On the Mathematics of Music: From Chords to Fourier Analysis

Mathematics is a far reaching discipline and its tools appear in many applications. In this paper we discuss its role in music and signal processing by revisiting the use of mathematics in algorithms that can extract chord information from recorded music. We begin with a light introduction to the theory of music and motivate the use of Fourier analysis in audio processing. We introduce the discrete and continuous Fourier transforms and investigate their use in extracting important information from audio data

Neural networks for musical chords recognition

peer reviewedIn this paper, we consider the challenging problem of music recognition and present an effective machine learning based method using a feed-forward neural network for chord recognition. The method uses the known feature vector for automatic chord recognition called the Pitch Class Profile (PCP). Although the PCP vector only provides attributes corresponding to 12 semi-tone values, we show that it is adequate for chord recognition. Part of our work also relates to the design of a database of chords. Our database is primarily designed for chords typical of Western Europe music. In particular, we have built a large dataset filled with recorded guitar chords under different acquisition conditions (instruments, microphones, etc), but also with samples obtained with other instruments. Our experiments establish a twofold result: (1) the PCP is well suited for describing chords in a machine learning context, and (2) the algorithm is also capable to recognize chords played with other instruments, even unknown from the training phase

Automatic chord transcription from audio using computational models of musical context

PhDThis thesis is concerned with the automatic transcription of chords from audio, with an emphasis on modern popular music. Musical context such as the key and the structural segmentation aid the interpretation of chords in human beings. In this thesis we propose computational models that integrate such musical context into the automatic chord estimation process. We present a novel dynamic Bayesian network (DBN) which integrates models of metric position, key, chord, bass note and two beat-synchronous audio features (bass and treble chroma) into a single high-level musical context model. We simultaneously infer the most probable sequence of metric positions, keys, chords and bass notes via Viterbi inference. Several experiments with real world data show that adding context parameters results in a significant increase in chord recognition accuracy and faithfulness of chord segmentation. The proposed, most complex method transcribes chords with a state-of-the-art accuracy of 73% on the song collection used for the 2009 MIREX Chord Detection tasks. This method is used as a baseline method for two further enhancements. Firstly, we aim to improve chord confusion behaviour by modifying the audio front end processing. We compare the effect of learning chord profiles as Gaussian mixtures to the effect of using chromagrams generated from an approximate pitch transcription method. We show that using chromagrams from approximate transcription results in the most substantial increase in accuracy. The best method achieves 79% accuracy and significantly outperforms the state of the art. Secondly, we propose a method by which chromagram information is shared between repeated structural segments (such as verses) in a song. This can be done fully automatically using a novel structural segmentation algorithm tailored to this task. We show that the technique leads to a significant increase in accuracy and readability. The segmentation algorithm itself also obtains state-of-the-art results. A method that combines both of the above enhancements reaches an accuracy of 81%, a statistically significant improvement over the best result (74%) in the 2009 MIREX Chord Detection tasks.Engineering and Physical Research Council U

Guitar Chords Classification Using Uncertainty Measurements of Frequency Bins

This paper presents a method to perform chord classification from recorded audio. The signal harmonics are obtained by using the Fast Fourier Transform, and timbral information is suppressed by spectral whitening. A multiple fundamental frequency estimation of whitened data is achieved by adding attenuated harmonics by a weighting function. This paper proposes a method that performs feature selection by using a thresholding of the uncertainty of all frequency bins. Those measurements under the threshold are removed from the signal in the frequency domain. This allows a reduction of 95.53% of the signal characteristics, and the other 4.47% of frequency bins are used as enhanced information for the classifier. An Artificial Neural Network was utilized to classify four types of chords: major, minor, major 7th, and minor 7th. Those, played in the twelve musical notes, give a total of 48 different chords. Two reference methods (based on Hidden Markov Models) were compared with the method proposed in this paper by having the same database for the evaluation test. In most of the performed tests, the proposed method achieved a reasonably high performance, with an accuracy of 93%

