Music as Science, The C Minor Series No. 11: In a Higher Domain—Beethoven's Late Quartets

DAILY DOSE of BEETHOVEN (July 16, 2020)

In today’s post, we do not seek to analyze the late quartets (although we have discussed a few in the Daily Dose, especially the Grosse Fuge.) Here, we simply wish to identify how the essentials of the C Minor investigation inform so many of these late quartets.

The question investigated—such as the C Minor Series—does not remain neutral, static, and unchanged outside of the process. The discoveries made by investigating the question, change the question itself.

Imagine posing 10,000 years ago the question: "What is justice?" The answer might have been brutal. Subsequent discoveries have changed the answer into something more civilized. Great knowledge has been developed through investigation of the C Minor Series. Different keys are involved. Different intervals are explored. Beethoven is now ready to examine the matter in new ways. For example, our half-tone motions have often surrounded the interval of a fifth such as C to G, in the case of G-Ab, C-B. Now Beethoven examines the interval of a minor sixth.

There are at least three of Beethoven’s late quartets that explore these matters. If Op. 111 took it to a higher level, the late quartets go even higher. We sense that all five of them (six counting the Grosse Fuge as a separate work), are united by the study of a single problem, or complex of problems. For now, we limit ourselves to identifying where Beethoven is pursuing the C Minor Series.

Today, we try a new approach to our use of examples. At various points throughout the 2 pages of scores (see the two pages below), we marked No. 1, 2, 3 etc, to denote the portion of the score under discussion. Since reading string quartet scores can be difficult, we offer a piano reduction. Please let us know if it works for you.

No. 1 and 2: simply show the mirror-image half-steps of C Minor transposed to A Minor.

No. 3: is the opening of string quartet No. 15, Op. 132. It's fugue-like, and upwards half-tones are played against downwards ones, in a manner reminiscent of Mozart's “Jupiter Symphony”.

No. 4: shows how, beginning at measure 75 of that movement, the half-tones, instead of surrounding a fifth A to E (G#-A F-E) now define a sixth F# to D (F-F# Eb-D.)

No. 5: shows that process in the main subject of the Grosse Fuge.

No. 6: shows 5-6 and 8-1 in C# Minor, and

No. 7 shows the opening of the String quartet No. 14, in C# minor, Op. 131. It's a fugue and Beethoven places great emphasis on the fourth note of the fugue subject, in this case the note A (tone 6 of the c# minor scale). Throughout the first movement, the dissonances will grow on the fourth tone of the subject.

Music as Science, The C Minor Series No. 11: Beethoven and Schubert—The Wanderer Fantasy

DAILY DOSE of BEETHOVEN (July 15, 2020)

Franz Schubert was born in Vienna on January 31, 1797. Beethoven was 27-years old and living in the same city. Haydn was 65 and still living there. Mozart had died young there, just 7 years earlier on December 5, 1791. Haydn, Mozart and Beethoven: these giants could be daunting shadows to grow up under. However, Schubert accepted the challenge and became one of the world's greatest composers.

But for Schubert, there was another shadow—poverty. His boyhood home in Vienna is now a museum. It looks OK until you realize that 14 families lived in that building! (See photo of the house below). Although they were in the same city, Beethoven and Schubert either never met, or only met briefly. Nonetheless, Schubert idolized Beethoven and learned from his music.

Waldstein/ Wanderer

The C Minor Series expands into other minor keys and their relationship to the tonic major. This included a C major/C minor relationship. Schubert's 1822 “Wanderer Fantasy” is such a unique and amazing work. It is in a dialogue with several compositions.

1. His own song from 6 years earlier, "The Wanderer." Schubert was probably the greatest song-writer who ever lived, composing over 500 "lieder." We include a performance of the song, with lyrics.

The second movement of the “Fantasy” quotes the song directly: 

The other three movements all have references to the song.

2. Beethoven's great Waldstein sonata. Compare the openings of the Waldstein (in C major), and the Wanderer (also in C major). (See photo below of the scores of the two compositions).

Here is a recording of the first movement of the Waldstein: 

3. The C Minor Series: The 4th movement represents one of Schubert's few ventures into fugal writing, and uses the characteristic interval of the dropping “diminished 7th” (major sixth). You will find it in the score provided with this recording of the entire thing by Paul Lewis.

Notice how all of the movements evolve into one another, in the style of a Fantasy.

The second movement begins at 5:43
The third movement begins at 12:12
The fourth movement begins at 16:59

Music as Science, the C Minor Series No. 10: The Mountain Top—Beethoven's Op. 111, Part 2

DAILY DOSE of BEETHOVEN (July 14, 2020)

Yesterday we examined the first measures of Beethoven's “Piano Sonata No. 32 in C Minor, Op. 111”, where he investigates musical space in the continuous domain.

We include the entire sonata by Mitsuko Uchida, with score, and give the appropriate times.

https://youtu.be/WGg9cE-ceso

A quick review:

1. In the first 5 measures, he examines the three possible double-lydians (or diminished 7th chords), and their relation to the dominant, tonic, and subdominant (5th, 1st, and 4th). He does this without a theme, or a key.

2. For the next 6 measures, he inverts Bach's chromatic descending scale into a rising one. There is still no theme, or key.

3. For the next 7 measures, he situates the opening dissonances on a pedal point of G, building tremendous tension, until he finally arrives at the note C in measure 18. (Example 1)

4. The next 4 measures constitute his moving from the continuous domain to the discrete, with a theme, in c minor. (Example 2, 1:50 in this recording.)

It's an odd theme to say the least. it's very agitated, very low, and in octaves only. Beethoven maintains Mozart's tradition of starting in octaves of C, and proceeding in octaves. We see the characteristic interval of Bach's “Musical Offering”—the “diminished 7th” in measure 20. It's the same two notes—Ab to B, except his time rising—B to Ab (as Mozart did in the third movement of his K475 Piano Sonata No. 14, and his Piano Concerto No. 24 in C Minor, K491.)

However, Measure 19 constitutes something different—three tones, C Eb B, with a “fermata” and “sforzando” on the B, which repeats in measure 20. What do those 3 notes do? They synopsize both Bach and Mozart. Play Bach's opening of the “Musical Offering”—C Eb G Ab B, then play only the first 2 notes followed by the last one. You have C Eb B! Play the opening of Mozart's “Fantasy”— C Eb F# G Ab C B, then play only the first 2 and the last one, you have again C Eb B!

The theme of Op. 111 should bring both the Bach and the Mozart to mind. Beethoven is quoting the entire process of the C Minor series, not just one work.

The movement is very agitated and proceeds relentlessly. Franz Schubert had a profound insight into it, and shortly after Beethoven's death, set a poem by Heinrich Heine, "Der Atlas", using the intervals of the main theme in a different key. Heine's poem goes as follows:

DER ATLAS

Ich unglücksel'ger Atlas! eine Welt, (I, the unfortunate Atlas, a World,)

Die ganze Welt der Schmerzen muß ich tragen,
(An entire world of pain I must bear,)

Ich trage Unerträgliches, und brechen (I bear what is unbearable)

Will mir das Herz im Leibe.
(And it will break my heart and body.)

Du stolzes Herz! du hast es ja gewollt, (You proud heart! You wanted it,)

Du wolltest glücklich seyn, unendlich glücklich
(You wanted to be happy, infinitely happy)

Oder unendlich elend, stolzes Herz, (Or infinitely miserable, proud heart,)

Und jetzo bist du elend. (And still you remain miserable.)

Here’s a video of Schubert's Der Atlas
https://youtu.be/aLH0mGjBjvA

Beethoven had had to hold up the world by himself, and now it is Schubert's turn!

The first movement of Op. 111 goes into a short fugue, which changes somewhat the intervals. Instead of C Eb B, it is G Ab D B (trill) C. (See example 3, 5:50 in this recording)

Amazingly, Beethoven goes for 4 measures with nothing but “diminished 7th” chords. (See Example 4, 6:10-6:18 in this recording.)

THE LAST MOVEMENT

The beautiful transcendent second movement seems to have nothing to do with the C Minor Series. But wait! A sudden loving tribute to Mozart's “Fantasy” emerges after the triple trill in this recording at 22:30 (see Example 5). Compare the bass line to both the main theme of the first movement of the Op. 111, and to the opening of the Mozart’s “Fantasy”. Then see how the bass line is in canon with the soprano. Ms. Uchida does not get it right. Nobody does.

But we can understand Beethoven’s concept. Because Beethoven’s power to allow us to hear the beauty of the entire process as a unified one has grown!

Music as Science, The C Minor Series No. 9: The Mountain-Top—Beethoven's Op. 111

DAILY DOSE of BEETHOVEN (July 13, 2020)

Recently, some readers have communicated difficulties in comprehending some aspects of the C Minor Series. Even professional musicians are likely to encounter that difficulty, because few are taught to think about music as constructive geometry, but rather as chord progressions. Therefore, we appreciate our readers working through these musical and scientific challenges.

Today, we arrive at the apex of this C Minor idea with Beethoven's “Piano Sonata No. 32 in C Minor, Op. 111,” and we hope that the power of the music itself will help clarify the idea.

The greatest works of art have a paradoxical quality to them. If you’ve only heard the music of JS Bach, but had never heard Mozart and Beethoven, you might think that it just couldn't get any better; there is a quality of beauty and perfection in his masterpieces. Indeed, there were associates of Bach who made the claim that it was not possible to advance beyond him. Yet when we encounter the next great work in the series, we realize that it does get better!

