Key-finding Algorithm Research Articles

A Real-Time Key-Finding Algorithm Based on the Signature of Fifths

The signature of fifths is a special kind of music representation technique enabling acquisition of musical knowledge. The technique is based on geometrical relationships existing between twelve polar vectors inscribed in the circle of fifths, which represent individual pitch-classes detected in a given composition. In this paper we introduce a real-time key-detection algorithm which utilizes the concept of the signature of fifths. We explain how to create the signature of fifths and how to derive its descriptors required by the algorithm, i.e., the main directed axis of the signature of fifths, the major/minor mode axis, the characteristic vector of the signature of fifths, the characteristic angle of the signature of fifths, and the angle of the major/minor mode. We performed a series of experiments to test the algorithm’s effectiveness. The results were compared with those obtained using key-detection approaches based on key-profiles. All experiments were conducted using works composed by J.S. Bach, F. Chopin, and D. Shostakovich. The distinctive features of the presented algorithm, with respect to the considered key-detection approaches, are computational simplicity and stability of the decision-making process.

A Key-Finding Algorithm Based on Music Signature

The paper presents the key-finding algorithm based on the music signature concept. The proposed music signature is a set of 2-D vectors which can be treated as a compressed form of representation of a musical content in the 2-D space. Each vector represents different pitch class. Its direction is determined by the position of the corresponding major key in the circle of fifths. The length of each vector reflects the multiplicity (i.e. number of occurrences) of the pitch class in a musical piece or its fragment. The paper presents the theoretical background, examples explaining the essence of the idea and the results of the conducted tests which confirm the effectiveness of the proposed algorithm for finding the key based on the analysis of the music signature. The developed method was compared with the key-finding algorithms using Krumhansl-Kessler, Temperley and Albrecht-Shanahan profiles. The experiments were performed on the set of Bach preludes, Bach fugues and Chopin preludes.

Key-finding by artificial neural networks that learn about key profiles.

We explore the ability of a very simple artificial neural network, a perceptron, to assert the musical key of novel stimuli. First, perceptrons are trained to associate standardized key profiles (taken from 1 of 3 different sources) to different musical keys. After training, we measured perceptron accuracy in asserting musical keys for 296 novel stimuli. Depending upon which key profiles were used during training, perceptrons can perform as well as established key-finding algorithms on this task. Further analyses indicate that perceptrons generate higher activity in a unit representing a selected key and much lower activities in the units representing the competing keys that are not selected than does a traditional algorithm. Finally, we examined the internal structure of trained perceptrons and discovered that they, unlike traditional algorithms, assign very different weights to different components of a key profile. Perceptrons learn that some profile components are more important for specifying musical key than are others. These differential weights could be incorporated into traditional algorithms that do not themselves employ artificial neural networks. (PsycINFO Database Record

Big Data, Big Questions: A Closer Look at the Yale–Classical Archives Corpus (c. 2015)

This paper responds to the article by Christopher White and Ian Quinn, in which these authors introduce the Yale-Classical Archives Corpus (YCAC). I begin by making some general observations about the corpus, especially with regard to ramifications of the keyboard-performance origins of many pieces in the original MIDI collection. I then assess the accuracy of the scale-degree and local-key fields in the database, which were generated by the Bellman-Budge key-finding algorithm. I point out that some of the inaccuracies from the key-finding algorithm's output may influence the results we obtain from statistical studies of this corpus. I also offer an alternative analysis to the authors' finding that the ratio of V7 to V chords increases over time in common-practice music. Specifically, I conjecture that this finding may be the result of (or related to) increasing instrumental resources over time. I close with some recommendations for future versions of the corpus, such as enabling end users to help repair transcription errors as well as offer ground truths for harmonic analyses and key area information.

Harmony Generation Driven by a Perceptually Motivated Tonal Interval Space

We present D'accord, a generative music system for creating harmonically compatible accompaniments of symbolic and musical audio inputs with any number of voices, instrumentation, and complexity. The main novelty of our approach centers on offering multiple ranked solutions between a database of pitch configurations and a given musical input based on tonal pitch relatedness and consonance indicators computed in a perceptually motivated Tonal Interval Space. Furthermore, we detail a method to estimate the key of symbolic and musical audio inputs based on attributes of the space, which underpins the generation of key-related pitch configurations. The system is controlled via an adaptive interface implemented for Ableton Live, MAX, and Pure Data, which facilitates music creation for users regardless of music expertise and simultaneously serves as a performance, entertainment, and learning tool. We perform a threefold evaluation of D'accord, which assesses the level of accuracy of our key-finding algorithm, the user enjoyment of generated harmonic accompaniments, and the usability and learnability of the system.

