Microtonal evaluation of blue notes in the early blues scale by empirical pitch measurement and statistical characterization has not yet been performed in existing research. To address this, fifteen recorded classic blues performances by acknowledged early masters of the blues were studied. Computer based methods were used to collect the audio frequencies of note samples from each performance. Each note had its frequency ratio with respect to the average tonic tone for the performance converted to microtonal cents format. Cluster analysis was performed on these note collections to identify individual note clusters. The fourth and fifth were clearly identified. Three principal "blue note" clusters were isolated with means of 319.1, 582.8, and 1037.9 cents. These values corresponded closely to the harmonic half diminished seventh chord (i.e. 1, ♭3, ♭5, ♭7 with harmonics 5:6:7:9). The "neutral" third was confirmed to occur in this sample. A similar blending of the perfect fourth and tritone was demonstrated in this study. The flat 7th presented as three separate clusters. Several clusters idiosyncratic to individual performers were also identified. Findings are discussed with regards to the array of theories proposed to explain the blues.

中文翻译：

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“蓝调音符”和蓝调音阶的微调分析

现有研究尚未进行通过经验音高测量和统计表征对蓝调音符进行早期布鲁斯音阶的微调评估。为了解决这个问题，研究了由公认的布鲁斯早期大师录制的十五首经典布鲁斯表演。使用基于计算机的方法从每种演奏中收集音符样本的音频频率。每个音符的频率比率相对于平均音调的转换为微音分制。对这些笔记集合进行了聚类分析，以识别各个笔记聚类。清楚地确定了第四和第五。分离出三个主要的“蓝调”簇，均值分别为319.1、582.8和1037.9美分。这些值非常接近于谐波半减的第七和弦（i。e。1，♭3，♭5，♭7，谐波5：6：7：9）。确认该样品中出现“中性”三分之一。在这项研究中，完美的第四色调和三色调完美融合。平面7呈现为三个独立的群集。还确定了个别表演者特有的几个聚类。讨论的结果与为解释忧郁症而提出的一系列理论有关。