Pitch Class Research Articles

Music Similarity Ranking: Case Study Fairphonic

Fairphonic Pte Ltd is a technology company operating in the music sector. Fairphonic provides services to detect content on social media that is suspected of copyright infringement. Fairphonic utilizes audio features for the detection process. The current algorithm used by Fairphonic requires pairwise comparison, and the content to be compared is collected through a scraping process immediately after the process is run. Fairphonic has hundreds of thousands of music data in their database. Fairphonic desires a more scalable algorithm to compare an input music piece with the entire Fairphonic music catalog. This research uses features such as Harmonic Pitch Class Profile (HPCP), Chroma, and Rhythm Pattern. The study compares previously researched algorithms, namely binary similarity matrix, Euclidean distance, and similarity matrix profile. The results show that the combination of HPCP with the binary similarity matrix yields the highest Mean Average Precision of 0.989. Speed testing by performing comparisons 10 times shows that the combination of Chroma and the similarity matrix profile is 72% faster compared to the combination of HPCP with the binary similarity matrix. The author recommends the Chroma and similarity matrix profile algorithm for music similarity ranking due to its faster process.

Computational modeling of interval distributions in tonal space reveals paradigmatic stylistic changes in Western music history

Diachronic stylistic changes in music are to a large extent affected by composers’ different choices, for example regarding the usage of tones, intervals, and harmonies. Analyzing the tonal content of pieces of music and observing them over time is thus informative about large-scale historical changes. In this study, we employ a computational model that formalizes music-theoretic conceptualizations of tonal space, and use it to infer the most likely interval distributions for pieces in a large corpus of music, represented as so-called ‘bags of tonal pitch classes’. Our results show that tonal interval relations become increasingly complex, that the interval of the perfect fifth dominates compositions for centuries, and that one can observe a stark increase in the usage of major and minor thirds during the 19th century, which coincides with the emergence of extended tonality. In complementing prior research on the historical evolution of tonality, our study thus demonstrates how example-based music theory can be informed by quantitative analyses of large corpora and computational models.

Phasic Dissonance, Timbral Contrast: Analysing 20th‐Century Guitar Harmonies with Discrete Fourier Transform

ABSTRACTOne of the six‐string classical guitar's most distinctive features is its unbalanced timbre. That is to say, only four pitches of the chromatic aggregate are overtonally supported by the resonances of the guitar's three bass strings. A common pitch‐ and structure‐generating strategy, exploited by twentieth‐century composers who wrote for the guitar, is bound up with this affordance. Local and global harmonic contrasts are often built around an antagonism between open‐string sets and fretted harmonies that largely avoid duplicating notes associated with the open strings. Open‐string/fretted binaries derive their sonic antagonism not just from timbral distinction, however, but from the fact that their pitch materials often lie at diametrically opposed positions on the circle of fifths. In many instances, this colouristic conflict replaces harmonic‐functional tension as a structure‐generating agent; the latter is reduced to a surface‐level topic. Representative works by Frank Martin and Leo Brouwer are taken as exemplifications of this trend.In demonstrating the subtle interactions between instrumental affordance and abstract pitch relationships and hierarchies, an invaluable theoretical approach developed by Ian Quinn and finessed by Jason Yust entails the study of harmonic quality through the discrete Fourier transform. This mathematical formula has been processed into an easy‐to‐use but powerful web application by Jennifer Harding – the Pitch Class DFT Vector Calculator – making its explanatory power available to music analysts without mathematical expertise. Part of the raison d’être of this article is to show how this application might be used and, more important, how the information that it yields might be interpreted.

