Introduction to the Mathematics of Music
暫譯: 音樂數學入門
Amiot, Emmanuel
- 出版商: A K Peters
- 出版日期: 2026-08-17
- 售價: $2,080
- 貴賓價: 9.5 折 $1,976
- 語言: 英文
- 頁數: 130
- 裝訂: Quality Paper - also called trade paper
- ISBN: 1041168160
- ISBN-13: 9781041168164
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相關分類:
離散數學 Discrete-mathematics
尚未上市，無法訂購
商品描述
Introduction to the Mathematics of Music is aimed at helping bridge the substantial gap between a classical musician culture and the universe of mathematical notions in music. It explains the necessary notions, starting from scratch, with rigour but without any unnecessary formalism. It was developed from a course given in Perpignan, France, for a bachelor in Music theory.
- After a mandatory outline of the seminal role of numbers in music, based on the equations of consonance, the book introduces the essential formalisation of pitch-classes and pc-sets as elements and subsets of the integers modulo 12.
- Transpositions and inversions, traditional musical operations, are formalized in that context. Symmetries and structures are studied efficiently with these tools -- for instance linking Olivier Messiaen's forgotten Modes of Limited Transposition with subgroups of the dihedral group D12.
- The book ends with a sampling of the geometrical models of musical spaces that mark the modern era in the discipline.
- A wealth of exercises (and indications of solutions) is provided, since the notions exposed are better assimilated with paper and pencil.
This text is primarily intended for serious music students who intend to develop the ability to understand the current research in mathematical music. Some prior knowledge of music theory (non mathematical) is an asset. It is hoped that the style of presentation, together with the numerous exercises, might also be a source of pedagogical inspiration for teachers and students even in so called pure' mathematics.
商品描述(中文翻譯)
《音樂數學導論》旨在幫助彌合古典音樂文化與音樂中數學概念之間的巨大鴻溝。它從零開始解釋必要的概念，既嚴謹又不過於形式化。該書是基於在法國佩皮尼昂（Perpignan）舉辦的一門音樂理論學士課程而開發的。
- 在強調數字在音樂中重要角色的必修大綱之後，基於和諧的方程式，書中介紹了音高類（pitch-classes）和音高集合（pc-sets）的基本形式化，作為模12整數的元素和子集。
- 轉調和反轉這些傳統音樂操作在此背景下被形式化。利用這些工具有效地研究對稱性和結構，例如將奧利維耶·梅西安（Olivier Messiaen）被遺忘的《有限轉調模式》（Modes of Limited Transposition）與二面體群 D12 的子群聯繫起來。
- 本書最後介紹了標誌著該學科現代時代的音樂空間幾何模型的取樣。
- 提供了大量的練習題（及解題指示），因為所揭示的概念更容易通過紙筆進行吸收。
本書主要針對有志於理解當前數學音樂研究的認真音樂學生。對音樂理論（非數學）的先前知識將是一項資產。希望這種呈現風格，加上眾多的練習，能成為所謂「純」數學的教師和學生的教學靈感來源。
作者簡介
Emmanuel AMIOT is a French mathematician and musician: alongside his studies at the Nice Conservatory (piano with Ms Audibert-Lambert in particular), he pursued his scientific studies (ENS Saint-Cloud, agrégation, PhD), and was able to synthesise these disciplines through the founding of the Society for Mathematics and Computation in Music, http: //www.smcm-net.info/ in 2007. Long time co-editor in chief of the Journal of Mathematics and Music (published by Taylor and Francis), he is an academician (EASA) and author of numerous conferences and reference articles on the topic, including the monography Music through Fourier Space. His work is authoritative on discrete Fourier transform of musical structures (scales, rhythms), rhythmic canons, and homometry, all subjects that will be carefully avoided in this book. Retired from the national education system, he devotes himself to his research, publications, conferences, and concerts.
作者簡介(中文翻譯)
艾曼紐·阿米奧特是一位法國數學家和音樂家：除了在尼斯音樂學院的學習（特別是跟隨奧迪貝特-蘭伯特女士學習鋼琴）外，他還進行了科學研究（ENS 聖克勞德、法學資格、博士學位），並通過於2007年創立音樂中的數學與計算社會（Society for Mathematics and Computation in Music，網址：http://www.smcm-net.info/）來綜合這些學科。他長期擔任《數學與音樂期刊》（Journal of Mathematics and Music，出版商為泰勒與法蘭西斯）的主編，並且是歐洲音樂科學學會（EASA）的學者，撰寫了許多關於該主題的會議和參考文章，包括專著《通過傅立葉空間的音樂》。他的研究在音樂結構（音階、節奏）的離散傅立葉變換、節奏佳能和同構性等主題上具有權威性，這些主題在本書中將被小心避免。退休於國家教育系統後，他專注於研究、出版、會議和音樂會。
