其他2016arxiv.org
和声解释：迈向音乐的科学理论
Harmony Explained: Progress Towards a Scientific Theory of Music
入门 · 约 45 分钟读完前置知识：基础乐理、信号处理基础
导读
这篇论文试图从物理与计算的角度为和声建立一个“科学理论”，作者批评传统乐理不是科学，并提出基于大脑计算基频、进化偏好低计算成本的解释框架。HN 读者普遍认为作者对乐理和科学方法论都存在误解：乐理本就是描述性、文化性的体系，而论文本身充满未经证实的猜想，并不满足可证伪等科学标准。
HN 关注点：焦点是“音乐理论是否应该/能否成为科学”，以及作者以科学名义批评乐理却缺乏严谨论证的做法。
HN 评论精选
这几条评论里：质疑 5 补充 3
质疑论文既不符合科学标准，覆盖面也远不及传统和声教材
我喜欢从物理/计算角度剖析和声，会细读这篇文章。但包装方式很让人反感：作者似乎对音乐理论和科学都误解得很深。要称为科学，需要有假设、可证伪、并经过实验检验——这些都没有，甚至连可验证的度量都没有。我看到只是用科学术语替代音乐术语来描述音的关系，这不是科学。讽刺的是，引言里那句 Feynman 的话（理论越简约、现象越涌现越令人满意）反而更好地解释了现有乐理。作者指责乐理是伪科学，可乐理从未试图成为科学；而作者自称科学的音乐理论反而不是科学。而且这套“理论”只覆盖了我那本《Harmony and Voice Leading》32 章中的前两章的内容，讲的是什么让音符好听，而不是什么让音乐好听。
dahart查看英文原文
I love the dissection of harmony from a physics/computation point of view; I'm going to read this in more detail. But the wrapping is quite off-putting to me; the author seems to misunderstand both music theory and science, and rather deeply. I don't see a scientific theory here at all. To be called science, it needs to have a hypothesis and be falsifiable, and after that get tested experimentally and proved - I don't see that, nor even a stab at a metric that is verifiable. What I see here is note relations described using science terminology instead of music terminology. That's not science, that's just someone using the terminology they're comfortable with rather than learn the accepted paradigm. "The more factored a theory and the more emergent the observed phenomena from the theory, the more satisfying the theory." - Feynman. It's ironic that this better explains existing music theory than the one presented here, even though Feynman wasn't talking about music theory. The author accuses music theory of being pseudo-science, when music theory is not and never was attempting to be science, and yet the author proposes a theory of music claiming to be science that in fact isn't science. Unfortunately, this 'theory' here only seems to contend with the first two of the 32 chapters in my copy of "Harmony and Voice Leading", and this mainly talks about what makes notes sound good, not what makes music sound good. Also unfortunately, the author doesn't seem to be aware of what's going on in modern music theory, which is exploring things like how to compose music out of the beat frequencies that exist as harmonic dissonances between two or more notes. A lot of the physics of harmonics is currently already being incorporated into music theory.
