music, but because he came to so dominate the French opera scene that a petition was circulated in 1740 seeking a royal order to limit his output in any given year.  Who doesn’t love output restraints in Baroque opera?

Back in the Baroque: An Introduction and Preview

The Baroque period covers roughly 150 years of music history, divided into the early (1605 to 1630), middle (1630 to 1680), and late (1680 to 1750) periods.  Just a quick detour into music theory.  Baroque music introduces the figured bass (also known as the thorough bass), as composers began what was to become an obsession with harmonic progressions that continue to this day and across all genres of music.  The figured bass part was played by one or more instruments (often a harpsichord, possibly joined by a cello or viola da gamba), collectively referred to as the basso continuo.  Here is a much more detailed explanation:  http://openmusictheory.com/thoroughbassFigures.html.

The figured bass also gave rise to the practice of basso ostinato or ground bass, essentially a repeating pattern in the bass line.  For example, listen to the first eight notes of the following—one of the most famous examples of ground bass in music history:

Johann Pachelbel, Canon in D:

Pachelbel creates the harmony from the ground up; hence, ground bass. This is no longer the fixed drone of Renaissance polyphony—harmony, beginning in the Baroque, is free to journey away from the home tonic chord, led by the bass line.  Chords, rather than individual notes, could provide a sense of emotional closure—something noted by Monteverdi in his seconda practica.  No longer just a piercing high C (think back to Allegri’s Miserere and its high notes), this is more the emotive satisfaction of riff based on power chords.    The notable effect of this new method of composition was to confine melody in a single voice (as opposed to multiple voices in polyphony), supported by accompaniment, i.e., monody, paving the way for opera, concertos, and more popular musical forms.  These basso continuo parts, and the concept of the basso ostinato, links Western music across the centuries, beginning in or around 1600 to the present, from Beethoven’s symphonies to Count Basie to some of the best-known rock tunes.

The Beatles, Day Tripper:

Led Zeppelin, Immigrant Song:

Baroque composers were now free to explore the relationships between the multiple melodic lines and the figured bass line, a compositional technique called “counterpoint”—literally point on point—which would come to dominate the Baroque Era.  Here is a short video that provides an excellent introduction to contrapuntal technique:

Although counterpoint was present prior to the seconda practica, Monteverdi’s embrace of dissonance led subsequent composers to explore a greater range of tone color in their music.  Harmonies therefore became more complex as composers both identified the natural affinity between chords, as well as how multiple tones could combine into new chords. 

The culmination of these explorations in counterpoint manifested in the fugue form.  Technically, a fugue is a “contrapuntal compositional technique in two or more voices, built on a subject (theme) that is introduced at the beginning in imitation (repetition at different pitches) and recurs frequently in the course of the composition.”  I think it is easiest to understand as the same basic melodic line (the subject) repeated at different times and at different pitches and meters, like Row, Row, Row Your Boat (in its most simplistic form).  It opens with a short main melody (ending with “stream”), which is then repeated successively in each ensuing voice.  When each voice has entered, the exposition is complete.  Most fugues will then move on to more complex “development”, exploring different keys where material previously heard is transformed and transfigured, before returning to the home key for the recapitulation.  Some fugues have a coda at the end.

Fugues are magical things.  All you need is a simple tune to start and, frankly, it doesn’t need to be anything great.  So, let’s pick a recent example from the top of the pop charts:

Ed Sheeran, Shape of You:

Not exactly great music.  But give the tune over to a talented composer, unleash the contrapuntal power of the fugue and—BOOM:

Ed Sheeran (arr. Giovanni Dettori), Shape of You: https://www.classicfm.com/discover-music/ed-sheeran-fugue/ (see embedded link)

And if you want to hear a shorter vocal-only version:

Ed Sheeran (arr. Giovanni Dettori and Chris Rupp):

Renaissance Music IX: The End of an Era, Claudio Monteverdi (1567-1643), Part I

We now arrive at the singular musical genius of Claudio Monteverdi.  In any list of the most important composers in history, he’s Top 10, easily.  As much as I love Tallis and Allegri, neither is on Monteverdi’s level artistically.  Unlike Bach, who fully embodied his age with such mastery that (at least for me) his death took the entire Baroque Period with him to the grave, Monteverdi’s genius for innovation ended the Renaissance, began the Baroque, while pretty much inventing and perfecting opera along the way.  More to say about him as a Baroque composer later, but for now, a true late Renaissance madrigal to close out that singularly gilded period.  A standard form to be sure, but for Monteverdi a chance to incite a revolution in sound—Monteverdi dabbles in that black art of dissonance to achieve a more dramatic effect to his music, a technique that he would use to great effect in his operas.  Instead of composing solely on closely related chords, Monteverdi experimented with combining chords that had no relationship to one another, adding additional color to his music and which enabled him to express a broader range of emotions. 

