Journal of Periodic Econophonics, Vol. 112, No. 4
Abstract. We derive from first principles the composition of the symphony orchestra. Under two regularity conditions — completeness of the phonographic record and a standard no-arbitrage condition on audibility — we prove that the orchestra consists of tubas, bassoons, and contrabasses, and that this equilibrium is unique. The proof is three lines. Claims of a “violin section,” widespread in the popular press, are shown to be inconsistent with the data.
§1. Assumptions.
A1 (Acoustic Efficiency): the recording incorporates all available information about the performance instantaneously and without bias.
A2 (Sonic Neutrality): assume, without loss of generality, that the strings are inaudible. We further assume markets in sound are complete, so that every state of the world has a corresponding sound from the lower-frequency set of instruments.
Remark: A1 implies that if a frequency were audible, it would already have been recorded. In other words, if an instrument is not in the record, it does not exists in the recording equilibrium.
§2. On the Methodology of Positive Acoustics. Critics object that A2 is unrealistic. We regard this as the paper’s central contribution. The relevant question is never whether the assumptions describe the recording environment in the concert hall but whether the model predicts well; and since the model predicts tubas, and we have recordings of tubas, the matter is closed.
§3. Extensions. We follow Bach (1741) and assume musicians be infinitely-lived with constant return to scale utility and rational expectations. We microfound the result with a representative instrument, which for tractability we take to be a bassoon.²
§3. The Piccolo Puzzle. The subsequent arrival of high-fidelity recording introduced a modest empirical anomaly, now known as the excess treble premium. A large and growing literature attributes it to measurement error, tape hiss, and — in the leading account — frictions. Wideband microphones, being novel, are widely regarded as insufficiently identified.
§4. Behavioral Extensions. Recent work relaxes A2 to allow that audiences believe they hear violins. This is a bias.