Indexing audio signals directly in the transform domain can potentially save a significant amount of computation when working on a large database of signals stored in a lossy compression format, without having to fully decode the signals. Here, we show that the representations used in standard transform-based audio codecs (e.g. MDCT for AAC, or hybrid PQF/MDCT for MP3) have a sufficient time resolution for some rhythmic features, but a poor frequency resolution, which prevents their use in tonality-related applications. Alternatively, a recently developed audio codec based on a sparse multi-scale MDCT transform has a good resolution both for time-and frequency-domain features. We show that this new audio codec allows efficient transform-domain audio indexing for 3 different applications, namely beat tracking, chord recognition and musical genre classification. We compare results obtained with this new audio codec and the two standard MP3 and AAC codecs, in terms of performance and computation time.