关于马佐拉（Mazzola）的段子是这样的：懂音乐懂到能看穿他理论的人，会被他的数学忽悠得团团转；反之亦然。如果你想探索那个领域，季莫茨科（Tymoczko）的《音乐几何学》（A Geometry of Music）更有嚼头。但这完全没切中要害。音乐不仅仅是数学上的协和与不协和。音乐是运用协和、不协和、音色、节奏、曲式以及历史与文化的实践……
The joke about Mazzola is that people who know enough about music to see through his theories are bamboozled by his maths, and vice versa. If you want to explore that space, Tymoczko's A Geometry of Music is more rewarding. But this misses the point. Music isn't just mathematical consonance and dissonance. Music is the practice of using consonance, dissonance, timbre, rhythm, form, and historic and cultural…
…people working on unified theories of harmonic/Western/tonal music. The author fails to reference the most interesting work done in this area. The ones I've found most convincing are: - Dmitri Tymoczko's Geometry of Music: http://dmitri.tymoczko.com/geometry-of-music.html - Bill Sethares's Tuning Timbre Spectrum Scale approach: http://sethares.engr.wisc.edu/ttss.html - Andrew Duncan's Combinatorial Music Theory: http://andrewduncan.net/cmt/…
……希望能自由地移调并在远关系调之间进行转调。这是个很深的话题，但如果有人感兴趣，我推荐两本书：- 威廉·塞萨雷斯的《音色、律制、频谱与音阶》（Timbre, Tuning, Spectrum, Scale） - 德米特里·季莫茨科的《音乐几何学》（A Geometry of Music）
…desire to be able to freely transpose and to modulate between distant keys. It's a deep topic, but if anyone's interested, I recommend two books: - Timbre, Tuning, Spectrum, Scale by William Sethares - A Geometry of Music by Dmitri Tymoczko
去看看德米特里·季莫茨科的《音乐几何学》（Geometry of Music）。https://www.amazon.com/Geometry-Music-Counterpoint-Extended-... https://www.youtube.com/watch?v=NnvynOyZI-Q
Check out Dmitri Tymoczko's "Geometry of Music". https://www.amazon.com/Geometry-Music-Counterpoint-Extended-... https://www.youtube.com/watch?v=NnvynOyZI-Q
Recommended: A Geometry of Music by Dmitri Tymoczko - http://dmitri.mycpanel.princeton.edu/geometry-of-music.html The Geometry of Musical Rhythm by Godfried Toussaint - Original paper - http://cgm.cs.mcgill.ca/~godfried/publications/geometry-of-r...…
关于马佐拉（Mazzola）的段子是这样的：懂音乐懂到能看穿他理论的人，会被他的数学忽悠得团团转；反之亦然。如果你想探索那个领域，季莫茨科（Tymoczko）的《音乐几何学》（A Geometry of Music）更有嚼头。但这完全没切中要害。音乐不仅仅是数学上的协和与不协和。音乐是运用协和、不协和、音色、节奏、曲式以及历史与文化的实践……
The joke about Mazzola is that people who know enough about music to see through his theories are bamboozled by his maths, and vice versa. If you want to explore that space, Tymoczko's A Geometry of Music is more rewarding. But this misses the point. Music isn't just mathematical consonance and dissonance. Music is the practice of using consonance, dissonance, timbre, rhythm, form, and historic and cultural…
……那些致力于构建和声/西方/调性音乐统一理论的人。作者漏掉了引用该领域最有趣的研究成果。我个人觉得最有说服力的是：- 德米特里·季莫茨科（Dmitri Tymoczko）的《音乐几何学》：http://dmitri.tymoczko.com/geometry-of-music.html - 比尔·塞萨雷斯（Bill Sethares）的“律制-音色-频谱-音阶”（Tuning Timbre Spectrum Scale）方法：http://sethares.engr.wisc.edu/ttss.html - 安德鲁·邓肯（Andrew Duncan）的《组合音乐理论》：http://andrewduncan.net/cmt/……
…people working on unified theories of harmonic/Western/tonal music. The author fails to reference the most interesting work done in this area. The ones I've found most convincing are: - Dmitri Tymoczko's Geometry of Music: http://dmitri.tymoczko.com/geometry-of-music.html - Bill Sethares's Tuning Timbre Spectrum Scale approach: http://sethares.engr.wisc.edu/ttss.html - Andrew Duncan's Combinatorial Music Theory: http://andrewduncan.net/cmt/…
……希望能自由地移调并在远关系调之间进行转调。这是个很深的话题，但如果有人感兴趣，我推荐两本书：- 威廉·塞萨雷斯的《音色、律制、频谱与音阶》（Timbre, Tuning, Spectrum, Scale） - 德米特里·季莫茨科的《音乐几何学》（A Geometry of Music）
…desire to be able to freely transpose and to modulate between distant keys. It's a deep topic, but if anyone's interested, I recommend two books: - Timbre, Tuning, Spectrum, Scale by William Sethares - A Geometry of Music by Dmitri Tymoczko
去看看德米特里·季莫茨科的《音乐几何学》（Geometry of Music）。https://www.amazon.com/Geometry-Music-Counterpoint-Extended-... https://www.youtube.com/watch?v=NnvynOyZI-Q
Check out Dmitri Tymoczko's "Geometry of Music". https://www.amazon.com/Geometry-Music-Counterpoint-Extended-... https://www.youtube.com/watch?v=NnvynOyZI-Q
推荐阅读：德米特里·季莫茨科的《音乐几何学》 - http://dmitri.mycpanel.princeton.edu/geometry-of-music.html 戈德弗里德·图桑（Godfried Toussaint）的《音乐节奏的几何学》（The Geometry of Musical Rhythm） - 原版论文 - http://cgm.cs.mcgill.ca/~godfried/publications/geometry-of-r...…
Recommended: A Geometry of Music by Dmitri Tymoczko - http://dmitri.mycpanel.princeton.edu/geometry-of-music.html The Geometry of Musical Rhythm by Godfried Toussaint - Original paper - http://cgm.cs.mcgill.ca/~godfried/publications/geometry-of-r...…
或者 http://dmitri.tymoczko.com/geometry-of-music.html
Or http://dmitri.tymoczko.com/geometry-of-music.html