My new edition of Reger’s solo violin sonata op. 91 no. 7 : now on IMSLP!

January 31, 2017

The violinists are the worst…I can’t tell you the number of students, violinists that I’ve had who said “Yes, I will learn the seventh sonata by Reger. I will have it on my next recital.” Never.

David Diamond

As of now (more specifically, earlier this month), it will perhaps be at least slightly easier for some of those violinists to follow through, because there is now a free edition available on IMSLP of the work I assume Diamond was referring to: the seventh of Max Reger’s Seven Sonatas for Solo Violin, op. 91.

(Of course, the phrase “seventh sonata by Reger” is hardly unambiguous, even when restricted to the realm of the violin: Reger had earlier published a collection of four solo sonatas as his op. 42, and in addition there is also his series of sonatas for violin and piano — a genre also commonly called “violin sonata”. Thus, in addition to op. 91 no. 7, “seventh [violin] sonata by Reger” could conceivably mean op. 91 no. 3, op. 103b no. 2, or even op. 42 no. 4. However, op. 91 no. 7 seems the most likely candidate.)

This rectifies a long-standing omission in the IMSLP catalog, which since 2011 has included the first six sonatas of op. 91, but, mysteriously, not the seventh, thereby tantalizing visitors who came in search of the famous Chaconne.

The Wonderful Month of May

May 31, 2016

This isn’t the post I promised, but I didn’t want to let the month of May pass without sharing my thoughts on a rather timely Schumann song, the first of his Dichterliebe cycle, “Im wunderschönen Monat Mai” (“In the wonderful month of May”). One or two readers may even find this song particularly timely.

The score can be found on IMSLP. Here is a recording sung by Christine Schäfer, otherwise known for intense twentieth-century repertory such as Berg and Boulez.

Now, I could almost get away with claiming that this was the post I meant to write, and that I had simply mixed up Schubert and Schumann. It’s arguably easy to do: their names share an initial syllable, they’re both German Romantic composers of…a bunch of things, including piano music, Lieder, chamber music, and symphonies; and Schumann was one of the first to “discover” Schubert (notably the “Great” C-major symphony), on one occasion writing one of his own works with a pen that Schubert had allegedly used.

But no one would actually believe me if I claimed that.

Not even if I pointed out that this post, like its would-have-been-predecessor, is also going to feature Schenker prominently. Even more specifically, is going to feature my disagreement with an analysis by Schenker.

All of that being, of course, a coincidence as timely as this song, and the other main coincidence of this soon-to-be-past month (about which more…next month).

Read the rest of this entry »

Mathemusicality is back

February 29, 2016

It’s February 29 again, which means it’s time to announce that this blog is being resurrected. Stay tuned for a post on Schubert (and Schenker).

Pachelbel’s Canon

April 23, 2008

As you might expect, the demise of the IMSLP has put something of a damper on my grandiose plans of analyzing musical works on this blog. Today, however, we’re in luck, as Wikipedia provides all the source material I’ll need for this post.

The context for this is a question, of sorts, posed by a commenter named “funkhauser” (the reason I say “of sorts” will hopefully become clear):

It seems to me that a surprisingly large number of progressions of 8 chords found in say, your favorite piece, have a IV chord as the “middle” chord (i.e., if each chord lasts a quarter note and we are in 4/4 time then the IV chord is the first chord of the second measure). Two familiar examples are Pachel[bel]’s Canon and the beginning of Bach’s Air on the G string. The chord progressions are, roughly:
I – V – vi – iii – IV – I – IV – V
I – iii – vi – vi7 – IV – V7/V – V – V7

(…)However, I can’t think of an 8-chord progression I’ve heard in which the V chord is the middle chord…Imagine putting the V in the place of the IV in Pachelbel’s Canon or Bach’s Air. It would completely change the feel of the piece (and arguably, it would ruin it).

(…)What I’m wondering is: In Westergaard’s theory can we derive the important difference in function between IV and V? And can we derive the fact that the IV should occupy stronger beats and larger time spans than V?

Tisk tisk. It’s obvious that the questioner has not yet managed to throw off the Rameauvian shackles, and is still laboring under the impression that musical passages are constructed by juxtaposing “chords” in time. Well, funkhauser, you’ve come to the right place — disabusing innocent souls of this mistaken notion has become one of my missions in life.