Harmonic Change Detection from Musical Audio

In this dissertation, we advance an enhanced method for computing Harte et al.’s [31] Harmonic Change Detection Function (HCDF). HCDF aims to detect harmonic transitions in musical audio signals. HCDF is crucial both for the chord recognition in Music Information Retrieval (MIR) and a wide range of creative applications. In light of recent advances in harmonic description and transformation, we depart from the original architecture of Harte et al.’s HCDF, to revisit each one of its component blocks, which are evaluated using an exhaustive grid search aimed to identify optimal parameters across four large style-specific musical datasets. Our results show that the newly proposed methods and parameter optimization improve the detection of harmonic changes, by 5.57% (f-score) with respect to previous methods. Furthermore, while guaranteeing recall values at > 99%, our method improves precision by 6.28%. Aiming to leverage novel strategies for real-time harmonic-content audio processing, the optimized HCDF is made available for Javascript and the MAX and Pure Data multimedia programming environments. Moreover, all the data as well as the Python code used to generate them, are made available.<br /

Computational Tonality Estimation: Signal Processing and Hidden Markov Models

PhDThis thesis investigates computational musical tonality estimation from an audio signal. We present a hidden Markov model (HMM) in which relationships between chords and keys are expressed as probabilities of emitting observable chords from a hidden key sequence. The model is tested first using symbolic chord annotations as observations, and gives excellent global key recognition rates on a set of Beatles songs. The initial model is extended for audio input by using an existing chord recognition algorithm, which allows it to be tested on a much larger database. We show that a simple model of the upper partials in the signal improves percentage scores. We also present a variant of the HMM which has a continuous observation probability density, but show that the discrete version gives better performance. Then follows a detailed analysis of the effects on key estimation and computation time of changing the low level signal processing parameters. We find that much of the high frequency information can be omitted without loss of accuracy, and significant computational savings can be made by applying a threshold to the transform kernels. Results show that there is no single ideal set of parameters for all music, but that tuning the parameters can make a difference to accuracy. We discuss methods of evaluating more complex tonal changes than a single global key, and compare a metric that measures similarity to a ground truth to metrics that are rooted in music retrieval. We show that the two measures give different results, and so recommend that the choice of evaluation metric is determined by the intended application. Finally we draw together our conclusions and use them to suggest areas for continuation of this research, in the areas of tonality model development, feature extraction, evaluation methodology, and applications of computational tonality estimation.Engineering and Physical Sciences Research Council (EPSRC)

PEMBUATAN DATABASE TRANSKRIP AKORD INSTRUMEN TUNGGAL MENGGUNAKAN METODE ENHANCED PITCH CLASS PROFILE (EPCP)

Playing music and recognize the chord being played are the two things are inseparable. However, recognizing the chord is not an easy case. Most beginners often have difficulty in determining the type of chord that consists of several tones. Therefore, people prefer to rely on private tutors to learn music. Based on human nature that likes the practical and easy way to solve the problem. So this final project, will be made a chord detection software automatically, so make easy to the beginner understand. By using EPCP (Enhanced Pitch Class Profile) which consists of 12 classes based on the range frequency of tones which generated from the detection of peaks in the FFT (Fast Fourier Transform) process. That process is able to recognize the type of chord being played, regardless of octave levels. By making the database of this software, it will be capable of storing data that has been processed through the sampling process and then thresholding process to take the dominant peak and will be continue to the frame blocking process, windowing, FFT and EPCP. The input data extension *.wav will be processed in audio files form. The system will detect the major and minor chords. Keywords: Method EPCP(Enhanced Pitch Class Profile), Sampling, FFT (Fast Fourier Transform), Akor

A novel chroma representation of polyphonic music based on multiple pitch tracking techniques

It is common practice to map the frequency content of music onto a chroma representation, but there exist many different schemes for constructing such a representation. In this paper, a new scheme is proposed. It comprises a detection of salient frequencies, a conversion of salient frequencies to notes, a psychophysically motivated weighting of harmonics in support of a note, a restriction of harmonic relations between different notes and a restriction of the deviations from a predefined pitch scale (e.g. the equally tempered western scale). A large-scale experimental evaluation has confirmed that the novel chroma representation more closely matches manual chord labels than the representations generated by six other tested schemes. Therefore, the new chroma representation is expected to improve applications such as song similarity matching and chord detection and labeling