补充推荐 Dmitri Tymoczko 的几何音乐理论及相关书籍与公开讲义
这个领域最好的工作是普林斯顿教授 Dmitri Tymoczko 做的。他发现了一些相当根本性的结果，用几何学把此前许多和声理论串联起来。他是首位在 Science 上发表论文的音乐理论家，还写了一本很棒的书《A Geometry of Music》（技术性强但可读，是真正想理解音乐为何好听的人的必读）。他在普林斯顿开设的两学期入门音乐课融入了自己的思想，讲义在网上公开，质量之高超过我所知的任何入门教材，尤其适合喜欢听科学解释的极客。
metaxy2查看英文原文
The best work happening in this area is by a Princeton professor named Dmitri Tymoczko [1]. He's discovered some pretty fundamental results that tie together a lot of the previous theories of harmony based on geometry. He was the first music theorist ever published in Science [2] and he wrote an amazing book called A Geometry of Music [3] (technical but readable, a must for anyone trying to really understand why music sounds good). He also teaches a 2-semester intro level music class at Princeton that is infused with his ideas, and makes the lecture notes available online [4]. Those notes are so good they're better than any intro music textbook I know of, especially for us geeks who like to hear the scientific explanation for everything. [1] http://dmitri.mycpanel.princeton.edu/bio.html [2] http://dmitri.tymoczko.com/sciencearticle.html [3] https://www.amazon.com/Geometry-Music-Counterpoint- Extended-Practice/dp/0195336674 [4] http://dmitri.tymoczko.com/teaching.html
质疑作者正确指出乐理缺乏科学性，但自己的核心论证同样全是无根据的猜想
作者抱怨现有乐理不科学，我完全同意——这个领域充斥着技术味十足、广为接受的教科书，里面包含完全未经证实或平凡错误的和声生物学“解释”。但他随后却一头扎进大量无根据的猜想：1. 大脑就是计算机；2. 进化激励更少的计算；3. 找出声音的基频是有价值的；4. 若其他频率和谐，找基频在计算上更容易；5. 这就是和声带来愉悦的原因。这是个不错的理论，但没有任何实质证据支撑。他唯一做对的是避开了常见误解：耳朵并不直接感知声波波形，而是感知耳蜗不同部位的共振，按原始波形的傅里叶变换直接发送神经信号——这是可以（科学地）测量的。
unholiness查看英文原文
The author starts out by complaining that current music theory is not scientific. I completely agree. The field is astoundingly full of technical-seeming, well-accepted textbooks containing a biological "explanation" of harmony that is either totally unproven or trivially false. But then he precedes to dive into a mountain of unsubstantiated conjecture, saying: 1. Our brains are just computers 2. Evolution motivates less computation 3. Finding the fundamental frequency of a sound is worthwhile 4. Doing that is computationally easier if all other frequencies are in harmony 5. That is what has lead to harmony giving us pleasure (The rest is essentially fluff around this core argument) It's a nice theory, but there's nothing to substantively back up any of these points. He comes the closest on point #4, but only by making strong assumptions about the flavor of #1. The whole thrust of his argument is just totally tangential to addressing his initial complaints about the lack of science and rigor within the subject of biological harmony. - One thing he does get right is avoiding most common mistake that textbooks and laymen alike think about hearing: Our ears do not perceive the waveform of sound directly (for the most part[1]). Rather, we perceive sympathy vibrations at different parts our cochlea, rather directly sending nerve signals according to the Fourier transform of the original waveform. This can be measured (scientifically)! This Vi Hart video does a remarkably good job at giving a layman's tour of our some of the phenomena in our ears: https://www.youtube.com/watch?v=i_0DXxNeaQ0 [1] If this were totally true, we wouldn't be able to perceive phase at all! But it is the case that these sympathy vibrations are perceived with much more sensitivity than our perception of phase, and are linked more closely to peoples' idea of harmony.
补充乐理本质是描述性的文化工具，本就不该归科学管
作者说音乐理论不是科学意义上的“理论”，这没错。但作为音乐人/制作人/作曲者，我根本不想要那种东西。研究过多种音乐形式后我知道音乐没有“正确答案”，一个规定性/预测性的音乐“理论”并非我们所求。音乐中的“正确”来自长期的文化集体推理，东西方音乐的发展差异就是明证：东方音乐对和声进行的重视低得多，且常用不同律制甚至“纯律”（西方音乐为支持灵活的和声运动必须放弃纯律）。由此我的论点是：乐理本质上是描述性的，存在许多由历史文化发展驱动的音乐理论。乐理应处于科学的领域之外——涉及人类反应等科学面向的领域是心理声学、信号处理和数学，而乐理关注的是科学之外的审美。
theabacus查看英文原文
The author is correct in saying that music theory is not a "theory" the scientific sense. But as a musician/producer/composer I'd never want that anyway. Having studied many forms of music, I know that there is no "right" and so a proscriptive/predictive "theory" of music is not at all what we want. On the contrary, what is "right" in music comes from a long line of collective cultural reasoning. This is much more evident in the distinctions between the development of eastern and western music, each having their own "theory". Notably, eastern music has a lot lower emphasis on harmonic progression and tends to use different tuning, sometimes "perfect" tuning (something which western music must eschew to support flexible harmonic motion). This leads me to my thesis, that music theory is primarily descriptive in nature and there are many theories of music, driven by historical-cultural development. Music "theory" should lie outside of the domain and concern of science. There are fields which address the human response and other scientific natures of this such as psychoacoustics, electrical engineering and signal processing, and mathematics. Music "theory" has in its view aesthetics which lie outside of the domain of science and is a tool for use in describing things which have been found pleasing aurally and culturally.
