To play 'slowly'
What is the correct measure of slowness in performance? Which perceived layer of the rhythmical structure should we relate to, and can slowness be measured with a metronome or should it be distinguished through listening alone? 
In dance music, there is a limit to how long a dancer can hang in the air when jumping (pas de sissonne in the Bourrée), or sustain a lift (temps de courante) in the Courante or Sarabande). The general tempo, established always on the metric level of the beat, will reveal the character of the dance, treating the metric subdivision as ornamental movements/notes.
One could argue that when playing Bach’s dance suites, which were not meant for actual dancing, we can adjust the tempo to the musical taste. This is true (and supported by historical sources) to the extent that the rhythmical structure will remain comprehensible at the beat level. The Sarabande must be still be played in three, not six, whatever the choice of tempo.
Informed and inspired by dance, I attempt to recognize a 'danceable' metric level and establish it as a beat even in the abstract concertos and sonatas. In the slow movement (Adagio) of Bach’s E major violin concerto, it is not unusual for performers to articulate the pulse on the level of eighth-notes, to give the violin figurations a calm quality.
Ex. 1: The figurative line of the solo part in the Adagio movement of Bach’s Violin Concerto in E major (Bach-Gesellshaft 1851-99).
However, if we turn our attention to the bass line, a structure of three quarter notes emerges (see example 2).
Ex. 2 The bass line from the Adagio of Bach’s Violin Concerto in E major, revealing a simple structure in 3/4 (Bach-Gesellshaft 1851-99).
Although the eighth-note pulse might bring a quality of 'calm' to the solo line, the amount of beats in the bar will result in a calm which is also static. With the quarter-note pulse, the calm is instead achieved through the quality of movement. The gesture on the downbeat (Ex. 1) executed as a dramatic lift will then be suspended over the sixteenth rest. This creates a tension that triggers a forward motion on the second and third beats, preparing the explosive sustained gesture on the next downbeat. Such a movement sequence has the air of a Sarabande. The step-unit of the pas grave is sustained over two beats and then moves forward, falling into an energetic élevé on the next downbeat.
The Adagio tempo can thus be as slow as possible, given that the 'utmost possible' slowness is measured by the timing of the sustained lift. The following video example demonstrates an attempt to incorporate the sustained gestures of the Sarabande into the slow movement of the E major concerto by Bach.
Vid. 1 Adagio from Bach’s Violin Concerto in E major, with Baroque Aros ensemble
At a PhD presentation, an organ piece was discussed. To express a religious dimension of eternity, one passage had the indication 'as slow as possible'. The PhD candidate presented several recordings with a range of perceived speeds, becoming slower and slower. A metronome was used, because at some point the tempo became impossible to judge by ear. The 'winning' recording was crowned, achieving a tempo twice as slow as the 'losing' recording, in which a slow metronome pulse was applied to the sixteenth-note metric level, whereas in the “losing” version the same pulse was applied to the eighth notes.
What is the limit of slowness? When applying a tempo designation 'As slow as possible' to an abstract piece of music, what can be considered 'impossibly' slow? I assume, in the slowest possible version, it must still be 'possible' to comprehend melodic motion or harmonic relations.