Temporary Notes (11)

Tempo, tempo!  Let me admit that I've been casual about tempo markings; in part this is because I want to have the latitude necessary to make a piece work under different performance conditions — different room acoustics and physical placements of players, different instruments (individual instruments often "speak" and resonate very differently), and, of course, different players — as well as to allow for the precise tempo and variations in tempo to remain, to some extent, an element within the interpretive domain.  And I'll further admit that my tempo markings have often been either completely intuitive (just keep adjusting that metronome until it sounds right) or completely pragmatic (i.e. setting a common pulse to a nice round number so that complicated rhythms are easier for players to rehearse), and sometimes they have been ambiguous or downright vague, particularly when I use words rather than a numerical indication.  I could probably get along reasonable well with this casualness, but in a performing environment with so many competing traditions and influences, it's definitely helpful to be clear about things whenever flexibility, ambiguity, or vagueness is not intended. (Also, as someone who does, for better or worse, think a lot about music, it's somewhat careless not to think through something as basic as tempo).

There is some very useful material online about tempo.  For more contemporary concerns, I recommend this webpage by composer John Greschak.  For an exhaustive treatment of a historical repertoire, I recommend this webpage on the time signature and tempo markings in Mozart. 

Greschak's page forced me to go back and read Mälzel's "Notice on the Metronome".  Beyond the mechanical interest of the device, the main interest for me is in his scaling of tempi, and, as a composer, this is a very useful place to begin thinking about tempo, regardless of the precise (or imprecise) relationship of his ideas and gadget to historical practice.  Mälzel basically envisioned four basic tempos, each measured by a different basic unit or pulse:  for Adagio, the eighth note, Andante, the quarter, Allegro, the half, and Presto, the whole.  Within a basic tempo, the  pulse may vary a bit up and down, with Mälzel describing 80 per minute as "moderate", meaning a typical or middling rate for the tempo in question.  (The number 80 seems to be taken from Quantz who identified it with the human heartbeat.  "Moderate" is a really problematic word: it can mean middling, or can indicate a slowing down (or retreat from an extreme position), in the sense of moderation; a good word to avoid in scores, Ithinks).   From this moderate value, one can interpolate the assais and moltos that vary down or up from the middling, and, also, interpolate tempi like Allegretto or Larghetto which fall about midway between the basic tempi.  What I draw most usefully from Mälzel is making the basic counting unit clear in the score, i.e. eighth = 80.  The words have their archaic and exotic charm, and if you are making a stylistic reference to historical repertoire, then go ahead and leave the words in, but not without the numerical markings.   The interpretation of these words has changed and will change over time, but my physicist friends assure me that we're unlikely to experience a change in values for a minute anytime soon.  In my case, I'll try to drop using words for the tempo, but this will not stop me from using words to indicate other expressive suggestions.

Now about the scaling of tempi.  Metronomes are still made set to Mälzel's original scale, which approximates, in whole numbers, a 16-step scale between 40 and 80: 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 63, 66, 69, 72, 76, 80.  Digital devices now widely available offer more precision than this, but these tempi are still likely to have been internalized by practicing musicians.  (Somewhat akin to perfect pitch, many musicians are able to memorize tempi, and some even execute the most complicated emsemble rhythms by drawing on their reserves of such internalized tempi.  What a piece of work!)  As Greschek points out, Cowell and Stockhausen each proposed tempo scales based on 12 divisions of a tempo "octave", in Cowell's case, just intonation-based "scales" dividing the tempi spaces 60-120 and 48-96, and in Stockhausen's case, an approximation of an equal tempered division between 60 and 120.  Stockhausen used these tempo markings throughout his work rather consistently.   Being personally unattached to the number 12, I can probably get along just fine with the conventional 16 values, but if I had to take 12, I would go with 60, 64, 68, 72, 76, 80, 84, 90, 96, 100, 106, 112, which uses only three speeds not found on the tradional metronome (64, 68, 90), one of which (90) is easy to accurately perform in proportion to the basic value of 60.