We have heard several pieces that examine what we termed the "Lydian" intervals in music. (Ft 1) The usual approach to composing a piece of music is to start out with a theme, in a specific key, and then broaden your investigation, working your way up, by developing new themes and keys. We have already seen how Mozart in his “Fantasy”, started out from a more universal musical space, and worked his way down, deriving passing keys from that higher dimension.

In Op. 111, Beethoven begins completely from that higher universal space, in what would be known in physics as the “continuous domain”. He begins in no key, and without a theme.

Today instead of an audio explanation of these matters, we post short sections of the score, alongside a complete performance of the first movement. We encourage our readers to listen to it one step at a time.

Here is the first movement with score, as performed by Mituko Uchida: https://youtu.be/WGg9cE-ceso

Example 1: presents the first 2 measures. It begins with the left hand playing an octave of Eb, followed by a drop to an F# octave. That is the “diminished seventh” interval we have encountered in several of the C Minor compositions. It is followed by F# A C Eb in the right hand, the first of our three “double-lydians”. It resolves tentatively, on G.

Then listen to Example 2: It repeats the same pattern but starts on the tones Ab-B, the “diminished seventh” from the opening of Bach's “Musical Offering”. The right hand follows with Ab D F Ab, the second of our “double-Lydians”, and comes to rest on an unstable C. Now we have covered two out of three of these configurations, and there should be only one left.

If Beethoven repeated the same pattern, he would play Db-E in the left hand, followed by Db E G Bb in the right, coming to rest on F. Then we would have a neat little package of the three double-lydians, as they resolve to C F and G. He almost does that but...The left hand does give us Db-E, and then it moves up to F, while the right hand is a surprise—Db F Bb Db. (See Example 3).

This a Bb minor chord! Why does he do that? We think likely to make the point that the double-lydians, because of their ambiguity, can resolve in many different ways to many keys. Any one of the four tones could be a "leading tone” that resolves upwards by a half-step. Beethoven has opened new pathways for composing!

Is Bach's “chromatic scale” present? Look at example 4 and you will see that Beethoven, like Mozart, has placed it in the bass line. You will also see it is an ascending chromatic scale, which is not so obvious at first. Up until 1:07 in this recording, there is no key established—a full keyless minute. After that, the note G (the dominant of C), grows until the piece actually resolves into a theme (Allegro Brio), and a key (C Minor) at 1:50.

Tomorrow, we will discuss this miraculous transformation.

Ft 1. The term "Lydian interval" comes from the medieval Lydian mode. That mode differs from an F major scale by one note. Whereas F major has a Bb for its fourth term, F G A Bb C D E F, the Lydian mode has B, F G A B C D E F.
Instead of a perfect 4th between notes 1 and 4 of the scale, we have an augmented fourth, a “tritone”. Beethoven explored the properties of the Lydian mode in the slow movement of his String Quartet Op. 132.

Here again is the first movement, performed by Mituko Uchida: https://youtu.be/WGg9cE-ceso

https://youtu.be/WGg9cE-ceso

(Example one)

Beethoven Rarity—Rondo in B flat for piano and orchestra

DAILY DOSE of BEETHOVEN (July 10, 2020)

The delightful and sunny “Rondo in B flat for piano and orchestra, WoO 6”, composed in 1793, was originally intended as the finale of Beethoven’s Second Piano Concerto. The “andante” section of this rondo is most likely inspired by the rondo ending of Mozart's “Piano Concerto No. 22 in E-flat Major”.

The composition was eventually published in 1829 by Beethoven’s student, Carl Czerny.

Here is a wonderful rendition performed by Sviatoslav Richter in 1963.

https://youtu.be/FBkbKbbACKg

Music as Science, The C Minor Series No. 8: The Pathetique Sonata Compared

DAILY DOSE of BEETHOVEN (July 9, 2020)

Now we will compare all three movements of the “Pathetique” Sonata with Mozart's work. Today’s post will rely largely on the audio, with the text as reference.

https://soundcloud.com/user-385773…/beethoven-mozart-c-minor

1. Beethoven is in a dialogue with both Mozart's Piano Sonata in C Minor and his Fantasy in C Minor.

2. Beethoven's slow introduction, which reappears (though changed) in the middle and end of his first movement, synopsizes Mozart's “Fantasy” and integrates it with the sonata, so that it is not a separate piece.

3. This is the first time that we might consider that Beethoven surpasses Mozart, but that does not in any way detract from Mozart's work, which was also a scientific discovery of the first order.

4. Mozart's signature opening of 3 octaves of c is compared to Bach and Beethoven.
5. Beethoven took virtuoso piano playing to a whole new level with this work.

6. A key transition to what is sometimes known as the " development section" is compared in both first movements.

7. Recently, we discussed the existence of three and only three double-lydian or diminished 7th chords:

F# A C Eb , B D F Ab, DbE G Bb.

Beethoven opens by repeating the same idea 3 times, but higher in pitch each time. You might expect him to use all three. He does not. He uses 1, then 2, then 1 again. In the coda though, he uses all 3, making it the most powerful statement of the slow section.

8. In the slow movements, Beethoven does not quote Mozart's first theme in Eb, but his second in Ab—giving us a most beloved song.

9. We take the ending of both third movements up to a point of discontinuity, and the return to the main idea. Several key points of similarity are identified. The endings of both third movements are compared. Mozart's is a tour de force.

Some ideas are better transmitted via audio. So please enjoy the audio.

https://soundcloud.com/user-385773…/beethoven-mozart-c-minor

We also leave you with a scored version, performed by Annie Fischer

1st movement
https://youtu.be/kqvBJc9IovI

2nd movement
https://youtu.be/iCL5sHzlDOI

3rd movement
https://youtu.be/Ifj8dwuAzAQ

Music as Science: The C Minor Series No. 7: Beethoven's "Pathetique" Sonata Part 1

DAILY DOSE of BEETHOVEN (July 8, 2020)

We now come to a real gem. Beethoven loved and admired Mozart's music. The challenge of matching it, let alone going beyond it, was daunting. Beethoven’s first great success in meeting that challenge was through his Piano Sonata No. 8, Op. 13, often called the "Pathetique." We examined several aspects of that sonata by itself on April 7-8 posts. Please feel free to revisit them.

Now let us compare it to Mozart. Beethoven's entire sonata is in a loving, and scientific dialogue with the “Fantasy in C minor, K. 475” and “Piano Sonata in C Minor K.457” by Mozart.

The “Fantasy” is often played as a prelude to the “piano sonata”, as done in the recording by Alicia de Larrocha posted on July 1st. Beethoven synopsized the entire Fantasy into a much shorter prelude.

A clear reference to the “Fantasy” is contained in the opening measures. The “Fantasy” opens with just three octaves of C, heavily stated, with middle C being the highest, deriving from Bach’s 6-part Ricercar. Beethoven's opening is also weighty, and straddles those same three octaves, but with the interstices filled out.

Mozart proceeds on to something in the second measure that we did not analyze in the last few days—a puzzling question in the higher voices: F#CEb to GBD, followed by AbCF# to GBG.

Beethoven does the same thing in his first measure, resolving from F#ACEb to GBD, but an octave lower. Just compare F#CEb-GBD, to F#ACEb-GBD. A necessarily provided audiotape helps you to hear it.

Audio: https://soundcloud.com/user-216951281/beetmozcminor1…

Is Beethoven merely quoting Mozart, or is he taking up a scientific problem?

We must examine this Lydian-Tritone question as a geometrical construction If we are to further comprehend it. The true nature of the musical system, as we have seen, had been investigated over the centuries, through a series of “12 half-steps” (chromatic scale), and the “circle of fifths”: a series of major and minor keys moving through a series of up to 12 fifths. Those investigations pushed the limits.

Now, we have something different. If you divide an octave at any but one note, you will get two different intervals. For instance, divide a C octave at G. C ascending to G is a fifth, but G ascending to C is a fourth. Try inverting those intervals. Descend by a fifth, and a fourth. Now the octave is divided at a different tone F. That is an elementary irony, and the development of that process has beautiful implications, which we addressed in our discussion of the very opening of Beethoven's Ninth Symphony on May 8th, as "Get out Your Ruler and Compass!"

The Tritone is the only interval that does not invert that way. It divides the octave exactly in half and inverts onto itself.(Ft 1). C ascending to F# is equivalent to F# ascending to C. That opens up different possibilities and ambiguities. Is F# dividing the C octave in half, or is C dividing the F# octave in half? The interval of a minor third divides the Tritone in half. C to Eb, is a minor third, as is Eb to F#(Gb). Keep ascending, and the note A functions that way. F# to a A is a minor third, as is A to C.

That gives you a very unstable configuration. You have two Lydian intervals C-F#, and Eb -A , and four minor thirds. What, if any, is the generating tone? This configuration can open up new pathways (Ironically, it can also be used as a cheap trick). It is also ironic, that when it is represented visually, it is very stable. Construct a circle with each of the twelve tones separated by 30 degrees, like a clock. Connect those points, C Eb F# A and C. You have inscribed a square. (See pic. 1)

Construct another such configuration by moving it up a half-tone. C Eb F# A, becomes Db E G Bb. Move up another half-step, to D F Ab B. Move up another half-step to Eb F# A C, and we have...Wait a minute! Isn't that the first one again? We have covered all twelve tones! There are only three of these things possible (Thank God!). Represent all three on a circle. (See diagram)

Sometimes a visual representation can do wonders. Notice that if we rearrange D F Ab B to B D F Ab, the outside terms, Ab to B, are our diminished 7th interval from the Musical Offering, .

