汎用的な声のリードスペース
Clifton Callender1, Ian Quinn, Dmitri Tymoczko
1College of Music, Florida State University, Tallahassee, FL 32306, USA.
Science (New York, N.Y.)
|April 19, 2008
まとめ
この研究は,音楽のピッチシーケンスを理解するための数学的モデルを導入し,コードの32の等価関係とシーケンスの243を明らかにします. このモデルは,コードの類似性に関する新しい分析ツールと洞察を提供します.
科学分野:
- 音楽理論 音楽理論
- 数学的モデリング
- コンピュータ音楽学
背景:
- 伝統的な西洋音楽理論は,音高の配列を分類し,オクターブシフトや転置のような変換を無視している.
- 音楽構造の既存の幾何学的な表現は,複雑で断片化することがあります.
研究 の 目的:
- 5つの主要な音楽の変形 (オクターブシフト,パルムテーション,トランポジション,反転,カーディナリティの変化) を説明する数学的モデルを開発する.
- コードとコードの配列の内にある基礎的な数学的構造と等価性を明らかにする.
- 音楽理論のための新しい分析ツールと,幾何学的な表現のための統一された枠組みを提供すること.
主な方法:
- ミュージカル変換の数学モデリング.
- コードとコードの配列の等価関係派生.
- ミュージカル要素のための幾何学的分数空間の構築.
主要な成果:
- アコードの32の異なる等価関係を特定する.
- アコードの配列の243の異なる等価関係を特定した.
- コードとシーケンスを表す32の幾何学定数空間ファミリーの開発.
結論:
- 数学的モデルは,音楽構造を理解するための統一された枠組みを提供します.
- このモデルは,音楽理論的な概念の間の新しいつながりを明らかにします.
- 新しい分析ツールと,コードの種類間の類似性を評価するための方法を提供します.
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