Great Masters In Dialogue: Part 1

Greetings!

On this, Ludwig van Beethoven’s 251st birthday, we continue our celebration and discovery of the great Master and his music-beginning with a six-part series entitled “Musical Masters in Dialogue”—which focuses on a single work: “Symphony No. 4 in E minor” of Johannes Brahms.

What? How, you may well ask, do we celebrate and refine our comprehension of Beethoven, by studying a work of Brahms? It requires many things, including an understanding of the dialogue between musical masters, and a challenge to the false division between Natural Sciences (Naturwissenschaft) and Art (Geisteswissenschaft), which was implemented through the Romantic movement of late 19th century.

According to this doctrine, the “Natural Sciences” consist of the study of objective nature, such as geometry and physics, outside of man, by a cold and calculating scientific method, that operates without emotion or creativity, both of which would stand in the way of said objectivity. Works of Art, however, were deemed to be creative, and passionate. They reflected the subjective inner life of humanity, and were often created impetuously, without being weighed down by thought or deliberation, both of which would stand in the way of said creativity.

Thus, we have, according to Romantic doctrine, either thinking without feeling, or feeling without thinking. Can such an artificial state of affairs actually exist? Could any great art have come into existence in such a world? Could any scientific discoveries have been made thus?

THE SPIRIT OF SCIENTIFIC DIALOGUE

There has long existed among great scientists, a spirit of collaboration in solving problems, and in happily passing some aspects of such problems on to future generations.

One such set of problems is characterized by what Leibniz called the “Principle of Least Action” (essentially, that nature will always follow the most efficient course). Contributions had been made earlier, including Fermat’s discovery that light will always take during the path of least time (this diagram, accounts for refraction of light according to least time).

1. Fermat Light -least time

The Principle of Least Action. Light will always follow the path of least time. Point P depicts a change in medium, say from air to water.

After Bernoulli issued a friendly challenge to solve the Brachistochrone problem (curve of least time), several responses were received, and these types of investigation, which had been carried forward from Fermat and others, extended into the future as well. Though scientific discovery is a good in itself, it usually led to the benefit of mankind.

2. Tautochrone ( all of the balls will reach the bottom at the same time.)

The time taken by an object sliding without friction in uniform gravity to its lowest point along the curve is independent of its starting point.

3. Brachistochrone curve (the curve of least time.)

In 1696, Johann Bernoulli issued the following friendly challenge to solve the Brachistochrone (least time) problem.

“I, Johann Bernoulli, address the most brilliant mathematicians in the world. Nothing is more attractive to intelligent people than an honest, challenging problem, whose possible solution will bestow fame and remain as a lasting monument. Following the example set by Pascal, Fermat, etc., I hope to gain the gratitude of the whole scientific community by placing before the finest mathematicians of our time a problem which will test their methods and the strength of their intellect. If someone communicates to me the solution of the proposed problem, I shall publicly declare him worthy of praise.”

THE SPIRIT OF MUSICAL DIALOGUE

Could such a dialogue exist in art, in music? Could an investigation into the Principle of Least Action take place there? The aforementioned Romantic doctrine would seem to say no. An artist has deep-seated emotions, and must undergo a strong catharsis in order to express them, to “get them out.” Such a view suggests a purely internal, and timeless origin for a creative work of art. It tends towards the idea of “Art for Art’s Sake”. Let Art speak for itself they say. It has no need of analysis, and need not justify its existence, nor benefit mankind.

Let us remember that this Romantic doctrine is fairly new. Though it has historical precedents, the deep connection between science and art used to be much better understood. Sometimes composers quote each other as a sign of respect. At others times, the quote is much deeper. They are quoting an essential discovery, and how to carry it much further, including with artists they never met.

Although Mozart was familiar with Bach’s sons, he first encountered J.S. Bach in 1782 at the salon of Baron von Swieten. Old Bach’s music was considered elitist, and too complex for ordinary people, so it was seldom played. Mozart took up the challenge. He began composing fugues, and incorporating other challenges from Bach into his music. Why? There are great difficulties involved. Mozart must have sensed that rather than being too complex, Bach’s counterpoint could elevate people to a higher level than the then popular melody and simple accompaniment.

Mozart responded in such a way to Bach’s “Musical Offering”, first with a fugue,K426, in 1783,

https://youtu.be/oNrM37AYxfc

then the next year with his his Piano sonata in C minor, K457. But then, he carried it much further in his Fantasy in C minor, K475.

Here is “The King’s Theme” from Bach: next, the opening of Mozart’s Fantasy. (See photo sample)

4. Musical Offering King's Theme (today we discuss just the first five notes.) Noted 4 and 5 (Ab and B) from the diminished 7th interval, which implies the Lydian intervals.

5. Mozart Fantasy First 7 notes

The notes are identical to the first five notes of Bach's Musical Offering, except for the repetition of C, and the crucial addition of F#.