Chord Recognition in Music Using a Robust Pitch Class Profile (PCP) Feature and Support Vector Machines (SVM)

Chord Recognition in Music Using a Robust Pitch Class Profile (PCP) Feature and Support Vector Machines (SVM)

The Tonnetz at First Sight: Cognitive Issues of Human–Computer Interaction with Pitch Spaces

Pitch spaces allow pitch relations to be expressed through geometrical representations for many different purposes. The Tonnetz is a well-known pitch space in the field of music theory; equivalent representations have been described in the field of cognitive science, especially Krumhansl's model of perceived triadic distance. Despite her empirical approach, we know very little about the way people interact, cognitively speaking, with Tonnetz-based computational platforms involving multimodal stimuli. Our study has approached this issue by means of empirical experimentation for the first time. A total of 88 participants, with varying backgrounds in music and mathematics, were asked to interact with a Tonnetz interface; they did not have prior knowledge of this pitch space. Results of our experiment confirmed our main hypotheses. On the one hand, strong skills in music theory are needed to partially grasp the overall structure of the Tonnetz at first sight; this aspect is mainly related to the quality recognition of triads and the detection of shared pitch classes in harmonic motions. On the other hand, the particular geometry of the Tonnetz may bias this understanding when non-functional harmonic sequences are displayed on it.

PMFCC Features for Music Classification Using the Modified KNN Algorithm

From ancient period Music is a integral part of human life. People prefered to listen Music while relaxing. All over the world nowadays music is used as supporting medication for healing mental illness and many other diseases. The origin of Indian Music is Indian Classical Raga, having a melodious combination of Rhythm and notes. There are various users like music-composers, e-learners, music therapists are frequently retrieving Indian classical Raga based music. The vast retrieval of Raga based music made it necessary to classify Indian music on Raga. This paper proposes an a new algorithm to classify an Indian Music using Raga information which further will be useful for song recommendation, personalizing collection, and musicologists for various purpose.
 In this paper, the combined Pitch and MFCC based PMFCC features are extracted and processed by Modified K Nearest Neighbor algorithm. The performance of PMFCC and Pitch Class Distribution features is compared using traditional machine learning classification algorithms and Modified Variant K Nearest Neighbor (MVKNN). The PMFCC features outperformed with the Modified KNN algorithm. The accuracy of PMFCC features with Modified KNN algorithm is found 96.11% for our Our dataset and 93.65% for Compmusic standard dataset.

Zhao Xiaosheng’s Tai Chi:


 The implementation of China Reform and Opening-up policy in 1978 gave birth to the Chinese new wave music, with an idiosyncratic manner of rebelliousness, individuality and innovation that brought a break-through in Chinese new music of the past. In this paper, we focused on a representative piano solo work Tai Chi (1987) by composer Zhao Xiaosheng who explored the ancient Chinese philosophy I Ching and the Tang Dynasty musical form Tang Daqu using Allen Forte’s pitch class set theory. We analyzed how Zhao employed the Western sonata and Chinese Tang Daqu to reflect the yin-yang dualism, based on the composer’s statement in the interview, researchers’ analyses, and authors’ suggestion. By decoding the pitch-class permutations that correspond to the 64 hexagrams of I Ching, the mathematical logic becomes the main way to combine the I Ching with serial music. Nevertheless, the compatibility between musical expression and commentaries of hexagrams is not reflected in the piano solo Tai Chi. Therefore, we discussed the entanglement of a compositional identity formation based on contradicting elements from that of the traditional Chinese musical culture and Western art music, with questions about the accretion and authenticity in the contemporaneity and musicalization of the ancient I Ching. 

Lutosławski's Mid-Century Harmony

Abstract This article proposes to expand our understanding of Witold Lutosławski's chordal space and its relation to formal processes. It argues that the traditional analytical focus on harmonic colors of isolated chords comes at the expense of understanding how chordal interactions shape form. How do individual chords participate in cogent, expressive, and sensuous long-range harmonic processes? The article explores how the arrangement of intervals in twelve-tone chords (especially the ordering, restriction, and modularity of intervals) not only imprint distinct coloristic qualities to single chordal entities but are also implicated in strategies of harmonic progression, relatedness, complementarity, and contrast. These analytical goals prompt a reconceptualization of chordal elements, which are understood as combinations of pitch class and modal quality rather than simply as pitches in register. The analytical focus is on Lutosławski's harmony of the mid- to late fifties, attending in particular to the Five Iłłakowicz Songs, the composer's inaugural effort in the use of vertical aggregates. Lutosławski's chordal space in these pieces is interpreted through a series of cyclic graphs and transpositional networks, prompting a novel understanding between twelve-tone chordal harmony and form. The study proposes to contribute to the analytical reappraisal of a set of pieces that anchor an influential harmonic practice in twentieth- and twenty-first-century music.

