This post is a followup to my previous post on the diesis in musical tuning. My earlier example of the so-called “greater diesis” involved a sequence of four ascending minor thirds. In equal temperament, four minor thirds add up to an octave, but when those thirds are tuned to a pure 6/5 ratio, the sequence lands quite sharp of an octave. In this post we’ll explore the same discrepancy, but we won’t traverse any minor thirds directly. To ascend by a minor third, we’ll first ascend by a perfect fifth and then descend by a major third. This way, we’ll hear perfect fifths and major thirds throughout the sequence, until the end when the destination pitch, Bbb, is contrasted against the starting A. Personally I find this example more shocking than the previous version, because the major thirds and perfect fifths are more “persuasive” to my ear than minor thirds. Although I sense that something funny might be happening as the sequence progresses, I’m convinced of the “rightness” of the destination pitch when it arrives, and when I then hear the original A, I just can’t believe that’s where the sequence started a little while earlier. The sound clips below use a sampled bassoon. (view score)
Ascending Fifths, Descending Major Thirds – Equal Temperament (bassoon): [audio http://rudiseitz1.files.wordpress.com/2013/12/diesisfifthsthirds12etbasoon.mp3]
Ascending Fifths, Descending Major Thirds – Pure Intervals (bassoon): [audio http://rudiseitz1.files.wordpress.com/2013/12/diesisfifthsthirdsbassoon.mp3]
Here is an alternate set of clips using a sampled organ:
Ascending Fifths, Descending Major Thirds – Equal Temperament (organ): [audio http://rudiseitz1.files.wordpress.com/2013/12/diesisascendignfifthsdescendingmajorthirds12etorgan.mp3]
Ascending Fifths, Descending Major Thirds – Pure Intervals (organ): [audio http://rudiseitz1.files.wordpress.com/2013/12/diesisascendingfifthsdescendingmajorthirdsorgan.mp3] ■