The crucial addition in the Mozart is the tone F#. Many productive hours may be spent, and have been spent (including by this author), in elaborating these works. However, we find it best to concentrate on the fundamentals before advancing. Sometimes the most elementary discoveries, are also the most profound.

Beethoven elevated this dialogue to a sublime level in his final Piano Sonata No. 32 in C minor, Op. 111. Bach had featured in his “Musical Offering” the large and dissonant interval—the diminished 7th—in the melody. That interval also implies what are sometimes termed Lydian intervals (tritones).

Beethoven, in the introduction to his Op. 111, abandoned melody, theme and key. There is no theme! There is no key! Is he lost in ambiguity then? No! It is a precise investigation. He decided that rather than examine Bach’s diminished 7th interval as part of a theme, and build up from there, he would open with it, outside of key or theme, as the beginning of an inquiry into the Well-Tempered System as an entirety.

6. Op. 111 Opening

It opens with the diminished 7th interval, Eb-F#, the interval which both Bach and Mozart highlighted

When Beethoven finally arrives at a theme, it truncates both Bach’s “King’s Theme” (Musical Offering) and the opening of Mozart’s “Fantasy in C minor”, so that they are a one in our minds.

7. Op. 111 Main Theme

The first three notes, C, Eb, and B, truncate both the King's Theme and Mozart's thus invoking them both. The diminished 7th interval is reversed, going from B to Ab.

Later, in a sublime movement, Beethoven recalls the entire opening of Mozart’s Fantasy.

Stay tuned for Part 2.

Great Masters In Dialogue: Part 2

Johannes Brahms’ “Symphony No. 4, 1st Movement”

The classically oriented successors to Beethoven faced a daunting task. They were committed to maintaining his tradition, but how could one match him, let alone advance over him?

Schumann, Mendelssohn, and Chopin all understood that the first step in continuing this great tradition required that Beethoven's music be anchored in the work of J.S. Bach.

BRAHMS’ EXTRAORDINARY SENSE OF MISSION

For the then young Johannes Brahms, Bach and Beethoven were seminal figures. A portrait of Beethoven guided him at the piano, and one of Bach guarded him over his bed. However, his own vast collection of musical scores included the complete works of Couperin, which he edited; Madrigals by Luca Marenzio; and many other Renaissance works. Brahms recognized that Bach did not come out of nowhere. There is a history of musical discovery leading up to Bach’s great works, and many of Brahms' own compositions were informed by what he learned from Renaissance music.

Something precious, and internal, was driving him to accept his role as the guardian of classical music, against what he saw as dangerous tendencies towards arbitrariness and caprice.

One of the least recognized events in history is the “Manifesto” of 1860. At the time, an effort was made to proclaim that the "Music of the Future'' of Liszt, Wagner et al, was a 'fait accompli'. Historians agree that, in opposition, Brahms led the effort to gather signatories for the “Manifesto”, which counters that idea, saying:

“The undersigned have long followed with regret the pursuits of a certain party, whose organ is Brendel's "Zeitschrift für Musik". The above journal continually spreads the view that musicians of more serious endeavor are fundamentally in accord with the tendencies it represents, that they recognize in the compositions of the leaders of this group works of artistic value, and that altogether, and especially in northern Germany, the contentions for and against the so-called ‘Music of the Future’ are concluded, and the dispute settled in its favor. To protest against such misinterpretation of facts is regarded as their duty by the undersigned, and they declare that, so far at least as they are concerned, the principles stated by Brendel's journal are not recognized, and that they regard the productions of the leaders and pupils of t he so-called New German School, which in part simply reinforce these principles in practice and in part again enforce new and unheard-of theories, as contrary to the innermost spirit of music, strongly to be deplored and condemned.”

There were at least twenty signatories lined up for the Manifesto. But that was sabotaged when it was leaked prematurely to the press with only three signatures, making it seem vindictive. From then on, the battle took place in music and in the concert halls. That battle was far more intense than we sense today.

Sometimes, a dialogue between masters is born out of necessity. No matter what the attitude to the Romantic composers is today, Brahms saw a great danger of increasing lack of rigor in the works of Liszt (whose works he labeled as "swindles"), and those of Bruckner (which he described as "symphonic boa constrictors"). This was not petty jealousy on Brahms' part. He took music far too seriously for that.

Brahms began work on this fourth symphony in 1884. He chose Beethoven and Bach as bookends for the first and last movements. It was a clear demonstration of classical rigor, as opposed to romantic wandering.

The first movement is a masterpiece of the “Principle of Least Action”—which is known in music as “motivfuhrung”—creating an entire movement out of a small group of notes known as a “motiv”. Brahms illustrated the nature of such motives.

What is the smallest unit in music—a note? An isolated tone tells you nothing. Does the single tone C establish C major? Play F after it, and you will hear otherwise. The smallest unit is a unit of action—of motion, an interval.

