Musical Scales and Their Mathematics
Schüffler, Karlheinz
- 出版商: Springer
- 出版日期: 2025-03-12
- 售價: $2,680
- 貴賓價: 9.5 折 $2,546
- 語言: 英文
- 頁數: 716
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3662695405
- ISBN-13: 9783662695401
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相關主題
商品描述
Are musical scales just trivial? This book explores this question, revealing the complexity of creating "harmony" in tonal systems.
Why 12 tones? Are there alternatives? Are 12 fifths equal 7 octaves? What is "consonance"? When are intervals "perfect" or "imperfect"? What is meant by "tonal characteristics", "whole tone" and "semitone"? "Ancient tuning" vs potentially new?
Answers need thoughtful explanations, revealing interconnectedness. In this context, mathematics is pivotal, explaining scale generation, temperament systems, etc.
Divided into three parts, this book covers:
- Modern interval arithmetic driven by prime numbers.
- Architectural principles of scales, with examples.
- Systematic nature of historical tunings and temperaments.
Understanding only requires school knowledge, developed into algebraic tools applied musically.
商品描述(中文翻譯)
音階只是微不足道的嗎？本書探討了這個問題，揭示了在音調系統中創造「和諧」的複雜性。
為什麼是12個音？有其他選擇嗎？12個五度等於7個八度嗎？什麼是「和諧」？何時音程是「完美」或「不完美」的？「音調特徵」、「全音」和「半音」是什麼意思？「古老的調音」與潛在的新調音有何不同？
答案需要深思熟慮的解釋，揭示彼此之間的聯繫。在這個背景下，數學是關鍵，解釋音階生成、音律系統等。
本書分為三個部分，涵蓋：
- 由質數驅動的現代音程算術。
- 音階的建築原則，並附有範例。
- 歷史調音和音律的系統性特徵。
理解只需要學校的知識，並發展成應用於音樂的代數工具。
作者簡介
Prof. Dr. Karlheinz Schüffler is a mathematician, organist, and choir conductor. As a mathematician, he teaches at the University of Düsseldorf and previously at the Niederrhein University of Applied Sciences (Krefeld). As a musician, he has been dedicated to church music since his youth, with both organ and mathematical music theory being his areas of expertise.
作者簡介(中文翻譯)
卡爾海因茲·舒夫勒教授是一位數學家、風琴師和合唱指揮。作為數學家，他在杜塞爾多夫大學任教，之前曾在尼德萊因應用科技大學（克雷費爾德）任教。作為音樂家，他自青年時期以來一直致力於教會音樂，風琴和數學音樂理論是他的專業領域。
