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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