An Algorithm for Harmonic Analysis

1997 ◽  
Vol 15 (1) ◽  
pp. 31-68 ◽  
Author(s):  
David Temperley
Keyword(s):  
Harmonic Analysis ◽  
Spatial Representation ◽  
Tonal Music ◽  
Pitch Class

An algorithm is proposed for performing harmonic analysis of tonal music. The algorithm begins with a representation of a piece as pitches and durations; it generates a representation in which the piece is divided into segments labeled with roots. This is a project of psychological interest, because much evidence exists that harmonic analysis is performed by trained and untrained listeners during listening; however, the perspective of the current project is computational rather than psychological, simply examining what has to be done computationally to produce "correct" analyses for pieces. One of the major innovations of the project is that pitches and chords are both represented on a spatial representation known as the "line of fifths"; this is similar to the circle of fifths except that distinctions are made between different spellings of the same pitch class. The algorithm uses preference rules to evaluate different possible interpretations, selecting the interpretation that most satisfies the preference rules. The algorithm has been computationally implemented; examples of the program's output are given and discussed.

The Interplay of Set Content and Temporal Context in a Functional Theory of Tonality Perception

1988 ◽  
Vol 5 (3) ◽  
pp. 219-249 ◽  
Author(s):  
Helen Brown
Keyword(s):  
Structural Characteristics ◽  
Perceptual Cues ◽  
Tonal Music ◽  
Critical Feature ◽  
Functional Interpretation ◽  
Pitch Class ◽  
Functional Relationships ◽  
Musical Excerpt ◽  
Musical Excerpts ◽  
Pitch Class Sets

The purpose of this study was to provide evidence for the perceptual component of an analysis of pitch relationships in tonal music that includes consideration of both formal analytic systems and musical listeners' responses to tonal relationships in musical contexts. It was hypothesized (1) that perception of tonal centers in music develops from listeners' interpretations of time-dependent contextual (functional) relationships among pitches, rather than primarily through knowledge of psychoacoustical or structural characteristics of the pitch content of sets or scales and (2) that critical perceptual cues to functional relationships among pitches are provided by the manner in which particular intervallic relationships are expressed in musical time. Excerpts of tonal music were chosen to represent familiar harmonic relationships across a spectrum of tonal ambiguity/specificity. The pitch-class sets derived from these excerpts were ordered: (1) to evoke the same tonic response as the corresponding musical excerpt, 2) to evoke another tonal center, and (3) to be tonally ambiguous. The effect of the intervallic contents of musical excerpts and strings of pitches in determining listeners' choices of tonic and the effect of contextual manipulations of tones in the strings in directing subjects' responses were measured and compared. Results showed that the musically trained listeners in the study were very sensitive to tonal implications of temporal orderings of pitches in determining tonal centers. Temporal manipulations of intervallic relationships in stimuli had significant effects on concurrences of tonic responses and on tonal clarity ratings reported by listeners. The interval rarest in the diatonic set, the tritone, was the interval most effective in guiding tonal choices. These data indicate that perception of tonality is too complex a phenomenon to be explained in the time-independent terms of psychoacoustics or pitch- class collections, that perceived tonal relationships are too flexible to be forced into static structural representations, and that a functional interpretation of rare intervals in optimal temporal orderings in musical contexts is a critical feature of tonal listening strategy.

Diatonic Connotations of Pitch-Class Sets

1997 ◽  
Vol 15 (1) ◽  
pp. 1-29 ◽  
Author(s):  
René Van Egmond ◽  
David Butler
Keyword(s):  
Set Theory ◽  
Theoretical Study ◽  
Class Relations ◽  
Tonal Music ◽  
Pitch Class ◽  
Tonal Pitch ◽  
Relationship Of ◽  
The Relationship ◽  
Pitch Class Sets

This is a music-theoretical study of the relationship of two-, three-, four-, five-, and six-member subsets of the major (pure minor), harmonic minor, and melodic (ascending) minor reference collections, using pitchclass set analytic techniques. These three collections will be referred to as the diatonic sets. Several new terms are introduced to facilitate the application of pitch-class set theory to descriptions of tonal pitch relations and to retain characteristic intervallic relationships in tonal music typically not found in discussions of atonal pitch-class relations. The description comprises three parts. First, pitch sets are converted to pitchclass sets. Second, the pitch- class sets are categorized by transpositional types. Third, the relations of these transpositional types are described in terms of their key center and modal references to the three diatonic sets. Further, it is suggested that the probability of a specific key interpretation by a listener may depend on the scale-degree functions of the tones.