质疑乐理是文化实践知识，否定从业者智慧无助于增进理解
乐理书籍从未声称自己是科学。西方音乐是文化建构，乐理书解释的是如何实践这个特定领域。对内行人来说，作者试图“烧掉”的那三句开场陈述完全说得通——音乐家说一段音乐处于某个“和声体系”中，就像我们说棒棒糖是“甜的”一样自然。我不会因为厨师不用分子成分描述味道而批评他们。从不同于音乐家的角度剖析音乐固然有趣，但完全否定本地专家的理解反而阻碍我们了解更多。农民根据某种花初开来决定何时播种，而不是根据地球相对太阳的精确位置，难道就是彻底的失败者吗？如果只读这位作者的乐理，我依然不知道怎么弹钢琴。他浪费大量笔墨，说的不过是 Metis（地方性经验知识）与 Techne（技术知识）的区别。
stfwn查看英文原文
> You can't start a science textbook like that. 'Music theory books' make no claim to be scientific. Western music is a cultural construct and there are books that explain how to practice this particular field. For insiders, the three initial statements the author attempts to burn down make perfect sense. What it means to locate a (part of) a music piece in a 'harmonic system' makes just as much sense to musicians as the rest of us calling a lollypop 'sweet'. I wouldn't criticise cooks for not describing taste by the molecular contents of their ingredients. While it's interesting to dissect music differently from how musicians may analyse it, completely rejecting local experts' understanding of a phenomenon runs counter to finding out more. Is a farmer a complete fail whale for knowing when to plant his crops based on when a certain type of flower first blooms, rather than the precise position of the earth relative to the sun? If I would only read music theory by this author, I would still not have a clue how to play the piano. He/she wastes a lot of words on what could otherwise be described as the difference between Metis and Techne, or local knowledge and technical knowledge. I pasted two long quotes about the distinction between Metis and Techne here: https://pastebin.com/ZYKJDFRN
质疑作者未做功课就全盘否定整个领域，令人失望
其他评论者已经很好地指出了作者论证的具体问题。一个有能力、在某个领域有见识的人，不做任何真正的研究和学习就试图插手另一个领域，总是令人沮丧；而当他们进而把整个领域斥为“迷信”和“不科学”，同时其所作所为却表明他们根本没去了解过去一百年音乐理论或心理声学的任何工作时，就更加令人沮丧。我通常很喜欢 HN 上音乐与计算交叉的文章，但这次实在遗憾。至少它引发了一些不错的讨论吧。
mazelife查看英文原文
Other commenters here have done a good job picking out specific problems with the author's arguments. It's always frustrating when someone who is capable and knowledgeable about one subject decides to try their hand in a different field without having bothered to do any real research or study in it. And it's doubly so when they proceed to then dismiss, literally, the entire field as "superstitions," and "unscientific" even as everything they've written betrays that they haven't bothered to familiarize themselves with basically any of the work that's been done in music theory or psychoacoustics in the last 100 years. I usually love it when articles about the intersection of music and computation show up on HN, but in this case it's really unfortunate. At least it's sparking some good discussion, I guess.