Sign recognition using key frame selection

This paper deals with static and dynamic hand gesture (digits) recognition. The method provides a threefold novel contribution: (1) segmentation algorithm gives better results on any skin colour and any size of hand on complex and non-uniform background; (2) key frame finding algorithm and (3) the recognition technique of signs (static digits, alphabets and dynamic digits). We separate out key frames from a sequence of static gestures, which include correct gestures from a video sequence. The recognition efficiency of key frame detection is 93% using the proposed algorithm. The segmentation efficiency is almost 95%. Features are extracted using the proposed feature extraction algorithm, and gestures are recognised. We propose a novel algorithm for static and dynamic gesture recognition. The proposed algorithm shows recognition efficiency of 94.8% for static gestures and 94% for dynamic gestures.

The KUSC Classical Music Dataset for Audio Key Finding

In this paper, we present a benchmark dataset based on the KUSC classical music collection and provide baseline key-finding comparison results. Audio key finding is a basic music information retrieval task; it forms an essential component of systems for music segmentation, similarity assessment, and mood detection. Due to copyright restrictions and a labor-intensive annotation process, audio key finding algorithms have only been evaluated using small proprietary datasets to date. To create a common base for systematic comparisons, we have constructed a dataset comprising of more than 3,000 excerpts of classical music. The excerpts are made publicly accessible via commonly used acoustic features such as pitch-based spectrograms and chromagrams. We introduce a hybrid annotation scheme that combines the use of title keys with expert validation and correction of only the challenging cases. The expert musicians also provide ratings of key recognition difficulty. Other meta-data include instrumentation. As demonstration of use of the dataset, and to provide initial benchmark comparisons for evaluating new algorithms, we conduct a series of experiments reporting key determination accuracy of four state-of-the-art algorithms. We further show the importance of considering factors such as estimated tuning frequency, key strength or confidence value, and key recognition difficulty in key finding. In the future, we plan to expand the dataset to include meta-data for other music information retrieval tasks.

Predicting Key Recognition Difficulty in Music Using Statistical Learning Techniques

In this paper, the authors use statistical models to predict the difficulty of recognizing musical keys from polyphonic audio signals. The key recognition difficulty provides important background information when comparing the performance of audio key finding algorithms that often evaluated using different private data sets. Given an audio recording, represented as extracted acoustic features, the authors applied multiple linear regression and proportional odds model to predict the difficulty level of the recording, annotated by three musicians as an integer on a 5-point Likert scale. The authors evaluated the predictions by using root mean square error, Pearson correlation coefficient, exact accuracy, and adjacent accuracy. The authors also discussed issues such as differences found between the musicians' annotations and the consistency of those annotations. To identify potential causes to the perceived difficulty for the individual musicians, the authors applied decision tree-based filtering with bagging. By using weighted naïve Bayes, the authors examined the effectiveness of each identified feature via a classification task.

Changing Styles, Changing Corpora, Changing Tonal Models

This article explores the historical development of common-practice musical style and how that development might connect to the cognition of key within the history of Western European tonality. First, musical corpora of 19 composers were divided into three-chord progressions, and these progressions were tallied. The chord tallies were used for a cluster analysis and for measurements of inter-corpus cross entropy. The cluster analysis divided the corpora in ways that conform to historical and stylistic intuitions, and inter-corpus cross entropy was found to correlate with the years separating the corpora. These findings show that the chronological distance between two musical corpora seems to predict compositional similarity and that chord-progression norms are connected to specific historical situations. In order to model how these changes might affect the cognition of musical key, a corpus-sensitive key-finding algorithm was used to decode key within a famous example of musical ambiguity, the opening of Beethoven’s “Eroica” symphony. Each corpus-trained model created a slightly different key interpretation, suggesting that historically situated models of tonal cognition might indeed interpret the same stimulus differently.

Distribuciones tonales en la música del renacimiento, un análisis comparativo

In this study we use the tone counting technique, the tonal hierarchies and the key-finding algorithm in order to quantitatively assess the similarity between the musical language of the Renaissance and the posterior tonal language. The results show that there is a huge correspondence between tonal distributions in both languages, and between these and the tonal hierarchies found by Krumhansl and Kessler (1982). This suggests that the differences are fewer than usually believed, and that in the Renaissance there is a tonal hierarchy similar to that of tonal system. Moreover, some problematic cases show that modal language favors tonal ambiguity. Finally, empirical evidence is provided to the notion that, in the Renaissance, the system tends progressively in time, to two poles: tonal major and minor.

