Wednesday, May 27, 2015

Mensuration and the Old Ways of Composing.

A few days ago I got a couple of very challenging comments on my blog. One was on the post "A Cathedral and a Motet" and asked the following:
Do you know of a book that explains how Dufay, Ockeghem, etc. wrote their more intricate compositions? Not just a simple explanation of isorhythm or a rudimentary explanation of 15th->16th century counterpoint, but: if I am Dufay and I am going to write the music above in your post, how exactly do I go about accomplishing that?
Now I spend most of my time trying to write, you know, 21st century music, not 15th century music, but this is such an interesting question that I wondered how it could be answered. First I went to my shelf to see what books might contain some answers. Composition is, for a very large part, notation. In other words, what we can write down and how we write it down IS the piece, or at least the definitive instructions for performing the piece. So I took down one of the oldest books in my library The Notation of Polyphonic Music 900 - 1600 by Willi Apel, originally published in 1942 and, I believe, still in print. It is the most thorough textbook on the old systems of notation. It contains facsimiles of a lot of older notation. Here, for example, is a three-part chanson in white mensural notation by Guillaume DuFay.

If you look very closely at the top, there is a little line of text above the staff that says "Guillermus du" and then a little bit of staff with the note "fa". This is often how he signed his name on a music score. But wait, this is not a music score in the modern sense. I will explain below.

There are two pieces on the page. At the top is Quel fronte signorille and the bottom is the chanson "Dona i ardenti". Transcribing this kind of notation into modern notation is the work of a graduate doctoral seminar in musicology. As you can see, reading the original manuscripts is not easy! For comparison, here is the beginning of that chanson in modern notation:

Click to enlarge
The transcription into a modern score does several things: it takes all the original pitches and puts them on modern clefs and also changes all those weird boxy hollow notes (hence, "white" mensural notation -- there is also black and even red) into modern rhythmic values. But one other very important thing happens. The original is three separate parts just stacked up. They are not aligned rhythmically at all. A big part of the problem of transcription is figuring out exactly how the parts align. At this point in music history the score, where the various parts are precisely aligned rhythmically and corralled within barlines, had not yet been invented.

This gives us an important clue about DuFay's compositional methods: he did not compose in score! Like most composers before the 17th century, DuFay was a singer. The others, like Francesco da Milano, were largely lutenists. As a singer, how he likely composed was each line separately. In other words, what he probably did was write down the tenor and then compose the cantus and then the countertenor. This is not how modern composers work, by the way.

In the text, the DuFay chanson is chosen as an example of [2, 2], meaning, in the orthography of the text, that the tempus and prolatio are both imperfect. Huh? Ah yes, nothing like a bit of Latin to brighten one's day. In answer to a question in the comments about mensuration, in modern notation there is, within the notation, only one kind of subdivision to any note: duple.* In other words, every whole note contains only two half notes, every half only two quarter notes and so on. But in white mensural notation they had two possibilities: duple and triple or imperfect and perfect. In this kind of notation the brevis and semibrevis (usually rendered in modern transcription as a whole note and a half note or a half note and a quarter note) are the ones where we see the division into three. The mensuration or subdivision of the brevis is called the tempus and the two possibilities are perfectum and imperfectum and this was indicated in the time signature. The mensuration or subdivision of the semibrevis is called prolatio and, again, there are the two possibilities of perfect and imperfect, i.e. triple or duple subdivision. There are, therefore, four possibilities as indicated in this handy chart from the text:

The old time signatures are interesting. For one thing, this is where our "C" time signature comes from, often called, by ill-educated music teachers, "common" time. As you can see it is the old white mensuration time signature for "tempus imperfectum cum prolatione imperfecta". The so called "cut" time, which is the same half-circle with a slash through it indicates in modern music that the half note takes the beat.

Now that doesn't tell you exactly how to write a mensuration canon à la Guillaume DuFay, but it will give you an idea of the notation at least. For practical exercises in modal counterpoint I can do no better than recommend another excellent text, this one by another McGill professor, Peter Schubert, titled Modal Counterpoint, Renaissance Style, which was published in 2008.

*In modern notation we can indicate any subdivision whatsoever, but we do it with a workaround, essentially going outside the notation itself. To indicate a triple subdivision we write a little 3 with a bracket. But we can also write a 5 or a 7 or anything. The most extreme I have seen is something like 13 in the time of 12. This is how we think of it: we stuff extra notes into a fixed beat. Works quite well.