Intervals open up a new and higher level of ambiguity. One of the strongest principles in musical discovery is “inversion”—as it is in the so-called "hard sciences." For example, mirror images in stereochemistry are known as 'chirality' (see example 1)—is the left and right-handed versions of the same molecule. They function differently. Musical intervals can also appear as mirror images. (See example 2).

Chirality: Mirror images in chemistry

Mirror images in music

Human creativity has a "pre-established harmony" with the laws of the universe, which will always follow the most efficient pathway. Try dipping a wire cube into the fluid you would use in making soap bubbles. You might expect the soap film to simply cover all six surfaces of the cube. It actually forms a smaller cube inside. Though it looks more complex, it is the minimal surface that the soap film can form. (See example 4)

Least action in soap bubbles

TEXT to Accompany the Audio Description (see below)

Brahms had been in a dialogue with Beethoven's “Hammerklavier”—Piano Sonata No. 29, Op. 106, for all of his life. His Piano Sonata No. 1 in C major, Op. 1, written in Hamburg in 1853, starts with a bold quote from the “Hammerklavier.” The first movement of his 4th Symphony is a response to a section of the slow movement in Beethoven’s Op. 106, in which Beethoven abandons the key signature, and concentrates on the essential movement.

Brahms begins with a simple descending interval in quarter notes—B to G—a major third. He follows with an inversion, an ascending minor 6th—E to C. Then, he moves the entire process down a scale step—A to F#, and D# to B. The entire opening theme looks like this. (See example 3).

Opening Theme of Brahms' 4th Symphony

Anyone who hears this opening will likely comment that it constitutes a "bare-bones " statement, a minimal one. Brahms is demonstrating "freedom necessity." True freedom doesn't come from the license to do whatever you please. Accepting the restrictions of physical reality (including humanity's need for great art), demands more creativity, and leads to more profound discoveries.

How does one make an entire movement out of this? It is not a linear, mechanistic process—not a Lego set. If you try to find the genesis of the movement in linear extensions of the theme, it won't work, and it will be boring. As you can see with the soap bubble, the process of construction according to the “Principle of Least Action” is not linear, but creative.

What? Nature shows creativity?

The second theme, in B minor, might seem unrelated. It is not! The main theme, like the opening, contrasts alternating inversions, in this case the minor seventh and major second. The bass line for that second theme, when put through a series of elementary transformations (mostly octave transpositions), reveals its derivation from the main theme (as illustrated in the audio.)

Brahms continued his experimentation with these transformations well beyond the symphony (as demonstrated in the audio).

Audio: https://drive.google.com/.../1eIj4L1HLDyPSuqe9DF2.../view...

Here is a performance of Brahms’ first moment: https://youtu.be/4uw0l00vb7Q

Great Masters In Dialogue: Part 3.1

Brahms' Symphony No. 4, 2nd Movement

"Who says there is nothing new under the sun?"

The 1st movement of this symphony came from Brahms' deep reflections upon Beethoven's discoveries, and the 4th movement from his equally deep study of Bach. The 2nd movement presents unique discoveries by Brahms himself. The written text complements the audio (see link below), which is primary. Some things just have to be heard.

The connections in this movement are so rigorous, that they may seem to derive from logic. Nothing could be further from the truth. Logic is superseded by reason, which in turn, is ruled by love, but without abandoning logic. Brahms is free to range, in the entire well-tempered musical system, and the opportunity for creative discovery it offers. Such beautiful new discoveries could never arise from mere logical connections.

A new composition cannot mean anything to anybody, if it merely follows the course of logic, especially if one has something to say to the world—something positive that might lead to positive change. That requires creativity, and original discovery. One must present people with the possibility for change, as reflected in one’s self! Is that a matter of deep feelings only? Get ready to get nerdy, but from the depths of your soul!

In the previous section, we examined one of Brahms' great discoveries in this movement: how he took the ancient principle of inversion, and applied it not just to themes, but the entire musical system. Inverting the entire scale of E major gave us the Phrygian mode, and thus the movement's paradoxical opening was resolved- or was it? (please review last post for Brahms 3.1)

Further investigation led to how Brahms' inverted the symmetrical tetrachords of the major scale. This is not the same as twentieth century composers fooling around with different arbitrary scales. Everything was lawfully constructed, everything was a discovery of principle, expanding the capabilities of the well-tempered system of tonality, but never abandoning it in an arbitrary or capricious way.

Brahms came, not to overthrow that system, but to fulfill it. He took part in realizing its ever-expanding potential!

Brahms inverted the tetrachords harmonically. The major scale goes as follows (with WT representing whole tones,or major seconds, and HT representing half-tones, or minor seconds)

WT WT HT WT WT HT

E F# G# A B C# D# E

In between lies the tritone, or Lydian interval, in this case A# (or Bb).

The tetrachords are symmetrical and even suggest polyphony.

If we play the upper tetrachord downwards, within the same scale, we invert the intervals.

