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A loosely sorted and lightly annotated catalogue of through the music posts on this blog.

With my flute waiting to be repaired, I found myself exiled from orchestra rehearsal, so I figured I’d go hear Yo-Yo Ma with the Chicago Symphony Orchestra. It was a patron-only concert. I fought hard for the ticket and paid $180 for the cheapest seat in the house. By the end of the night, I rather wished I’d grabbed my Nuvo plastic flute and gone to rehearsal after all. The $180 view, from literally above the stage. Yo-Yo Ma is down there somewhere. Rachmaninoff was not. ...

Sibelius’s No. 5 out of his Six Impromptus (Op. 5) is a petite B minor Vivace written in 1893. It’s only three and a half minutes, sounds mysterious, and somewhat very cool. Sibelius was never really a piano composer, and you can hear him thinking in strings. He seems to have agreed. Within months he arranged this impromptu for string orchestra, later pairing it with No. 6, and the arrangement premiered in February 1894. ...

I’ve written about this nocturne twice already, through Sokolov and Pollini. I’m still not done. It’s so pretty. It opens with two bars of chords: a plagal cadence, the “amen” at the end of a hymn. The piece starts where most music ends. Then the melody, over rocking triplets in the left hand. The middle turns stormy, through F minor to F-sharp minor, and finds its way back. At the end the same two bars return. Amen again. ...

Fauré wrote his Fantaisie in 1898 for the Paris Conservatoire’s annual flute competition. Paul Taffanel, who had taken over the flute class in 1893, commissioned it and is its dedicatee. At the premiere that July, all eight of his students played it, one after another. It comes in two parts: a singing Andantino, then a quick Allegro. Taffanel matters as much as the piece. The flute was a star in the Baroque (Quantz wrote some three hundred concertos for Frederick the Great), then spent most of the 19th century as a section instrument behind the violin and the piano. The French school brought it back as a solo voice, partly through these commissions. Godard had already written for Taffanel; after Fauré came competition pieces by Chaminade, Enescu and Gaubert, and decades later Dutilleux and Messiaen. Add Debussy’s Faune and Syrinx, and most of what a flutist plays as a soloist was written in French, for a French sound. How lucky we are. ...

I’m preparing Castelnuovo-Tedesco’s Sonatina for flute and guitar, Op. 205, for this quarter’s chamber program. He wrote it in 1965, a small piece in three movements: a graceful Allegretto, a melancholy Siciliana, and a Scherzo-Rondo to finish. This piece is a shock for a flutist, not because the notes are hard. Usually, orchestral and classic-classical chamber playing trains flutists to project, blend, and phrase music the way it has always been phrased. None of that helps here. In a flute and guitar duo, the textures are thin, every detail is exposed, and where a phrase leans, how long a note lasts, how much time to take, even for a vibrato or half a note’s crescendo, are all decisions I actually have to make. ...

Having been playing Stravinsky’s Four Études for Orchestra, my main reaction has been: what? Here’s some background. Despite the title, these were never orchestral studies. Three are orchestrations of his Three Pieces for String Quartet (1914). The fourth, Madrid, began as an Étude for Pianola (1917), written for a player piano. Its score needs six staves, three pianists’ worth of notes, because no human was supposed to play it. In 1928 Stravinsky gave all four titles and an orchestra; Ansermet premiered them in Berlin in 1930. So we’re playing music written for four soloists and a machine. ...

Notes on Chapter 2 of Professor MacKenzie’s Mechanizing Proof: why anyone wanted to prove programs correct.

Prof Ortner gave a talk on Tuesday about his recent working paper, “Leader-Driven Collusion” (19 August 2026). The paper finds that a patient cartel leader’s best scheme opens with gradually rising prices before settling at the monopoly price. The method is as interesting as the result. In place of the recursive machinery of Abreu, Pearce and Stacchetti (APS, 1990), the field’s standard tool, the paper uses Lagrangian duality. One constraint, two readings. In repeated Bertrand with zero cost, a firm that undercuts takes the whole market today and earns nothing thereafter. A fringe firm therefore stays in the cartel only if ...

This note came out of the first sessions of a PhD course in monetary economics. The opening question was what “fiat” money is. The word is Latin for “let it be done”; it has nothing to do with the car. Fiat money is an object that is intrinsically worthless and inconvertible: it gives no utility, has no use in production, and cannot be redeemed for anything that does (Wallace, 1980). That definition is the source of the difficulty. In Arrow–Debreu general equilibrium, markets are complete and all trades for all dates and states clear at date 0 under a single budget constraint. An intermediate object has no function there, and its equilibrium price is zero. ...