A Novel System for Music Learning using Low Complexity Algorithms

This paper introduces a music learning system that uses new low complexity algorithms and aims to solve the four most common problems faced by self-learning beginner pianists: reading music sheets, playing fast tempo music pieces, verifying the key of a music piece, and finally evaluating their own performances. In order to achieve these aims, the system proposes a monophonic automatic music transcription system capable of detecting notes in the range from G2 to G6. It uses an autocorrelation algorithm along with a binary search based algorithm in order to map the detected frequencies of the individual notes of a musical piece to the nearest musical frequencies. To enable playing fast music, the system uses a MIDI player equipped with a virtual piano as well as section looping and speed manipulation functionalities to enable the user to start learning a musical piece slowly and build up speed. Furthermore, it applies the Krumhansl-Schmuckler key-finding algorithm along with the correlation algorithm to identify the key of a musical piece. A musical performance evaluation algorithm is also introduced which compares the original performance with that of the learner’s producing a quantitative similarity measure between the two. The experimental evaluation shows that the system is capable of detecting notes in the range from G2 to G6 with an accuracy of 88.7% in addition to identifying the key of a musical piece with an accuracy of 97.1%.

The Use of Large Corpora to Train a New Type of Key-Finding Algorithm

Computational models of key estimation have struggled to emulate the accuracy levels of human listeners, especially with pieces in the minor mode. The current study proposes a new key-finding algorithm, which utilizes Euclidean distance, rather than correlation, and is trained on the statistical properties of a large musical sample. A model was trained on a dataset of 490 pieces encoded into the Humdrum “kern” format, in which the key was known. This model was tested on a reserve dataset of 492 pieces, and was found to have a significantly higher overall accuracy than previous models. In addition, we determined separate accuracy ratings for major mode and minor mode works for the existing key-finding models and report that most existing models provide greater accuracy for major mode rather than minor mode works. The proposed key-finding algorithm performs more accurately on minor mode works than all of the other models tested, although it does not perform significantly better than the models created by Aarden (2003), Bellman (2005), or Sapp (2011). Finally, an algorithm that combines the Aarden-Essen model (2003) and the proposed algorithm is suggested, and results in significantly more accurate key assessments than all of the other extant models.

Perceptual Tests of an Algorithm for Musical Key-Finding.

Perceiving the tonality of a musical passage is a fundamental aspect of the experience of hearing music. Models for determining tonality have thus occupied a central place in music cognition research. Three experiments investigated 1 well-known model of tonal determination: the Krumhansl-Schmuckler key-finding algorithm. In Experiment 1, listeners' percepts of tonality following short musical fragments derived from preludes by Bach and Chopin were compared with predictions of tonality produced by the algorithm; these predictions were very accurate for the Bach preludes but considerably less so for the Chopin preludes. Experiment 2 explored a subset of the Chopin preludes, finding that the algorithm could predict tonal percepts on a measure-by-measure basis. In Experiment 3, the algorithm predicted listeners' percepts of tonal movement throughout a complete Chopin prelude. These studies support the viability of the Krumhansl-Schmuckler key-finding algorithm as well as a model of listeners' tonal perceptions of musical passages.

Correction of Misclassifications Using a Proximity-Based Estimation Method

An estimation method for correcting misclassifications in signal and image processing is presented. The method is based on the use of context-based (temporal or spatial) information in a sliding-window fashion. The classes can be purely nominal, that is, an ordering of the classes is not required. The method employs nonlinear operations based on class proximities defined by a proximity matrix. Two case studies are presented. In the first, the proposed method is applied to one-dimensional signals for processing data that are obtained by a musical key-finding algorithm. In the second, the estimation method is applied to two-dimensional signals for correction of misclassifications in images. In the first case study, the proximity matrix employed by the estimation method follows directly from music perception studies, whereas in the second case study, the optimal proximity matrix is obtained with genetic algorithms as the learning rule in a training-based optimization framework. Simulation results are presented in both case studies and the degree of improvement in classification accuracy that is obtained by the proposed method is assessed statistically using Kappa analysis.

Localized Key Finding: Algorithms and Applications

We consider the problem of determining a localized tonal context in a musical composition. Our method is based in part on a key-finding algorithm developed by Krumhansl and Schmuckler (Krumhansl, 1990) and is applied in a sliding-window fashion, producing a sequence of key assignments. These assignments constitute so-called class data in that they possess no natural numerical properties and can be considered as arising from a classification process. A new approach for smoothing such class data using graph theoretic norm estimates is applied to the sequence of key assignments. The effectiveness of the proposed method is evaluated by comparing it with judgments made by experts. Then, the problem is placed in the context of machine recognition of music patterns. We discuss a music pattern recognition system proposed by Coyle and Shmulevich (1998) that relies on robust determination of localized tonal context. This, in turn, allows the system to incorporate perceptual error criteria.