WT WT HT HT WT HT

E F# G# A E D# C# B

If we maintain the intervals, we invert the tones, into the upper tetrachord of e natural minor:

WT WT HT WT WT HT

E F# G# A E D C B

Brahms invented a new modality that is minor and major at the same time, though in a precise manner. The section beginning at measure 5 is in E major and e minor at the same time. Except for one tone, that modality is employed strictly through the inverted tetrachords. The major tones derive from the first tetrachord E F# G# A , and the minor ones from the inverted second tetrachord E D C B.

Scales and keys are no longer self-evident—a priori existences, as unchallengeable as The Ten Commandments. They are created anew, and new modalities can be lawfully created. I put extra emphasis on "lawfully", because, as the 20th century has shown us, the arbitrary creation of new modalities does not work. The principles of tonality can be expanded, but never abandoned. It is the method by which one discovers new modalities that counts. Don't just memorize the keys, chords and scales of the well-tempered system, look at how that system came into existence! (Why do we think Brahms studied so much early music?)

Brahms elaborates on his discovery throughout the movement. At measure 30, a beautiful new theme emerges.

E E F# G# E D# E C# E B E F# G# E

It seems miles away from the quizzical opening. Invert the intervals though, and you have the opening horn solo, with a few rhythmic differences.

E E F G E D E C E B.

Brahms continues to insist on inverting the tetrachord in a simple up and down motion. A good example is this begins at measure 36 at a quick tempo.

F# G# A# B A G F# D E F#

He could have done this with a major tetrachord up and down, and nobody might have noticed. Instead, he inverts the tetrachord, thus maintaining his idea of change as the substantial (Again, this is made much more clear in the audio).

Soon after this, another beautiful new theme emerges at measure 41, in the cellos, stated in B Major.

B C# D# E D# C# B G# A# F#

Again, is this new? The opening statement, which reached up to a third, and down to a third, now expands to reaching up by a 4th, and down by the same. This identifies the qualities of the tetrachords, which were both the discovery and the source of the opening paradox. The theme reaches up by a tetrachord B C# D# E then down the same tones E D# C# B. It then descends B A# G# F#. Like the opening, it centers on a certain tone (in this case B and rises up, and reaches down in the same space, but with inverted intervals (in this case WT WT HT rising from B, and HT WT WT descending from.

This might seem to be an unambiguous B Major, but the inversion of WT WT HT continues, and Brahms may well have created B Major anew.

The climax of the piece begins at measure 88, and reaches its height at measure 98.

Despite the syncopation, and octave transpositions at that high point, the theme is basically the same as what we heard earlier at measure 88, and even earlier in the cellos at measure 41, but now it is in a newly created E major

E F# G# A G# F# E C# D# B.

The Coda is amazing! In Part 3, we discussed how the opening horn theme could exist in several modalities, including the Phrygian mode, but also A minor and especially, C major. Brahms ends the movement by having the horn repeat its opening, first against a bass pedal point of E and then C, so we hear how it might have sounded in C, except that he brings in astounding dissonances, all based on the opening. It ends, not with a perfect cadence of B to E, but F natural to E, thus exploiting the characteristic dissonance of the entire work.

For Brahms, the point is not " finally arriving" at E major, but the process of discovery, and generation of new modalities itself. This writer remembers a composition teacher glowering at him and saying, "Just remember, everything that can be said in this language (tonality) has been said." That was the argument for atonality, and serialism. The harmonic language of tonality had been exhausted. If you see music theory as reductionist chord progressions, you might have a case. Brahms was proving that the system of Bach was not only still viable, its potential was infinite, and he did create something new under the sun.

Reading this installment alone might be difficult to understand. We urge you to please listen to the audio in conjunction with the written text!

https://drive.google.com/.../1hjlg90cBUpeRdOBWmZw.../view...

Great Masters In Dialogue: Part 3.2

Brahms Symphony No. 4- 2nd movement

WHO SAYS THERE IS NOTHING NEW UNDER THE SUN?

By Brahms’ time, a great gulf existed between music theory and musical practice. The essence of musical composition lies in creativity, and discoveries made by the human mind, including discoveries of new possibilities in the musical system, such as scales and keys. Music theory often leaves the human mind out of it, and presents scales, keys, and chords as fixed and unchanging, as "The Law." (In the 20th century there were many law-breakers, but you really want "not to overthrow the law, but to fulfill it.")

New Modalities in the Second Movement

In the first movement, we heard an unprecedented development of the “motivfuhrung”—the “Principle of Least Action” in music. Do we get a break from this idea and its gravitas in the second movement? No way, it intensifies! Brahms is fighting against the romantic idea that artistic creativity lies in an arbitrary notion of freedom to do whatever one wants.

I will explain this in words as much as possible, but the accompanying audio is indispensable. Some things have to be heard.

(Audio link: https://drive.google.com/.../14q7ApMEVFrEvdxS364V.../view...)