Now we see three different pathways to investigate the actual nature of the musical system in which we live:

1. The investigation of half-steps, and their necessary generation of twelve tones.

C C# D D# E F F# G G# A A# B C, ascending, and C B Bb A Ab G Gb F E Eb D Db C descending. These half steps are anything but self evident.

2. The progression of the “circle of fifths”, which also generates 12 tones. They are also not self-evident, and here, the question of tempering arises once again.

C G D A E B F# Db Ab Eb Bb F C.

3. The investigation of the musical system as determined by the Lydian or Trione interval, including the double Lydian or diminished 7th. This configuration also approaches the 12 tones, but perhaps from a higher standpoint, C Eb F# A, Db F A Bb, and E G Bb Db. Have fun experimenting at the piano with it! (please refer back to the audio.)

The actual higher standpoint though, is how these harmonic systems INTERACT with one another. The best musical compositions examine this. They don't work in isolation.

We shall proceed more quickly in the next few days. An important topic has been breached!

(Ft 1). Why do we call the Tritone the "Lydian' Interval? The medieval Lydian mode went from F to F, but the 4th tone, instead of Bb, as in an F major scale, was B. Instead of a perfect 4th, F to Bb, we have an augmented 4th, F to B. That creates an instability, and a tendency for a modulation to C major to be built into the scale. When Beethoven declared the 3rd movement of his “String Quartet Op. 132” to be in the Lydian Mode, musical formalists simply refused to believe him!

Music as Science, the C Minor Series No. 6: Mozart’s “Fantasy” Part 3

DAILY DOSE of BEETHOVEN (July 7, 2020)

CPE Bach tells us that although a “Fantasy” requires a thorough knowledge of harmony, a written-out work, such as a “Sonata”, requires a far more comprehensive knowledge of composition. Mozart seems to challenge that notion by finding an even higher degree of rigor in an improvisation than in a sonata.

Today, we examine key transitions in the rest of Mozart's K. 475 “Fantasy”. Again, we provide Mitsuko Uchida’s performance with score:

https://youtu.be/Ui9pyxdVX6Y

1. A quick review: Mozart changes Bach’s 5-note theme from the “Musical Offering”: C Eb G Ab B, by adding two tones—F# and another C, to a 7-note theme: C Eb F# G Ab C B. Both of these changes make an important difference. The last four tones, G-Ab C-B, give us mirror image half-tone motifs.

Mozart employs Bach's descending "chromatic" line brilliantly by changing only one note every measure, and placing it in the bass line, so that it determines the harmonic ordering, rather than function as a melody. That descending bass line does not stop at G (the dominant of C Minor), but in measures 15-17, comes to rest on Gb-F#.

This is a turning point in the work. The tritone, or "Lydian" interval, which divides the C octave exactly in half (at F#), has been introduced both in the first-measure theme starting from C. and the bass line starting from C. Mozart is investigating a different generating principle of the musical system.

2. For the next few measures, Mozart plays around with B Minor and Major, alternating D natural and D #. The tone F# always bears a crucial role. After a lot of questions, that tone F# is isolated as the fifth of B Minor. At measure 24, F# repeats, alone, then becomes the third of D major. That is a magical, but lawful moment! It emerges between 2:50 and 3:03, in this recording (right around the repeat sign, or measures 22-26 in the score.)

3. After a long melodic section, the half-tone motions reappear at about 5:33. We hear E to F in the bass again and again. We are now in A Minor, and E to F corresponds to the same interval as G to Ab in C Minor. A few measures later, at 5:43, a turn marked P, on the notes A Bb G# A, A Bb G# A, reminds us again of the opening.

At 6:02, we wander into F major. It is a very simple idea. But again derives from the theme. The right hand plays on C and D, then descends to F-E. In F major, C and D are tunes 5 and 6 in the scale, and F and E are 1 and 7. That in turn, proceeds 5-6 and 1-7. The last 4 tones of the theme, G Ab C B were 5-6,and 1-7 in C Minor. The left hand also reflects it a bit.

Starting at 6:18, for about one minute, A Major change is prepared by a bass line descending in half-steps! A long “Andantino” in Bb follows, and at 9:30 climaxes in a “Piu Allegro” section reminiscent of the Bach’s “Prelude in C Minor” from the Well-Tempered Clavier, Book I. This section fills CPE Bach's recommendation that at some point the improviser proceed through a part of the Circle of Fifths. Since the days of Pythagoras, investigating that circle had been a means of trying to determine the true nature of the musical universe. Proceed as the bass line does here, G to C to F to Bb, to Eb to Ab etc. If that were done 12 times you would end up back at G.

Mozart almost does that but his concern is to lead us back to the opening. At 10:00, he continues to move through this circle, and gradually introduces more of these "Lydian" or tritone intervals. At about 10:41, a few measures before the opening returns at "Tempo Primo", he contrasts two rising tones, with two descending ones. What are they? The descending tones are C-B, and Ab-G, over three octaves! After a long pause, we feel fully prepared to hear that powerful opening once again.

But is it an exact repetition? Of course not. It's Mozart. This time though, it really does behave like C Minor and it comes to a glorious end in that key.

This “Fantasy in C Minor, K475” became the "meat and potatoes" for future composers. They all studied it. His revolutionary use of the Lydian mode will be the basis for an intense, continuous dialogue, particularly with Beethoven, who also recognized the central nature of Bach's “Musical Offering”, thus composing particularly his Op. 13 "Pathetique" Piano Sonata in C Minor, as well as his last Piano Sonata Op. 111, in which Beethoven explicitly "quotes by paraphrase" Mozart's “Fantasy” just after the famous "double trill" section.

We shall go to Beethoven’s innovation in the next days. In the meanwhile, we leave you with a seldom-heard work: the then sixteen year-old Franz Schubert's Fantasy in C Minor. See if it rings a bell!

https://youtu.be/5JjMTf-7lgI

Music and Science, the C Minor Series No. 5: Mozart’s Fantasy—Part 2

DAILY DOSE of BEETHOVEN (July 6, 2020)

In the last C Minor Series post, we traced the first 25 measures of Mozart’s “Fantasy in C Minor”, and found ourselves even in that short time, in terra incognita (certainly for 1785), as we worked through the implications of Mozart’s treatment of Bach's discoveries.

Here again is Uchida’s performance of the Fantasy with score:

https://youtu.be/Ui9pyxdVX6Y?list=RDUi9pyxdVX6Y

“Fantasy” meant something different back then than it does now. “Fantasy”, or “Fantasia”, and “Fancy” all referred to free improvisation—a free flight of the imagination, but guided by rigour, rather than "doing whatever one felt like." In 1753, J.S. Bach's son, Carl Philipp Emanuel Bach (CPE Bach), wrote a book called "Essay on the True Art of Playing Keyboard Instruments''. Joseph Haydn swore by this book. In the last chapter called "Improvisation: The Free Fantasia," he tells the reader how one goes about improvising such a work:

“It is quite possible for a person to have studied composition with good success...without having any gift for improvisation. But, on the other hand, a good future in composition can be assuredly predicted for anyone who can improvise, provided that he writes profusely, and does not start too late.”

CPE Bach states that the “Fantasy” will proceed through more keys than usual, and that the player would do well to limit his bass lines to the scales of the keys he is passing though.

Here we provide an example: A “Fantasy” by CPE Bach, who was the most famous improviser of his day. Listen to as much or as little as "Suits your Fancy."

https://youtu.be/LOT_nUPvE98

Such "Flights of Fancy" usually do pass through several keys, and produce very different ideas, often unrelated. CPE Bach highly recommends what is sometimes known as the "double Lydian", or diminished 7th chord, as an aide to change keys. Mozart uses them in a very different way.

Compare Mozart's “Fantasy”, with CPE Bach's.

We already seen how Mozart challenged CPE's advice about bass lines, and took the bold move of employing J S Bach's descending half-tones as his bass-line, leading into a process of constant ambiguity of key. We can hear how Mozart is advancing over CPE Bach.

The comparison would be easy, had we left out CPE's father. Now, listen to J.S. Bach's “Chromatic “Fantasy in D Minor”, as performed by the great Bach scholar and artist, Rosalyn Turreck:

https://youtu.be/rZmfRM4WH8s

Progress among human genii is not so linear! Kepler was a unique genius and contributed a huge breakthrough that allowed JS Bach to make that next huge leap in innovation, and now, its Mozart’s turn. This progress is not linear. It would not be human, were it otherwise.

What is it about JS Bach's “Chromatic Fantasia (and Fugue)”? This work is probably composed between 1717-1723. We get the sense of anger, expressing dissatisfaction that the breakthroughs he had so long sought in the Well-tempered System had yet to occur. Could that be so? He never composed anything like it, before or after. It is a unique moment in a great mind. When in the 1800s, Johannes Brahms and Clara Schumann were asked to submit a piece of scientific music to the University of Gottingen, this was their choice. We wonder if they were hoping the scientists would help them figure it out.

