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).

Imminent resurrection possible

February 29, 2012

Continuing a tradition begun last February 29, I am posting to announce that…I may start posting again.

(The hiatus was a bit longer this time, of course. But perhaps the coming non-hiatus may be also.)

I would be picking up where I left off, more or less.


Every continuous function bounded implies compact

February 18, 2009

It occurs to me that it might be nice to post solutions to miscellaneous mathematical exercises at least once in a while.

I saw this one on a chalkboard earlier today; evidently the room was serving as the venue for an analysis class. It’s exactly the sort of elementary exercise that usually takes me a day to solve, if I’m lucky. But this time, I’m happy to report, I managed to figure it out in just a few minutes (while ostensibly listening to a lecture on something else).

Problem: Let U \subset \mathbf{R}^n be such that every real-valued continuous function on {}U is bounded. Prove that U is compact.

Read the rest of this entry »

Bach by popular demand…

December 31, 2008

Well, as requested, at any rate…

Here is an analysis of the first two measures of the B-flat major Prelude from WTC I.

Warning: this analysis breaks some of the rules (well, one in particular) of strict Westergaardian theory as expounded in ITT. In fact, it does so twice (at two distinct stages). Exercise: see if you can identify the rule that is broken, and give a convincing rationale for relaxing it.

1. The basic structure:

2. Segment the final two beats of the first span with: an incomplete neighbor in the bass, a complete neighbor in the soprano, a borrowing from the bass in the alto, and a rearticulated suspension in the tenor:

3. Anticipate the G in the soprano:

4. Borrow from these structural lines to create the texture of the passage:

5. Delay the fourth half-note:

6. Elaborate further (the operations being, I hope, clear):

7. Elaborate still further to obtain the passage as Bach gave it to us:

Happy New Year!

J.S. Bach: Air from Orchestral Suite No. 3, mm.1-2

May 31, 2008

Recall that in a previous post I challenged readers to analyze the first two measures of the Air from Bach’s Orchestral Suite No. 3 in D major (a piece, incidentally, that might be better referred to as “Air Off The G-String” than by its usual nickname). The time has come to reveal the answer.

In the Pachelbel analysis, we started from the underlying basic structure and showed how the passage was constructed via the Westergaardian operations. This time, for the sake of variety, we’ll proceed in the reverse direction, starting from the passage itself and “undoing” the operations until the basic structure is revealed.

Our passage is the following:

Stage 1

Call this Stage 12. The first thing we’ll undo are the explicit arpeggiations in the first violin and continuo lines:


Actually, I did a bit more than that, as you can see. I skipped a stage in which the first violin part looks like:

How did I know that D was the span pitch of the second half of beat 2 rather than C#? That is, why did the first violin part not reduce to:

Is it because G#-E-B (or even G#-E-B-D) is a Certified Chord, whereas G#-E-B-C# isn’t? Fat chance! As an exercise in eliminating harmony, see if you can explain the real reason. (I’ll likely explain it in a future post, but probably only after we’ve formally developed more Westergaardian theory. Hint: It has nothing to do with Certified Chords.)

Eliminating the borrowed G and B from the first violin, we obtain stage 10:


What an odd interpretation of beat 2! Instead of hearing a passing motion from E to C, I am interpreting the E as a borrowing from the viola line:


(Note also the elimination of the A borrowed from the second violin line.) Why on Earth is this interpretation to be preferred to the seemingly simpler one? The answer is that the seemingly simpler one isn’t in fact so simple. Notice that the D in the second violin line is left hanging (ITT, p. 30), and therefore not displaced, after beat 1. If the D in the first violin line were to be interpreted as a passing tone, that would leave us without a D among the sounding span pitches of beat 2. However, we know from the C# of beat 3, as well as from the fact that D was left hanging in the second violin, that D must be a span pitch for some span that includes beat 2 (deeper levels will make this clearer; see below). We would therefore be compelled to regard the second violins’ D as being temporarily displaced during beat 2; that is, it must move by step to some note borrowed from another line. (The only alternative would be to regard it as (entirely) undisplaced during beat 2, but this is made difficult because of the simultaneous E: since in this scenario we’re not considering D as a local span pitch of beat 2, we’re left with understanding an implicit dissonance, which is quite problematic indeed.) Since E is a span pitch of beat 2 and C# is not, we must therefore hear the D-line as moving up to a borrowed E during beat 2. But why should we go through the trouble of understanding such a conceptually difficult situation as the D-line effectively “merging” temporarily into the F#-E line? Given the stated step motion D-C# in the first violin, isn’t it easier to regard that D as a span pitch over the span of beat 2?

Stage 8 shows transferred pitches (ITT, sec. 7.7) reassigned to their rightful homes:

Stage 1

This stage represents the transition from instrumental lines to structural lines; I have symbolized this by switching from the alto clef to the treble clef in the third line.

Next the transferred pitches are reassigned to their rightful registers:


The suspension in the top line is removed:


Rearticulations in the bottom three lines:


Rearticulation of a suspension in the second and third lines; chromatic step motion in bass:


Suspensions eliminated:


Neighbor note removed:


Finally, then, we have the basic structure of the phrase: