Octaves Above Milstein's Prokofiev is...Sort of the Same Prokofiev

It is not too far-fetched, or at least not unprecedented, to identify an even division of time too slow to be heard as a pitch with a label that customarily is assigned to a pitch. For example, the sound waves emanating from a black hole in the Perseus Cluster have been identified as a B flat, although they are too low to be heard: indeed, the crests of the waves are millions of years apart. But to label this frequency with a pitch is simple enough. Multiplying or dividing a frequency by 2ⁿ moves it up or down, respectively, by n octaves. This transfer by one or more octaves both preserves its letter name and potentially puts it within the range of human hearing where we typically categorize frequencies with letters. For example, 440 Hz is an A, and so is 880 Hz, 1760 Hz, 220 Hz, 110 Hz, and the rate at which the moon goes around the earth (the sidereal month of 27.321661 days). Well, actually the sidereal month is a rather high A (30 octaves lower than ~459 Hz); in fact, it is closer to the black hole's B flat (of which one is ~466 Hz).

With this in mind, consider the opening of Prokofiev's Second Violin Concerto in G minor, which was premiered in Madrid on this day 81 years ago. It begins with a G, B-flat, D, E-flat, C sharp, and another D played by the soloist, and then this rising motive repeats in its entirety. The frequency at which the rising motive appears can also be labeled as a pitch. Prokofiev indicated a tempo of quarter = 108, which makes the motive's frequency a slightly low F sharp. While some commercially recorded performers roughly take that tempo, many others tend to go slower: around an F or even around an E for the rising motive. But Nathan Milstein, in a live recording from 51 years ago, not only plays it faster than what Prokofiev requests (and with relatively little rubato), but also plays the rising motive "at a G," several octaves below the open-string G he plays to begin the concerto, a G that matches the opening tonal center of the concerto.

Prokofiev follows this rising motive and its repetition with a descending motive (D-C-Bb) and its embellished repetitions that extend the motive lower and longer by one suffixed note with each repetition. However, thanks to durational reductions of interior notes, each descending motive still takes up the same amount of time; therefore, the frequency of the descending motive can still be labeled by a single pitch letter. Milstein's tempo for this portion puts the descending motive's frequency at around a B. Although the descending motives neither contain a B nor are in B, the immediately following orchestral statement of the ascending and descending motives is transposed to start on, and position the tonal center on, B.

The movie below demonstrates these pitch-tempo relationships.

Thanks to Debbie Rifkin for encouraging me to think about this concerto.