Statistical Learning of Chord-Transition Regularities in a Novel Equitempered Scale: An MMN Study

In music and language domains, it has been suggested that patterned transitions of sounds can be acquired implicitly through statistical learning. Previous studies have investigated the statistical learning of auditory regularities by recording early neural responses to a sequence of tones presented at high or low transition probabilities. However, it remains unclear whether the statistical learning of musical chord transitions is reflected in endogenous, regularity-dependent components of the event-related potential (ERP). The present study aimed to record the mismatch negativity (MMN) elicited by chord transitions that deviated from newly learned transitional regularities. Chords were generated in a novel 18 equal temperament pitch class scale to avoid interference from the existing tonal representations of the 12 equal temperament pitch class system. Thirty-six adults without professional musical training listened to a sequence of randomly inverted chords in which certain chords were presented with high (standard) or low (deviant) transition probabilities. An irrelevant timbre change detection task was assigned to make them attend to the sequence during the ERP recording. After that, a familiarity test was administered in which the participants were asked to choose the more familiar chord sequence out of two successive sequences. The results showed that deviant transitions elicited the MMN, although the participants could not recognize the standard transition beyond the level of chance. These findings suggest that humans can statistically learn new transitional regularities of chords in a novel musical scale, even though they did not recognize them explicitly. This study provides further evidence that music-syntactic regularities can be acquired implicitly through statistical learning.

A different kind of meantone temperament and a novel mapping from the harmonic series to Pythagorean pitch classes

The logarithm mapping of natural numbers is a sum of products of coefficients. If these coefficients are arbitrary parameters, a new mapping of natural numbers to some subset of real numbers appears. This mapping preserves some crucial logarithm properties and constructs a new musical sound with a spectrum of inharmonic overtones. The simplest one-parameter mapping to a subset of polynomials with integer coefficients is constructed. The parameter defines a new “perfect fifth” similarly to the meantone temperament. It is an interesting case when the mapping parameter is defined from the linear relation between the new “major third” and the new “perfect fifth.” The most interesting case of a linear relation is the condition of zeroing the syntonic comma. Here, the new meantone temperament, based on the new “perfect fifth,” simultaneously coincides with Pythagorean- and five-limit-like tunings.

Parsimonious sequences of finite sets and their applications to chord progressions and music composition

Parsimony is a broad concept with applications in music theory and composition. Two sets A and B of finite cardinality n (n-sets) are in parsimonious relation if there exists a (n–1)-set C that is included in both A and B. A sequence of n-sets is parsimonious if any two successive sets in the sequence are in parsimonious relation. This work demonstrates that for any set of finite cardinality p, there exist sequences of its n-subsets (n ≤ p) that are circular, non-redundant, exhaustive and parsimonious, and it describes the corresponding algorithm. The image of such a sequence by a bijection and the retrograde sequence keep the same four properties. The consequences of these results for the pitch class (pc) subsets of cardinality n (or n-chords) of a pc set of finite cardinality p (p-tonic scale) are derived and discussed in the context of music harmony, microtonality and composition.

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.

Fingerprints, barcode sequences and quasi-phylogenies-Tools for analysing polyphonic music.

A data flow is presented for visualising the evolution of elementary structures of polyphonic music from early Baroque to late Romantic, using quasi-phylogenies based on fingerprint diagrams and barcode sequence data of 2-tuples of consecutive vertical pitch class sets (pcs). The present methodological study, which sees itself as a proof of concept for a data-driven approach, uses examples of music from the Baroque, the Viennese School and the Romantic era to show that such quasi-phylogenies can be generated from multi-track MIDI (v. 1) files that largely correspond to the eras and the chronology of compositions and composers. The method presented is considered to have the potential to support the analysis of a wide range of musicological questions. In the context of collaborative work on quasi-phylogenies of polyphonic music, a public data archive could be established that provides multi-track MIDI files with contextual data.

