Pitch-Class Sets

The described method yields ten heptatonic scales with an augmented fifth and ten pentatonic scales with a diminished fifth. But there are other scales that have an augmented or diminished fifth. So this feature is not the determining factor for these classes of scales.

This paper explores parsimonious voice leading transformations within pitch-class sets, from the perspective of three distinct voice leading states: static retention, increasing intervals, and decreasing intervals, all under the condition of preserving the invariance of pitch-class sets with prime form. It introduces concepts related to the number of voices, rules of voice leading, transformational outcomes in sets, and classification and relational theories in the normal form of pitch-class sets. The significance of this theory extends the practical applications of bridging, hooking invariance, and hybrid relational combinations in transformations from trichords to hexachords. Furthermore, it broadens the scope of post-tonal triadic invariance in Neo-Riemannian theory by applying these characteristics to the overall pitch-class sets space, ultimately forming a comprehensive theory of parsimonious voice leading and the invariance of pitch-class sets with prime form within this space.

In this paper we address the problem of designing an algorithm that, when given a representation of a passage of music as input, discovers all and only instances of perceptually significant repetition in the passage. The algorithm must be able to discover perceptually significant instances of repetition where the occurrences of the pattern are identical (exact repetition) and instances where the occurrences differ but are nonetheless perceived to be 'versions' of the same thing (modified repetition). Such an algorithm would ...

This study examines one of the most important composer of the 20th century, György Sándor Ligeti and his work Musica Ricercata. In structural terms, this work, which is written in Hungary, is the first and only in the musical repertoire. What makes Musica Ricercata unique in the musical world is it’s controlled approach to pitch material. The work consists of eleven movements and pitch class used in the work increases one by one in each successive movement. When it comes to the last movement, the work ends with a fugue which twelve pitch classes are used. Before analyzing the work, Ligeti’s life and musical language is examined in detail. The style and works of the composer, who has produced works in many different styles, are discussed under three different titles as the Hungarian years, the European years and the last period. Under these headings, his musical style is introduced over his works, and lastly Musica Ricercata, one of his early work, is analyzed.

Chord recognition task is to split up a piece of music into segments and assign each of them a chord label according to the analysis of the harmonic content. Making the chord recognition task process audio recordings automatically will be of great help for music information retrieval. Most of the existing chord recognition systems proceed as follows. In the first step, a given audio recording is converted into a sequence of chroma features. In the second step, the feature sequence is passed into chord recognition module in which the features are assigned with chord labels. However, although much research has been done, there is little understanding of the effect of the different processing stages and of the various parameter settings on the final recognition result. In this thesis we analyze the different stages of typical automated chord recognition systems. In particular, we consider several types of chroma features as well as several chord recognition methods based on simple temp...

In this preliminary work, we seek to present a brief historical review of the use of partitions in music, to provide a concise introduction to the theory of partitions, and lastly, through an extensive bibliographic revision and a thoughtful theoretical reflection, to lay the foundations of what we call partitional harmony – a comprehensive harmonic conception which relates the theory of partitions to several fields of post-tonal music theory. At the end, some basic operations (pitch, transposition, inversion, and multiplication) are defined and an illustrative musical application is provided, followed by our research prospects.

In this paper, we introduce a novel collection of educational material for teaching and learning fundamentals of music processing (FMP) with a particular focus on the audio domain. This collection, referred to as FMP notebooks, discusses well-established topics in Music Information Retrieval (MIR) as motivating application scenarios. The FMP notebooks provide detailed textbook-like explanations of central techniques and algorithms in combination with Python code examples that illustrate how to implement the theory. All components including the introductions of MIR scenarios, illustrations, sound examples, technical concepts, mathematical details, and code examples are integrated into a consistent and comprehensive framework based on Jupyter notebooks. The FMP notebooks are suited for studying the theory and practice, for generating educational material for lectures, as well as for providing baseline implementations for many MIR tasks, thus addressing students, teachers, and research...

Pitch Class Profiles (PCP) [Fujishima 1999] are largely used for all applications involving harmonic content. Although the main steps of the PCP calculation are generally equal over all the scientific literature, some implementation details may vary, specially the impact of the distance between the frequency of the FFT bins and their closest note. This paper compares 6 ways of using this distance to weight the contribution of each FFT bin in the final PCP vector. We present the results of the 6 computed PCPs when used in a chord recognizer, a tonality estimator and a key detector.

