The Meaning of Music

The title to this post is ambiguous.   So much so that its intended meaning might not strike the reader at all.  What I mean is that certain music phrases have been used, for centuries, to convey certain musical feelings and moods; so much is obvious.  But we expect that they convey different feelings to different people.  No!  From hearing the same phrases used with the same meaning (by different composers) so often, music lovers can begin to understand a conventional meaning to these phrases, which the composer could (I'm not saying they consciously do, but they could choose to do so) use them to underline particular feelings!

On my own, I had begun to think this way as a teenager.  But then, I came across a book by Deryck Cooke, a somewhat specialized British author and musicologist—now dead—called The Language of Music, in which he tried to prove this very thesis: that certain musical phrases can be used intentionally to convey specific emotions. 

Cooke is best known for his thematic analysis of Richard Wagner's Ring of the Nibelungs.  This is a cycle of four operas, based on an epic poem, and—I believe—certain germanic myths and legends.  These matters could take an interested music lover a lifetime to get to the bottom of, but the basic idea is that Wagner deliberately used musical melodic fragments—called Leimotifs—to convey the dramatic logic, the cause and effect, of the thoughts and actions of the protagonists of the opera.

Soon after I had learned about Deryck Cooke, I stumbled on a two-CD album, with copious accompanying notes and musical illustrations—today easily available in almost any public library; certainly in our own—in which he sets out his analysis of the Leitmotifs of Wagner's Ring Cycle, and I for one think his analysis is exactly on the money.  It is a huge edifice; and that's what the opera cycle needed, lasting close to fifteen hours, total, to hold it together.

I'm not going into the Wagner operas today.  But the old hymns of Easter illustrate one of the family of musical phrases that are most obvious, in those that I recognized as a youth: triumph, and joy!

Those two words, more than any others, encapsulate what Believers feel at Easter.  (In the interest of full disclosure, I'm an atheist, but anyway ...)  Actually, there are two emotions I want to talk about: the feeling of triumph; and the feeling of completion.

The rising scale.  In the scale of C, the notes C, D, E, F, G, in sequence, convey a feeling of assertion, a feeling of having something to say.  Even just the rising triad, C, E, G, which sounds like the beginning of a fanfare, sounds like a challenge, or even a defiant challenge.  And there is a feeling of uncompleted business.  (Note that, almost necessarily, the meanings I'm trying to convey are vague.  There is no exact correspondence between musical meanings, and literary meaning.  The phrase can be abbreviated to just a rising fifth: C-G, and still convey that feeling of a challenge, or just a question: What?!

The second phrase I want to describe is the descending scale: C' B A G F E D C.  As Deryck Cooke describes it, this musical phrase conveys a feeling of coming home, of closure.  The two half- phrases C' B A G, and F E D C convey parts of this idea of conclusion. 

In a lot of Easter music, these two phrases are combined, to convey a challenge, triumph, satisfaction, the conclusion of an argument.  The easiest examples are, of course, Easter hymns. 

One of the oldest, and most famous Easter hymns is: The strife is o'er, the battle won.  The tune by Palestrina sorry  Melchior Vulpius, I believe, incorporates both the challenge tune, and the satisfaction tune. 

There is another hymn, not as ancient, nor as well known as the Palestrina: This joyful Easter tide, often used as an anthem for Easter.  This tune, too, incorporates the two phrases, for a challenge, and for a successful conclusion.  If I can, I will color-code the examples. 

Here is the music of The Strife is O'er, the tune of Melchior Vulpius.  Again, the tune dates from around 1611:

The tune for the first two measures has the descending phrase, which I described as conclusive, satisfaction.  The next phrase or two, in the example, raise the challenges; the ending descending scale repeats the satisfactory conclusion.  In fact, the entire tune is replete with satisfaction, confidence, and, I suppose, celebration.
 

Here is a reconstruction of This Joyful Eastertide, which is apparently derived from a Dutch tune of the 17th century, harmonized by the well-known arranger of sacred music, Charles Wood (but here by me).

The first complete measure has the ascending tune of assertion and challenge.

The last three complete measures have the complete descending scale of F major!  As a treble, I loved to sing this line, and I'm sure, so does anyone singing this part.

Conclusions

Both these examples are from the 17th century, and that's not a coincidence; that was the era of protestant congregational singing, and that doubtless had a lot to do with establishing the emotional content of musical phrases.  Some would argue that this entire phenomenon flows from hymnody.

Arch

'Bist du bei mir'

Anna Magdalena's Notebook

 Johann Sebastian Bach's second wife—to whom he was married at the time he died—was Anna Magdalena, a woman much loved by many generations of music-lovers, and certainly Bach-lovers.  Anna Magdalena maintained an album, in which she copied many short pieces by her husband, and many other pieces that took her fancy.

