1. The Avoidance of Part-Crossing in Polyphonic Music: Perceptual Evidence and Musical Practice David Huron Presented by Zhenyao Mo

2. Dowling ’ s Observation Two Concurrent interleaved melodies Without pitch overlay Easy to segregate “ Part Crossing ” Hard to segregate Transpose

3. Three Hypothesis Tessitura Range Overlap Local Crossing Pitch DomainTime Domain

4. Two Questions Is the avoidance of part-crossing on purpose or just because the different pitch distributions for various voices? Is the avoidance of part-crossing on purpose or just because the different pitch distributions for various voices? Is the purpose of such avoidance to prevent the sort of perceptual confusions, say, can not segregate different parts? Is the purpose of such avoidance to prevent the sort of perceptual confusions, say, can not segregate different parts?

5. Subjects: 105 polyphonic keyboard works by Bach Why??? As for choral works, different parts have their own instrumental or vocal range, while keyboard music parts are relatively free to traverse whole range As for choral works, different parts have their own instrumental or vocal range, while keyboard music parts are relatively free to traverse whole range In keyboard music the parts maintain homogeneous timbers In keyboard music the parts maintain homogeneous timbers

6. Measurement of Part-Crossing Sonority : each novel vertical pitch arrangement between two voices can be deemed a distinct sonority Sonority : each novel vertical pitch arrangement between two voices can be deemed a distinct sonority Degree of part-crossing : proportion of vertical sonorities in which a part crossing has occurred Degree of part-crossing : proportion of vertical sonorities in which a part crossing has occurred

7. Some Facts Number of Parts TwoThreeFourFiveSix Degree of part-crossing Mean (%) 0.180.791.783.116.11 Standard Deviation of Pitch 5.654.714.474.333.94

8. Auto-Phase Method Aim : To distinguish Local crossing from tessitura and range overlap Basic idea : keep the pitch range, but regenerate the order or correspondence

9. More Facts

11. Two Questions Is the avoidance of part-crossing on purpose or just because the different pitch distributions for various voices? Is the avoidance of part-crossing on purpose or just because the different pitch distributions for various voices? NO NO Is the purpose of such avoidance to prevent the sort of perceptual confusions, say, can not segregate different parts? Is the purpose of such avoidance to prevent the sort of perceptual confusions, say, can not segregate different parts? YES, we got evidence. YES, we got evidence.