Nello spazio temperato dodecafonico, basato sulla divisione dell'ottava in dodici parti uguali, alcune collezioni di note possono trasporsi un numero di volte inferiore a 12, prima di riprodursi identiche. Queste collezioni sono legate ai circoli di intervalli sottomultipli di 12 (cioè 1,2,3,4,6) ed alla suddivisione dell'ottava in parti uguali; le più semplici sono il tritono e la triade aumentata: il primo è sei volte trasponibile e divide l'ottava in due parti uguali, la seconda è quattro volte trasponibile e divide l'ottava in tre parti uguali. Tutte le collezioni simmetriche per trasposizione devono essere composte da tritoni e/o triadi aumentate: non possono essere composte da 5 o 7 note, perché 5 e 7 non sono multipli né del numero 2 né del numero 3; tuttavia, in qualsiasi modo si voglia sovrapporre un tritono ed una triade aumentata, senza raddoppi, il risultato sarà sempre equivalente alla stessa collezione di 5 note (0,1,4,7,8), e in qualsiasi modo si vogliano sovrapporre due tritoni ed una triade aumentata, senza raddoppi, il risultato sarà sempre equivalente alla stessa collezione di 7 note (0,1,2,5,6,8,9), complementare dell'altra. Queste due collezioni sono le uniche costituite da soli tritoni o triadi aumentate a non essere simmetriche per trasposizione Le collezioni simmetriche per trasposizione sono 16, ossia:-il totale cromatico-il tritono e la sua collezione complementare di 10 note-la triade aumentata e la sua collezione complementare di 9 note-tre collezioni di 4 note (formati da diverse sovrapposizioni di due tritoni), e le loro complementari di 8 note-cinque collezioni di 6 note, di cui due costruite sulla sovrapposizione di due triadi aumentate, e tre formate da diverse sovrapposizioni di tre tritoni.

Some tendencies in post-tonal music are regarded as very “cerebral” or “cryptic”, and are often
misunderstood, when not rejected, by the uninitiated public and even by some professional
musicians. As an effort to overcome my resistance to this languages, I designed an interactive
application in MAX that allow to improvise using Allen Forte’s set theory. So, rather than being
forced to do a bunch of arithmetic calculations by heart before play a single note, musicians can
hear instantly the aural qualities of determined pitch class sets by playing a simple chord in a MIDI
keyboard to generate variations of a previously played musical gesture. An iterative design process
was carried on, and the results, conclusions and reflections during the different stages of the
work showed the relevance of the music theory applied and its relation to constraint satisfaction
techniques in music composing processes.

A partir de la segunda mitad del siglo XX se verificó un cambio imprevisto en la metodología de las ciencias no físicas, revolucionando el modo tradicional de investigación en esos dominios al realzar el valor de las teorías formuladas con la ayuda de la matemática (Bunge, M., 1972). Ello supone, epistemológicamente hablando, la transformación progresiva de la teoría fenomenológica a su teoría representacional correspondiente, lo cual es asimilable, se acepta, a un proceso evolutivo de teoría-metateoría.

This paper speculates on the potential of a limited set of interacting particles to produce interesting temporal structures in a two dimensional world. Particles exchange information locally though global complex behavior emerges spontaneously. The imaginary physics of the world is described in an ensemble of 2D arrays. An autonomous genetic algorithm continuously aims to optimize the arrays in an effort to maximize diversity. In addition, an external user may interfere in a subtle way; external gestures are integrated into the arrays in proportion to their strength. A quite elaborate mapping scheme creates relationships between complex system behavior and parametric MIDI events.

The Composers Toolbox is a Macintosh Common Lisp-based environment designed to facilitate ease of data manipulation during the precompositional sketching process. The package provides a series of tools, many with graphic interfaces, which allow the user to work with both MIDI and sampled sound data in a free and flexible fashion.

This paper describes a simple and efficient template-based chord recognition algorithm and its statistical evaluation. A Pitch Class Profile calculation is introduced, based on a STFT, peak extraction and a two-octave frequency range limitation. It includes also simple binary templates, realized for standard schemes to extract the chord information. By correlating these templates with the signal, it is possible to generate a time-depending chord sequence. To decrease the amount of miss-matches, a correlation coefficient threshold and a mode filter were applied. As part of the statistical evaluation, hand annotated test files were used as well as pre-annotated Bea-tles songs. Our algorithm is able to achieve an evaluation score of 49% for several of the songs by the Beatles. However it scored less than state-of-the-art algorithms, but it is acceptable as debut work in the field of Music Information Retrieval.

Course Description: The purpose of this class is to present students with a general overview of the repertoire of the 20th-century as well as several different approaches for the analysis of these works. Additionally, this class strives to place each composer and their works into the appropriate historical context. By understanding the motivations of the composer, the context in which they were writing, and the compositional methods used, and in many instances developed, the diligent student will ultimately arrive at a more in-depth understanding of this era's music. Through listening and score study students will learn what analytic tools would be most appropriate for extracting the meaning of the compositions being considered by trying to answer the questions, " Why/ when/how was this piece written? " and uncovering a composer's stylistic traits. Score study and analysis will be supplemented by readings that include short biographies, journal articles and other important historic accounts. Students will also put some practices to use in short compositions of their own based upon some of the techniques learned in class.

The Composers Toolbox is a Macintosh Common Lisp-based environment designed to facilitate ease of data manipulation during the precompositional sketching process. The package provides a series of tools, many with graphic interfaces, which allow the user to work with both MIDI and sampled sound data in a free and flexible fashion.

Advances in chord recognition research using machine learning are hampered by two factors: the scarcity of annotated training data, and the limited complexity of the features and models used. Both problems are intertwined, as with few training examples, increasing the complexity of the model would inevitably lead to overfitting. In this paper we develop a way to address the first problem by exploiting chord annotations from online chord data- bases. We show how such chord annotations, despite being noisy and lacking exact chord onset times, can be put to use both during the recognition and training stage. We note that the ability to exploit this large untapped resource may enable researchers to also address the second problem: with more training data, one may be able to use more complex models without running the same high risk of overfitting.