.
I have an indifferent voice, at best, but just this evening I was visiting my brother, and got drawn into singing in the choir for a wedding! This is a thrill, since we atheists rarely get invited to sing in church choirs. Luckily for me, this was an amateur choral society, and they were short of male voices.
Everyone has their own way of getting their head in the choir game. Some folks need to learn the melodies. Some can simply read off from the notes. Some have to hear their place in the rest of the choir sound. Some have to understand the
chord for each note they sing. Me, I have to understand the
geography of the piece.
Back in the old days of plainchant, the tune stuck to just a few notes, and once you knew the Home Note (the so-called tonal center, or Tonic), you learned all your notes relative to that one. They could have called the Home Note 1, and then numbered the remaining notes 2, 3, 4 and so on, and of course note 8 was (essentially) the same as note 1, but an octave higher, so you could call it 1', and the next note 2', and so on. (You have a problem going
downwards. You could call the note below 1 by 7*, the next lower one 6*, all the way down to 1*, etc, etc.)
As many of us know, the notes were actually called "doh, re, me, fa, soh, la, ti, doh," etc, as charmingly described by Maria in
The Sound of Music. This system is called Tonic Sol-Fa.
Here is an account in Wikipedia. (Actually, there seems to have been a medieval verse of music of eight lines, the first line starting on the home note, and each successive line starting on the next higher note. The lines are said to have started with the syllables Ut, re, mi, fa, so, ... , but someone replaced Ut with Do. Probably got canonized for this innovation. If anyone can give me a reference to a performance of this verse, I shall be eternally grateful.)
[Added later: Here is a depiction of the original latin hymn to which I referred, and an
explanation by Mr Neil Hawes:
]
Centuries passed, and by the time Palestrina was composing (Giovanni da Palestrina -- probably not his real name, but I could be wrong)
harmony had been discovered, and people were singing many melodies simultaneously, creating a tapestry of sounds at a single instant. This meant that a given note could be
harmonized in many ways.
As a side-effect, it became possible --and desirable!-- to
change the home note temporarily, to create tension, and the feeling of
travel. Many tunes depart from their home note by the second sentence, to coin a phrase. By the time Bach came around, the skill of changing home notes was not just one of many procedural techniques for composers, but almost their most important stock in trade.
How was music notated, once the home note was changed? The new Doh could be the old Soh, or practically any note! To be honest, I don't know how this situation was dealt with in the world of Tonic Sol-Fa, as the Do-re-mi system is called. But Bach, and even many composers before him had begun to use an
absolute notation system that simply showed the notes, and new notes that were required because of moving away from the Home Note were indicated with symbols (so-called
accidentals: sharps and flats that were inserted right in front of the note).
So when we're singing along, and a whole lot of accidentals suddenly crop up, of
course we know that we're traveling, and incidentally, what note to sing, as well. But for those of us who are hard to please, we need to know
where we are relative to the original key; hence my remark about the geography of the music.
Several months ago, I described a system used by Stephen Malinowski which illustrated relationships between notes. He actually used several methods, I'm referring to one of them: The Interval Lattice. Here it is:
Here, the Home Note is represented by
1. You could think of it as C major, if you like. Surrounding it are six other notes: counting
counter-clockwise from the note immediately to the "east" is
5, or G major;
3, or E major/minor;
6, or A major/minor;
4, or F major;
5#, or
6Flat, G Sharp or A Flat; and finally
3Flat, or E Flat major.
Of course, some folks consider
every note to be related to every other note. This particular scheme gives priority to these 6 notes, but if you take
their immediate neighbors, you get all the possible notes included, at (at most) a distance of one (additional) note away.
To help out novices, I should say that some of these 6 notes are closer than others; actually G major, F major, and A minor are the most closely related. These are most often the first destination when Bach, for instance, leaves home. Next favorites are D minor and E minor, closely followed by G minor, and C minor. (By this time, you're seeing that this lattice is not that helpful, really! Maybe some 3-dimensional lattice might be of help...) So when I say that I want to know
where I am, I don't mean simply which new Home Note; I want to trace the sequence of Home Notes that got me where I am.
Where do Riemann, Columbus and those people come in?