Development of Tonality Induction: Plasticity, Exposure, and Training

Tonality induction is the natural outcome of acoustic redundancies in music and the predisposition of the brain to represent these redundancies. In the simplest case, tonality induction relies on frequency resolution and a memory accumulator. A review of the literature suggests that these and other more sophisticated building blocks (analysis of complex tones and sensitivity to sequential characteristics of musical patterns) are in place to contribute to tonality induction in the first year of life. As further revealed by life-span studies of preference and recognition for stylistically different popular music excerpts, two other constraints must also be considered: (1) brain plasticity and (2) degree of exposure to music of particular styles. The importance of a final factor, (3) formal music performance training, is shown in studies of (a) the benefits of the major triad frequency ratio relations (4: 5: 6) on memory (absolute judgment) for tones in an unfamiliar context (b) the applicability of a model based on a key-finding algorithm to pitch memory in a tonal context, and (c) the probe-tone task.

What's Key for Key? The Krumhansl-Schmuckler Key-Finding Algorithm Reconsidered

This study examines the Krumhansl-Schmuckler key-finding model, in which the distribution of pitch classes in a piece is compared with an ideal distribution or "key profile" for each key. Several changes are proposed. First, the formula used for the matching process is somewhat simplified. Second, alternative values are proposed for the key profiles themselves. Third, rather than summing the durations of all events of each pitch class, the revised model divides the piece into short segments and labels each pitch class as present or absent in each segment. Fourth, a mechanism for modulation is proposed; a penalty is imposed for changing key from one segment to the next. An implementation of this model was subjected to two tests. First, the model was tested on the fugue subjects from Bach's Well-Tempered Clavier; the model's performance on this corpus is compared with the performances of other models. Second, the model was tested on a corpus of excerpts from the Kostka and Payne harmony textbook (as analyzed by Kostka). Several problems with the modified algorithm are discussed, concerning the rate of modulation, the role of harmony in key finding, and the role of pitch "spellings." The model is also compared with Huron and Parncutt's exponential decay model. The tests presented here suggest that the key-profile model, with the modifications proposed, can provide a highly successful approach to key finding.

Using the Krumhansl and Schmuckler Key-Finding Algorithm to Quantify the Effects of Tonality in the Interpolated-Tone Pitch-Comparison Task

We examined two models that quantified the effects of tonality on accuracy and reaction time in an intervening-tone pitch-comparison task. In each of 16 task conditions (standard tone-interpolated sequence-test tone, abbreviated as S-seq-T), the S and T tones, C₄ and/or C#₄, were separated by a three-tone sequence that was a random arrangement of one of the four triads, ${\rm{C}}_{{\rm{4Major}}} ,{\rm{C}}_{{\rm{4Minor}}} ,{\rm{C\# }}_{\rm{4}} _{{\rm{Major}}} $ or ${\rm{C\# }}_{{\rm{4Minor}}} $ . Both models were based on the tonal hierarchy (Krumhansl, 1990a; Krumhansl & Shepard, 1979) and the key-finding algorithm (Krumhansl & Schmuckler, cited in Krumhansl, 1990a); the key- finding algorithm was used to determine the best-fitting key for the first four notes of the condition (i.e., the S-seq combination). Model 1 (S-Tone Stability) determined the stability of the S tone given that key. Model 2 (T-Tone Expectancy) determined the expectancy for the T tone given that key. Over the 16 conditions, for three groups of 12 subjects, differing by level of training, mean proportion correct discrimination ranged from .53 to .95 and increased significantly across levels of musical experience. For the musically trained subjects, both models predicted performance well but neither model was dramatically more effective than the other; the combination of both models did produce an increase in predictability. For untrained subjects, tonality, as assessed by the key-finding algorithm in either model, was not significantly correlated with performance.

Maximum key-profile correlation (MKC) as a measure of tonal structure in music.

Tonal structure is musical organization on the basis of pitch, in which pitches vary in importance and rate of occurrence according to their relationship to a tonal center. Experiment 1 evaluated the maximum key-profile correlation (MKC), a product of Krumhansl and Schmuckler's key-finding algorithm (Krumhansl, 1990), as a measure of tonal structure. The MKC is the maximum correlation coefficient between the pitch class distribution in a musical sample and key profiles, which indicate the stability of pitches with respect to particular tonal centers. The MKC values of melodies correlated strongly with listeners' ratings of tonal structure. To measure the influence of the temporal order of pitches on perceived tonal structure, three measures (fifth span, semitone span, and pitch contour) taken from previous studies of melody perception were also correlated with tonal structure ratings. None of the temporal measures correlated as strongly or as consistently with tonal structure ratings as did the MKC, and nor did combining them with the MKC improve prediction of tonal structure ratings. In Experiment 2, the MKC did not correlate with recognition memory of melodies. However, melodies with very low MKC values were recognized less accurately than melodies with very high MKC values. Although it does not incorporate temporal, rhythmic, or harmonic factors that may influence perceived tonal structure, the MKC can be interpreted as a measure of tonal structure, at least for brief melodies.