Luckily we can find the DuFay chanson on YouTube. Here is Dona i ardenti with unknown performers:

Tuesday, May 26, 2015

Concerto Guide:

I know I didn't put up a Concerto Guide post last week. Every time I sat down to start one that old New Yorker cartoon kept popping into my head and I lost the will to write. You know the one: there is this little kid standing on stage next to a piano. He is dressed in evening garb and addressing the audience saying: "and now, God help us all, Rach three."  I just couldn't get that out of my head, especially as it looked like the next concerto I was going to do was either Rachmaninoff Two or Three.

The problem is that I just don't think I can do a Music Salon post on a Rachmaninoff piano concerto. Usually I am on the other side of the ideological divide between the Serialists and the Traditionalists. Usually I think that the Serialists and their fellow travelers were simply dogmatic in their insistence that the traditional forms were tired, exhausted clichés. But when I listen to Rachmaninoff I think, well, perhaps in this case they were right. Rachmaninoff's piano concertos are all that piano concertos should be: noble, virtuosic, then tender and lyrical. They are a bit like what Chopin might have written if he had written a mature concerto. So what's the problem?

As I see it, a composer can write a concerto that we hear as being noble, adventurous or tender and lyrical and it can be a great success. But if the composer's goal is to show us how noble and virtuoso or tender and lyrical he can be, in other words if that is his actual goal instead of making a piece of music, then the result will be, sorry to say, kitsch. Kitsch as in a painting by Thomas Kinkaid:

Or a movie by Steven Spielberg that does nothing but push our emotional buttons from beginning to end.

See, that's everything that we like, right there. A pretty little country church, just like the one we wished we had attended when we were young; tall trees, mountains in the distance, a babbling brook and over all the delicate hues of sentiment. With Rachmaninoff we have an extension of the romanticism of Tchaikovsky, but, to me at least, it is genuine passion turned to mere sentiment, a haunting melody become a nice pretty tune. It is very well done, the technique, both pianistic and compositional, but you can certainly see why composers like Schoenberg and Stravinsky would think that this is exactly what had to be killed in order for music, their music that is, to move forward.

So that's why I can't do a Concerto Guide on Rachmaninoff. (For an interesting discussion of the ideological differences and compositional practices of Stravinsky and Rachmaninoff, see this paper by Richard Taruskin: Stravinsky and Rachmaninoff: A Comparative Study of Their Musical Ideologies.)

But you really have to hear this for yourself, so here is Yuja Wang with Yuri Temirkanov conducting the Verbier Festival Orchestra in the Piano Concerto No. 2 of Sergei Rachmaninoff:

That was composed around 1900 so it brings this phase of the Concerto Guide to an end. Next up is the 20th century and a surprising revival of the energy and adventure of the solo concerto with remarkable works by Schoenberg, Bartók, Shostakovich, Prokofiev, Berg, Glass, Salonen and just about everyone else.

See you next week.

Monday, May 25, 2015

Discovery of the Week

To balance out my unkind remarks about Bruckner (and Mahler), let me direct your attention to one of those many interesting composers whose work was completely overshadowed by the relentless march of Modernism. I am talking about Vagn Holmboe. Who? Yes, exactly. Holmboe was a Danish composer who wrote, among other things, thirteen symphonies. A while ago I ran across an appreciation of him by Richard Taruskin that was written, I think, on the occasion of Holmboe's death in 1996. [UPDATE: Actually it was written in 1994, just a couple of years before.] He was born in Jutland in 1909. He is Denmark's second symphonist after Carl Nielsen.

In any case, I finally got around to listening to some Holmboe and, not surprisingly, given the praise from Taruskin, I was quite impressed. Here is his Symphony No. 8, "Sinfonia boreale" conducted by Owain Arwel Hughes with the Århus Symphony Orchestra:

That is pretty good, isn't it? Rather more interesting than Bruckner, wouldn't you say? Perhaps, and I say this very tentatively, even more interesting than Mahler? But the music of people like Holmboe was anathema to the modernists. For one thing it is tonal and makes expressive gestures instead of perplexing the audience with musical structures that have no real expressive content. So it had to be banned, or at least sneered at with every opportunity. They, the modernist intelligentsia, did the same with Shostakovich, but his music seems to have won itself an ever-growing audience despite their best efforts. Maybe it is time to give Holmboe a chance. Here is his Symphony No. 5 with the same performers:

Malicious Review of the Week

Via Norman Lebrecht I ran across this rather amusing review. Or rather, allegorical satire of a review. Instead of an actual review of an actual concert with actual performers we have a Personal Experience of a Performance of a Bruckner Symphony directed by a Famous Conductor! Here is a sample:
“I was somewhat ambivalent about staying for the second half,” she recalls, “especially after Legendary Violinist gave a great reading of Obscure 20th-Century Piece That No One Else Wanted to Hear. But I had heard that the Famous Conductor is a Bruckner specialist, so I thought maybe he could make it listenable.”
But McBrahmsFan was wrong. “Basically I had forgotten how bad Bruckner is,” she explains, sipping a comforting cup of tea in her apartment. “Even in that historic hall with a great symphony orchestra, there was no saving the music from itself. I’d say Bruckner is a lot of ‘sound and fury signifying nothing,’ but that is too poetic a phrase for its sprawling expanse of Wagnerian brass clichés and proto-minimalistic repetitions of diatonic tetrachords. I almost died.”
“At one point I caught myself thinking, ‘How did this man ever write four-part motets? He can’t even write basic soprano-bass counterpoint.’ The one time the bass did anything it was that tired descending line borrowed from Meistersinger, which created only a momentary interest of passing dissonance. And that trite scherzo – I spent the whole time wishing Mahler had written it.”
Heh. But as funny as this is, it is a mere Shadow on the wall of the cave of what might have been an even better, and even more merciless, scourging of Bruckner.

I was just listening to the Symphony No. 6 of Bruckner yesterday and yes, I was wondering to myself, as I was trying to stay awake, why isn't this better music? Why are the rhythms either sodden plodding or disquieting nasal marches? I hear this music and it just seems to imply gargantuan Imperial German militarism (which, historically, was just around the corner). But, pace the allegorical Sally McBrahmsFan, I was not wishing Mahler had written it, I was rather thankful that it was just Bruckner and not Mahler who seems to have most of Bruckner's failings with an added dose of fervid neuroticism.

I know that there are lots of Mahler fans among my readers--it is one of those rare aesthetic items about which we differ. Perhaps in time I will come around. Or they will...

Let's have a listen to the Bruckner Symphony No. 6. This is the BBC Philharmonic with Juanjo Mena conductor at the 2012 Proms:

Sunday, May 24, 2015

Time Signatures: Compound, Composite and Straight Up

I spent a lot of yesterday re-metering a section of a symphony. I thought I was being clever by writing in a simple 9/8 meter with a variety of subdivisions, but it was pointed out to me that this was actually concealing what was really going on. So I re-wrote the notation to bring the music into focus. But this got me thinking that I may not have talked much about time signatures. If you type "time signatures" into the search box to the right, it will turn up several posts, but they are mostly specific to particular pieces. What I want to do here is talk about time signatures generally.

Going back in history we notice that the hardest aspect of musical notation to get right is the notation of rhythm. Once the staff of lines and spaces was discovered (or invented, traditionally ascribed to Guido of Arezzo), it took another 500 years of experimentation before efficient solutions to the problem of rhythmic notation were discovered.

In music we have different specific words for time. The "timing" of a piece is its duration in minutes and seconds. But we also have the concepts of "beat" or "pulse", of "meter" and of "rhythm" itself. The pulse is the recurring, regular beat that underlies most music. Its speed is indicated in a score with a "metronome mark". The metronome was invented shortly after 1800 and Beethoven was one of the first composers to give specific indications in his scores. The sign for a quarter note followed by an equal sign and a number tells you that there are so many quarter notes per minute. This is usually seen in the top left of the score right after a tempo word. These tempo words are usually Italian (such as Allegro or Adagio), but are often German or French, or even English. They give a rough idea of tempo and mood whereas the metronome mark gives a precise indication.

Another crucial element of the notation of rhythm is meter. We feel the pulses of music in little packages of two, three, four or more beats. Each package is shown in the score with a barline to separate it from surrounding packages. The typical meter of most pop music is 4/4, meaning each measure or bar has four beats. In pop music usually the 2nd and 4th are stressed. This is what is called the "backbeat" because it is actually a variation from the norm. The regular stress in 4/4 is ONE two three four (to show that one is really stressed and three a bit less). Another common meter is 3/4 which is used in minuets and waltzes. Again, the first beat is stressed. Here, let me show you what this looks like. Here are some examples:

This was done in Finale, which can do just about anything. First off we have the tempo word, Adagio, which means "slowly", followed by a quarter note being equal to 60. So the pulse is one beat per second. The first measure is 4/4, with four quarter notes. Note that this is just for example. You can write pretty well any kind of rhythm you like within that basic meter by using a pattern of short and long notes. But it has to add up to four quarters or the equivalent. Next is a measure of 3/4 with just three beats.

