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Harmony and nonharmonic partials

 

作者: Max V. Mathews,   John R. Pierce,  

 

期刊: The Journal of the Acoustical Society of America  (AIP Available online 1980)
卷期: Volume 68, issue 5  

页码: 1252-1257

 

ISSN:0001-4966

 

年代: 1980

 

DOI:10.1121/1.385116

 

出版商: Acoustical Society of America

 

数据来源: AIP

 

摘要:

We have explored some musical effects of tones with nonharmonic partials. The spacing of partials can be stretched so that each partial frequencyfijpresent in tones sounded singly or together is given byfij=Ai/12+log2j. Hereiis the scale step in semitones,jis the partial number, andAis the frequency ratio of a pseudo‐octave (A=2 for a true octave). We find that subjects can match the keys of stretched (A=2.4) as well as unstretched passages. Stretched cadences (A=2.4) do not seem final. But, a stretched ’’cadence’’ with equally spaced partials that goes from closely spaced (tonally dissonant) to widely spaced (tonally consonant) partials does seem final. Our experiments do not decide finally among three views of harmony: that harmony depends on a fundamental bass or periodicity pitch (Rameau), that harmony depends on the spacing of partials (Helmholtz and Plomp) or that harmony is a matter of brainwashing.

 

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