我强烈建议对这个话题感兴趣的人读读赫姆霍兹（Helmholtz）的《论音的感觉》（On the sensations of tone），这是一部迷人的 19 世纪杰作，试图从物理原理去理解音乐感知，从第一性原理推导出标准的西方音程以及协和/不协和音……
I urge anyone interested in this topic to read Helmholtz's "On the sensations of tone", a fascinating 19th-century tour-de-force trying to understand music sensation as coming from physical principles, deriving the standard western intervals and consonance/dissonance from first principles…
On the Sensations of Tone by Hermann von Helmholtz The Road by Jack London all of the Oz books by L. Frank Baum The Scottish Students' Song Book Heart Songs The Age of Reason The Art of Money Getting by Barnum
Next to this interesting article and comments, I think mention should be made of von Helmholtz's XIX century book "On the sensations of tone". He is considered to be the father of acoustics, and derived the consonance/dissonance of the notes in the diatonic scale from first physical principles. He extracted and computed what is described as…
…random or arbitrary, it has some nice dual mathematical and musical properties: intervals between the notes in the scale have special frequency ratios that sound pleasing to the ear (read Helmholtz's "On the sensations of tone" for a fascinating physically-based take on why it is like that -- he is known as "the father of acoustics", and that book contains the distillation of 8 years of deep, smart research way before we had…
我强烈建议对这个话题感兴趣的人读读赫姆霍兹（Helmholtz）的《论音的感觉》（On the sensations of tone），这是一部迷人的 19 世纪杰作，试图从物理原理去理解音乐感知，从第一性原理推导出标准的西方音程以及协和/不协和音……
I urge anyone interested in this topic to read Helmholtz's "On the sensations of tone", a fascinating 19th-century tour-de-force trying to understand music sensation as coming from physical principles, deriving the standard western intervals and consonance/dissonance from first principles…
赫尔曼·冯·亥姆霍兹的《论音的感觉》、杰克·伦敦的《大路》、L. 弗兰克·鲍姆的所有《奥兹国》系列、苏格兰学生歌集、心灵之歌、理智时代、巴纳姆的《致富的艺术》
On the Sensations of Tone by Hermann von Helmholtz The Road by Jack London all of the Oz books by L. Frank Baum The Scottish Students' Song Book Heart Songs The Age of Reason The Art of Money Getting by Barnum
在这篇有趣的文章和评论之余，我认为应该提一下冯·亥姆霍兹 19 世纪的书《论音的感觉》。他被认为是声学之父，从物理第一性原理推导出了自然音阶中音符的协和与不协和。他提取并计算出了被描述为……的东西
Next to this interesting article and comments, I think mention should be made of von Helmholtz's XIX century book "On the sensations of tone". He is considered to be the father of acoustics, and derived the consonance/dissonance of the notes in the diatonic scale from first physical principles. He extracted and computed what is described as…
……并非随意的或偶然的，它有一些很好的数学和音乐双重属性：音阶中音符之间的音程具有特殊的频率比，听起来很悦耳（想了解这种基于物理特性的迷人解读，可以读读赫姆霍兹的《论音的感觉》——他被誉为“声学之父”，那本书凝聚了在我们拥有……之前，他长达 8 年深刻而聪慧的研究精华）
…random or arbitrary, it has some nice dual mathematical and musical properties: intervals between the notes in the scale have special frequency ratios that sound pleasing to the ear (read Helmholtz's "On the sensations of tone" for a fascinating physically-based take on why it is like that -- he is known as "the father of acoustics", and that book contains the distillation of 8 years of deep, smart research way before we had…