The first movement began in a bare-bones way, but the opening of the second movement is even more stark. While the first movement flowed in up-and-down motions of an interval and its inversions (with other instruments playing related things), the second movement is even more restricted. It begins with a solo horn playing an unaccompanied phrase. Other instruments join in, but either in unison or at the octave. There is only one theme. It centers around the tone E, moving up by a half-step and a whole step, and then down by two whole steps—an up and down motion that cannot but help remind us of the first movement.

E E F G, E E D C, E E F G, EE F G E (hear it in the audio)

It is relentless, unique and challenging.

What should our reaction be, A or B?

A. Brahms is challenging us with something that cannot be comprehended from any known theory! He gives us the key signature of E major, with its 4 sharps, and immediately, all 4 of them are negated in that opening. F# C# G# and D# all become naturals. What is he doing, and where is he going with this?

B. No worries. It's in the Phrygian mode.

Brahms is posing a problem for us to solve. Most musical theory avoids problem-solving. If we cannot explain something, we feel uneasy, and slap a name on it. That allows us to relax, and feel that we understand what is going on. Do we really understand it though, just by naming it?

In analyzing music, one has to have the courage to experiment, to re-situate the tones, and examine how they might have been done differently. This helps us understand the nature of the actual creative discovery made by the composer.

The opening tones (E E F G, E E D C, E E ) are more of a question than a statement. Let us assume for a minute that we have never heard of the Phrygian mode. How then does one account for these tones? They sound somewhat like e minor, but that key has F# as the second step, and here we have F natural instead. They could also be in C major, or A minor (as demonstrated in the audio). That ambiguity brings us into the realm of hypothesis. It is not a theme in one mode based on sense-certainty, like a simple statement in the indicative mood in language; it has the potential to exist in many modes, and its meaning differs in each mode. That potential sets our minds on fire, in a way that a "self-evident" simple statement of a single meaning could not.

What Brahms does is more like a play on words by Shakespeare. Take, from the opening of King Lear, the pun on the verb "to conceive", in Gloucester's acknowledgment of his bastard son Edmund:

KENT

Is not this your son, my lord?

GLOUCESTER

His breeding, sir, hath been at my charge: I have

so often blushed to acknowledge him, that now I am

brazed to it.

KENT

I cannot conceive you.

GLOUCESTER

Sir, this young fellow's mother could...

This is not Shakespeare entertaining himself with his own wit. The question of "what is legitimate" grows, as the play proceeds. Likewise, the ambiguities introduced by Brahms, develop and grow in their importance.

After the first 8 measures, the theme repeats a 3rd higher, on the clarinet, in the key of E major. Should we now say:

A. "It is as if he started on the Earth, and now is on the Moon. How, exactly, did he get there?"

or,

B. " No worries. He begins in the Phrygian mode, then continues in E major."

Further Enigmas in this Movement

This author has seen failed attempts to explain this movement from standard theory, where keys become absurd, and chords absurder. You have to step outside of the musical system as taught and invoke a principle.

How did he get from the Phrygian mode to E major, from earth to the moon? One of the great principles in science, including musical science, is that of inversion. Inversion usually works by inverting themes, then developing the ironies invoked. Brahms revived inverting entire scales. Now you are practicing the role of inversion in the entire musical system itself.

What is the relationship of the Phrygian mode to E major? It is a mirror image! Take the E major scale, E F# G# A -B C# D# E, and invert it. That is, make it descend by the same intervals as it ascends (WT WT HT- WT WT HT), and you obtain E D C B -A G F E, the Phrygian mode. (see example 1)

Aha! Now we have the two modes as "a One" (just as a violinist's two hands, though different, function as a one), through the process of inversion. Does the second movement begin then, in the Phrygian mode, and proceed to its inversion E major, or vice-versa? Can we now just slap names on scales and keys, or must we comprehend a process of transformation as fundamental?

Again, should our verdict be:

A. " This helps, but there is something unsettling about this E major."

B. "Worries solved! E major and the Phrygian mode are inversions of one another. Let's go home, and watch TV!"

There is indeed something unsettling in the supposed E major section that begins at measure 5! Brahms advances the process of inversion further. The major scale has two symmetrical tetra-chords. Both proceed WT WT HT: In the case of E major:

WT WT HT

E F# G# A and,

WT WT HT

B C# D# E.

The Lydian interval, or tritone (in this case A#), lies between them (see audio).

What if we invert the tetra-chords? If we match the ascending

WT WT HT

pattern E F# G# A, with the same intervals descending. That gives us:

WT WT HT

E D C B from the e minor scale, another mirror image!

That gives us a scale of E F# G# A / B C D E . That is exactly what Brahms employs! This author has heard Bach, Mozart, and Beethoven play between major and minor, invoking their in-betweenness. He has never heard any of them dwell in that "uncomfort zone" of both modes at once. Brahms is not in both major and minor in some nebulous way. With only a couple of exceptions, this passage is major in the first tetra-chord (E F# G# A), and minor in the second (B C D E).

As far as I know, that is an invention of Brahms. Again, please listen to the audio, where we help clarify that quality, including by demonstrating how the passage might sound in either E major or e minor.