The best way to start, I think, is to take a look at these passages and see what’s actually going on. Here’s how to construct the opening of Pachelbel’s canon:

1. The underlying basic structure is the usual \hat{3} - \hat{2} descent (with the \hat{2} on its way to \hat{1}, of course):

2. These structural lines will be realized as three textural lines, with span pitches assigned as follows:

(When I say “assigned” I technically mean borrowed, of course.)

3. The top two lines will both descend from the upper note to the lower:

4. The A is delayed by a lower neighbor, in familiar fashion:

5. We connect the F# to the A and the D to the F# by step motion. In fact, we’d like to have continuous quarter notes in these two voices, so on beat 3 of m.2 we’ll also elaborate the C# by a lower neighbor passing tone in the top voice (producing functional parallelism alignment with the bass) and borrow a G from the bass for the middle voice:

6. Actually, we’d like to have quarter notes in all three voices, so we elaborate the bass by means of borrowing :

(The A and the F# are of course borrowed from the span pitches of stage 2 above.)

7. Now, since this is supposed to be a canon, we’ll present the voices one by one.

8. Finally, this is how the texture is actually realized, in terms of which instruments play what.

Now, having analyzed the passage, let’s see if we can address funkhauser’s question. The first thing to note is that nowhere in the above derivation sequence is there any mention of “chords” at all. As a matter of fact, I didn’t even bother to check whether the progression claimed by funkhauser

I – V – vi – iii – IV – I – IV – V

is “accurate” or not — so that as I’m typing this, I literally don’t know what the “chords” of this passage are! I It’s important to emphasize this, because I just got through analyzing the passage in precise detail, attributing a specific function to every single note, and I have the passage itself, as well as my analysis of it, firmly entrenched in memory. Indeed, I can’t mentally replay the passage without instantly and simultaneously reconstructing my analysis. And yet — and yet — when it comes to selecting the appropriate Roman numeral for each of these quarter-note simultaneities, I am — at least at this immediate moment — about as clueless as a typical freshman theory student. (Though I do already know the first one will be I and the last one V.)

Having made that point, let me now pause to reflect on what the chords are…Okay, yes, funkhauser has got it “right”; though I suppose there is an ambiguity about beat 3 of m.1, since there are only two distinct pitch-classes in that simultaneity. Come to think of it, the same is true of both “IV” chords in m.2. Oh, and it’s also true of the very first chord!

(Notice how very different this type of thought is from the instinctive, intuitive reasoning that I used to construct the above analysis. Actually, “instinctive, intuitive” is not the correct description; what I meant to say was specifically musical. Whereas what I am doing here, in verifying funkhauser’s chord progression, is the totally abstract (if trivial) mathematical problem of verifying that two finite sets are equal to each other.)

Funkhauser asks about the difference in function of the IV and V chords. What I would like to point out is that there is no “IV chord” at all! The simultaneity on beat 1 of m.2 is just the coincidence of two passing tones, and that on beat 3 is just the coincidence of two neighbors a passing tone and a neighbor. To pick out these chords as fundamental objects in their own right (and as the same fundamental object, no less!), is to carve up musical reality in the wrong way, like putting dolphins in the same category as fish.

Strictly speaking, then, the answer to funkhauser’s question is “mu” — i.e., “your question depends on incorrect assumptions”. The “chords” of harmonic theory are simply not legitimate music-theoretical entities, any more than Earth, Air, Water, and Fire are chemical elements. Yes, these four things do exist, but they don’t play anything like the theoretical role that people once attributed to them. In fact, today we understand that not only are they not fundamental, but they’re not even the same kind of thing: “Earth” is a planet, “air” is a state of matter (gas), “water” is a chemical compound (H2O), and “fire” is a process (combustion).

So it is with “IV”, “V”, and all the rest. Yes, there are collections of notes in musical compositions to which you could give these labels, but to do so is to presuppose the wrong theory of music.

Like Aristotelian chemistry, harmonic theory may not seem obviously wrong until you’ve had considerable experience with the alternative. This explains why I invariably get reactions like “But…but…of course harmonic theory is correct (or useful) — look how ubiquitous progressions like I-IV-V-I are!”

Yes, and the “Four Elements” are also ubiquitous in the natural world.

For the moment, I will leave it as an exercise to come up with the correct analysis (or at least an analysis of the correct type) of the first two measures of the Air from Bach’s Third Orchestral Suite. Here’s a big hint: