Pythagorean tuning, which derives all musical intervals of a Western chromatic scale from repeated application of a fifth and subsequent reduction (collapse) into a single octave, results in an octave interval slightly larger than 2:1, and the difference between a Pythagorean octave and a 2:1 octave is referred to as the Pythagorean comma. Empirical studies suggest that listeners prefer a stretched octave, that is, an octave interval slightly larger than 2:1. The magnitudes of the Pythagorean comma and of the stretch from a 2:1 ratio in preferred octave tuning are similar, and it is suggested these phenomena might be connected. Implications of such a similarity that are addressed include (a) how the Pythagorean comma predicts preference for a stretched octave, (b) rejection of uncertainties in tuning as a cause of preference for a stretched octave, (c) how the Pythagorean comma and preference for a stretched octave might be related to tension and musical aesthetics, (d) the nature of “scales” and “intervals” in musical and psychophysical senses, (e) the role of motion through auditory pitch space in the Pythagorean comma and preference for a stretched octave, and (f) incorporation of elements of Pythagorean tuning into the representation of the octave.

勾股定律的调音是通过重复应用第五次和随后的减少（折叠）到一个八度来获得西方色阶的所有音乐区间，导致八度区间略大于2：1，而勾股八度与2：1八度音阶称为毕达哥拉斯逗号。实证研究表明，听众更喜欢拉伸的八度音程，即，一个八度音程间隔略大于2：1。在优选的八度音阶调音中，毕达哥拉斯逗号的幅度和从2：1比率开始的拉伸幅度相似，建议将这些现象联系起来。解决的此类相似性含义包括（a）毕达哥拉斯逗号如何预测对扩展八度音阶的偏爱；（b）拒绝不确定性作为对倍频拉伸八度音阶偏爱的原因；（c）毕达哥拉斯逗号和偏好如何因为张开的八度音可能与张力和音乐美学有关，（d）音乐和心理物理意义上的“音阶”和“音程”的性质，（e）勾股引号中听觉音调空间中运动的作用以及对音调的偏爱舒展的八度音阶