Harmonic analysis based on Tonal Pitch Space

Sakamoto, Shoki; Arn, Sean; Matsubara, Masaki; Tojo, Satoshi

doi:10.1109/kse.2016.7758058

Cited by 3 publications

(10 citation statements)

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“…Based on the distance defined by TPS and the principle of the shortest distance, Sakamoto et al [9] have proposed a method to find the most plausible interpretation of a given chord sequence. Given a chord sequence, first, their method extends each chord to its interpretations and constructs a graph whose edges have weights that correspond to the distances on TPS.…”

Section: Former Approaches Based On Tpsmentioning

confidence: 99%

“…Yamamoto and Tojo [10] have tried to generalize TPS and proposed several functions called "distance elements (DEs)" and a way to train them with annotated datasets. Based on the method of [9], their method replaces the TPS with the proposed generalized TPS then convert path distance to path probability such that the shortest path should have the highest probability, and finally apply SGD to update parameters.…”

Section: Former Approaches Based On Tpsmentioning

confidence: 99%

“…TPS claims the principle of the shortest distance, that is, we can find the most plausible chord interpretation as the one which minimizes the distances between neighboring chord interpretations. Utilizing this property of the distance defined by TPS, Sakamoto et al [9] proposed a method to find the most plausible interpretation sequence for a chord sequence as the shortest path in the interpretation graph (Figure 1), that is a directed graph whose edges are weighted by the TPS' distances and expresses all possible chord interpretation sequences. However, it has been found that this method's prediction accuracy was only around 40%.…”

Section: Introductionmentioning

confidence: 99%

“…However, it has been found that this method's prediction accuracy was only around 40%. Yamamoto and Tojo [10], assuming that one of the reasons is the calculation of TPS is based on classical music theory and/or expert's intuition but not on optimized with actual data, tried to find a better distance model by generalizing the distance function in TPS and proposed a method by which we can automatically fit its parameters with annotated dataset. They succeeded to find some combinations that achieve over 80% accuracy with less than a hundred parameters but, they tested only a few candidate combinations.…”

Section: Introductionmentioning

confidence: 99%

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Effective Features for Finding Chord Interpretation Paths

Yamamoto

Tojo

2023

IIAI Letters on Informatics and Interdisciplinary Research

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We humans naturally feel tonality when we hear music, but its actual mechanism is still unknown. There have been many approaches to understand this mechanism, but one promising method is to measure the distance between chords, as was proposed in Tonal Pitch Space (TPS). Although the theory seems theoretically convincing, we could not know which features contribute most and which others are useless in an objective manner. In this study, we try to define a new distance model by clarifying the effective set of features among them. Based on the principle of the shortest distance, which is claimed by TPS, we estimate each distance by optimizing features to obtain the most plausible chord interpretation (i.e., a degree/key pair for a chord name). We propose the set of functions based on these features and we evaluate all simple combinations of them exhaustively. It turns out that accuracies almost max out with around 20 effective parameters in the functions, achieving about 80-90% accuracy, that outperforms the original TPS.

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Section: Former Approaches Based On Tpsmentioning

confidence: 99%

Section: Former Approaches Based On Tpsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Effective Features for Finding Chord Interpretation Paths

Yamamoto

Tojo

2023

IIAI Letters on Informatics and Interdisciplinary Research

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“…Even when we add the information on duration for each pitch event, the tree cannot be fixed uniquely, as there remains the arbitrariness as to the height of junction point of branches. Matsubara et al [10,8] have tried to fix the junction height, regarding the number of beats, e.g., 2 n beats ≤ L n < 2 n+1 beats (Fig. 2), however, when they tried to include cadential retention the height still remained ambiguous.…”

Section: Introductionmentioning

confidence: 99%

On Linear Algebraic Representation of Time-span and Prolongational Trees

Tojo

Marsden

Hirata

2018

Lecture Notes in Computer Science

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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.

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