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Automatically identifying keys in music recordings is an integral step in many content-based music indexing and retrieval tasks. In Western tonal music, the key creates a system that defines the roles of fundamental music elements such as pitch and chord. Pioneering research work (Pauws, 2004; İzmirli, 2005; Gómez, 2006b) on audio key finding heavily relies on key templates developed via the theoretical and perception-based approaches by Krumhansl (1990) and Temperley (1999). Systems based on geometrical models (Chew, 2000) can also perform real-time key extraction (Chuan & Chew, 2005). Currently, rule-based approaches based on music theory (Weiβ, 2013) remain popular. Data-driven approaches have also been applied to audio key finding. For example, hidden Markov models have been used to determine key (Peeters, 2006) as well as key and chord simultaneously (Burgoyne & Saul, 2005; Chai & Vercoe, 2005; Noland & Sandler, 2007; Papadopoulous & Peeters, 2012). Support vector machines have also been used to determine the key (Mandel & Ellis, 2005; Gómez, 2006a; Schuller & Gollan, 2012).
Although various audio key finding algorithms have been proposed, evaluating their effectiveness is difficult. Because music compositions are complex, it is not straightforward to determine a ground truth (the key considered correct in this case) to be compared with the system-generated answer. For example, it is not unusual for a composition to use more than one key or for musicians to disagree about the key or keys it uses. To ensure that the ground truth is determined objectively, many researchers focus on classical pieces from the common practice period and use the title key as the ground truth (Pauws, 2004; Chuan & Chew, 2005; Peeters, 2006). However, a particular composition may not use the title key throughout the entire piece (Chuan & Chew, 2012). Another way to obtain a ground truth is to ask musicians to manually annotate the key throughout a composition (Chai & Vercoe, 2005; Schuller & Gollan, 2012; Papadopoulous & Peeters, 2012; Weiβ, 2013). However, this process is extremely time-consuming, which limits the size of the research using it, and can be problematic when musicians’ annotations disagree (Chuan & Chew, 2012). To enable large-scale evaluations without sacrificing the accuracy of the ground truth, it would be desirable to have an automated process that identifies pieces with less uncertainty in their ground truths, leaving musicians with fewer pieces in question that would require manual examination.
In this paper, we propose methods to predict key recognition difficulty from audio signals by using statistical learning. Modeling the key recognition difficulty rather than directly detecting the key provides another way to select pieces that need manual annotation. Not only will correctly predicting the difficulty levels quicken the key finding process by filtering out the easy-to-judge tracks, it will also provide important background information about the private data set used to evaluate the algorithm. With this information, the reported accuracy can be compared and interpreted more meaningfully when evaluating systems that use different private data sets.
To predict the key recognition difficulty, we first extracted low-level features from audio recordings using Mel-frequency cepstral coefficients and features related to harmony and timbre. We then applied multiple linear regression and proportional odds model to predict the perceived key recognition difficulty. We conducted experiments using 1083 classical pieces, each manually annotated by three musicians. In addition to examining the prediction accuracy, we also examined the differences between the musicians’ annotations and the consistency of their annotated labels.