melodic lemons

Yesterday, I suggested several reasons why the Melodic Difference
Limen (MDL) should not be used as the sole basis of choosing a
tuning system. Today, I would like to take the stronger position that
while MDL does have the *appearence* of a well defined psycho-
acoustic term, the idea is actually quite ambiguous.

To bring this into focus, consider the following two experiments:

Experiment (1): C D E D C

Experment (2): C C C D C

Suppose first that these notes are given their normal 12-tet
meanings. We can explore the MDL in experiment (1) by minutely
adjusting the frequencies of the tones. As the extensive previous
discussion on this list suggests, very small changes in pitch do not
cause a different melody to be perceived, while large changes will
cause a different melody to be heard. While the exact values needed
to change the melody will undoubtedly differ depending on which
note is changed, who is listening, the timbre of the tones, etc., a value
of 1/3 tone for a MDL does indeed seems reasonable.

[Digression: Say the E note is slowly flattened. The melody with E at
200 cents above D is surely heard as the same as the melody with E
199 cents above D, is the same as the melody 198 cents above D, etc.,
and thus there is a continuum of minute changes, each of which is
judged the same. Yet at the extreme they are judged different. This
suggests one interesting kind of "modulation" that is possible in
tunings that have very fine pitch gradations... the "same" melody can
be "repeated" over and over, yet at the end of the repeats it is a
"different" melody. Has anyone explored this compositional idea?]

Now consider experiment (2). Say that the D note is 10 cents above
the C note. Such a 10 cent difference is clearly audible (no extreme
"hypersensitivity" is required - all we're talking about here is the
ability to perceive that the pitches are different), and the melody is

X X X up X

But if the D note was 10 cents *below* the C (if you excuse the
notation), then the melody is

X X X down X

which is indeed a very different melody! Of course, if the D were
perceptibly the same as C, the melody would be

X X X X X

which is different yet again. This highlights the idea that the
*contour* of a melody is aurally far more significant than the details
of the pitches. The reason the MDL appears large in experiment (1) is
because the contour of the melody does not change, but the MDL
appears very small in experiment (2) because the contour does
change. Thus the MDL is very different depending on the musical
context (in this case the contour of the melody) in which it is
investigated. Surely, one should not wish to choose a tuning system
based on only a small subset of possible melodic contexts.

Bill Sethares


SMTPOriginator: tuning@eartha.mills.edu
From: Gregg Gibson
Subject: Arabs and the 17-tone equal
PostedDate: 18-12-97 17:45:18
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