ABSTRACT
Stumpf (1898) maintained that melodies played on micro- and macroscales (that is, on scales where the usual ratio between the frequencies limiting the octave is lessened or enlarged, being nevertheless divided in 12 tempered semitones) could preserve their tonal content rather well. Werner (1926) maintained a similar view, emphasizing the fact that even visual figures preserve their attributes when lessened or enlarged in visual space. An experiment conducted with six widely known melodies played on 12 special scales ranging from the proportional compression of the octave to one semitone, to the dilatation to the double octave, shows that the recognition of melodies rapidly drops under the 50% level when the compression reaches 40% of frequency, and the dilatation 30%. Trained subjects (undergraduate musicians) show a significant peak of 91% of recognition when the compression of the octave reaches seven semitones (i. e., the fifth, the most consonant interval except the octave itself). The experiment and the introspective reports of both trained and untrained subjects show that such a comparison between tonal and visual space is strongly dubious, and that factors not yet investigated may play a significant role in the Erscheiniingswei.se(mode of appearance) of the micro- and macromelodies. For instance, the use of unconventional intervals upsets the correct forming of the tonic (that is, the tonal frame of reference), supposedly preventing listeners from recognizing the original melody in its compressed or dilatated versions.