Now we get a bit fancy. The next measure is a compound time signature, meaning that the beat-unit is not a simple note like a quarter note, but a dotted note. Each beat contains within it three smaller note values instead of two. This time signature is used a lot in dances such as the gigue. It has rather a lilting feel. 6/8 is called compound duple time because it consists of two beats, each of which is a dotted note. The next measure, 9/8, is compound triple time because it has three beats, each of which is a dotted note.

The next line shows what weird things you can do with composite time signatures. A composite time signature is one that has a variety of beat units, not just quarter notes or dotted quarter notes, but a mixture of, perhaps, quarter and eighth note beat units. The first measure in the second line, with the time signature 1/2 + 5/8 means that each measure consists of a half note followed by five eighth notes or a group of four eights followed by a group of five eighths. The last measure is a quarter beat followed by another quarter beat, then three eights, then a final quarter beat. So those are two examples of composite time signatures. A popular piece using a composite time signature is "Take Five" by Dave Brubeck which is in 5/4 divided into two groups of three quarter notes followed by two quarter notes.

But obviously, no-one would be crazy enough to actually use the two composite time signatures I showed as examples, right? Right? In fact, they are both found in the second movement of my second symphony. I originally had them all notated in 9/8, but I realized that this was concealing the real subdivisions. What you see there, plus a couple of others, is what is actually going on in the meter of the piece!

Let's have a little listen to "Take Five" just to show you how natural a composite time signature can feel.

Saturday, May 23, 2015

A Cathedral and a Motet

The Wall Street Journal has an excellent article about the construction of the Santa Maria del Fiore cathedral in Florence, often called more simply the "Duomo", which is one of the most remarkable and beautiful pieces of architecture ever created.

Click to enlarge
The WSJ comments:
The cathedral’s 140-foot span was so wide that traditional methods of covering it were inapplicable. 
...Brunelleschi set out with his friend Donatello to Rome to study its ancient structures, especially the Pantheon, with its own huge dome. He found that the Pantheon’s designers had employed some clever techniques, counteracting the natural forces of push and pull (downward and outward) on its vault by making the walls thicker where the stress was greatest, at the base. Higher up, they used lightweight materials, including concrete, to create a double-layered dome that got thinner as it rose, allowing it to bend and curve. He collected these ideas, added some of his own, and returned to Florence. 
...once the project was under way, Brunelleschi’s inventiveness seemed unbounded. He created a floating platform on beams cantilevered from the dome’s base that rose nearly 197 feet above the ground. He designed a double-layered dome with hidden circular chains of stone, iron and wood for support. He instructed the workmen to lay bricks in a unique herringbone pattern, with larger bricks interrupting smaller ones at right angles, to create a more solid bond, and invented machines to facilitate the project, like a magna rota or “great wheel” to lift materials, and a new kind of tower crane called a castello to move them at great heights.
Most remarkably, and the reason I am posting about this today, is that the inventiveness of the architecture was matched by a musical composition commissioned to be performed at the 25 of March 1436 consecration of the cathedral, Pope Eugene IV officiating.

To understand something about how the piece of music, titled Nuper rosarum flores by Guillaume DuFay, is in its way as remarkable as the cathedral itself, I have to introduce a couple of musical terms. One is talea which refers to a rhythmic pattern; and the other is color, which refers to a melodic sequence. A talea is repeated a number of times and so is a color, but what is interesting is that they are normally not the same length. In a typical example, the talea might consist of four durations and the color of 28 pitches so before the melody has finished, the talea will have been heard seven times. A piece, such as a motet for voices and instruments, using this kind of structure is called an isorhythmic motet (isorhythmic means "same rhythm") because of the repeating rhythmic pattern.