Implicit Absolute Pitch Representation Affects Basic Tonal Perception

2017 ◽  
Vol 34 (5) ◽  
pp. 569-584 ◽  
Author(s):  
Zohar Eitan ◽  
Moshe Shay Ben-Haim ◽  
Elizabeth Hellmuth Margulis
Keyword(s):  
Absolute Pitch ◽  
Occurrence Frequency ◽  
Tonal Music ◽  
Pitch Class ◽  
Harmonic Progression ◽  
Relative Pitch ◽  
Preceding Context ◽  
Tonal Hierarchy ◽  
Tonal Perception ◽  
Tonal Context

It is undisputed that the cognition of tonal music is primarily established by pitch relationships set within a tonal scheme such as a major or minor key. The corresponding notion—that absolute pitch and absolute key are largely inconsequential for tonal cognition—thus seems inevitable. Here, we challenge the latter notion, presenting data suggesting that absolute pitch and absolute key significantly modify listeners’ judgments of tonal fit and tonal tension. In two experiments extending the probe tone technique (as applied in Krumhansl & Kessler, 1982) participants heard a brief tonal context (a major triad in Experiment 1, a harmonic progression in Experiment 2) followed by individual probe tones, and rated how well each probe fitted the preceding context, as well as the musical tension conveyed by each probe. Two maximally distant key contexts, G major and D♭ major, were used in both experiments and in both tasks. Ratings revealed significant absolute pitch effects in both tasks, though in different ways. In the tonal fit task, diatonic pitches in G major were rated higher than those in D♭ major; in contrast, chromatic pitches were rated higher in D♭ major, compared to G. In the tension task, overall ratings were significantly higher for D♭ major contexts than for G major context (Experiment 1). Importantly, these effects reflect the occurrence frequency of pitch classes and keys in the tonal repertory: frequent pitch classes were rated as better fits than rarer ones, and a rarer key (D♭) rated tenser than a frequently-occurring key (G). Absolute pitch effects were most strongly manifested by participants without formal training, for whom the relative pitch effects of the tonal hierarchy were weak, and were stronger when tonal context was weaker (Experiment 1 as compared to Experiment 2). Results suggest that implicit absolute pitch perception, reflecting key and pitch class occurrence frequency, significantly affects tonal music processing; such absolute pitch effects may be activated principally when tonal perception or tonal cues are lacking.

scholarly journals A Glimpse at Iuriĭ Kholopov’s Garmonicheskiĭ analiz

2014 ◽  
Vol 20 (3) ◽  
Author(s):  
Zachary A. Cairns
Keyword(s):  
Twentieth Century ◽  
Harmonic Analysis ◽  
Tonal Music ◽  
String Trio ◽  
Romantic Music ◽  
Analytical System

Iuriĭ Kholopov’s Garmonicheskiĭ analiz (Harmonic analysis) is a three-volume anthology, intended to accompany his textbook Garmoniia: Prakticheskiĭ kurs (Harmony: a practical course), which formed the basis of the harmony courses he taught at the Moscow Conservatory in the 1980s. This paper provides a small glimpse into the anthology, particularly volume 3. This volume, which deals primarily with non-tonal music of the twentieth century, is the only one with its own subtitle: hemitonicism. The subtitle refers to a simple, intuitive analytical system in which groups of intervals that involve one or more semitones play a prominent role. The paper concludes with an examination of Kholopov’s analysis of Denisov’s Romanticheskaia muzyka (Romantic Music) for oboe, harp, and string trio (1968), a representative example of the analyses in Garmonicheskiĭ analiz’s third volume.