Decoding Imagined Musical Pitch From Human Scalp Electroencephalograms.

Brain-computer interfaces (BCIs) can restore impaired cognitive functions in people with neurological disorders such as stroke. Musical ability is a cognitive function that is correlated with non-musical cognitive functions, and restoring it can enhance other cognitive functions. Pitch sense is the most relevant function to musical ability according to previous studies of amusia, and thus decoding pitch information is crucial for BCIs to be able to restore musical ability. This study evaluated the feasibility of decoding pitch imagery information directly from human electroencephalography (EEG). Twenty participants performed a random imagery task with seven musical pitches (C4-B4). We used two approaches to explore EEG features of pitch imagery: multiband spectral power at individual channels (IC) and differences between bilaterally symmetric channels (DC). The selected spectral power features revealed remarkable contrasts between left and right hemispheres, low- (< 13 Hz) and high-frequency ( 13 Hz) bands, and frontal and parietal areas. We classified two EEG feature sets, IC and DC, into seven pitch classes using five types of classifiers. The best classification performance for seven pitches was obtained using IC and multiclass Support Vector Machine with an average accuracy of 35.68±7.47% (max. 50%) and an information transfer rate (ITR) of 0.37±0.22 bits/sec. When grouping the pitches to vary the number of classes (K = 2-6), the ITR was similar across K and feature sets, suggesting the efficiency of DC. This study demonstrates for the first time the feasibility of decoding imagined musical pitch directly from human EEG.

Modulation Mining—Computer-Aided Exploration of Functional Chord Forms

The different labelling systems defined by the functional theories of harmony have been developed from about 1870 to 1950, without the help of computers. The complexity of harmonic labels spans from pure triads over added characteristic dissonances, over alterations of the fifth, up to non-chord notes like suspensions. Computer-based evaluation of functional label expressions shows that thereby their cardinality increases up to several thousands. For this, we present the basic theory, a concrete program implemented in Prolog, and some empirical results. The software is capable of analysing historic published analyses by inductively collecting all appearing labels, as well as theories as such, where the set of labels is given deductively, by regular expressions. A major application is the mining for possible modulation chords, i.e. different functional labels which result in (enharmonically) the same pitch classes. That this strategy had actually been applied by composers manually is explained by significant examples from the Romantic period.

FluidHarmony: Defining an equal-tempered and hierarchical harmonic lexicon in the Fourier space

FluidHarmony is an algorithmic method for defining a hierarchical harmonic lexicon in equal temperaments. It utilizes an enharmonic weighted Fourier transform space to represent pitch class set (pcsets) relations. The method ranks pcsets based on user-defined constraints: the importance of interval classes (ICs) and a reference pcset. Evaluation of 5,184 Western musical pieces from the 16th to 20th centuries shows FluidHarmony captures 8% of the corpus's harmony in its top pcsets. This highlights the role of ICs and a reference pcset in regulating harmony in Western tonal music while enabling systematic approaches to define hierarchies and establish metrics beyond 12-TET.