It has to do with
maps. A map, of course, is an abstract representation of a geographic area. (We've obviously gotten away from thinking of a map as a representation of The World --here be dragons, etc, etc. Maps of The World are, at best, laughable approximations, because adjacent points are often at opposite ends of the map.) If we think about it, our system of scales is a map from a set of sounds into the numbers 1, 2, 3, ... , 7. Mathematicians and geographers soon cottoned onto the fact that any shape other than a plane, such as the Earth,
cannot be represented by a single map.
One of the big things-to-do in mathematics is to
calculate gradients, such as the
pressure gradient, or the
temperature gradient, and so on. A lot of physics is all about gradients, but we math folks
own the idea of gradients. It so happened that everyone knew how to do gradients when
using a single map. Riemann's brilliant contribution to mathematics was to show how to do gradients while
using a patchwork of maps! By and by, Einstein came along, and said that
all maps were equally good for physics (though of course some maps were a little more equal than others).
[Added later: As to the mathematics-- A surface such as a cylinder or sphere (or Möbius Strip, for that matter)
cannot be represented by a single map. So you need several maps to represent the whole thing, and these maps
must overlap, and there has to be a minimal degree of smoothness in the equations that connect the two maps in the overlap. These sorts of surfaces, together with all their maps, are called
Manifolds, for the simple reason that multiple maps are necessary. So, all manifolds are
locally Cartesian; in other words, a small neighborhood of every point is one at least one of the maps. Compare this with the remark that Wagner's music is
locally diatonic in the following paragraphs. Later composers have written music that is totally
atonal, that is, there is no tonal center at any moment. In fact, they go out of their way to destroy any feeling of tonality --any feeling that there exists a Home Note, even a temporary one-- in the entire piece. I must confess that atonal music is not satisfying to me personally, but I might have enjoyed a few seconds of it while my defenses were down.]
Then along came a fellow called Richard Wagner. I doubt whether he knew anything about Riemann or Einstein, but he was writing music that seemed to
completely disregard the home note. At any given instant in time, one can hear an implied home note. But unlike Bach, Handel, Mozart and Beethoven, all of whom
traveled widely in respect to their home notes, but who always took the time to
travel back to the home note, Wagner sometimes set out from the home note, never to go back again in the same piece. Like Riemann, though, who insisted that
every point should be on some regular map that looked more or less like the X-Y grid, Wagner's music is, in a small neighborhood of any moment in the music, like the music of Bach, which is to say,
locally diatonic. This makes Wagner's music easy to apprehend, so long as you did not have a driving urge to "go back home" to the initial Home Note. [Wagner changed home notes --
modulated, which is the technical term for it-- based on the imperatives of the melody he was building.]
Many Wagner tunes are perfectly diatonic. Some of them, however, are not. So Wagner is, for music, something like what Riemann (or Einstein) was to mathematics (and Physics).
So, you see, geography is not too far removed from music, conceptually. To conclude, Merv Griffin's tune used in Final Jeopardy (named by Griffin
Think) is an instance of a tune that leaves home in one direction, and arrives home from the opposite direction, having gone completely around the world!
Arch
The first opera in the tetralogy (actually written last) was Rhinegold. This brilliantly written opera serves as a prologue to the action of the remaining three operas: A Dwarf, Alberich, steals the magic Rhinegold from the Rhinemaidens. Meanwhile, the Giants have built Valhalla for the gods, and need repayment. The trickster god Loge (Loki) steals the magic Ring forged by the Dwarves of the Rhinegold, and gives it to the Giants. For the moment, everyone is happy, except the Dwarves and the Rhinemaidens. (Back then the Dwarves had their own eminent domain principle, except for when people stole things from them!) [The painting at right is a depiction of Alberich and a Rhinemaiden by Arthur Rackham.]
Wagner's peculiar invention was the concept of the Leitmotif: a tiny musical fragment that is highly recognizable, which would serve not merely as the basis for mood music, but very specific aural allusions to persons, feelings, incidents, objects, principles and events. So when in Star Wars the score recalls Darth Vader, or The Empire, or The Rebellion, or The Force, we must remember that Wagner, decades earlier, invented the means to do this in a way perhaps a little too subtle to succeed in modern Cinema. Modern Cinema has embraced the idea of broad musical themes that refer to persons, places or events, but not at the miniscule, atomic level of Wagner's Leitmotifs. (The score for Gone With the Wind, by Max Steiner, for example embodied this modified Leitmotif principle.)