Stay tuned for part 2, where we will follow the development of the movement!

Great Masters In Dialogue: Part 4

Brahms Titanic (and truly unsinkable) Fourth Symphony: Finale

INTRODUCTION

The story of Johannes Brahms should be an inspiration for us all. There was nothing in his background that suggested the great role he was to play. He was born into poverty—an oppressive poverty. There were no great musicians in Hamburg to teach him. His father was an itinerant bass player, who only supported a musical career for Johannes if it would pay off financially, such as playing in ad-hoc orchestras. For that reason, he discouraged his son's piano lessons, and especially a career in composition. It didn't pay the bills!

His father, seeking to feed his family, sent him to play in brothels for sailors. The women tormented him and teased him. The sailors laughed at him, and poured beer down his throat! The then boy Johannes Brahms staggered home drunk at the age of 14!

How did he maintain his sanity? He memorized the polkas and reels he was obliged to play, and while he rattled them off, studied the poetry he had set upon the piano's music stand.

Something drove him, and it was not just a desire to become great, but a sense of responsibility for the future of music. Where did that come from? Was it divine inspiration? Perhaps, but bear in mind that divine inspiration can come from without and from within; that the word "enthusiasm" means "The God within you."

THE FOURTH SYMPHONY

Let us summarize what we have discovered so far:

1. Despite the late 19th-century effort to drive a wedge between art and science—claiming that one emphasizes wild and ungrounded emotion, and the other, dry forensic reason—the universe will not submit to such an artificial division. The spirit of joyful discovery is not different in art than it is in science! Emotion and reason are unified, in the act of discovery!

2. Great scientists delighted in passing unsolved problems on to future generations. Whatever tendency towards egoism they may have had, those tendencies were subordinated to their love of humanity, and of future generations. The solutions to such scientific problems would change the lives of future generations. But, so would the solutions to artistic problems.

3. Brahms was alarmed at the degree of arbitrariness and caprice in musical composition. He understood that music is not just about the composer's personal angst, but about shaping future history. Classical music had a responsibility to that future, which the unbridled passion of the Romantics did not.

4. In his Fourth Symphony, he set out to strip the principle of least-action down to its essentials, free of all decoration, of everything superfluous, and make that principle of least-action clear, by constructing themes of the most bare-bones origins. From such elemental themes, he would develop the most universal and all-encompassing polyphony.

5. I must caution that it is not a linear process. Perhaps it can be compared to embryology. Human beings start out with two cells, which become a zygote. From this, wonders of differentiation occur. Organs, membranes, nerve cells, and most importantly, a human brain, rather than an animal one. Yet, it all flows from the continued division and replication of cells. Nothing extraneous is introduced. It is embedded. But, it is not a linear process at all.

Such is the “motivfuhrung” in music.

6. Though Brahms took all of musical history into his heart, the bookends for this work are Beethoven and Bach. The first movement explores the “Motivfuhrung” (motive-leading) from the highest standpoint. Brahms takes a passage from the third movement of Beethoven's Hammerklavier sonata, where Beethoven abandons the key signature, and posits descending 3rds, against their inversions, ascending 6ths. Brahms makes those intervallic motions the main theme of the first movement. All potential distractions and embellishments are stripped away. The principle has to stand, or fall, on its own. (See example 1)

Example 1: Brahms

7. The principle of inversion, expanded: In the 2nd movement, Brahms creates new modalities by inverting entire scales, and the tetrachords within a scale, thus making it possible to play in minor and major at the same time.

8. The principle of least-action—nature will always follow the most efficient course. The most reasonable course exists in both science and art. This does not always mean simple, and it could easily be confused with Ockham's Razor—the idea that the simplest answer is usually the right one. That is a mistake. If this measly theme had to thrive based on purely linear extensions, it would fall flat, as would a zygote that never stopped being a zygote. The theme exists, not in itself, but in its relationship with the entire musical universe, and its ongoing development.

9. Let us take an example in physics. Take a wire cube, and dip it in soapy water. You might expect that the application of the principle of least action, might result in a soap film covering all six squares that form the cube's surface.

Not so.

The soap bubbles will take this shape.

(See example 2: soap bubble)

Example 2: Soap Bubble

Notice the curved surfaces on the inner cube. The principle of least action does not confine itself to two-dimensional Euclidean space. We have passed from apparent linearity to higher dimensionalities, simply by following the principle of least action. This is actually the least possible surface area, and the least action taken to get there, although it looks more complex.

The same is true for the symphony. Do not expect Brahms to make his case from mere linear extensions of the theme. That theme exists in an entire universe of musical motion, and draws upon it, but never in an arbitrary way.

THE OTHER BOOKEND: BACH

May I suggest an experiment you may try with friends who don't know the work. Play the first few minutes of the fourth movement, then stop! Ask them if it evolves lawfully, or jumps around from one thing to another. My friends all said:" It jumps around."