We will return in the next installment for the remainder portion of Mozart's great work.

Beethoven Rarities: Civilized BBQ Music

DAILY DOSE of BEETHOVEN (July 4, 2020)

Normally, we are not fans of Classical music as background music. But Beethoven did also had to make a living out of his music. In his time, a “Serenade”, like a “Divertimento”, was meant to be light entertainment, and was often performed outdoors. We can imagine some paying close attention while others chatted. We can also imagine the chef loving every minute while chopping vegetables.

We offer two versions, a civilized modern one, and a recording taken straight from vinyl, with all the noises. That may bring an element of nostalgia to some, and it features the great Marcel Moyse on flute, so we could not resist. If you are too young to remember vinyl, just pretend it's hamburgers sizzling. 😉

https://youtu.be/RcAUUH1-pD8

https://youtu.be/LNkrwWPC2JY

Happy Fouth of July!

Beethoven Rarities—La Marmotte

DAILY DOSE OF BEETHOVEN (July 3, 2020)

The children's song “Marmotte”, is another example of folk songs that Beethoven set to music. “Marmotte” was composed between 1790-1805, as one of a set of 8 songs (8 Lieder, Op. 52, No. 7).

Around 1770, Beethoven attended a play by his friend, the poet Johann Wolfgang von Goethe, and was very moved by the poem about the begging, playing children with their little marmottes. (Marmots are relatively large ground squirrels that lives in Asia, Europe and North America. They were often used by travelling musicians with hurdy-gurdies (or bag-pipes), to perform various tricks.)

Beethoven took Goethe’s poem, which was in a mix of Austrian and French, and wrote a song for Baritone and piano, of a child singing about his begging and traveling as he played his hurdy-gurdy with his dancing Marmotte. 

Original Text:

Ich komme schon durch manche Land,
Avecque la marmotte,
Und immer was zu essen fand
Avecque la marmotte,
Avecque si, avecque la,
Avecque la marmotte.

Ich hab’ gesehn gar manchen Herrn,
Avecque la marmotte,
Der hätt die Jungfern gar zu gern,
Avecque la marmotte,
Avecque si, avecque la,
Avecque la marmotte.

Hab' auch gesehn die Jungfer schön,
Avecque la marmotte,
Die täte nach mir Kleinem sehn,
Avecque la marmotte,
Avecque si, avecque la,
Avecque la marmotte.

Nun laßt mich nicht so gehn, ihr Herrn,
Avecque la marmotte,
Die Burschen essen und trinken gern,
Avecque la marmotte,
Avecque si, avecque la,
Avecque la marmotte.

Translation:

I have come already through many a land,
with the marmot
and always found something to eat
with the marmot,
here and there,
with the marmot.

I have seen so many men
with the marmot
that love the maidens all so well,
with the marmot,
hhere and there,
with the marmot.

I've also seen the fair maiden
with the marmot
who look at the little man that I am,
with the marmot,
here and there,
with the marmot.

Now do not let me go like this, you gentlemen,
with the marmot
the fellows love to eat and drink,
with the marmot,
here and there,
with the marmot.

Here is a professional version performed by Dietrich Fischer-Dieskau.

https://youtu.be/JS_QDwurtsw

and here is a version performed by children:

https://youtu.be/ZI_OKLsRVeA

We love how adorable these children are as they got ready to perform!

Music and Science, the C Minor Series No. 4: Mozart’s Fantasy in C Minor, K475

DAILY DOSE OF BEETHOVEN (July 2, 2020)

Wolfgang Amadeus Mozart (January 27, 1756 – December 5, 1791) was born six years after the death of Johann Sebastian Bach. Universally recognized as one of the greatest minds in history, it is often overlooked that Mozart made it a practice to learn as much as possible from others—he was one of the greatest students of all time.

So, when in 1782, the 26-year old Mozart encountered the instrumental works of Bach, through the Vienna salon of Baron Gottfried van Swieten, and his friend Christian Gottlieb Neefe (an organist, opera composer, and musical director of the theater in Bonn), he made over the course of the three year period of 1782-85, a complete transformation of his, and Bach's, approach to composition, and a correlate "revolution in musical affairs". (It should be noted that in that same year, 1782, Neefe would become the teacher of the 12 year old Beethoven.)

Within days, Mozart began working to assimilate everything he could from Bach's compositional method from the musical scores owned by Baron van Swieten. The “Fantasy in C Minor K475,” is said to have been composed in 1785, and the “Piano Sonata in C Minor, K457” for pianoforte is usually dated as composed in 1784. Though it is possible that he was composing them both in his head at the same time, the Fantasy does strike us as more advanced, and thus probably a later work. Mozart may not have been satisfied that his sonata K457, treated Bach's ideas adequately.

BACH’s BREAKTHROUGH

The “Fantasy” is a dialogue with J.S. Bach's 1747 “Musical Offering”, also composed in the key of C Minor. The “Musical Offering” was Bach's treatise on the art of rigorous improvisation. Bach had successfully improvised a six-part fugue in the presence of Frederick the Great of Prussia, an intellectual feat that was considered to be impossible, in May 1747 at the age of 62. Bach had also extemporized a three-part fugue on a theme provided for him by the King, who was an accomplished flutist. The King's request had been that Bach "double the voices" in his improvisation, but Bach had declined for that moment, preferring to consider more deeply the implications of the "royal theme".

Bach then wrote, over the course of the two months(!) of May and June, a multi-faceted work, composed of canons, fugues, and a trio sonata, demonstrating the tools and approaches that were required to know how to achieve such a magnificent feat of invention. Bach believed, and demonstrated by composition, that his method of musical discovery was reproducible. His earlier Two and Three-Part "Inventions", composed for his son, were his "rules" for how to compose, including improvisation ("how to have good Inventions [ideas], and more, how to develop them".)

The work included "puzzle canons." Only part of the canon was written out. Clues were provided for how the reader could write out the missing voices. Was Bach bold enough to try and educate a King, by making him write out exercises? Would the working out of the exercises provide the King with an idea of how the seemingly impossible task of setting the King's Theme in 6 voices became possible?

The significance of the six-voiced fugue is that the six species of human voice: soprano, mezzo-soprano, and alto (female), and tenor, baritone, and bass (male) types of the human voice(or instruments that capture the registral qualities of those voice species), and their simultaneous interactions, through the science of counterpoint, provide the widest possible canvas upon which a composer can work. Improvising such a composition would demonstrate the highest freedom of thought that the mind might, in principle, attain.

The addition of each voice does not represent linear or additive growth, but exponential growth, that generates a "density of singularities." In this case dissonances, that when lawfully prepared and resolved sound, paradoxically, beautiful, rather than ugly.

Although we presented the “6-part Ricercar” on June 29, we give you a different version today, not only to directly compare to Mozart, but also so that you can directly hear and SEE that exponential growth. See where each instrument enters, and hear some semblance of its full power and glory with the entrance of the sixth voice at 1:55.

https://youtu.be/3i6MorFy3YE

MOZART’S RESPONSE

The “Fantasy” is Mozart's reflection on Bach's compositional method as developed in the “Musical Offering”. He did not necessarily feel that it required composing a fugue. Bach's contrapuntal ideas could also work on a new modern level.

Here, we provide a scored version with Miksudo Uchida:

https://youtu.be/Ui9pyxdVX6Y

In the first two measures, we hear a question, a pause, and an answer. But is it an answer, or a question being answered by another question? (see rolling score.) Then, the same question, pause and answer is played slightly lower, in the third and fourth measures. A third time, the question is posed, but there is no pause this time. The composition continues, stating the question in various ways, including inversion, resolving, but only momentarily, in three separate, different "thematic" sections, climaxing in a “Piu Allegro” section reminiscent of the Bach’s “Prelude in C Minor” from the Well-Tempered Clavier Book I and the reassertion of the now-transformed opening of the piece.

ABOUT THE METHOD

Mozart's dialogue with Bach, like many great works of art, such as “The Decameron”, “The Canterbury Tales”, and “Gargantua”, pose the same questions, but at ever deeper levels. The “King’s Theme”, or “royal theme” question that Bach has answered one way, is answered by Mozart in another, deeper way.

In the Fantasy, that "question" begins with the same five notes as the first measure of the "royal theme" (C, Eb, G, Ab, B ). But Mozart changes the Bach by adding two notes, making it a total of seven. One is an F#. Mozart, in doing so, has not merely introduced a new "tone"; he has introduced something sometimes called the Lydian, or Tritone interval. It divides the C octave exactly in half, and that interval—C-F#—is also divided in half at Eb. ( C-Eb is a minor third. Eb- F# an augmented second, the "enharmonic equivalent" of a minor third.)

In the opening measure of the Uchida recording, we hear those changes. Instead of Bach’s C Eb G Ab B, we have C Eb F# G Ab C B. Mozart has also added an extra C. What does that do? We discussed the mirror image half-tone motions of G-Ab and C-B in Bach. Here, they are made explicit. Both new tones are there for a reason.

A wise man once insisted that the addition of the F# was revolutionary in that it overturned formalist notions of keys and scales. If one looks at it in and of itself, in the opening phrase, it is hard to discern. What is needed is a physical notion of dimensionalities.

