Music, Science, and Software

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When you study physics, it is common—or at least it was when I was a student—for textbooks to present mathematical identities without explanation. You become accustomed to using tables of integrals and other precalculated artifacts as a means to solve problems without necessarily understanding why a particular identity holds true. Some form of the Gaussian function appears as a probability density function in different corners of physics, usually with little explanation. Integrating it is a necessary part of finding an expected value, but the process is rarely explained.

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Years ago, I opened a book to refresh my knowledge of the mathematics of general relativity and the foundations of quantum computing (same math, different domains). Unfortunately, the book suffered from the poor organization and opaque writing that characterizes many textbooks. If you already know the material, these books can serve as useful reference sources. If you are learning the material for the first time, they usually make the learning process much more difficult than it has to be.

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La Catedral is perhaps Agustín Barrios's best known and most played composition. Even though La Catedral is one of Barrios's early works (written in 1921), it didn't assume a final form until the last years of Barrios's life, when the Costa Rica (1939) and El Salvador (1943) manuscripts were written. Throughout his career, Barrios evolved how he played La Catedral, adding and removing parts, changing fingerings, and renotating entire movements. As a result, you will find that nobody plays it exactly the same way, depending on which transcription they are working from and how their preferences shape the bits they incorporate or omit to create their own unique renditions. Part of the joy of listening to or performing La Catedral is the variety of arrangements and interpretations it makes possible, providing something new to discover each time it is played.

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Für Elise is a posthumously published—and possibly unfinished—work for the piano by Ludwig van Beethoven. The original manuscript is now lost, but a copy was published in 1867 and the transcriber claimed the original was dated April 27, 1810. The piece was dedicated to “Elise”, whose identity has been much speculated upon but never confirmed. Even though the dedication was not a title, it is how the piece is most commonly known. The WoO number is a sequential catalog number assigned to Beethoven's works without an opus number, making the piece his 59th known work without an opus number. Despite having been published long after his death, Für Elise is one of his most popular works, even inspiring Wolf Hoffmann's solo on the title track of Accept's 1985 album, Metal Heart.

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