in meantone tuning is so unpleasant, and such an obstacle, that by the late seventeenth
century it was being substantially modified in practice.
Modified meantone temperament
This was probably the most appropriate temperament for most of the early organ music
we now hear. Even though Buxtehude and Bach were among those exploring new
temperaments their compositional technique remained informed by the meantone system.
The pure thirds of meantone are de-tuned a little in order to try and lessen the ‘wolf’.
Modified meantone temperament was still being used by English organ builders,
including Willis, as late as the 1850s. This included fifth-comma meantone and sixth-
comma meantone (‘Silbermann’ temperament). Modified meantone temperament allows
the composer to modulate a little more freely and frequently, even occasionally into five
sharps or flats, before returning to the home key.
Well tempered or circulating temperaments
These came into being in the late seventeenth century as musical theorists started to
experiment with ways of hiding the ‘wolf’ and making all keys usable. It was perfectly
obvious that this could be done by distributing the intervals equally across the scale, but
this was not the path they took. The reason they did not take this path was that these
circulating (no-wolf) temperaments are those which allow the widest exploration of key
colour. Musicians of the eighteenth century were happy with the expressive possibilities
offered by writing in different keys and sought to exploit the quite different character of
each in their writing.
These temperaments include the various tunings by Werckmeister (organ expert, 1691,
Kirnberger (Bach pupil, early eighteenth century), Neidhardt (1724) and Vallotti (about
1730). Werckmeister III is notable for its purity in the best keys and its suitability for
organs with large quint mixtures, as many of the fourths and fifths are in tune, but is
irregular and bumpy in the way it deals with modulation and key colour. Vallotti is
smooth and regular but the key colour is generally rather mild. In all these systems it is
possible to play in any key but the more remote keys may sound unpleasant and
enharmonic modulation is not always happy.
Other circulating temperaments have been devised in modern times. Nearly all of them
suffer from the grave defect that they are difficult to commit to memory and are therefore
difficult to use in practice as one cannot tune an organ with a book in one hand.
Equal temperament
This has been known since 350 BC but this very obvious solution did not become
widespread until the late eighteenth century, or fifty to a hundred years later in the
English speaking world. The advantages are clear. All keys are usable and full
enharmonic modulation is possible. The disadvantages are also clear. Not one interval is