Next, familiarize them with Brahms’ 8-note Passacaglia theme:

E F# G A A# B B(8va) E.

Then have them listen to the same measures again, and if possible, sing the Passacaglia theme as it repeats. As soon as they hear it, the piece will seem well-ordered to them. Accessing the ordering principle, changes how they hear it. It is one of the most striking examples I know of.

Brahms sat down at the piano one day, before Hans von Bülow (German conductor) and Joseph Joachim (the great Jewish German violinist) He played the last movement of Bach's Cantata 150 (https://youtu.be/lC8UErdK_XE) for them, and asked what they would think about it as the foundation for the last movement of a symphony. Later, Joachim wrote that he did not respond at the time, because he knew that his friend had already made up his mind to do it.

In Bach’s Cantata, it proceeds: A A B B C C DEE(8va) A. It is an early work by Bach, and that "Ground Bass" changes key, whereas in his later works, it does not. (Hear the final movement, Ciaconna, of Bach's Cantata #150 ,https://youtu.be/fgZF896c6ZA click on the last section in description for “Ciaconna”)

Mozart revived much of Bach's genius, including fugal writing, after his studies at the salon of Baron van Swieten at age 26. Beethoven took it further. Neither of them composed a Passacaglia, or Chaconne. Perhaps even van Swieten did not know of this Platonic form. Brahms, who saw himself as the man who would receive and transmit classical rigor to the future, must have seen it as necessary. The Passacaglia, or Chaconne, is one of the great developers of the principle of least action, sometimes known as freedom-necessity. Let a student composer have free reign with a sonata, or worse, a tone poem, with no restrictions, and he or she may flail about wildly, like an architect who cares little for a foundation, or support: and act, like the men Jonathan Swift ridicules as "building a house from the top down." Freedom must be reigned in, and defined by necessity. Freedom comes from responding to demands of necessity.

Bach's mentor Buxtehude, composed a beautiful Chaconne (or Ciaccona) for organ, based on an 8-note bass theme. Notice how that bass line plays with the intervals of Bach's later “Musical Offering”.

C Ab G B C Eb D G

Here it is played on a well-nuanced Schnittger organ: https://youtu.be/8gu5r_SyWz4

What glories Buxtehude archives with such a repetitive bass line! What worlds the registration of this instrument opens!

Yet, it begs to be surpassed. This brings me to a great paradox.

One might compare the difference between Bach and his predecessors as the difference between polygons inscribed in a circle, and the circle itself. (See example 3)

Example 3

At the end you will see a square inscribed in a circle. In terms of area, it is far from the circle. The remains after the square are huge. Next is a hexagon inscribed in a circle. (See example 4). Is it closer to, or further from a circle? The remaining area is less, but the singularities, as changes in direction are now 6, instead of 4. It is closer in a way, but further in another. The circle is continuous. It has no changes in its movement. Lastly, we see a multi-sided polygon inscribed in a circle. It seems definitely to be closer. The difference in area between the circle and the inscribed polygon is becoming minimal. Yet, the number of singularities, as changes in direction, is huge, and increasingly separated from circular rotation, which is a different, simple species of action.

Example 4

In comparing Bach with his predecessors, I often feel the paradox. At times, he seems so close to them, that you could not imagine him without their accomplishments. At other times, I sense an unbridgeable gulf. Listen now to Bach's Passacaglia in C minor for Organ, BWV582. The bass line is now 15 notes, instead of 8. At one point, Bach marks it "fugued": not Passacaglia and Fugue, but the Passacaglia is now fugued, and the first 8 tones of the bass become the fugue subject.

The opening bass is: C G Eb F, G Ab F G, D Eb, B C, F G C.

https://youtu.be/FpZfvlWJbjg

Robert Schumann loved this work, but did not dare to take it further. That remained for Brahms. As you listen, do you get the same eerie sense as I, of how much Bach owes to his predecessors, but at the same time, how he eclipses them: how a single, seemingly simple discovery, changes everything?

..and we have not even yet heard what Brahms does with the Passacaglia!

Great Masters In Dialogue: Part 5 (really Part 6):

Brahms and Bach

Now we arrive at the sixth and last installment on Brahms' Fourth Symphony. This work is revered, but its revolutionary importance is often missed, because the world has come to accept the very arbitrariness against which Brahms was fighting. It may seem odd to label this symphony as revolutionary, when Brahms is so often characterized as a reactionary, resisting everything new; but new does not always mean better, or even good. Sometimes, defending classical rigor IS a revolutionary act, especially as in this case, where Brahms defends that rigor by creating something new, really new!

We began this series by identifying the least action principle: that nature always acts for the good, and in the most efficient way. We examined it in physics, and whether that principle of efficiency and goodness could apply in music as well.

So far, Brahms has shown brilliantly that it does. (However, when Brahms first presented this work to his friends at the piano, played by himself and Ignaz Brull, it was met with a deafening silence. In that silence, the music critic and champion of Brahms, Eduard Hanslick, said, "I feel as though I have just been beaten up by two very intelligent men."

