Tuning logarithmic spectrum analyzers for music analysis

Abstract

Logarithmic filter banks for the real‐time analysis of musical signals permit the examination of the partials of notes in real time for transcription or analysis using low‐cost digital signal processors. However, many recordings (even CDs) are mistuned, sometimes approaching a quarter‐tone. Therefore, a tuning technique has been developed to allow the alteration of the filter center frequency, or all the filter center frequencies. The basis of the technique is to use a filter bank that results in complex outputs (magnitude and phase). The algorithm detects the imaginary part of the product of the filter output and the conjugate of the product of the filter output at the previous sample time and the expected phase shift. This quantity is positive for a sine wave below the filter center frequency and negative above, thus permitting a correction to the center frequency, and it is readily computed. Applications will be presented using a Motorola 56000 DSP and covering 7 octaves at the highest 85 piano frequencies.