Here is the story.  In 1598, a group of composers and performers met in Ferrara in connection with the wedding of Philip III.  Details of what emerged during those concerts was memorialized in the writings of Giovanni Artusi, a noted music theorist.  Monteverdi used this occasion to trot out some of his more inventive compositions, which Artusi described as “harsh and little pleasing to the ear.”  Chief among Artusi’s complaints was Monteverdi’s “open and exposed” use of dissonance, breaking Palestrina’s golden rules of harmony and counterpoint.  The Artusi-Monteverdi debate raged without cessation much of the next decade—Artusi published his anti-modernist treatise on music theory in 1603 and Monteverdi responded in kind.  Best not to debate a genius on his own turf:  Monteverdi’s landmark Fifth Book of Madrigals compiled these innovative compositions and, in the introduction, the composer announced his intention to publish a treatise of his own, one that has come to be known as the Seconda practica, although Monteverdi’s full title was Seconda practica, overo Perfettione della moderna musica.  Translation is probably not needed there.

The first selection, Cruda Amerilli, leads off the Fifth Book.  Monteverdi undoubtedly placed it first, since this madrigal and come in for the harshest criticism from Artusi.  In it, Monteverdi uses dissonances in the opening bars to convey the wounds of love suffered by the protagonists, the shepherdess Amaryllis and the shepherd Mirtillo:

Cruel Amaryllis, who even with your name, to love, alas,
instruct bitterly;
Amaryllis, more pure and beautiful
than the white privet,
but more deaf and more fierce and more fleeting than the deaf asp;
since in speaking I offend you,
I will die in silence.

Claudio Monteverdi, Cruda Amarilli:

The next selection, which closes the Fifth Book, has become the most famous of the lot.  Here, Monteverdi takes harmony to new places, creating dissonances and ambiguity, augmenting the lyrics musically to drive the emotionally points home.  The lyrics and music, in Monteverdi’s skilled hands, are fused to one.  While these brief dissonances fall relatively easily on our 21st century ears, they would have seemed like harsh daggers to the brain in 1605.  This pain, this music, is all too real—we are still singing songs about it today:

O Mirtillo, Mirtillo, my love,
if only you could see
the inner life and feelings of her
whom you call most cruel Amarilli,
I know well that you would feel for her
that same pity which you ask of her.
Oh, our souls are too unhappy in love!
What joy is there, my heart, in being loved?
What joy is there for me in having so dear a lover? Why, cruel Destiny,
do you divide us when Love unites us?
And why do you unite us,
treacherous Love, when Destiny divides us?

Claudio Monteverdi, O Mirtillo, Mirtillo anima mia:

The use of dissonance has become more common over the centuries, but it still can be effectively employed to convey emotional pain.  By 1964, The Beatles, and John Lennon in particular, had reached a tipping point.  The extreme popularity of the Fab Four had completely eroded their privacy, subjecting The Beatles to constant attention—the pressure of fame had become literally physical as photos of the band from that era will attest.  Lennon wrote a song about his emotional pain, which The Beatles would predictably lampoon in a movie by the same name.  But the title and that remarkable opening chord tell a story as old as time.

The Beatles, A Hard Day’s Night:

Monteverdi’s Fifth Book was a landmark in music history—this is where Monteverdi slams the door on the Renaissance for good, in compositions that would influence scores of musicians, from Mozart to Beethoven and right through to The Beatles and beyond.  Bigger things to come next time, as Monteverdi’s genius reaches its full flowering; but for now, a farewell to the Renaissance and, oh, what a way to close out that glorious age.

Renaissance Music V: Giovanni Pierluigi da Palestrina (1525-1594)

All visits to Rome trace (at least in part) the career of Giovanni Palestrina, who at times was employed at Santa Maria Maggiore, the Vatican, and San Giovanni in Laterano. Palestrina is also arguably the most important composer in history, even if the most celebrated story about him turns out not to be true. No composer was more revered or studies by other composers. Bach’s titanic B Minor Mass (which will get an entry all to itself later on), for example, reflects his careful study of Palestrina. In sum, Palestrina’s music is the embodiment of the Renaissance ideal.

In Palestrina’s music, Renaissance polyphony reaches its zenith, utilizing a somewhat reduced counterpoint to create the luminous harmonies that would so inspire Bach a century plus later. Reducing his use of counterpoint also enabled Palestrina to limit dissonance. Palestrina’s rules of composition, especially regarding the succession of intervals, produced a gorgeous harmony known as “the Palestrina style”—arguably, the most beautiful sonority ever achieved in vocal music. Led by the Catholic Church in full Counter-Reformation zeal, composers sought to codify Palestrina’s style, creating rules that would govern composition for more than 200 years:

  1. The flow of music should be dynamic, not rigid or static.
  2. Melody should contain few leaps between notes.
  3. If a leap occurs, it must be small and immediately countered by stepwise motion in the opposite direction.
  4. Dissonances are to be confined to suspensions, passing notes and weak beats. If one falls on a strong beat (in a suspension) it must be immediately resolved.