But what key are we in? Are we even in a key? The key signature for C Minor should be three flats. Look at the score! There is no key signature! No flats are indicated at all. Is Mozart perhaps operating in the continuous domain of the entire Well-Tempered system, generating particular keys from that domain, as he proceeds? The " key" is not the key! Imagine observing the earth from the Space Shuttle. You name the nations as they come into view, including your own beloved homeland. But, you are no longer viewing the planet as, say, an Oklahoman who never left the state. You're grasping the entire planet, as a member of the human race, and zeroing in on your home state from that higher standpoint.

The entire piece has an improvisational quality. In fact, strictly speaking, the piece is not in a "key", as one can see by looking at the beginning of the score— The key is created by Mozart, who treats "keys" not as pre-assigned fixed structures, but as regions, created for, and through investigation.

THE DESCENDING CHROMATIC SCALE

We heard how the five-note (C Eb G Ab B ) opening of the “Musical Offering” was altered into seven (C Eb F# G Ab C B ). Where did the descending chromatic scale of the “King’sTheme” go?

Here lies Mozart's genius. In the “King's Theme”, that descending chromatic scale was part of the theme, the melody. Mozart moves it into another dimensionality, an harmonic series that changes with each measure of the bass voice. C B Bb A in the first 4 measures. Do you hear it as a melody? Not at all! It governs harmonic change in the seven-tone melody. They are doubly-connected in physical terms. We hear one process—the changing seven-note theme, interacting with another—the more slowly changing half-steps of the bass. It is not simply a matter of being in two voices. Perhaps it could be compared to the chaos of observing just the passage of days, but measuring and stabilizing those days by the passage of months, or even years.

Such a descending bass line is known as a ground-bass. In every previous composition, it descended from the tonic to the fifth, then back up to the tonic, i.e: C B Bb A Ab G - C. (For example: Bach's Crucifixus from his B Minor Mass, or “Dido's Lament” by Purcell).

This bass line however, surprises us and continues on to Gb (F#), and rests there for a while. Now, the introduction of the dissonance F#, is functioning and interacting at two different levels. One takes place in the first bar; the other takes 15 measures to unfold. Both are measured against C.

Before continuing, let us ask the simple question: Why do people say classical music is relaxing? Is it not often energizing? It is! But, do you not get the feeling, that while you listen to the notes as they fly by, that there is also a slower harmonic process unfolding, that provides that calm?

At 2:37, F# takes on a third role. At first it functions as the fifth of B Minor, then changes its role to the third of D major. (Beethoven will take this idea and run with this in his Ninth Symphony.) We have now heard this tone, F#, function at three different levels. This may contradict reductionist and linear concepts of mind and thought, but please contemplate how your mind really works. The mind is subtle, it does not think merely at one level. When contemplating an idea, does your mind not play with it, at different levels?

We will stop here and return in the next installment for the rest of the C-Minor Fantasy’s innovations.

We provide here a non-scored, but perhaps more poetic rendition, by Mieczyslaw Horszowsk, from 1962.

https://youtu.be/ct34rmS2Yg8?list=RDct34rmS2Yg8

Music as Science: The C Minor Series No. 3--Wolfgang Amadeus Mozart & Baron van Swieten

DAILY DOSE OF BEETHOVEN (July 1, 2020)

In the C Minor Series No. 1, we presented Johann Sebastian Bach and his revolutionary 1747 "Musical Offering". It may seem hard to believe, but after Bach's death in 1750, his music was relegated to such obscurity that even Haydn and Mozart knew little of him. Bach's music was seen as elitist, written for the court and the erudite, rather than the people. "Enlightenment" tastes of the late 1700s favored more simplistic music, such as song and accompaniment. One key player in this shift was Jean Jacques Rousseau, author of the philosophical school of Social Contract. Rousseau's book, "Social Contract," published in 1762, argues that individuals should consent to surrender some of their freedoms and submit to the authority in exchange for the protection of their remaining rights and the maintenance of social order. Rousseau was also a prominent musical theorist and composer. He tried, unsuccessfully, to "simplify" music theory, and insisted on the "Unity of Melody," which argues that melody should be one, and have primacy over all other parameters. He wrote:

"For a Music to become interesting, for it to convey to the soul the feelings it is intended to excite, all the parts must concur to fortify the expression of the subject; the harmony must serve only to make it more energetic; the accompaniment must embellish it without covering or disfiguring it; the bass must, by a uniform and simple progression, somehow guide the person who sings and the one who listens, without either of them perceiving it.

"The unity of melody requires indeed that one never hear two melodies at the same.

"The whole together must convey only one melody to the ear and only one idea to the mind."

Never hear two melodies at the same time?! No wonder Bach’s contrupentual compositions are out of favor!

Van Swieten's Salon

Baron Gottfried van Swieten (October 1733- March 1803), was a Dutch-born Austrian diplomat, librarian, and amateur musician. Van Swieten spent some of his diplomatic careers in Berlin, where the musical circle of Princess Anna Amalia performed and admired the works of Bach and Handel. Historian David Shavin documented that Baron von Swieten also visited Frederick the Great and that the King sang the theme he gave to Bach for the visiting diplomat. For the rest of his life, Van Swieten became a champion of Bach. He expressed his view about the value of Bach's work in the prominent German publication, "Allgemeine musikalische Zeitung:

"I belong, as far as music is concerned, to a generation that considered it necessary to study an art form thoroughly and systematically before attempting to practice it. I find in such a conviction, food for the spirit and for the heart and I return to it for strength every time I am oppressed by new evidence of decadence in the arts. My principal comforters at such times are Handel and the Bach's and those few great men of our own day who, taking these as their masters, follow resolutely in the same quest for greatness and truth."

Upon returning to Vienna in 1777, Van Swieten began inviting young musicians to his home, holding musical salons that performed the then, out of favor and obscure works of J.S. Bach and Handel—thus reviving their tradition of counterpoint. Among these young musicians was the 26-year-old Wolfgang Amadeus Mozart.

Mozart grabbed on powerfully to the musical discoveries of Bach. Among the many works of Mozart where we can clearly hear the ideas of the "Musical Offering," are the "Adagio and Fugue in C Minor, K546," the "Piano Concerto No. 24 in C Minor, K491," and the "Piano Sonata No. 14 in C Minor, K457". We include short audio comparing all of these works. One extraordinary moment compares the Fugue theme from Bach's "Fugue in A Minor" from WTC Book 2 (From June 29's C Minor Series No. 1), with Handel's fugue "And With his Stripes" from the Messiah, and Mozart's double-fugue "Kyrie Eleison" from his Requiem. We hope that you will enjoy the unveiling of these unexpected gems.

https://soundcloud.com/user-216951281/music-as-science-the-c-minor-series

Tomorrow we will examine the great "Fantasy in C Minor, K475". Some say it is an introduction to the "Piano Sonata No. 14 in C Minor, K457". We feel that Mozart may not have been entirely satisfied with the sonata, and composed this to advance his experiments and discoveries of Bach's work.

Mozart takes Bach's 5 note opening, and extends it to 7, by adding, in particular an F#. We ask our readers what difference does that make? Also, where is Bach's descending chromatic scale?

Bach C - Eb - G - Ab - B

Mozart C - Eb - F# - G - Ab - C- B

We include a performance of the Fantasy followed by the piano sonata, performed by Alicia de Larrocha.

https://youtu.be/kMsTV0XscQ8

We also include a performance of the Piano Concerto in C Minor, performed by Andras Schiff:

1st movement: https://youtu.be/nqTHzgh7Fok

2nd movement: https://youtu.be/H5zY44vaPNo

3rd movement: https://youtu.be/_AAO64LFM5w

Music as Science: the C Minor Series No. 2–Kepler and Bach--The Great Secret

DAILY DOSE OF BEETHOVEN (June 30, 2020)

Today, we will delve deeper into Johannes Kepler’s role in the development of the Well-tempered System. We will discuss Kepler's discoveries in Astronomy and music, which innovated both fields of studies.

Johannes Kepler (December 1571 – November 1630), as an astronomer, is universally recognized for his discoveries in astronomy, including the discovery of universal gravitation. Yet, his equally rigorous discoveries in music, which changed our understanding of the very nature of the musical system, are dismissed as mystical. Kepler, in 1619, published one of the most important scientific treatises to date, which is titled “The Harmony of the World.” For context, the Thirty Years War began in 1618, which is at the end of over 100 years of religious war that destroyed Europe, which only ended in 1648 with the Treaty of Westphalia. At the time, the earth is still viewed as the center of our solar system (geocentric). It was only in the year 1623 that Galileo published his “Dialogue Concerning the Two Chief World Systems”, which discussed heliocentricity among three people: one who supports Copernicus' heliocentric theory of the universe, one who argues against it, and one who is impartial. This caused Galileo to be interrogated by the inquisition and forced to recant his heliocentric theory. It is in this political atmosphere that Kepler, whose own mother was burned as a witch, published his discoveries.

KEPLER'S STRONG HYPOTHESIS

Kepler wrote that he KNEW that the musical ratios would be found in the organization of the solar system and spent 25 years looking for it, including in all the wrong places, such as the masses of the planets and his earlier discovery of the planets' ordering according to the "platonic solids." (See diagram). How could he be so sure? What was his evidence?