Now Wagner's ideal was to present the entire saga of the Rhinegold using all these media of music, art, dance, poetry and drama. He started with his own script (libretto), written all in verse of an appropriate epic meter, and set about creating a score that had the highly imaginative principle of the Leitmotif at its heart.
The opening scene of the entire four-opera tetralogy (some 13 hours of music-drama) opens under the surface of the river Rhine. Before the curtain goes up, the Overture to Das Rheingold begins simply with a huge B Flat chord.
Deryck Cooke, a well-known British musicologist who has spent a large proportion of his life in studying the Leitmotifs of Der Ring des Nibelungen, suggests that this theme is the basic theme of Nature. (Note: Wagner himself has written at length about his own Leitmotifs for the Ring; I simply use Deryck Cooke's description because I'm more familiar with it.)
Gradually the Nature theme transforms into a more 'churning' theme, that of the River Rhine. Here you get the first, simplest example how Wagner developed musical ideas via transformation of these atoms of meaning, to represent related ideas by related atoms of musical melody and harmony. (He adds that the pentatonic theme of the Rhinemaidens, from whom the Dwarves stole the gold in the first place, as characteristic of nature elementals in the story, such as the Wood bird, who appears in the third opera, Siegfried.)
Later, in subsequent operas, Wagner introduces variants of the opening Nature motif to represent the World Ash Tree, from which Wotan cuts himself a staff, or spear. A similar, but minor-key theme represents Erda, the earth-goddess. Here is her first appearance, her minor-key theme a counterpart to the major theme of the River Rhine. (After warning Wotan of sad consequences of his actions, she foretells the downfall of the gods, and under her words is an ominous descending, major version of her rising, minor theme.)
Here is a sequence of scene fragments from Rheingold, staged by the San Francisco Opera. In this clip we have (1) the Rhinemaidens frolicking, shortly before being robbed of their gold, (2) Wotan, the King of the gods, (3) Wotan being talked at by his consort, (4) the two giants, Fasolt and Fafnir talking about not getting paid for their construction work, (5) The Dwarf Alberich, (6), (7), (8) scenes I don't recognize, and (9) Wotan leading the way over the Rainbow Bridge into the (finally paid-for) Valhalla.
The giants, who are given the Ring, fight among themselves, and one kills the other. The survivor, Fafnir, turns himself into a dragon, the better to guard the Ring. (The fight among the Giants is echoed in Smeagol killing his brother Deagol in Tolkien's Ring Saga.) The gold is cursed, and has an appropriate theme, which one hears in the orchestra at critical moments when the Ring influences events around it, usually ending in death, war or destruction.
The second opera (the first of the real operas after the prologue, Rhinegold) is Die Walküre. In it, Wotan puts into motion his devious plan to retrieve the Ring from the Giants, and, maybe, return it to the Rhinemaidens. Wotan arranges for a man and a woman to be born, who would be the parents of a great hero. But the plans go wrong, and the woman (Sieglinde) ends up married to the wrong man. But Wotan arranges for the man he intends should be Sieglinde's lover to stumble into her home during a storm. They fall in love, and run away together while the husband lies sleeping. The betrayed husband follows, and there is a mighty battle where both men die, but luckily Sieglinde already bears the child who is to be the hero.
During the duel, the valkyrie Brunhilde aids the lover, in defiance of Wotan's explicit instructions, because she has pity on the pregnant woman and her lover. (This is a poignant moment, because Wotan, in his heart of hearts, supports Brunhilde's action, while his instructions to Brunhilde were in obedience to his wife Fricka's command. Wotan's wife Fricka is the deity who guards the sanctity of marriage, and is naturally appalled at Wotan's plot to have this lover come between a man and his wife.) Now Brunhilde faces Wotan, and after a lengthy accusation of treachery, he condemns her to a magical sleep, after which she has to marry the mortal who wakes her, which takes away her immortality, of course. Losing immortality is a major deal, as we have learned from Tolkien's Ballad of Luthien Tinuviel. The opera ends with the magic fire music, representing the magical ring of fire Wotan arranges to be placed around the sleeping Brunhilde, to ensure that only the exceptional hero can wake her.
