The new and practical equal temperament
tuning is central to Werckmeister's argument here.
On the piano, with equal temperament
, all three pitches are identical--there is only one note on the keyboard for them.
This has been the most fundamental source of errors, misapprehensions and confusions since the 16th century." In this connection, Koukal points out that today's equal temperament
, within which the octave is divided into iq equal semitones, asserted itself gradually during the course of the 19th century, and the concert pitch set at 440 Hz was only officially agreed as the international standard in 1939.
This may even result in a retuning of the sounds of the past: "Equal temperament
is now universally accepted, but ...
While it listens to you play, your pitch is charted in relation to equal temperament
. You can watch it while you are playing, like a traditional tuner, or as Wakefield did, it can also be used to show the pitch of an Audacity recording played back over the computer's speakers.
His two published books, How Equal Temperament
Ruined Harmony (and Why You Should Care) and Shakespeare's Songbook, have gained international renown.
38a (tuned in Kellner) and two portatives built by David Petty & Associates, one in equal temperament
and the other in meantone.
He pairs music and math concepts such as scales and modular arithmetic, octave identification and equivalence relation, intervals and logarithms, equal temperament
and exponents, overtones and integers, tone and trigonometry, and tuning and rationality.
It might happen to prick up your ears from a purely avant-garde perspective, but it still doesn't add anything new to our understanding of Bach's lessons in well-temperament as a technological, namely reproducible way forward in musicking (and which incidentally was itself eventually supplanted by the modern system of true equal temperament
, which is also what makes playing Das wohltemperierte Klavier on the piano such an ironic exercise to begin with).
How Equal Temperament
Ruined Harmony: And Why You Should Care, by Ross.