THE PASSACAGLIA

The last post began by citing Beethoven and Bach as bookends for this great composition, and indeed they were. Brahms had a portrait of Beethoven looming over his piano, and one of Bach over his bed. Brahms remarked that the greatest events of his lifetime were the unification of Germany, and the publication of the complete works of Bach. When a new work was published by Handel, Brahms studied it within a few days. When a new work was published by Bach, all work stopped immediately, to examine the new treasure.

People sometimes ask how Brahms advanced music over Beethoven. There are many things I could point to, but my answer often surprises them. Brahms had a huge collection of scores, going back to the Renaissance. He recognized valuable traditions that had been lost, and needed to be restored, if classical culture is to be advanced. One of those traditions was the “Passacaglia”, or “Chaconne”—an ancient, rigorous and binding form, and a necessary form, in an age increasingly defined by "anything goes”.

Neither Mozart or Beethoven, despite their revival of Bach and Handel, including in fugues, investigated this form (although Beethoven's 32 Variations in C Minor, woO 80 might qualify as an attempt. We include a link for those interested). https://youtu.be/sfQsrf3cofA

Brahms had to develop his skills in a prototype, before composing a full-fledged Passacaglia, with 30 variations. (This is not new. Beethoven wrote his Choral Fantasy as preparation for the far more difficult task of setting Schiller's “Ode to Joy” to his Ninth Symphony.)

The most important foray for Brahms was his 1873 "Variations on a Theme by Haydn" for orchestra. It begins with a theme in two sections, A and B, of 15 measures each, but with repeats, for a total of 60 measures (although only thirty in the score, since repeats are not counted as measures). Seven long variations follow. Brahms has followed, for now, the format of a proper Theme and Variations.

At measure 361, the Finale begins. Brahms suddenly condenses the entire bass line into a mere ten-notes, occupying only 5 measures, which he repeats twenty times, for over 100 measures:

Bb Bb Eb D C Bb Eb C F F(8va).

The Theme and Variations is now transformed into a “Passacaglia”, and it makes the Finale wondrous and powerful. Even when the opening theme returns, the ten-note bass figure keeps going. You will hear it in the accompanying audio. (Here’s the finale: https://youtu.be/0IzEMDjHJZY?t=909 starting at 15:09)

To compose an entire movement of thirty variations as a Passacaglia, while making that thirty-times repetition always new, and fresh, was something that had not been attempted since Bach. It was a monumental challenge.

We have already discussed Bach’s Cantata #150 (Nach dir, Herr, verlanget mich, BWV 150, https://youtu.be/lC8UErdK_XE?t=676) from whence came the theme, and the magnificent Passacaglia for organ in c minor as a model (https://youtu.be/zzBXZ__LN_M)

There was another prototype for Brahms, Bach's Chaconne for solo violin (Partita No. 2 in D minor BWV1004). Brahms loved this work, but was also awed by it. Whenever his violinist friend Joseph Joachim was in town, Brahms demanded to hear it. He made an arrangement for it for piano, left hand only. However, he also commented that he could not have written it, because he might have died from the excitement. (Here’s Hilary Hahn: https://youtu.be/ngjEVKxQCWs)

Bach was not the first to do this. Heinrich Biber composed a passacaglia for solo violin over forty years earlier on a four-note bass. Here’s a link:

https://youtu.be/sgcR183f8gA?list=TLPQMzAwNDIwMjIE3W9PvMfU4w

Such works pale though, when compared to Bach's Chaconne, a work 256 measures long, with 64 variations, based on a simple 4 measure foundation. The piece is a triptych of three sections. The beginning and end are in D minor, and the middle in D major. Brahms follows suit, except in E minor, E major, and back to E minor.

As already discussed, Brahms took the bass line of the last movement of the Ciacona in Bach's Cantata, 150, in A minor as his theme: A A B B C C D E E A, transposed it to e minor, and added a chromatic tone: E F# G A A# B B E.

Though the Chaconne is not quoted directly, it defines the architecture. At the center of the triptych, in the major key section, is a tender, soft-spoken, and loving "Chorale", or hymn. (See audio link below. See example of a triptych painting.)

The chorale in the Bach may be the master's tribute to his recently deceased wife. Brahms honors Bach in this case.

Many such works were written after Brahms' revival of this ancient lost form—the Passacaglia—some of them worthwhile, such as those by Rheinberger, Reger, Taneyev, and Shostakovitch. But the new direction in late 19th century music was such that nothing fulfilled the promise of Brahms.

We include a performance of the movement with analysis: https://youtu.be/ajoUNA4LLKk

and a stunning video of Furtwangler leading the Berlin Philharmonic in a rehearsal in London in 1948: https://youtu.be/leYbb5KZYDg

Audio File https://drive.google.com/.../161MX2S48Hgtwudjhij.../view...

No doubt, the Passacaglia and the Chaconne shall inspire great works in the future.