# Psychoacoustic Approaches for Harmonic Music Mixing +
## 4 Evaluation
### Results  
#### 4.2.1 Statistical Analysis  
To examine the data collected in the listening experiment, we separately analyzed the consonance and pleasantness ratings using the non-parametric Friedman test where we treated participants and mixes as random effects. For both the consonance and pleasantness ratings, the main effect of the conditions was highly significant (consonance: chi-square = 181.60, \(p\) < 0.00001; pleasantness: chi-square = 240.73, \(p\) < 0.00001). With regard to the interaction across conditions, we performed a _post hoc_ analysis via a multiple comparison of means with Bonferroni correction for which the mean rankings and 95% confidence intervals are shown in Figure 11a,b for consonance and pleasantness ratings, respectively. There is a very large separation between Conditions **B**, **D** and **E**, _i.e._, those conditions that attempt to find a good harmonic alignment, and Conditions **A** and **C**, which do not. No significant difference was found between Conditions **A** and **C** (consonance: \(p\) > 0.45; pleasantness: \(p\) > 0.07) and likewise for conditions **B** and **E** (consonance: \(p\) > 0.90; pleasantness: \(p\) = 1.00). For consonance, the difference between Conditions **D** and **B** is not significant, \(p\) > 0.08; however it is significant for pleasantness \(p\) < 0.05. Inspection of Figure 11 reveals similar patterns regarding consonance and pleasantness ratings, which are generally consistent with our hypotheses stated in Section 4.1. Ratings for Condition **C** (max roughness) are significantly smaller (worse) than for all other conditions, except Condition **A** (no shift). Pitch shifts in Condition **D** (min roughness) are rated significantly highest (best) in terms of pleasantness ratings. While there is a large separation between the ratings for Conditions **D** and **E**, _i.e._, our two proposed methods for consonance, such a result should be examined within the context of the experimental design and additional inspection of Table 1. Here, we find that close to 43% of the 900 combinations resulted in an identical choice of pitch shift, implying that both methods often converged on the same result and to a far greater degree than any of the other condition pairs. Since there is no significant difference between the ratings of Conditions **E** and **B** and because  
Figure 11: Summary of multiple comparisons of mean rankings (with Bonferroni correction) between conditions for (**a**) consonance and (**b**) pleasantness ratings. Both mixes and participants are treated as random effects. Error bars (95% confidence intervals) without overlap indicate statistically-significant differences in the mean rankings. these were rated towards the higher end of the (zero to five) scale, we could consider any of three methods to be a valid means of harmonically mixing music signals, nevertheless with Condition **D** the preferred choice. Looking again at the key-based approach (Condition **B**), it is useful to consider the impact of any misestimation of the key made by [PERSON]. To this end, we asked a musical expert to annotate the ground truth keys for each of the 20 excerpts used to make the listening test. These annotated keys are shown in Table 2. Despite the apparent simplicity of this type of music from a harmonic perspective, our music expert was unable to precisely label the key in six out of the 20 cases. This was due to the short duration of the excerpts and an insufficient number of different notes to unambiguously choose between a major or minor key. In these cases, the most predominant pitch class was annotated instead. Traktor, on the other hand, always selects a major or minor key (irrespective of the tonality of the music), and in fact, it only agreed with our expert in six of the cases. In addition, we used Traktor to extract the key for the full-length recordings, and in these cases, the key matched between the excerpt and full-length recording only eight out of 20 times.