From that visit I retain a treasured souvenir extended play recording of the “Moonlight” sonata played on the composer’s last piano, the quadruple-stringed Graf-Flügel, an instrument specially made to compensate for the composer’s failing hearing. How unlike a modern grand piano it sounds! And yet, this brittle tone of leather-covered hammers on thin strings has something vital to tell us about the aesthetic of the time, and of Beethoven’s musical intentions.

As an editorial assistant to John Mansfield Thomson in the formative years of the quarterly Early Music during the 1970s, I became more closely involved with the early music revival, and its founding principle that the acoustics of period musical instruments and performing spaces have a great deal to tell the listener and student about a composer’s original intentions. It became clear to me that the early music movement had a great deal in common with the avant-garde, in drawing attention to the contribution of authentic instruments to a composer’s aesthetic objectives, and the composer’s role as a philosopher in tonal relations. Accordingly, the progressivist view that a modern grand piano is better for performing Beethoven than an instrument of the period, because it is more powerful in tone, misses the point that the more powerful tone of a modern instrument is achieved by sacrificing the tonal coherence of equal stringing across the range. So when I hear a modern performance of the third movement of the “Moonlight” sonata, the up and down movement from bass to treble conveys nothing like the impression of a fountain surging upward, but is reduced to no more than a cheap thrill, a technical display. But the same passage played on an instrument of the period evokes a turbulence as exciting as the electronic music from Stockhausen’s Gesang der Jünglinge, because the tone colour is continuous and coherent throughout.

“But the same passage played on an instrument of the period evokes a turbulence as exciting as the electronic music from Stockhausen’s Gesang der Jünglinge…”

The hidden science of instrument construction in relation to music aesthetics still awaits proper scholarly attention. A fortepiano is coupled to a wooden floor or platform by its legs, just as a tuning fork is coupled to a table. The great variety of piano leg designs through the 18th and 19th centuries suggests a great deal of experimentation in finding the shape and style of piano legs most suited to the instrument, though as far as I know, the subject is never mentioned.

Beethoven’s forceful pianism in 1802 can also be understood as a deliberate response to the popularization of mechanical keyboards. The first keyboards were designed for evenness and lightness of touch, properties associated with a particular style of virtuoso pianism in the 19th century, one seemingly adapted to the rattling automation of the piano roll era. But imagine an attempt to reproduce the “Waldstein” sonata on a mechanical keyboard, rather than a valse by Chopin. A mechanical instrument has a constant reserve of energy to distribute, so in a passage of dense repeated chords the tempo is likely to slow down, only to speed up again when the chords give way to a melody. Think of Mozart’s witty “Rondo alla Turca”, a piece of parody Clementi, alternating fast melody verses and slow chordal refrains in exact imitation of a period mechanical instrument. By a similar analogy the Beethoven “Waldstein” sonata is making a statement about only a live performer being able by brute force to maintain a constant tempo through thick and thin (as it were): a trick a mechanical instrument of the period cannot match.

Having read Peter Pesic’s new book Music and the Making of Modern Science (MIT Press, 2014), I am equally convinced that the great mathematician Leonhard Euler, and Hermann Helmholz more than a century after him, were inspired to speculate at length about the ratios of consonance by the invention and availability of the hammer-action keyboard acting as a desktop calculator in tone combinations. Euler’s ultimately fruitless inquiry into squaring the circle of fifths, a subject inspired by the practical problem of piano tuning in equal temperament, leads me to imagine Beethoven himself studying Euler and seeking in his own way to resolve the same mathematical problems in his keyboard compositions. Beginning from middle C, the cycle of fifths leads ultimately to a twelfth note G sharp which is distinctly out of unison with A flat. Hence Beethoven’s “Moonlight” sonata, set in the dark and mysterious key of C sharp minor, then in A flat major, and finally in C sharp minor, provides a perfect forum for the composer to discuss the “gap in the circle of fifths” — the troubled and ambiguous relationship of G sharp and A flat within a tuning system based on just intonation. Listen for yourself, at how in every movement, across a range of emotions from pensive to joyful and energetic, pivotal or stressful moments in the musical argument coincide with the signal “false” intonation of a G sharp or A flat persistently striking a warning note, whether in the high treble, mid-range, or deep bass registers.

Some of this tonal and emotional uncertainty is captured in the website recording of the first movement on the Stein piano. In comparison to the Graf-Flügel, this instrument is warmer in tone, and profoundly and wonderfully resonant, a depth of tone that draws the listener in and brings tears to the eyes. Here it is easy to grasp the composition as the composer in dialogue with the instrument, sending a message about vainly striving to find harmony in life and having to be reconciled to its unattainability, the repeating G sharp of the first movement sounding the same warning as the raven’s refrain “Nevermore!” in the poem by Edgar Allan Poe.