These rules would hold sway over Western music at least until Ludwig van Beethoven’s final years.  And while Beethoven would go off to explore soundscapes that only he could imagine, Palestrina’s rules continued to provide the grounding structure of musical composition until Richard Wagner intentionally and purposefully shattered them in his Ring cycle of operas in 1874. 

Palestrina’s magnum opus is the Missa Papae Marcelli.  Even if the Church was unwilling to hand over responsibility for singing to the congregation as Protestants had, Church leaders wanted the word of God to be clearly articulated.  Polyphony, as practiced in the high Renaissance, involved overlapping voices making many of the words totally unrecognizable.  According to legend, a panel of cardinals at the Council of Trent threatened to put an end to beautiful music forever.  But music had a savior: because Palestrina’s music was so beautiful, not even these draconian cardinals would dream of banning it.  For this, Palestrina earned both the sobriquet “The Prince of Music” and everlasting glory. Unlike most composers, who saw their fortunes ebb and wane both during and after their lifetimes (even Mozart went out of fashion for a while)—the legend of Palestrina endured, as did his rules of composition.

Despite the indelible image of Palestrina composing music so beautiful as to persuade the Church to preserve polyphony, that story is, sadly, apocryphal.  Here is the entry from Wikipedia: “According to this tale, it was composed in order to persuade the Council of Trent that a draconian ban on the polyphonic treatment of text in sacred music (as opposed, that is, to a more directly intelligible homophonic treatment) was unnecessary. However, more recent scholarship shows that this mass was in fact composed before the cardinals convened to discuss the ban (possibly as much as 10 years before). Historical data indicates that the Council of Trent, as an official body, never actually banned any church music and failed to make any ruling or official statement on the subject.” 

Regardless of the truth, here is Palestrina’s Missa, in all of its glory, sung by the incomparable Tallis Scholars. In it, we can hear three distinct styles of music. First, we get all of the power and the glory of High Renaissance polyphony (Kyrie, Sanctus, Agnus I). Second, Palestrina presents a newer form of composition, which seems to incorporate the Church’s movement towards shorter phrases and clearer word-setting. Palestrina adopts this style during arguably the highlight of the mass (Gloria) and the most important (Credo). Third, a proto-Baroque style appears to emerge during the Agnus II, in which counterpoint predominates. Palestrina. Genius. Bringer of Light.

Palestrina, Missa Papae Marcelli:

Renaissance Music I: John Dunstable (1390-1453)

It was the English composer John Dunstable who introduced the third to music, creating the unique color palette that allowed Western music to flourish. In short, a “third” is simply the third note above the root note: If your root note is a C, the third interval is an E.  Thirds are referred to in music as imperfect because they can be both major and minor (depending on where you start).  And, of course, when you stack two thirds together, you get the 1-3-5 triad—the foundation of all Western music through to that pop tune that came out last week. 

Dunstable also found that there was an inherent logic that knitted together different triads, since each triad is composed of two notes of a different triad.  Moving from one closely related triad to another gives a logic to music that has informed our understanding of harmony to this day.  This video gives a great introduction to triads and chord theory:

Don’t worry about diminished and augmented chords, as they won’t become really relevant for a few hundred years.

Of Dunstable’s other major developments, his revolutionary decision to move the melody from the tenor line to the top treble line is the most significant. In this, he broke the continental preference for dissonance and the primacy of lower voices. Before Dunstable, music was, with very few exceptions, dull, sparse and predictable. Dunstable is responsible for bringing the color of the Renaissance to music and with his music that we start our musical journey in earnest.

John Dunstable, Quam Pulchra Es

Several hundred years later, a retired miner in the north of England composed a song based on a traditional Yorkshire ballad. Drawing his musical inspiration from the Middle English period (roughly from the 5th to 16th centuries), Ewan MacColl’s remarkable 1947 Canticle has been performed by many bands over the years, including most memorably by Simon and Garfunkel. From their legendary concert in Central Park, when these two brilliant musicians transported 1980s New York back to the English Renaissance, if just for a few minutes.

Simon and Garfunkel, Scarborough Fair:

Incidentally, I should note that my personal Rosetta Stone for Early Music was the Kronos Quartet’s remarkable album “Early Music” from the late 1990s. Kronos was, and remains, on the vanguard of contemporary music, but this album saw the group reach back across the centuries to find the inspiration for much of what they had been performing. The album effectively presents contemporary music along side music written several hundred years ago. The effect, for me, was remarkable and I recommend the album highly. It is one of my Desert Island Discs.

