To make post-tonal harmony more accessible, many music scholars derive various theories, which rely on the traditional notions of consonance and dissonance, to describe the quality of a chord. Most of these theories use the quality of an interval as the criterion to measure the proportion between the consonances and dissonances within a chord. All intervals can be categorized as either consonances or dissonances except for one—the tritone. Although traditionally in tonal music, the tritone was perceived as a dissonance; its quality in twentieth-century music, however, has been challenged by many scholars. It may sound like a dissonant (Paul Hindemith), a consonant (Joseph Straus), or a neutral interval (Charles Seeger). If different viewpoints abound in the tritone’s quality, do we hear it as adding the consonant or dissonant sound to a chord? Confronted with this issue, this article suggests an alternative way of perceiving all intervals—their space—and further proposes a method that assists us in hearing a chord in terms of its degree of compactness. Based on this method, we can experience the dynamics created by the confrontation between spatial and compact chords, and find post-tonal harmony more accessible.

中文翻译：

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当质量达到极限时：理解音调后和声的新解释方法

为了使音调和声更容易获得，许多音乐学者派生了各种理论，这些理论依靠和声与不和弦的传统概念来描述和弦的质量。这些理论中的大多数都使用间隔的质量作为衡量和弦中和声与不和声之间比例的标准。除一个音调外，所有音程都可以分为谐音或不谐音。尽管传统上在音调音乐中，三音被认为是一种不和谐。然而，它在20世纪音乐中的质量却受到许多学者的挑战。听起来像是不和谐（Paul Hindemith），辅音（Joseph Straus）或中立音调（Charles Seeger）。如果在三音的质量上有很多不同的观点，我们听到它是在和弦中添加辅音还是不谐音？面对这个问题，本文提出了一种感知所有间隔的另一种方法，即它们的空间，并进一步提出了一种方法，可以帮助我们从和弦的紧迫度方面来聆听和弦。基于这种方法，我们可以体验到空间和紧缩和弦之间的对抗所产生的动力，并发现调和后的和声更容易获得。