But what DuFay did in Nuper rosarum flores was no mere isorhythmic motet. Oh no. The piece is actually a mensuration canon, meaning that when the talea repeats, each time it is in a different meter! The four different meters used are 6/2, 4/2, 4/4 and 6/4. This technique is used in the lower voices, the tenors I and II. The upper voices are a freely written duet that make use of certain thematic material over and over and are therefore described as isomelic, meaning "using the same melody". The quite good Wikipedia article on the piece has this illustration that may help:

Structural plan of the motet and its tenor. Top: Pre-existing Gregorian cantus firmus; middle: Tenor in original notation, with four mensuration signs defining the diminution scheme; bottom: Total structural scheme: Through fourfold repetition of the tenor at different speeds, the motet has a structure of 4x2 parts, with length proportions of 6:4:2:3.

Or it may not! This is an extraordinarily complex piece and a unique one. Analyzing it in enough detail to fully understand how it is put together is a very large project indeed. So instead, let's just listen to it:

The upper voices are sung and the lower ones played by brass instruments. The score is rather complex as well. At first you will hear just the two upper voices, though you will see a score with four staves. This is because the tenors have a lot of rests at the beginning. Later on little red boxes will identify which staves are actually sounding. Enjoy!

Friday, May 22, 2015

Friday Miscellanea

Ex-drummer for The Police Stewart Copland talks about what he is into nowadays with the Globe and Mail. Groovin' with classical musicians and composing film scores is what.

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A glimpse into a typical blogger therapy session:

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A rather confusing article in the Guardian by Tom Service sort-of praises Sistema Scotland (based on the Venezuelan music education system) for early successes. But it is larded with so many caveats I'm not sure what it is saying. Here's what I think: if you get a bunch of kids interested in music involved in rehearsing and playing orchestral music and if you give them some decent instruction, you can transform their lives--especially if they come from economically depressed and cultural vacuous environments. This is pretty much a no-brainer, isn't it?

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What is it about a piece of music that either engages us or causes us to lose interest? No, I'm not going to scribble down the answer to that right here! But I am going to put up a clip from YouTube. This is s piece for 14 musicians by Harrison Birtwhistle called Cortege. It is well-played and the video quality is excellent:

So why is it that it never sparked any interest in hearing it to the end and I paused the clip at the 3:19 mark? Comments welcome. But don't say, "because you sir, are an idiot!"

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I heard an interesting concert last night with a young orchestra. The program was devoted to film music with suites from The Lion King, James Bond, Spiderman, Gladiator, Harry Potter, Indiana Jones, and, of course, Star Wars. The hall, a big one seating about 2000 people, was absolutely full and 95% of the audience were under 40 years old. They were also very enthusiastic. So what is all this moaning about the ageing symphonic audience? Perhaps the audience would be different for a different program, but I recently saw a small orchestra concert of two guitar concertos, one new, and two pieces by Gustav Holst and Arvo Pärt and, while not packed, it was pretty full, 80%, and again, the audience was nearly all under 40. But both these concerts were here in Mexico, so perhaps that is the difference...

So I won't suffer alone, here is the Indiana Jones theme so that you also will have it in your head for the next week:

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Years ago on this blog I did a post called "One Hit Wonders" in which I talked about a few composers who are known mostly for a single, solitary piece. In that post I just talked about the earlier composers, but musing over Gustav Holst reminds me that there have been quite a few more recent ones. Gustav Holst is overwhelming known for one single piece, his suite for orchestra titled "The Planets", which really is a spectacular piece of music. Here is  James Levine and the Chicago Symphony Orchestra with the movement "Mars, the Bringer of War":

He never wrote another piece that achieved similar recognition. Another composer with a single hit is the Spanish composer Joaquin Rodrigo who wrote one spectacular guitar concerto and a bunch of other music that is much less often heard. Here is the middle movement with its extraordinary theme. The performers are John Williams (guitar) and Paul Daniel (conductor) with the BBC Symphony Orchestra. Williams has to tune between movements because the first movement requires a scordatura:

And how about Modest Mussorgsky who is known almost exclusively for his amazing suite for piano (orchestrated by Ravel), "Pictures at an Exhibition". This is Sir Georg Solti with the Chicago Symphony:

Lastly, there is the Polish composer who wrote one exceptional symphony that was so popular it even made the British pop album charts. This is the Symphony No. 3 by Henryk Górecki, but I am not sure of the artists:

That is a pretty unlikely pop crossover hit, but it touches some very deep chords in a lot of listeners. Again, I pose my question from above: "What is it about a piece of music that either engages us or causes us to lose interest?" Why does this piece, despite its so modest beginnings way down in the subterranean register of the contrabasses, so transfix us while the Birtwhistle leaves us (or me at least) completely uninterested and uninvolved?

And that's it for this Friday's miscellanea.