Diesis II

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 then 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): 

Ascending Fifths, Descending Major Thirds — Pure Intervals (bassoon):

Here is an alternate set of clips using a sampled organ:

Ascending Fifths, Descending Major Thirds — Equal Temperament (organ):

Ascending Fifths, Descending Major Thirds — Pure Intervals (organ): 

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