In Book Three of “Harmonice Mundi” (The Harmonies of the World), Kepler said that he intended to overthrow the axiomatic assumptions held for 2,000 years that the cause of the intervals lies in rational numbers, such as 3/2 for the fifth. This assumption had held music back, because those ratios almost, but didn’t exactly work. They have to be tempered. Kepler says this of the cause of the intervals:

“Since the terms of the consonant intervals are continuous quantities, the causes which set them apart from the discords must also be sought for among the family of continuous quantities, not among abstract numbers, that is, in discrete numbers, since it is MIND which shaped human intellects in such a way that they would delight in such an interval..”

WHERE HE FOUND IT!

In Book Five, Kepler took his life-long study of the solar system, and found the musical intervals with amazing accuracy, in the ratios of a planetary orbit, between the angular velocities at the perihelion and aphelion. For simplification, look at the animated orbit of a planet provided (https://giphy.com/gifs/MYCbbIYhv6MO3wE1CT). Notice that it moves faster when closer to the sun (perihelion), and slower when farther away (aphelion).

But wait! That is also one of Kepler's great breakthroughs in astronomy! His second law states that the orbit of a planet will sweep out equal areas in equal times. (see the diagram of an elliptical orbit). Before Kepler, a false axiomatic assumption prevailed. It assumed that the orbits of the planets must correspond to perfect circles. This in a way, is similar to the false axiomatic assumption that musical intervals must correspond exactly to rational numbers (fractions).

As long as the assumption of circular orbits persisted, even Copernicus' (1473 –1543) heliocentric model oblige the planets to perform loop-de-loops known as epicycles, in order to fit observations (see comparison of the Ptolemaic geocentric model, and the Copernican heliocentric model. Both require epicycles.) The theory, and the physics, did not match. Kepler's discovery of the actual elliptical nature of the orbits brought theory and practice into coherence. Without that elliptical nature, the orbits would not have different angular velocities, and there would be no musical ratios.

SCALES

Kepler found the ratios of individual intervals in each planet. When he compared the ratios between planets, he found two scales, corresponding closely to our modern major and minor scales.

TEMPERING

What about the other false axiom: rational numbers alone as determining the harmonic values of intervals? In Book Three, Kepler criticized those who tried to base music on mathematics.

“The Pythagoreans were so much given over to this method of philosophizing by numbers, that they did not even stand by the judgment of their ears…they marked out what was melodic and unmelodic, and what was consonant and what was dissonant from their numbers alone, doing violence to the natural prompting of hearing. “

In another word, human voices cannot distinguish these odd intervals, he says, but:

“It is possible for strings to be tuned that way, since they are inanimate and do not impose their own judgment, but follow the hand of the foolish theorist without the least resistance.”

Even though the ratios Kepler found in the planetary orbits correspond very closely to those numerical values, in Book Five, he sets up a table showing how the ratio of the angular velocity at the perihelion and aphelion of a planet, varies slightly over the course of a year. They are not fixed "perfect" ratios. Thus the possibility of tempering, of making the slight changes necessary is something the musical system can adopt from the solar system. Kepler's notion of tempering is not a practical adjustment, but again, has its origin in Mind. From Book Three:

“Friendships are given life by harmonic tempering. For what concord is to proportion, that love, which is the foundation of friendship, is to the whole compass of human life…Although friendship cannot survive frequent injustices, yet it rejects laws (strict rules), and refers everything to the sound and sober judgment of love, dispensing now equally, now proportionally, and when neither, always dispensing what seems to be in the immediate situation to make for the preservation of love, which is also goaded on, as harmony is by discords…by a few injustices, and receives its strength by free forgiveness of them.”

The Well-Tempered system is not a set of fixed ratios. Tempering is a human activity, in industry as well as music, that calls for the human mind to bring nature into accord with itself!

Kepler was known to many musicians who preceded Bach. Andreas Werckmeister, in his “Hypomnemata Musica”, a work calling to establish a Well-Tempered system, wrote:

“I wish to say something more about the excellent imperial mathematician, Johannes Kepler’s opinion, which he stated in the five volumes of Harmonice Mundi…that the Archetype is the cause in that it not only moves the stars to a more beautiful harmony (indeed not sensuous) but even more that it prepares the minds and souls of men so that they exist in such harmony and are moved through the heavenly motions, and are made joyful through sensuous, earthly music.”

Kepler overthrew the false axioms that held back both astronomy and music, and put both into harmony with the laws of the universe and its Creation. He is absolutely unique.

Music as Science: The C Minor Series, No. 1--Bach's "Musical Offering"

DAILY DOSE OF BEETHOVEN (June 29, 2020)

We've discussed the musical dialogue between Beethoven and other great composers in several of our past posts. In this C-minor series, we intend to delve deeper into the discoveries of Beethoven's predecessors and successors, and extraordinary dialogue through time, that took place among them. We hope that our readers will enjoy this journey through time.

The romantic notion of "art for art's sake" locates the source of a great work of art in the passion of the artist, which he or she must 'externalize'. Each work is thus seen as an autonomous expression of the artist's deep feelings. Yet, while great passion lies within a great work, scientific problem-solving also lies within it. Like a scientist, the great artist sees what they are doing not as mere entertainment, but as also advancing civilization. Such individuals are always making new discoveries that expand our collective knowledge of the world around us. Thus, just as scientists are happy to pass problems and questions, such as "What is the nature of light?" down to subsequent generations, the same is true of great composers.

Johann Sebastian Bach's name is synonymous with what is called "Classical music" throughout the Western world. His perfection of the well-tempered system of musical composition laid the groundwork for future great composers such as Mozart and Beethoven. His advanced innovations in musical composition were realized in well over a thousand surviving masterworks. Several of these, such as the "St. Matthew Passion", "The Art of Fugue", "Mass in B Minor", "The Well-Tempered Clavier" and "A Musical Offering" are acknowledged as fundamental contributions to human thought. They make him the bedrock of any serious attempt to study, write, or perform Classical music.

Bach's discoveries did not come out of nowhere. He build them upon the work of his contemporaries and predecessors, such as Andreas Werckmeister, Dieterich Buxtehude, and Italian composers such as Corelli. Many of Bach's predecessors were engaged in the effort to establish a Well-Tempered system. They followed the work of even earlier composers, as well as that of the great astronomer Johannes Kepler, whose discoveries (reported in his 1618 Harmonice Mundi--Harmonies of the World) proved that the orbits of the planets correspond to the musical intervals. This discovery overthrew Aristotle's insistence that the Music of the World and the Music of the Spheres were two different things, and that the latter was inaudible and unknowable to man. Kepler proved that the musical system was ordered according to the laws of the universe. It was not something invented by mankind, but something discovered by us, and earthly music was not vulgar, but divine!

Werckmeister wrote several works on the need for a Well-Tempered System, and insisted that he found its basis in Kepler's astronomy. Many of Bach's earlier predecessors also saw the need for such a system. This is not just a matter of how to tune the keyboard. Some of their works were scientific experiments that were not only investigations of problems within the Well-Tempered System, but also investigations into the VERY NATURE of the musical system, in order to help establish the new Well-Tempered System. The Modal system that came before, which had governed music for centuries, produced some beautiful works. But it was limited. It was difficult to change modalities within it. The Well-Tempered System advanced and changed this.

In his 1722 Well-Tempered Clavier (Bach wrote two books of Well-Tempered Clavier "WTC", 20 years apart), Bach composed for all 24 major and minor keys. For the first time, they all could be played in tune, on the same instrument. Within a piece, he could modulate lawfully to any other key. Some of these keys had never been effectively used before. A tremendous degree of freedom was opened up!

THE MUSICAL OFFERING

In 1747, as an old man, Bach visited the court of Frederick the Great in Potsdam. His son, Carl Philipp Emmanuel Bach (CPE Bach), was the King's music master. The King, an avid music lover and amateur musician, was eager to test out "Old Bach" 's legendary abilities. He played a theme of his own invention on the flute, and reportedly asked Bach to compose a 6 part Ricercare (basically a fugue) on it. Bach replied, "let me start with something in 3-part" and improvised a rather amazing work right on the spot!

here is a scored version: https://youtu.be/NG7H8TQfGmQ

Performance by Tatyana Nikolayeva: https://youtu.be/WTVXQE9GCWA

Upon returning home, Bach composed the "Thema Regium" ("King's Theme"). The theme, in the key of C minor, was not only difficult, took some of the questions that had been posed for over a century to a new level. For example, the second half of the theme is a descending chromatic scale. The necessity for twelve different tones was known 2,000 years earlier by the Greeks. Investigating the chromatic scale by composing with it was crucial for the attempt to break out of the modal system. Several composers wrote chromatic experimental works in the early 1600's, such as J P Sweelinck, John Bull, and Girolamo Frescabaldi. Here's an example of "The Fantasia Chromatica" by Sweelinck (https://youtu.be/9zHWp9nEL0s).

The other idea addressed in the "Thema Regium" lies in the first 5 notes: C Eb G Ab B. The first three tones comprise a C-Minor triad. The tones C and G, a Fifth, is in the strong tonic-dominant relationship. Ab is a half-step up from G, and B is a half-step down from C. Thus we have a half-step motion in inversion, a mirror image. G-Ab, and C-B. Bach had experimented with this configuration 25 years earlier in the "G Minor Fugue" of his WTC Book 1, which begins D-Eb G-F# G. However, the "Thema Regium" explores something new: the large, dissonant leap from Ab to B, which is a diminished 7th. We will see the importance of that interval for investigating the scientific nature of the musical system in future postings.