Among these is a remarkable aria: Bist du bei Mir, which was, identified last century, to have been written by Heinrich Gottfried Stölzel, a talented contemporary of Bach's.  (In fact, a biographer of Stölzel is said to have declared that Bach and Stölzel were equally talented.  However, Stölzel did not have nearly as great an impact on music as did Bach.)

I've joined the New Horizons band for seniors in our hometown, and this spring, we're performing Bist du bei mir, arranged for band.  When I was 17 or so, a friend of my parents was anxious to teach me violin.  So I was given the loan of a violin, and asked to practice this very piece.  At that time, I had never heard it before, and thought it a fussy little tune; I had been told it was by Bach himself, and I told myself that it couldn't possibly be by Bach, whom I revered.  Soon my violin teacher gave up on me, saying that my intonation was too 'piano-like', by which she meant that my ear wasn't good enough to tune my fifths according to the just intonation that string players use, but that I was playing 'piano fifths', that were just a tiny bit out of tune to the ears of violinists.  (Hardly anyone today can tell the difference, unless they're temperament experts, which I certainly am not.)

The Stölzel aria, I have come to recognize for half a century, is just a gem.  Early in the aria, there is a chord that I described in the post about Harmonica Harmony, the dominant ninth but without the root.  There are numerous features in the song that provide 'hooks' for anyone wanting to hear it, but no hooks are necessary; it is a brilliant tune, evidently recognized by Anna Magdalena Bach, who was an extremely musical person.

Bear in mind that the tune is, basically, an aria, that is, a song.  Most of the recordings of it on YouTube emphasize the soprano line.  But to me, the counterpoint is wonderful.  Without being obtrusive, the parts caress the melody, giving the accompaniment a lot of character.  In orchestral arrangements, the counterpoint is usually smothered, but here is one, FWIW.

General Education

I just read, today, that the great Canadian pianist, Glenn Gould, did not complete high school. This is only the last in a series of stories about various—quite intelligent—historical figures who, for one reason or another, either struggled with, or gave up on, education.  Einstein is said to have struggled with simple mathematics.  Many important artists and musicians gave up school.  Actors have abandoned school, but have in some cases, gone back to school to try and complete their education. 

What are we to make of this?  Education is the imparting of certain skills from a knowledgeable person, to a (usually) younger person.  In modern times, the recipients are usually a group (a class), who are all taught together. 

I worry that this failure of the educational process could encourage young people in their belief that the education process is seriously flawed.  Well, we've all known that the educational process is flawed to some degree.  It does not take into account the great variation in the mental equipment of the members of a class; their different degrees of predisposition to learn; their psychological resistance to being taught; their emotional incompatibility with the instructor.  It's quite easy for a student to reject his or her teacher; "It's just not working out."

In case anyone thinks that all those future celebrities who bailed on school were incapable of completing school, I'd say that many of them had a firm grasp of most subjects in the curriculum; certainly Glenn Gould did, and probably Einstein.

What prevents modern schools from customizing the curriculum yet more than it is now, to match the preferences of the students (and parents) perfectly, is the cost.  In many ways, College accommodates this desire to have a more varied curriculum.

Pi Day Once Again

 [Apologies, readers; this post belongs in the—mostly—nonmusical blog I could be Totally Wrong, but.]

Well, it's π day in the USA, and though we wish it's an international feast, it really isn't!

I, and I'm sure many other mathematicians, sneer at this celebration, but I'm thinking: who am I to spoil the fun of so many mathematician wannabes?  Let them eat π, to paraphrase Marie Antoinette!

A few bits of trivia about the fabled mathematical constant:

1.  Though it's commonly thought of as 3.14, one of the cardinal properties of the number is that it could not possibly be represented by a decimal number that stops.  Cannot be done.  However, you can represent it as accurately as you want, but it will never be exact.  It can't be written as any fraction, either.

2.  HOWEVER: Archimedes had discovered an excellent approximation to the number Pi, namely 22/7.  If you've got a circle of radius 10 inches, and if you want to know what its circumference is, we know that, in the abstract, it will be 10 inches × Pi × 2.  This will be perfectly accurate.  But since we cannot represent Pi exactly, we can only find this circumference approximately.  (This means not exactly, but closely—in fact as closely as desired.)  If you want an estimate to as close as 1/1000th of an inch, we need to use about 6 decimal places of the value of Pi.  (It's  been 10 years since I've done this sort of thing, so I might be off by a couple of decimal places!)  So basically, what approximate value of Pi you must use depends on how close you want your calculation to be.  You can easily Google Pi, and compare it with 22/7, and you'll find that they agree to more than 5 decimal places. 

3.  But guess what.  It was known by Eastern mathematicians (Indians, Persians, Egyptians, Chinese, etcetera) that 355/113 was even a better approximation to Pi!  The miracle of these two approximations to Pi is how close they come using such small numbers!  The next fraction that comes even closer, is a fraction of two enormous integers. Google sends us to a website that gives 100798/32085 ~ 3.14159264,correct to 8 decimal places. But see how huge the numbers in the fraction are?