In this work we have compared two indexing algorithms that have been used to index and retrieve Carnatic music songs. We have compared a modified algorithm of the Dual ternary indexing algorithm for music indexing and retrieval with the multi-key hashing indexing algorithm proposed by us. The modification in the dual ternary algorithm was essential to handle variable length query phrase and to accommodate features specific to Carnatic music. The dual ternary indexing algorithm is adapted for Carnatic music by segmenting using the segmentation technique for Carnatic music. The dual ternary algorithm is compared with the multi-key hashing algorithm designed by us for indexing and retrieval in which features like MFCC, spectral flux, melody string and spectral centroid are used as features for indexing data into a hash table. The way in which collision resolution was handled by this hash table is different than the normal hash table approaches. It was observed that multi-key hashing based retrieval had a lesser time complexity than dual-ternary based indexing The algorithms were also compared for their precision and recall in which multi-key hashing had a better recall than modified dual ternary indexing for the sample data considered.