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美国作曲家、作曲理论家霍华德·汉森在1960年出版了一部全面阐述十二平均律音阶中音高材料的理论著作,在著作中汉森采用映射法从简单到复杂地计算出了所有音高组合形式,并形成了较为完整的“音高材料库”。该论著作为教材在美国一些院校至今仍在教授,但在国内知之甚少。汉森的研究方法和成果不仅为理解音高组织的各种形式提供了新的途径和方法,也为十二平均律音阶中音高组织的再研究打下了坚实的基础。
In 1960, American composer and composer theorist Howard Hansen published a theoretical work that comprehensively expounded the mid-pitched mid-scale material. Hansen used the mapping method to calculate everything from simple to complex in his book Pitch combination, and formed a more complete “Pitch Material Library ”. The book as a textbook in some colleges and universities in the United States is still professor, but little is known in the country. Hansen’s research methods and achievements not only provide new ways and means for understanding the various forms of pitch organization, but also lay a solid foundation for the reanalysis of pitch organization in the twelve-mean law scales.