Bach explored both of these ideas in the same piece, but not at the same time. The "A Minor Prelude and Fugue" from his WTC Book 2 (composed around 1742, some 20 years after he composed Book 1), explore the chromatic scale in its long prelude, and the diminished-7th leap in the fugue, starting at 6:10 in this recording. ( Friedrich Gulda plays on the Clavichord, an instrument which Bach loved, but played only in private settings, as it was too quiet for a public concert. Unlike the harpsichord, it can play louder and softer, and even with vibrato, which you will hear at the opening of the fugue.)

https://youtu.be/Em9tZaphIPM

The "Thema Regium", to our knowledge, was the first time that the two ideas were addressed together. We suspect that CPE Bach may have had a hand in coaching the King on posting a true challenge to his father. How fortunate for us that this came to pass!

Two months after returning home, Bach sent the King a package called the "Musical Offering", which employed the "Thema Regium" in many ways, including a spectacular 6-part Ricercare, that represented a great breakthrough in composition.

https://youtu.be/OSm9LEYixvA

Goethe and Beethoven: "Getting Along with Girls"

DAILY DOSE OF BEETHOVEN (June 28, 2020)

The Classics are often associated with imagery of stuffy-old-white-male who have nothing relatable for the contemporary youth generation. We beg to differ.

Goethe's Mit Mädeln sich Vertragen (Getting Along with Girls), written in 1787, is a poem that makes hilarious fun of the "machismo" mentality of any young, over-confident, would be Don Juan. Beethoven captures Goethe's imagery perfectly (including a mock sword fight), in this short work for Bass and Orchestra, WoO 90 (composed around 1790-92).

https://youtu.be/Lnboxr-Vngw

Mit Mädeln sich Vertragen:

Mit Mädeln sich vertragen,

Mit Männern 'rumgeschlagen,

Und mehr Credit als Geld;

So kommt man durch die Welt.

Ein Lied, am Abend warm gesungen,

Hat mir schon manches Herz errungen;

Und steht der Neider an der Wand,

Hervor den Degen in der Hand;

'Raus, feurig, frisch,

Den Flederwisch!

Kling! Kling! Klang! Klang!

Dik! Dik! Dak! Dak!

Krik! Krak!

Mit Mädeln sich vertragen,

Mit Männern 'rumgeschlagen,

Und mehr Credit als Geld;

So kommt man durch die Welt.

With girls I get along,

With men I brawl,

With more credit than money;

This how one goes through the world.

A song, sung on a warm evening,

Has already won many a heart for me;

And I back the jealous one against the wall, His sword in his hand; Out, fiery, fresh, The feather duster!

Clink! Clink! Clang! Clang!

Dick! Dick! Dack! Dack!

Crick! Crack!

With girls I get along,

With men I brawl,

With more credit than money;

This is how one goes through the world.

Beethoven's Piano Concerto No. 3 in C minor--On the C Minor Dialogue

DAILY DOSE OF BEETHOVEN (June 27, 2020)

We have made several references to dialogue among the great composers, especially through those compositions in C minor. The Piano Concerto No. 3 in C minor, composed approximately in 1800, was a continuation of that musical dialogue that Beethoven conducted for years with the composers Johann Sebastian Bach (1685-1750) and Wolfgang Amadeus Mozart (1756-1791). Bach’s Musical Offering, from the key of C Minor that he composed at the end of his life, is a benchmark in the entire classical repertoire and has given birth to more compositions in dialogue among Classical composers than perhaps any other work.

In this concerto, Beethoven is conversing particularly with Mozart’s own Concerto No. 24 in C Minor treatment of Bach’s breakthrough, composed in 1785, fifteen years before. Mozart’s first movement, longer than any other he had ever written in the piano concerto form, is echoed in Beethoven’s opening first movement’s tones, which outline the same Bach theme, but in a new way. Beethoven’s third movement commences by referencing Bach’s theme, also known as the Royal Theme.

The surprise of this concerto, however, is the second movement, sung as a piano aria in the key of E major. This is called a “distant key". That is, a key other than the expected keys of E Flat Major (relative Major), A Flat Major (subdominant parallel), or C Major (tonic major). It doesn’t follow the rules, in other words, and the reason is, neither Beethoven nor any other true Classical composer, ever created a great composition by “following the rules.” Beethoven, one of the greatest improvisers—and it was he who first premiered this piece—leads the orchestra, and the audience, to discover a new path, showing that there is a principle of creativity behind and above the rules, that is harmonious, intelligible, and reproducible in the mind of a receptive audience.

We present here two great performances. The first, Mozart's Piano Concerto No. 24, with Murray Perahia and the Finnish Radio Symphony Orchestra.

https://youtu.be/s8j-1u2ndZo

00:00 - Allegro

13:28 - Larghetto

20:41 - Allegretto

The second, Beethoven's Piano Concerto No. 3 in C minor, performed by the extraordinary Italian pianist, Arturo Benedetti Michelangeli, conducted by Carlo Maria Giulini, with the Vienna Symphony Orchestra.

https://youtu.be/2t29tFSwqrE

00:00 - Allegro con brio

17:55 - Largo

30:00 - Rondo – Allegro

If you have a favorite version of either piano concertos, please share it with us!

Is Beethoven’s “Fidelio” about the American Revolutionary Hero and Political Prisoner, Marquis de Lafayette?

DAILY DOSE of BEETHOVEN (June 26, 2020)

Forty-two years ago, a young passionate republican, Donald Phau, published the simple and straightforward case that Beethoven’s opera “Fidelio”, was based upon the actions of Gilbert and Adrienne Lafayette. His discovery was met with a deafening silence. Today, historian and musician, David Shavin, re-opened the case with some rather astounding research.

With Mr. Shavin's permission, we reprint from his findings.

Beethoven was hired to write an opera for Emmanuel Schickaneder (who commissioned Mozart's Magic Flute) and his Theater an der Wien. However, he was not satisfied with the libretto provided to him. Instead, near the end of 1803, Beethoven decides upon the French playwright Bouilly’s “Leonore, ou L’amour conjugal” (Leonore, or Married Love). Beethoven’s collaborator, Joseph Sonnleithner, prepared a German-language libretto.

The play is about a political prisoner and freedom fighter named Florestan, and his wife Leonore. When Florestan was imprisoned, Leonore disguises herself as a boy, Fidelio, and gets a job in the prison where her husband is imprisoned, in order to free him. The play parallels exactly the story of the Marquis de Lafayette, hero of the American Revolution, and his wife Adrienne.

In 1792, three years into the French Revolution, Lafayette was the leader of the Northern French Army, assigned to defend France against an expected invasion by Austria and Prussia. When he came into opposition with the blood-thirsty Jacobin leadership of France and their guillotine, he sought asylum at the U.S. Embassy in the Hague (He later wrote from prison to a friend, that “I supported the progress of the French Revolution down to the time when I thought it inconsistent with the rights of the people at large, the sentiments of the majority of their representatives, and the true notions of liberty, to unite with partial acts of violence, and I was of course obliged momentarily to seek for a neutral ground."). He was intercepted and placed under arrest by the Coalition of Britain, Austria and Prussia. Since they were going to war with Revolutionary France, linear thinking might conclude that they ought to have welcomed Lafayette as an ally, since he was breaking with the Jacobin leadership. But nothing in life is actually linear. Instead, they held Lafayette prisoner, outside of any rules that applied to war, simply because he represented the American solution for Europe and was a threat to the established rule. He was imprisoned in Prussia for two years, then transferred to Austria, for a total of about five years.

The similarity of Bouilly's play to the case of Lafayette is much amplified by the fact that in both cases, a loving wife intervening to save her husband through "L'amour conjugal", or married love.

Adrienne Lafayette herself was imprisoned in France, in late 1792-- shortly after her husband was imprisoned by the anti-France Coalition. She was there in the summer of 1794, when her sister, her mother and her grandmother were taken from her and guillotined. She only escaped the same fate due to pressures exerted by America – from

George Washington through his representatives in Paris, Gouverneur Morris and James Monroe. When finally released, a few months after the fall of Robespierre and the subsidence of the Terror, she proceeded to organize a confrontation with the Austrian Emperor, Francis II —demanding that he release her husband, or that he imprison her in the same dungeon. James Monroe and other Americans aided her with a passport as an American citizen. When a friend warned her that it was too dangerous, she assured him: “In this my decision is firm, and nothing in the world can bring me from it.” She did meet with the Emperor, who protested meekly to Adrienne that “his hands were tied” as “it was a complicated matter.” She was imprisoned at Olmuetz with her husband, but was taken away for medical treatment, and only later told that she could not return. She wrote: “They will not tear me away from here except with M. Lafayette; unless, perhaps, they drag me away dead.”

We ask our readers to re-examine our study of “Leonore's Aria”, posted on April 16, 2020. Could Leonore possibly represent anyone but Adrienne Lafayette? Are the arias of Leonore and Florestan not those of equals?

The courage and the fate of these two was a cause celebre at the time. Since the U.S. could not enter the fray openly, Alexander Hamilton led the unofficial effort to free Lafayette, including his friends in London, and attempted prison escapes. The playwright, Gottfried Lessing, led the Hamburg Republicans who managed to smuggle his letters from prison and publish them. By 1797, the international pressure to free Lafayette had reached a high point, and he was finally released.

