研究人员Daniel Wilkerson在2012年发表的论文《和声解释：音乐科学理论的进展》中，建立了音乐和声的科学理论框架1。该研究从物理现象和计算现象两个角度出发，推导出大调音阶、标准和弦字典以及大小三和弦感受差异等三个音乐基本现象1。
论文对19世纪物理学家赫尔姆霍兹的理论提出了批评1。赫尔姆霍兹认为音符和谐是因为一起演奏时比其他音符"更不差"，但这个理论存在逻辑矛盾——按照该理论，单个音符应该最和谐，和声现象本不应该存在1。该论文于2012年2月20日首次提交，最后修订于2014年6月9日1。
A research paper titled "Harmony Explained: Progress Towards a Scientific Theory of Music" presents a scientific framework for understanding musical harmony by deriving three fundamental musical phenomena from both physical and computational perspectives 1. The study, initially submitted on February 20, 2012, and revised through June 9, 2014, was authored by Daniel Wilkerson 1. The paper derives the major scale, a standard chord dictionary, and explanations for the perceptual differences between major and minor triads 1.
The work critiques nineteenth-century physicist Hermann von Helmholtz's theory of harmony, identifying significant logical flaws in his approach 1. Helmholtz's theory posits that musical notes harmonize because they sound "less bad" when played together compared to other combinations, yet this reasoning creates a paradox: according to this logic, individual notes should be most harmonious, and harmonic phenomena should not exist at all 1.
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