Matanya Ophee's Strange Arithmetic

The story you are about to read is true.

Matanya Ophee is a well-regarded publisher of classical music, primarily for guitar, which he himself plays. Mr Ophee owns one of the world's largest collections of guitar music, and knows a great deal about the repertoire and history of classical guitar. He has written lettered articles on those subjects, not to mention his many epistolary and acroatic works.

Mr Ophee also fancies himself to be something of a music critic.

Our story begins in 1995, with Mr Ophee's belated critical attack on a 1982 recording of the prelude to Bach's fourth lute suite, BWV 1006a, as performed by a well-known Classical Performer (henceforth CP). CP played the prelude in three minutes and thirty-five seconds (3:35), which works out to approximately 126 beats per minute (bpm). That was a fast tempo for a difficult piece with four sixteenths to the beat throughout, leading Mr Ophee to exclaim:

By all accounts, an astounding piece of digital pyrotechnics, a true virtuoso playing on the highest level. To place this in perspective, we note that the majority of guitarists who play this, usually take from 4:30 to 5:00 full minutes to play it.

Here is where our story turns tricky. Mr Ophee concluded that the recording must have been performed at a slower tempo and sped up by the recording engineer. To reach that conclusion, Mr Ophee committed several major blunders of arithmetic and musicianship.

First of all, Ophee reported that CP's recording was made at the truly astounding tempo of 157 bpm. In reality, the tempo was 126 bpm: fast, but not superhuman. At least three other virtuosos have recorded the prelude at or near that tempo.

Ophee compared CP's recording of the BWV 1006a prelude to a tape of CP playing an arrangement for guitar of the Sinfonia from Bach's BWV 29. The guitar plays the same notes in both; the prelude is a solo work, to which the Sinfonia adds an orchestral accompaniment. Ophee reported that, in a careful side-by-side comparison on his "well calibrated" equipment, he could hear no differences between the guitar tracks of the two recordings:

there is a good question in my mind if the actual guitar track on both recording is not, God Forbid, the very same recording....the articulations of the entire piece sound to me identical in both the LP and the tape. With today's technology, it is possible to prove or disprove the point with absolute precision.

Ophee's point is disproved by a great many differences between the two guitar tracks. Some of those differences are subtle, and would be noticed only by competent musicians. Others become obvious within the first few measures, even to non-musicians. The prelude, for example, scoots along at 126 bpm, while the orchestral Sinfonia flows along at the more majestic tempo of 112 bpm.

When asked why he is unable to hear these differences, Mr Ophee says it is only a matter of opinion whether they are audible.

Evidently Mr Ophee believes it is only a matter of opinion whether 112 is equal to 126, because he has been repeating the same mistakes and allegations for more than a decade [op19991104, op20030219, op20050808].

Some have suspected Mr Ophee of dishonesty, but he says he did not lie, so that explanation is right out. All of his errors, including his apparently sincere belief that 112 equals 126, are to be regarded as Honest Mistakes.

To continue our story, I must explain why Ophee thought he could bolster his argument by confessing his tin ear. He appears to have been suggesting---without actually saying so, which would have been libelous---that the recording of the prelude had been obtained by taking a tape of the guitar track for the Sinfonia and playing it back at a higher speed. In 1982, when the prelude was recorded, that was the only practical way to increase the tempo of a recording.

That brings us back to arithmetic because, as a matter of physics, increasing the speed of tape playback inevitably raises the pitch in direct proportion to the increase in tempo. A 6% increase in tempo raises the pitch by one semitone (half-step).

Ophee knew this, because he had spent a year working as sales manager for a company that made tape recorders. What he didn't know was how to do the arithmetic [er19991105, op20030219].

Mr Ophee thought the difference in speed between CP's recording of the prelude and the recordings by most other guitarists was on the order of 6%, and that he could attribute that difference to the recording engineer by finding or inventing evidence for a semitone (half-step) increase in pitch.

In reality, CP recorded the prelude about 25% faster than most other guitarists. By suggesting that so large a speedup had been achieved by manipulating the tape speed, Mr Ophee set for himself the impossible task of manufacturing evidence for a four-semitone increase in pitch (a major third).

Ophee, alas, did not comprehend the futility of his project. Instead of abandoning his theory, he went looking for something that could be construed as evidence for a semitone transposition.

What Ophee found was his own tape recorder. Unbeknownst to Ophee, his recorder was out of calibration and running 6% slow. That made his tape of the orchestral Sinfonia sound like it had been recorded in E major, one semitone lower than the F major recording of the prelude to BWV 1006a. To Mr Ophee, his defective tape recorder was the smoking gun that proved the fast tempo of the prelude had been achieved by artificial means.

In reality, both recordings are in F major.

F major is an unusual key for these works; most guitarists play the prelude in its original E major, and Bach's organ Sinfonia from BWV 29 was originally in D major. The key of the prelude is explained by CP's use of a capo on the first fret, which raises the pitch by one semitone; transposing the Sinfonia into the same key would then do away with the need to learn a second fingering for essentially the same piece.

Ophee knew that CP's published arrangement for the prelude recommends the use of a capo on the first fret, but chose not to believe that CP had followed his own recommendation when recording. In response to Ophee's allegations, CP's producer wrote a letter stating that CP had indeed used a capo during the recordings and during live performances, and that the orchestral parts for the Sinfonia from BWV 29 had been transposed to F major. Mr Ophee admitted that the cover photograph that came with his tape showed CP with a capo at the first fret. Someone cited a videotape of CP playing the prelude with a capo on the first fret, but Ophee seems to have doubted the existence of that video. (Eight years later, after offering to apologize to CP if I could locate a copy of the video and send it to him, Ophee acknowledged that the video shows CP using a capo to play the prelude.)

To Mr Ophee, however, none of the above counts as evidence that CP had used a capo on the recordings. To Mr Ophee, it is evidence of a vast conspiracy to cover up the truth [op19950403, op19991104, op20030219, op20030530, cl20030603].

As years went by, and the mathematical and musical impossibility of his allegations began to erode his credibility, Mr Ophee dreamed up several alternative fantasies. His most memorable theory was that a tape recorder with a "rotating" head would somehow be able to increase the tempo without raising the pitch. Before experts could even begin to scoff at this idea, Mr Ophee cited a 1988 advertisement for a variable-speed tape recorder, and claimed that recorder as an example of the technology he had hallucinated. Unfortunately for Mr Ophee, that advertisement clearly stated that changing the speed would also change the pitch [ya20030222, we20030222].

None of these setbacks have discouraged Ophee from insisting he was right all along [op20030530, op20050808]. One can only marvel at Mr Ophee's commitment to proclaiming the truth, as that truth must appear to a man with Ophee's command of arithmetic and music.

Two days after the article above first went online, Mr Ophee suggested I had taken him all too seriously, and should learn to QUESTION AUTHORITY. Many others, however, have taken Ophee's story far more seriously than I ever did. My retelling may not be as funny as Ophee's original tale, but my version is a lot shorter.

Any factual errors in this article are inadvertent, and will be corrected promptly after I learn of them. I will also attempt to answer frequently asked questions about Ophee's hoax.

Copyright 2005 William D Clinger.

Last updated 20 August 2005.