Note: I send emails to the class via the registrar's email lists for this course. Please make sure that you have registered your email with the university. Unfortunately some service providers see this as an indication that this is spam and dumps the mail into a junk, or spam, or other labeled folder. I do not know how to get around this as I do not want to give everyone everyone else's email, I do not want to enter all 50 separate email addresses as separate emails, but I want people to get them. Please remember to look into your junk/spam/... folder as well if you do not get the emails for this class.
Here is Bach's Prelude C major, no. 1 from the Well Tempered Clavier, played in the Lehman temperament, equal temperament, and another unequal temperament (Werkmeister III) from the the 18th century, played via midi, so all three are exactly the same as far as the notes that are played, it is just the tunings that differ. It is best to page through the file and play similar sections in each of the tunings to compare them. Or Just try to get a feel for the piece, esp the tone colour and feel of the piece in the different temperament. This piece is in the key that comes closest to just tuning in this temperament as opposed to equal temperament although the modulation throught means that one is effectively hearing many different keys in the one piece. The form of the piece means it could easily become boring (and for me does a bit in equal temperament) but the slight varitions in tunings of intervals throught the piece make the Lehman much more interesting for me. Sometimes the major thirds are sharp and bright, sometimes more sombre. Similarly the minor thirds can be brighter of more closed. Listen also to the C major final chord at the end of the piece. It is more harmonious (less beating or wavering) in the Lehman than the equal temperament.
Here is the last 17 seconds of that Prelude #1 from above in the Lehman Temperament and in Equal temperament. I find the Lehman more interesting-- there is more variety-- tnan in equal temperament. But see what you think. Listen also to the last chords in each case. (Note that these require an HTML5 aware browser which also understands .wav files. Almost all, except Internet Explorer, do, even though Microsoft invented the .wav files. )
All Material on this page including all course notes, assignments, course notes, solutions on documents linked to from this page hosted on theory.physics.ubc.ca are copyright W. G Unruh. 1998-2016