In the months after Lafayette was finally freed, Beethoven was a frequent visitor of the French Ambassador to Vienna, Jean Bernadotte, a friend of LaFayette. It has long been thought that it was Bernadotte who suggested that Beethoven create a “Bonaparte” Symphony (The Eroica). It has been suggested that Lafayette helped keep Bonaparte in the republican circles and away from oligarchical influence, from 1798 until 1804. Thus the symphony might not just have been praise of Napoleon, but an intervention, to keep him on the republican pathway.

Much later Bouilly denied any connection of his play to the story of the Lafayettes. That was at a time that it would have been very dangerous for him to say otherwise. Just as Leonore's aria could not be based on anyone but Adrienne Lafayette, Florestan's aria can not be based on anyone but her husband. Like Leonore's aria, it is in three parts. Here are the words:

Recitativ

Gott! welch ein Dunkel hier!

O grauenvolle Stille!

O'd ist es um mich her,

Nichts lebet ausser mir.

O schwere Prüfung! doch gerecht ist Gottes Wille,

Ich murre nicht, das Maass der Leiden steht bei dir.

Aria

In des Lebens Frühlingstagen,

Ist das Glück von mir gefloh’n.

Wahrheit wagt ich kühn zu sagen,

Und die Ketten sind mein Lohn.

Willig duld’ ich alle Schmerzen,

Ende schmählich meine Bahn;

Süsser Trost in meinem Herzen:

Meine Pflicht hab’ ich gethan,

Allegro

Und spür' ich nicht linde, sanft säuselnde Luft?

Und ist nicht mein Grab mir erhellet?

Ich seh', wie ein Engel im rosigen Duft

Sich tröstend zur Seite mir stellet,

Ein Engel, Leonoren, der Gattin, so gleich,

Der führt mich zur Freiheit ins himmlische Reich.

English translation:

Recitativ

Alas! what darkness here!

Oh gray silence!

All is wasted here.

Nothing lives but me!

Oh, heavy trial! But God's will is just

I will not complain.

The measure of suffering rests with you.

Aria

In the springtime of my life

Happiness has flown from me:

I dared to speak the truth openly,

And chains were my reward

I will gladly bear my pain

And end my days in disgrace.

But it is a sweet comfort to my heart,

That I have done my duty.

Allegro

Do I feel a soft air flowing about me?

Has my tomb become brighter?

I see, like an Angel wafting of Roses,

Standing by, and comforting me,

An Angel, Leonore, my wife, my equal

Who leads me to freedom in a heavenly realm.

We present here, three versions by three different generations of musicians:

1. Julius Patzak, with Wilhelm Furtwangler as conductor, from 1948.

https://youtu.be/YWICkSDz-Y0

2. Canadian tenor, Jon Vickers, with Otto Klemporer as conductor, from 1962.

https://youtu.be/m1QqZbkgeag

3. Tenor Jonas Kaufman, from 2004.

https://youtu.be/q407GBv3wjY

There are several things about this aria, that suggest that Bouilly had Lafayette in mind as the real-life Florestan, despite his later

denials.

1. Accounts given by Lafayette, Adrienne and others of the filthy conditions he was kept in, including open latrines beneath him:

Alas! what darkness her!

Oh gray silence!

All is wasted here.

Nothing lives but me!

2. Accounts of his isolation:

In Olmuetz he was known as prisoner number two. They wished to keep him a secret. In the opera, Leonore only gradually finds out where he is. His existence has been kept a secret.

3. Her account of his physical weakness, but moral strength.

"We found him in the most absolute solitude, not knowing our frightful misfortunes; that it had been expressly prohibited to tell him if we existed, his children and I, that his wasting away is frightful, his chest a source of horrible suffering.“ Yet, despite his physical condition, she was able to report: “He is morally as you left him. You know the force and sweetness of his soul, and despite the moral and physical tortures that [his captors] have chosen to heap upon him, there is not the least alteration in his character, nor the least imbalance in his temper"

That quality sings out in the aria.

4. Bouilly's play was only one of many to celebrate the idea, and was written after Lafayette's release in 1798. Bouilly drew on earlier influences.

The first play on the subject was “Le Prisonnier d’Olmutz, ou le devouement conjugal,” (The prisoner of Olmutz, or conjugal devotion), by P.A. Prefontaine. It was dedicated to Adrienne Lafayette. The play opened in 1797, and triggered a profound reaction when premiered in Paris.

LaFayette’s former aide, Philippe Charles d’Agrain, published “Captivite de LaFayette”. It included a poem, “The Castle of Olmutz.” A translated portion reads: "/ In this abyss where light barely descends, / Must I, in my wrenching pains without relief,/ Die by intervals in the sight of my oppressors?” Then, while contemplating what he had sacrificed, Adrienne appears.

Friedrich August Baumbach’s “Le songe de LaFayette” (The Dream of Lafayette), was put to music in a mini-drama, “Lafayette’s Dream,” by Friedrich von Oertel. There, LaFayette, in his dungeon, is “emasculated by the poison of loneliness” and tortured by visions of the guillotines and angry mobs. Then, the guardian spirit of America visits him, showing him a celebration of LaFayette in Boston and a warm reunion with Washington. The success in America even spills over into solving France’s turmoil. "LaFayette’s dream" clarifies his sense of mission and newly invigorates him. This 1794 scene of the guardian angel would also find its way into Bouilly’s play, in Florestan’s inspiration from above, but by his real-life wife as a guardian angel.

After all he had been through, Lafayette certainly deserved the right to retire. However, in 1824-25, at the age of 67, he undertook a successful year-long tour of the USA, in order to renew the spirit of the American Revolution.

We encourage historians, seeker of truth, and our readers to engage in a discussion on this most fascinating gem of American history. There is everything to be gained!

Beethoven Rarities: Song for Piano Four-Hand

DAILY DOSE of BEETHOVEN (June 25, 2020)

Beethoven composed ”ch denke dein, Song with Six-variations for Piano Four-hand, WoO74, in 1803.

Under the theme, Beethoven printed the words from the first verse of Goethe's poem “Nähe des Geliebten”:

Ich denke dein, wenn mir der Sonne Schimmer

Vom Meere strahlt;

Ich denke dein, wenn sich des Mondes Flimmer

In Quellen malt.

I think of you when the gleam of sunlight

Shines upon the sea;

I think of you when the shimmer of the moon

Is painted on the fountains.

Should the pianists sing it, or not? These variations are no too difficult but fun for middle level players.

Here is a not-too-fast version:

https://youtu.be/2M7ZxY91WW8

If you like, you can compare it to Schubert’s magnificent setting of the entire poem, “Nahe des Geliebten”. It is not without reason that Robert Schumann said the only progress made since Beethoven had been in Lieder.

https://youtu.be/m_dKPI9L_IY

Beethoven: Piano Concerto No. 4–the Final Movement

DAILY DOSE of BEETHOVEN (June 24, 2020)

How will Beethoven follow up the tearful farewell of the second movement? The answer might surprise us: with a playful Rondo!

On June 17th, we examined how a limited dance form, the Minuet, became transformed by Haydn, Mozart, and Beethoven, first into a more creative Minuet, and then the playful Scherzo, or musical joke. Today we will do the same for the Rondo. A “Rondo” is a form that constantly returns to the same theme, thus its name, meaning round. The form is taught to undergraduate music students as ABA, or ABACA, or even ABACADA—the invariant being the return to A. Unfortunately it seldom gets past that.

Like the Minuet, it was created in 17th century France. This Rondeau by Chambonnieres is so predictable you could set your clock by it.

A (8 measures) 0:02

A repeats (8 measures) 0:12

B (16 measures) 0:21

A (8 measures) 0:42

A repeats (8 measures) 0:51

C a variant of B (16 measures) 1:01

A (8 measures) 1:24

A repeats (8 measures) 1:33

For Haydn, Mozart and Beethoven there is little of interest in something that predictable: they increasingly want new developments! Thus, they will make a return to A seem like a surprise, or new discovery, every time. They will also play with your expectations, and give you something different. The transitions are often like long cadenzas, and prepare those surprises for us.

Let us follow just the basic outline of the third movement. Today we give the times for the recording performed by Alfred Brendel and Simon Rattle.

We also include the recording by Furtwangler and Conrad Henson for comparison.

You can find Grimaud's rendition in yesterday's posting of the entire work.

The 3rd movement starts with the A theme, but not in the main key of G major; it's in C major. Why? It is to provide a continuity with the second movement’s E minor. The single note E, connects the two movements. At about 0:45 a long transition begins, until the piano arrives at B, at 1:11. The seemingly simple piano melody has an equal counterpart in the left hand.

At 1:39 another transition begins. Where will it end up? When we return to A at 2:32, does it sound like the same-old, same -old, or is it refreshing? At 3:22, another short transition, into another surprise beginning at 3:49. The first few notes of A are in canon. Listen for the pizzicati in the strings. At 4:23 the solo piano once again slows down to approach a change, To our surprise at 4:34, B sings again, but more beautifully and in a different key than the first time.

At 5:02 we begin to transition again. Notice that the transitions are usually based on motifs of the main themes. At 5:37, another surprise: a slow and gentle version of A slips in without a long cadential build-up. Then such a cadenza leads us back to a full statement of A at 6:10. B pokes its head in at 7:10. Are we still dealing with different themes here? At 7:50 we hear a written-out formal cadenza.

We will you leave you, our readers ad libitum, to characterize the ending.