New Approaches to the Linear Analysis of Music

1988 ◽  
Vol 41 (2) ◽  
pp. 315-348 ◽  
Author(s):  
Allen Forte
Keyword(s):  
Analytical Techniques ◽  
Linear Analysis ◽  
Tonal Music ◽  
Pitch Class ◽  
New Approaches ◽  
Historical Importance ◽  
Varying Length ◽  
Analytical Research ◽  
New Procedures

A number of recent studies incorporate linear analysis of non-standard tonal music and non-tonal music. Although the author takes issue with the application of strict Schenkerian paradigms to such music he acknowledges the historical importance of the Schenkerian canon. Invoking new procedures, among them pitch-class set-analytical techniques, the author presents a series of analyses which reveal linear-motivic features held to be essential to the music under consideration over temporal spans of varying length. The study, which includes works by Stravinsky, Wagner, and Scriabin, ends by suggesting three guidelines for subsequent efforts in this new area of analytical research.

Pitch-Class Distribution and the Identification of Key

2008 ◽  
Vol 25 (3) ◽  
pp. 193-212 ◽  
Author(s):  
David Temperley ◽  
Elizabeth West Marvin
Keyword(s):  
Absolute Pitch ◽  
Tonal Music ◽  
Pitch Class ◽  
Class Distribution ◽  
Better Than

THIS STUDY EXAMINES THE DISTRIBUTIONAL VIEW OF key-finding, which holds that listeners identify key by monitoring the distribution of pitch-classes in a piece and comparing this to an ideal distribution for each key. In our experiment, participants judged the key of melodies generated randomly from pitch-class distributions characteristic of tonal music. Slightly more than half of listeners' judgments matched the generating keys, on both the untimed and the timed conditions. While this performance is much better than chance, it also indicates that the distributional view is far from a complete explanation of human key identification. No difference was found between participants with regard to absolute pitch ability, either in the speed or accuracy of their key judgments. Several key-finding models were tested on the melodies to see which yielded the best match to participants' responses.

Identifying groups of airborne particles by ordination

1994 ◽  
Vol 52 ◽  
pp. 856-857
Author(s):  
M. Shlepr ◽  
C. M. Vicroy
Keyword(s):  
Elemental Analysis ◽  
Energy Dispersive Spectroscopy ◽  
Manufacturing Process ◽  
Spatial Representation ◽  
Airborne Particles ◽  
Common Source ◽  
Data Set ◽  
Microelectronics Industry ◽  
Induced Changes ◽  
Source Materials

The microelectronics industry is heavily tasked with minimizing contaminates at all steps of the manufacturing process. Particles are generated by physical and/or chemical fragmentation from a mothersource. The tools and macrovolumes of chemicals used for processing, the environment surrounding the process, and the circuits themselves are all potential particle sources. A first step in eliminating these contaminants is to identify their source. Elemental analysis of the particles often proves useful toward this goal, and energy dispersive spectroscopy (EDS) is a commonly used technique. However, the large variety of source materials and process induced changes in the particles often make it difficult to discern if the particles are from a common source.Ordination is commonly used in ecology to understand community relationships. This technique usespair-wise measures of similarity. Separation of the data set is based on discrimination functions. Theend product is a spatial representation of the data with the distance between points equaling the degree of dissimilarity.

Harmonic Analysis and Representation Theory for Groups Acting on Homogenous Trees

1991 ◽  
Author(s):  
Alessandro Figá-Talamanca ◽  
Claudio Nebbia
Keyword(s):  
Representation Theory ◽  
Harmonic Analysis

Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups

2009 ◽  
Author(s):  
Tullio Ceccherini-Silberstein ◽  
Fabio Scarabotti ◽  
Filippo Tolli
Keyword(s):  
Representation Theory ◽  
Harmonic Analysis ◽  
Finite Groups ◽  
Wreath Products
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