1. Localized Key-Finding: Algorithms and Applications Ilya Shmulevich, Olli Yli-Harja Tampere University of Technology Tampere, Finland October 4, 1999

2. Outline Review of key-finding algorithms Median-based filters Graph-based smoothing of class data Application of algorithm to music pattern recognition

3. Key-Finding Algorithm Most stable pitch classes should occur most often. probe tone profile – set of 12 probe tone ratings for a given key 24 profiles (12 major and 12 minor) Input to algorithm is a 12 element vector d with elements of total duration of the 12 tones in the examined music. Correlate vector d with 24 profile vectors and produce 24 element vector of correlations r. The highest correlation is the key. Slide window across sequence of notes and run algorithm. The vector of results is t. d r max t

4. Median-Based Filters A filter window with length k scans through a set of elements and sorts them. The middle value is selected as the filter value. The window moves one element to the right and repeats the steps. Recursive median filters replace some of the input elements with previously selected output elements. Disadvantage: Class data cannot be ordered.

5. Graph-Based Smoothing Relax requirements of metric space to allow for “distance” between elements of class data. “Distance” – Based on similarity between two keys. High similarity corresponds to small distance. Testing was done using this method. The output of the algorithm was almost identical to the results from analysis done by ‘experts’.

6. Application to MPR Used methods discussed to correct pitch error Types of Pitch Error: Objective Perceptual Less stable elements are poorly remembered. To compute perceptual pitch error, must have knowledge of the key. The localized key- finding algorithm may be used to obtain this.