…computer science end of things, and this is recommended reading for anyone that works on my team. If you prefer to have an actual book, it is directly available for purchase on Amazon: http://www.amazon.com/Music-Mathematical-Offering-Dave-Benso...
如果你在找书的话，《Music: A Mathematical Offering》挺不错的：https://www.amazon.com/Music-Mathematical-Offering-Dave-Bens...。不过你的递归也快见底了。维基百科应该能带你搞定剩下的……
If you're looking for a book, Music: A Mathematical Offering https://www.amazon.com/Music-Mathematical-Offering-Dave-Bens... is pretty good. But you're nearly a the end of your recursion, though. Wikipedia ought to take you the rest of…
……升降号（sharps and flats）而不是用更多的字母？音符的数量以及它们频率之间的比例才是最底层的本质。其余的都只是历史的巧合。一个很好的入门起点是 David Benson 的《Music: a Mathematical Offering》。可以在这里免费在线阅读：https://homepages.abdn.ac.uk/d.j.benson/pages/html/maths-mus....
…sharps and flats instead of just more letters? The number of notes and the ratios between their frequencies are fundamental. The rest are historical accidents. A good place to start is David Benson's 'Music: a Mathematical Offering'. Available free online here: https://homepages.abdn.ac.uk/d.j.benson/pages/html/maths-mus....
……彻底被取代了。不过勋伯格《和声学》（Theory of Harmony）里的那些科学内容基本是垃圾。如果你有兴趣进一步了解现代对音乐物理特性的认识，我推荐《Musimathics: The Mathematical Foundations of Music》以及 Benson 的《Music: A Mathematical Offering》。至于从认知层面探讨音乐结构的尝试，我很喜欢《The……
…completely replaced. The scientific stuff in Schoenberg's Theory of Harmony is mostly garbage though. If you're interested in reading more about the modern understanding of the physical properties of music I'd recommend "Musimathics: The Mathematical Foundations of Music," and Benson's "Music: A Mathematical Offering." For an attempt to look at musical structure in terms of its cognition, I enjoyed "The…
万一有人还没看过：Dave Benson 写的《Music: A Mathematical Offering》方向差不多，但要深入得多，链接在此：https://logosfoundation.org/kursus/music_math.pdf
In case some folks have not seen it: along something of the same lines but in very much more depth is Music: A Mathematical Offering by Dave Benson, at https://logosfoundation.org/kursus/music_math.pdf
……计算机科学那一端，这是我团队里所有人的必读书目。如果你更喜欢读实体书，可以直接在亚马逊上买：http://www.amazon.com/Music-Mathematical-Offering-Dave-Benso...
…computer science end of things, and this is recommended reading for anyone that works on my team. If you prefer to have an actual book, it is directly available for purchase on Amazon: http://www.amazon.com/Music-Mathematical-Offering-Dave-Benso...
如果你在找书的话，《Music: A Mathematical Offering》挺不错的：https://www.amazon.com/Music-Mathematical-Offering-Dave-Bens...。不过你的递归也快见底了。维基百科应该能带你搞定剩下的……
If you're looking for a book, Music: A Mathematical Offering https://www.amazon.com/Music-Mathematical-Offering-Dave-Bens... is pretty good. But you're nearly a the end of your recursion, though. Wikipedia ought to take you the rest of…
……升降号（sharps and flats）而不是用更多的字母？音符的数量以及它们频率之间的比例才是最底层的本质。其余的都只是历史的巧合。一个很好的入门起点是 David Benson 的《Music: a Mathematical Offering》。可以在这里免费在线阅读：https://homepages.abdn.ac.uk/d.j.benson/pages/html/maths-mus....
…sharps and flats instead of just more letters? The number of notes and the ratios between their frequencies are fundamental. The rest are historical accidents. A good place to start is David Benson's 'Music: a Mathematical Offering'. Available free online here: https://homepages.abdn.ac.uk/d.j.benson/pages/html/maths-mus....
同一方向上另一本好书是 Dave Benson 的《Music: a Mathematical Offering》。https://homepages.abdn.ac.uk/d.j.benson/pages/html/maths-mus...
Another good book in the same vein is Dave Benson's 'Music: a Mathematical Offering'. https://homepages.abdn.ac.uk/d.j.benson/pages/html/maths-mus...
……彻底被取代了。不过勋伯格《和声学》（Theory of Harmony）里的那些科学内容基本是垃圾。如果你有兴趣进一步了解现代对音乐物理特性的认识，我推荐《Musimathics: The Mathematical Foundations of Music》以及 Benson 的《Music: A Mathematical Offering》。至于从认知层面探讨音乐结构的尝试，我很喜欢《The……
…completely replaced. The scientific stuff in Schoenberg's Theory of Harmony is mostly garbage though. If you're interested in reading more about the modern understanding of the physical properties of music I'd recommend "Musimathics: The Mathematical Foundations of Music," and Benson's "Music: A Mathematical Offering." For an attempt to look at musical structure in terms of its cognition, I enjoyed "The…
万一有人还没看过：Dave Benson 写的《Music: A Mathematical Offering》方向差不多，但要深入得多，链接在此：https://logosfoundation.org/kursus/music_math.pdf
In case some folks have not seen it: along something of the same lines but in very much more depth is Music: A Mathematical Offering by Dave Benson, at https://logosfoundation.org/kursus/music_math.pdf