GiantMIDI-Piano: A Large-Scale MIDI Dataset for Classical Piano Music

Symbolic music datasets are important for music information retrieval and musical analysis. However, there is a lack of large-scale symbolic datasets for classical piano music. In this article, we describe the creation of the GiantMIDI-Piano (GP) dataset containing 38,700,838 transcribed notes and 10,855 unique solo piano works composed by 2,786 composers. We extract the names of music works and the names of composers from the International Music Score Library Project (IMSLP). We search and download their corresponding audio recordings from the Internet. We further create a curated subset containing 7,236 works composed by 1,787 composers where the titles of downloaded audio recordings contain the surnames of composers. We apply a convolutional neural network to detect solo piano works. Then, we transcribe those solo piano recordings into Musical Instrument Digital Interface (MIDI) files using a high-resolution piano transcription system. Each transcribed MIDI file contains the onset, offset, pitch, and velocity attributes of piano notes and pedals. GiantMIDI-Piano includes 90% live performance MIDI files and 10% sequence input MIDI files. We analyse the statistics of GiantMIDI-Piano and show pitch class, interval, trichord, and tetrachord frequencies of six composers from different eras to show that GiantMIDI-Piano can be used for musical analysis. We evaluate the quality of GiantMIDI-Piano in terms of solo piano detection F1 scores, metadata accuracy, and transcription error rates. We release the source code for acquiring the GiantMIDI-Piano dataset at <a href="https://github.com/bytedance/GiantMIDI-Piano" target="_blank">https://github.com/bytedance/GiantMIDI-Piano</a>.

Melodic Transformation in George Garzone’s Triadic Chromatic Approach; or, Jazz, Math, and Basket Weaving

Abstract The Triadic Chromatic Approach (TCA) is a melodic improvisation technique, created by the saxophonist and jazz educator George Garzone. With the TCA, successive triads are connected by a semitone and must have different inversions. The resulting lines mysteriously resolve to any underlying harmony. This article develops transformational and Markov-chain models of the TCA, showing how this melodic process approaches a probability distribution where every pitch class is equally likely to appear. Nonetheless, theorizing the TCA is different from performing it, and insights from Garzone’s students—and the anthropology of weaving—suggest that goals are less fundamental here than characteristic gestures.

Mechanisms of absolute pitch: I. Acoustical beating

Musicologists and philosophers have commonly attributed distinctive qualities to individual musical pitches, and absolute pitch (AP) possessors recognize and recall notes and keys with immediacy and accuracy, leaving little doubt that they are aware of such characteristics. Bachem proposed that these distinct tonal qualities underlie the rapid and accurate judgments that he identified as genuine AP, and he defined the qualities as tone chroma (TC). The TCs of notes and keys, and of notes separated by a musical octave ( pitch class) are frequently expressed in visual terms, and studies of synaesthesia, the association of intersensory stimuli, provide clues to the systematic variation of TC qualities. The historical literature relating to note and key characteristics is commonly overlooked in the study of AP, however, and the article seeks to address this problem. Long-standing conclusions are reviewed, leading to the hypothesis that TC sensitivity can derive from an awareness of variations in the acoustical beats that occur in the tuning of instruments to equal temperament and which are perceived with particular clarity in organ tuning. This acoustical hypothesis is supported by modern neuroscientific findings and was predicted by theoretical observations in the literature as long ago as three centuries. In a follow-up article, Thurlow and Baggaley discuss the role of synaesthesia-type judgments in musical skills not previously regarded as absolute: for example, a perfect touch capacity observed in keyboard players.

From Ramos to Rameau

Abstract This article explores the advent of two foundational characteristics of the modern concept of harmony inaugurated by Rameau's Traité de l'harmonie (1722): first, that its principal objects are sonorities of three or more distinct pitch classes, that is, consonant and dissonant chords; and second, that these chords “move” from one to the next in ways determined by certain inherent relations among them, in a process in which dissonances, as well as consonances, play a significant if not crucial role. This article shows that the ancestors of these two fundamental properties of harmony, newly understood as a specifically polyphonic phenomenon, first emerged into theoretical discourse in polemical writings of the Northern Italian theorists Nicolò Burzio (1487), Giovanni Spataro (1491), and Franchino Gaffurio (1496, 1518), sparked by the inflammatory views of Bartolomeo Ramos de Pareia (1482). Moreover, while these ideas about harmony come to cohabit in Gioseffo Zarlino's Istitutioni harmoniche (1558), they were initially proposed not as complementary but as explicitly competing new conceptions of the nature of harmony, advanced to support their authors' polemical positions and attacks on each other.