质疑文章对主观审美问题过度客观化，且错误解释乐理概念
我不喜欢这篇文章的语气，它太纠结于“理论”这个词的字面含义，还一边侮辱一边错误地解释许多乐理概念。比如五度圈：文章完全没解释这个圈为什么有用——和弦转调时沿圈旋转，每次只改变一个音，这绝非巧合。文章对主观事物也过于“客观化”：其他文化使用有限或不同的音阶和律制，是因为他们错过了“真正的和声”？大三和弦最好听是因为因子 3 和 5 是“最有趣”的音程？4.3 节我就弃读了：说在钢琴上弹 C 和 F# 听起来很糟，还把喜欢不协和音乐的人比作“把自己虐待到重新校准预期、觉得被鞭打很爽或麦当劳好吃的人”。所以我不喜欢不协和音乐就是自欺欺人？后面引 Ben Franklin 的话也不过是把流行音乐和其他音乐作比较，不会因为是 Franklin 说的就成了定论。
squeaky-clean查看英文原文
I don't like the tone of this book, it gets too hung up on the literal word "theory" in music theory, and also badly explains a lot of concepts in music theory while insulting them. For example, the circle of fifths doesn't explain at all why the circle is cool or useful for chord transitions. It's not a coincidence at all. By rotating around the circle, your key changes by only one note at a time. It's also just waaaay to objective about subjective things. Other cultures use of limited or different musical scales or temperaments is because they are missing out on real harmony? A major triad sounds best because a factor of 3 and 5 are the "most interesting" intervals? Section 4.3 is where I'm just quitting. > "Play C and F# on a piano; it sounds awful" [...] " because someone has even written a piece of music based entirely in the most un-harmonic of intervals, the Augmented Fourth, and gotten away with it." [...] "There are people who can abuse themselves to the point of re-calibrating their expectations to all kinds of strange inputs, including thinking that getting beaten with whips is fun or that McDonald's tastes good. That doesn't mean that those inputs are natural or good or beautiful or true. " So I don't really like dissonant music, I've only tricked myself into thinking it's good? The Ben Franklin quote after it just sounds like someone comparing pop music to anything else. Just because it's Ben Franklin doesn't make it definitive. It starts by insulting the assumptions that the diatonic scale and triads are a given in conventional music theory. But then goes on to make even greater assumptions as to why some harmonies sound "better" than others. Please prove it, or it's just as meaningless as the work you're insulting.
补充西方古典和声只是众多深厚音乐传统之一，文章暴露了文化傲慢
提醒一下：巴赫所编码的西方古典和声只是众多和声体系中的一种。无视那些不含于西方古典音乐的极其深厚的音乐传统，是无意间流露的极度傲慢，因为它们对和声有不同的理解。音乐的一大好处就是让我看清了这种文化近视——它明显隐含在这类自命不凡的分析中，即使内容有趣且正确，作者们显然相信西方音乐才是“真正的音乐”。我们中很多人被训练成这样想，但事实并非如此：西方音乐不比其他音乐优越，也不低劣。我曾是巴赫音乐的忠实爱好者，也一度这样想，但研究了罗姆人、印度古典音乐、美国爵士、蓝草、弗拉门戈、罗马尼亚民间音乐、土耳其音乐等传统后，我发现这些传统同样深厚、同样有近乎疯狂的投入。请丢掉“巴赫的音乐是唯一真正音乐”的想法。同样的文化自恋也发生在语言领域对“正确”用法的争论上，是一回事。
the_cat_kittles查看英文原文
hey guess what, western classical harmony that bach kind of codified, is but one harmonic system. its accidentally super arrogant to ignore the insanely deep musical traditions that are not present in western classical music, since they have different ideas about harmony. one of the great things about music is that it has really opened my eyes to this kind of of cultural myopia. its so obviously implicit in pretentious analyses like these, even if their content is interesting and correct, that the writers believe that western music is the real music. its trained into alot of us that that is the case. well, its not. its not superior, nor inferior. someone is going to read this and think im being an sjw, but i assure you! i once implicitly thought this way too, but i studied other music besides my first love, which was the music of bach, and its true! the musical traditions of roma people, indian classical music, american jazz, bluegrass, flamenco, romanian folk music, turkish music (just whatever is coming to me in this moment) etc etc these things are so deep, and have such rich traditions of insane dedication. so, dispose of this idea that bach's music is the only real music. the same kind of weird cultural narcissism / racism / whatever it is happens in language, with "correct" usage of words. its the same damn thing. and can i just add, for all the overly left brained harmonic analysers out there- it would be nice to see someone address the fact that harmony, even in the restricted western classical sense, i guess "diatonic", depends greatly on timbre and range as well. of course i didnt read this paper, and instead ranted somewhat incoherently about topics which might not even apply to the paper, but hey, i had a good time!
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