A brief introduction

At its core, music is as much mathematics as art: The godfather of Western music—all Western music—is none other than Pythagoras, the Triangle King himself.  In or around 500 BC, Pythagoras developed the modern scale by taking metal bars and dividing them sequentially by 2/3 to create successive notes.  Pythagoras’ scale had 12 tones—you can see these on any modern-day keyboard, where there are 12 keys within each octave.  These are not, however, Pythagoras’ original tones, but their modern counterparts.  The basics of western music are organized around a series of “perfect” fifths—called perfect because they are easily tuned by ear.  The math, for those interested, is explained here:  https://pages.mtu.edu/~suits/fifths.html.

But Pythagoras’ scale had a problem—although his 12-tone scale replicated natural tones perfectly, the spacing between the notes was off and increasingly so as you went up the scale. So much so, in fact, that the octave note was considerably higher and thus “off”.  Mathematically, this can be reduced to the basic premise that no power of two can equal any power of 3.  Pythagoras’ solution to what became known as the Pythagorean Comma was to simply throw out all notes above 12 and 5 of the 12 tones he had discovered.  The remaining seven form the bedrock of all Western music—they are literally the Do, Re, Me, Fa, So, La, and Ti that Julie Andrews sang about in the Sound of Music (bonus points to anyone who had that song as the first one I’d mention in this series).  Again, the math stuff is here:  https://pages.mtu.edu/~suits/pythagorean.html

As a side note, there are far more tones possible than the 12 set out on a modern keyboard.  This may be summarized in the adage that G# is not the same thing as Ab.  Surely, our resident cellist, The Professor, can attest to that.  While we consider semitone composition to be a 20th century phenomenon (influenced largely by Arabic music), experimentation with additional semitones goes back more than 500 years.  Check out this video of an Archicembalo, which has 31 keys per octave, play an early experiment with 24-tone music:

But the bedrock for Western music is that familiar seven note scale and, with that established, it is time to start.

Not to endlessly quote Julie Andrews, but the beginning is indeed a very good place to start.  Well, not really the beginning, since we know that music has existed pretty much as long as mankind has.  Jazz musicians are known to lament all of the great music that disappeared, unrecorded, into the walls of jazz clubs—but that is nothing compared with the centuries, if not millennia, of music that have fallen silent, forever.  There is a reason why a Greek chorus was given that name—its part was more than likely sung.  It was the rise of what became modern staff notation in 11th century that allowed for modern musicians to replicate the music of the past (take a bow, Friar Guido of Arezzo—paying homage to Friar Guido is the second best reason to visit Arezzo, after the staggering Piero della Francesca fresco cycle depicting the Golden Legend, perhaps the greatest fresco cycle ever painted: http://www.travelingintuscany.com/art/pierodellafrancesca2.htm).  

At the beginning, Western music was monophonic, that is a single line of melody only. Here is a classic example, and one we will return to in a few hundred years.

Anon., Crux fidelis:

I’d like to think it was the acoustics in churches that got composers thinking about harmony.  Sound reverberates in a Gothic cathedral, producing direct and indirect sounds that overlap with each other.  This is the primary reason why music composed for church performances should be heard in situ, and not in a sterile concert hall with its perfected acoustics.  Regardless of the inspiration, late Gothic composers added a second line of music to their works. This was called organum.

Anon., Dies Irae:

Anon., Advocatam innocemus

Commonly, that second line of melody was sung by a boys’ choir.  In the Dies Irae selection, the two musical lines come together at around the 7:10 mark to produce the sound that is so characteristic of late Gothic music.  Alternatively, composers created organum by having one voice sing a continuous unchanging note, around which the plainchant is sung.  An example of this comes at the 1:30 mark of the second selection. This is, hilariously, called a drone and one of the more popular late Gothic instruments was called a drone organum, since it played only one note continuously. 

Incidentally, the concept of a drone has endured through the centuries.  The Velvet Underground used a drone extensively (and, no, I’m not talking about Lou Reed’s voice):

The Velvet Underground, Heroin:

Eventually, these new melodic lines would become independent on the main plainchant melody.  Reflecting church hierarchy, the primary melody continued to be sung in the lower male voices (the cantus firmus), while the higher voices were given faster lines to decorate the basic plainchant. The invention of harmony, however, created a problem.  While monophonic plainchant was easy enough to learn orally, multiple melodic lines needed to fit together precisely.  Eventually, the unmeasured rhythm that characterizes early Western music gave way to measured rhythm—the allocation of precise time values to individual notes, allowing singers to remain both rhythmically and melodically together as the composer had intended.  The need for measured rhythm gave rise to a need for written music.  Enter Friar Guido and his neumes. (https://brianjump.net/2015/08/29/the-origin-of-notation/).