Sieglinde has already been smuggled away from the scene of the battle by Brunhilde, and hidden away in a cave in a forest, near which it happens that the Dragon Fafnir has his lair. She is given shelter by the brother of Alberich the dwarf, and gives birth to the hero Siegfried.
Siegfried, the third opera, recounts how the young hero, brought up by the dwarf in the forest out of sight of humans, forges his father's broken sword, kills the dwarf, kills the dragon Fafnir, get
s the Ring, and proceeds to discover the sleeping valkyrie Brunhilde, who wakes and falls in love with him. Siegfried gazes at her in amazement; he has finally found a human woman, the first one he has ever seen.
But the Ring causes trouble, and Götterdämmerung, the last episode, recounts how when the couple arrive at a nearby court, Siegfried is offered another bride, and amid the cross-currents of jealousy, suspicion and avarice, Siegfried is murdered, Brunhilde in grief rides her horse into the flames of the funeral pyre, Valhalla catches aflame from the burning pyre (!!), and the Ring falls into the Rhine, where it belongs. [The painting at right is a depiction by Arthur Rackham of Brunhilde riding her horse Grane into Siegfried's funeral pyre. Equine actors in operas have famously been reluctant to do this bit.]
Wagner appears to have looked for a story in which the true hero is presented with a series of dilemmas, in which the choices were invariably inevitable but regrettable. To that extent, Wagner's choice of this tortured storyline is understandable, though the inevitability of the choices are occasionally questionable. Wagner's hero is, of course, not Siegfried, but Wotan. While, on the surface he appears to manipulate everything, he is simply the puppet of blind fate, the way Wagner seems to have seen life.
To conclude, the entire cycle of four operas (three operas and one opera-length prologue) is driven by the lyrics sung by the actor-singers, the fantastic scenery (nowadays too often substituted with modern interpretations, such as the California Gold Rush, etc), and the amazing score, played by Wagner's enormous orchestra, featuring special instruments for the purpose, such as special tubas to represent the the dragon Fafnir.
The story of the Ring of the Nibelungen is a variant of a German-Norse epic, the Nibelungenlied, written by an author whose identity remains a mystery. Wagner conflated this story with that of another legend, the Vollsung Saga, to portray a net of deception and disappointment intense enough to motivate his dramatic requirements. The sequence of betrayals is painful enough on which for Wagner to build the ultimate destruction of Valhalla, and the return of the Ring to the Rhinemaidens at the end of the whole drama. Today, to modern eyes, the melodrama seems too unreal and too long-drawn to be taken seriously. But granted that it was going to be realized in some medium, it is hard to think of a better one than Wagner used, or a more effective execution, if one takes into account the amazing musical creativity and planning that Wagner undertook, and achieved.
With the medium of Cinema available today, such projects can be implemented with much greater success, as we see in the Lord of the Rings project with J.R.R. Tolkien's book and Peter Jackson's movie trilogy. Since these were created by an author rather than a composer, the literary characterization is certainly more successful. Understandably so, since Tolkien had not only all German mythology and epic poetry for his sources, but Wagner's work as well. The musical score of the movie, however, takes a secondary place. While it is entirely possible that the score could have been written with the fine attention to detail of Wagner's Ring Cycle score, the needs of modern cinematic production procedures and the level of sophistication of movie-going audiences (compared to opera audiences) all dictate a simpler approach to movie scores.
The music community is divided over Wagner's music, especially his Ring cycle. Many musicians and aficionados regard Wagner's music overblown, heavy and self-indulgent, and one can see why. (Many composers after Wagner absorbed a lot of his ideas --Verdi, Mahler, Humperdinck-- but managed to keep their music more agile and their orchestras more compact, thus avoiding the worst of the criticisms that followed Wagner everywhere.) Still, we in the 20th and 21st centuries are accustomed to being indulgent with artists whose egos and ideas would probably dwarf those of Wagner. Perhaps Wagner's greatest mistake was that of being born too early!
In later posts, I plan to look at other operas by Wagner that are greater successes, artistically, and which reflect a more mature personality in the composer: Parsifal, and Die Meistersinger von Nürnberg.
Archimedes
