## 7 Conclusions  
The search functionality of online sound effect repositories is limited by the quality and quantity of user-supplied metadata. It would therefore be beneficial if metadata could be generated automatically. In terms of timbral metadata, the most-searched term on the freesound.org repository is \"hardness\". Previously, no perceptual model existed that could predict timbral hardness for a wide range of sound sources. The research documented in this paper aimed to develop a model that can do this.  
With a training dataset of 202 stimuli, comprising hardness ratings of 36 source types, the developed model achieved an \(R^{2}\) of 0.76 and [PERSON]'s rho of 0.84. With a new dataset, the model achieved an \(R^{2}\) of 0.57 and [PERSON]'s rho of 0.79; allowing for subjective variance within the dataset produced rho* = 0.98 and tau* = 0.92. Inspection of several outlying stimuli suggested that deficiencies in the audio recordings may have led to over-prediction of hardness, with clicks and excessive sibilance captured by the model of hardness but potentially ignored by the listeners. Without these outliers, the model's performance improved to \(R^{2}\) = 0.69 and rho = 0.83, closer to its performance with the training dataset. With a further dataset, where listeners had directly compared the hardness of multiple sounds generated by a particular source type, the model achieved rho* and tau* of 1.0.  
This model of hardness achieves similar performance to the PEAQ standardised model of audio quality assessment, and exceeds the performance of the average human (in this study's listening panel). It is therefore suitable for use in the generation of hardness metadata and, indeed, has now been incorporated into the freesound.org website for this purpose, with its automatically generated metadata available through the freesound API. For the Audio Commons project, this will facilitate the use of CC-licensed audio by improving the search functionality available to repository users. Future research in this area could focus on (i) developing algorithms to detect recording deficiencies and identifying how these could be included in the model of hardness to improve the results; and/or (ii) developing models of other timbral attributes that may also be beneficial for filtering and sorting search results.  
Conceptualization, A.P., T.B. and R.M.; Data curation, A.P., T.B. and R.M.; Formal analysis, A.P.; Funding acquisition, T.B. and R.M.; Investigation, A.P.; Methodology, A.P., T.B. and R.M.; Project administration, T.B. and R.M.; Software, A.P.; Supervision, T.B. and R.M.; Validation, A.P.; Writing, original draft, A.P.; Writing, review & editing, A.P., T.B. and R.M.  
This research was completed as part of the AudioCommons research project. This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No. 688382.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.  
The following abbreviations are used in this manuscript:  
CC Creative Commons RMS Root Mean Square VIF Variance Inflation Factor RMSE Root Mean Square Error CI Confidence Interval