This paper presents a methodology for analyzing polyphonic musical passages composed of notes with a harmonically fixed spectral profile, such as piano notes. The approach uses a linear basis transform and non-negative matrix decomposition to estimate the spectral profile and temporal information of each note. This results in a simple, compact system that learns notes by observation rather than relying on prior knowledge. The paper discusses non-negative matrix factorization (NMF) as a method for polyphonic music transcription. NMF is used to decompose a non-negative matrix into two smaller non-negative matrices, W and H, which represent the spectral and temporal information of the notes. The method is based on the concept of redundancy reduction, which has been applied to various perceptual applications, including polyphonic music transcription. The paper demonstrates the effectiveness of NMF on magnitude spectra of real piano recordings. It shows that NMF can accurately transcribe polyphonic music, even when notes overlap. The results indicate that NMF can effectively separate overlapping notes and identify their spectral and temporal characteristics. However, the method requires music passages from instruments with notes that exhibit a static harmonic profile. Future work aims to address this limitation by exploring alternative decomposition methods with greater expressive power. The paper also presents algorithms for NMF, including steepest descent and a multiplicative algorithm. These algorithms are used to optimize the cost function and ensure the non-negativity of the matrices W and H. The results show that NMF can produce accurate transcriptions of polyphonic music with a simple and compact system. The method is data-driven and does not rely on prior knowledge of musical structure.This paper presents a methodology for analyzing polyphonic musical passages composed of notes with a harmonically fixed spectral profile, such as piano notes. The approach uses a linear basis transform and non-negative matrix decomposition to estimate the spectral profile and temporal information of each note. This results in a simple, compact system that learns notes by observation rather than relying on prior knowledge. The paper discusses non-negative matrix factorization (NMF) as a method for polyphonic music transcription. NMF is used to decompose a non-negative matrix into two smaller non-negative matrices, W and H, which represent the spectral and temporal information of the notes. The method is based on the concept of redundancy reduction, which has been applied to various perceptual applications, including polyphonic music transcription. The paper demonstrates the effectiveness of NMF on magnitude spectra of real piano recordings. It shows that NMF can accurately transcribe polyphonic music, even when notes overlap. The results indicate that NMF can effectively separate overlapping notes and identify their spectral and temporal characteristics. However, the method requires music passages from instruments with notes that exhibit a static harmonic profile. Future work aims to address this limitation by exploring alternative decomposition methods with greater expressive power. The paper also presents algorithms for NMF, including steepest descent and a multiplicative algorithm. These algorithms are used to optimize the cost function and ensure the non-negativity of the matrices W and H. The results show that NMF can produce accurate transcriptions of polyphonic music with a simple and compact system. The method is data-driven and does not rely on prior knowledge of musical structure.