Cognitive Similarity Grounded by Tree Distance from the Analysis of K.265/300e

Hirata, Keiji; Tojo, Satoshi; Hamanaka, Masatoshi

doi:10.1007/978-3-319-12976-1_36

Cited by 8 publications

(8 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In earlier work, the concept of maximum time-span (MTS) has been shown to be useful [6,18]. If a pitch event does not have branching, i.e., there is no more subordinate pitch event and it is a leaf of the tree, its MTS is the original pitch length.…”

Section: Tree Structure and Saliencementioning

confidence: 99%

See 1 more Smart Citation

No longer 'somewhat arbitrary'

Marsden

Tojo

Hirata

2018

Proceedings of the 5th International Conference on Digital Libraries for Musicology

Self Cite

View full text Add to dashboard Cite

Following earlier work on the formalisation of Lerdahl and Jackendoff's Generative Theory of Tonal Music (GTTM), we present a measure of the salience of events in a reduction tree, based on calculations relating the duration of time-spans to the structure of the tree. This allows for the proper graphical rendition of a tree on the basis of its time-spans and topology alone. It also has the potential to contribute to the development of sophisticated digital library systems able to operate on music in a musically intelligent manner. We present results of an empirical study of branch heights in the figures in GTTM which shows that salience calculated according to our proposals correlates better with branch height than alternatives. We also discuss the possible musical significance of this measure of salience. Finally we compare some results using salience in the calculation of melodic similarity on the basis of reduction trees to earlier results using time-span. While the correlation between these measures and human ratings of the similarity of the melodies is poor, using salience shows a definite improvement. Overall, the results suggest that the proposed definition of salience gives a potentially useful measure of an event's importance in a musical structure.

show abstract

Section: Tree Structure and Saliencementioning

confidence: 99%

“…Human ratings of the similarity between each pair of melodies were obtained from a panel of 11 listeners. For details, see [6,7].…”

Section: Salience and Similaritymentioning

confidence: 99%

No longer 'somewhat arbitrary'

Marsden

Tojo

Hirata

2018

Proceedings of the 5th International Conference on Digital Libraries for Musicology

Self Cite

View full text Add to dashboard Cite

show abstract

“…Hirata et al [16] proposed to measure similarity of For example, "IP" in Fig. 1 includes three tones in a bracket and is assigned the feature of "down sound up a narrow pitch".…”

Section: A Implication-realization Model (Irm)mentioning

confidence: 99%

Subjective Evaluation of Correlation of Melody Length and Melodic Similarity Based on a Music Theory

Yazawa

Hamanaka

Utsuro

2016

IJSPS

Self Cite

View full text Add to dashboard Cite

This paper studies to measure similarity of melodies based on Implication-Realization Model (IRM), a music theory that abstracts music and then expresses music through symbol sequences based on information constituting the music such as pitch, rhythm, and rests and so on. The model employed in this paper is an extended one that is much more appropriate to measuring similarity of melodies. Compared with the symbols of the original IRM, the extended model employs finer grained symbols by simply distinguishing up and down of interval directions and by dividing each most symbols of the original IRM into two extended symbols. Based on such a fundamental framework of measuring similarity of melodies by an extended IRM, the major focus of this paper is to claim that the similarity measure studied in this paper has a certain correlation with subjective human judgments on melodic similarities. Furthermore, this paper examines the correlation between melody length and subjective human judgments on melodic similarities. It is quite remarkable to note the result of this analysis: i.e., the smaller the melody length is, the more similar the pair of melodies is judged to be by human subjects, even though their similarities based on the extended IRM are measured to be almost in the same range. Thus, we conclude that it is necessary to invent a much finer-grained similarity measure which is designed to be more sensitive to melody length and to be coincide with the results of subjective human judgments.

show abstract

“…2. Junction height by the number of beats [8] We have proposed the notion of Maximum Time-span (MTS) of each pitch event, as the longest temporal interval during which the event is most salient [11,2]. If a pitch event does not have branching, i.e., there is no more subordinate pitch event and is a leaf of the tree, its MTS is the original pitch length.…”

Section: Introductionmentioning

confidence: 99%

On Linear Algebraic Representation of Time-span and Prolongational Trees

Tojo

Marsden

Hirata

2018

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

In constructive music theory, such as Schenkerian analysis and the Generative Theory of Tonal Music (GTTM), the hierarchical importance of pitch events is conveniently represented by a tree structure. Although a tree is easy to recognize and has high visibility, such an intuitive representation can hardly be treated in mathematical formalization. Especially in GTTM, the conjunction height of two branches is often arbitrary, contrary to the notion of hierarchy. Since a tree is a kind of graph, and a graph is often represented by a matrix, we show the linear algebraic representation of trees, specifying conjunction heights. Thereafter, we explain the 'reachability' between pitch events (corresponding to information about reduction) by the multiplication of matrices. In addition we discuss multiplication with vectors representing a sequence of harmonic functions, and suggest the notion of stability. Finally, we discuss operations between matrices to model compositional processes with simple algebraic operations.

show abstract

Cognitive Similarity Grounded by Tree Distance from the Analysis of K.265/300e

Cited by 8 publications

References 5 publications

No longer 'somewhat arbitrary'

No longer 'somewhat arbitrary'

Subjective Evaluation of Correlation of Melody Length and Melodic Similarity Based on a Music Theory

On Linear Algebraic Representation of Time-span and Prolongational Trees

Contact Info

Product

Resources

About