一般化语音领导空间
Clifton Callender1, Ian Quinn, Dmitri Tymoczko
1College of Music, Florida State University, Tallahassee, FL 32306, USA.
概括
本研究介绍了一种用于理解音乐音调序列的数学模型,揭示了和弦的32个等价关系和序列的243个等价关系. 该模型提供了新的分析工具和对和弦相似性的见解.
科学领域:
- 音乐理论 音乐理论
- 数学建模的数学建模
- 计算音乐学 计算音乐学
背景情况:
- 传统的西方音乐理论分类了音调序列,而忽略了八度移动和转换等转换.
- 现有的音乐结构的几何表示可能是复杂的和碎片化的.
研究的目的:
- 开发一个数学模型,可以解释五个关键的音乐转换 (八度移动,变换,转换,反转,枢机变化).
- 揭示在和弦和和弦序列中的潜在数学结构和等价值.
- 为音乐理论提供新的分析工具,并为几何表示提供统一的框架.
主要方法:
- 音乐转换的数学建模.
- 对和弦和和弦序列的等价关系的推导.
- 为音乐元素构建几何分数空间.
主要成果:
- 识别了32个不同的和弦等价关系.
- 识别了243个不同的和弦序列等价关系.
- 开发了32个几何位数空间的家族,代表了和弦和序列.
结论:
- 数学模型为理解音乐结构提供了一个统一的框架.
- 该模型揭示了音乐理论概念之间的新联系.
- 它提供了新的分析工具和评估和弦类型之间的相似性的方法.
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