arXiv subjects

Ken Ito

Publications and source records attributed to Ken Ito.

4 recordsLinked to original sources

arXiv2026

Klangfarbenakkord and Klangfarbenharmonien Metric Space Models for Music on Informational Geometry 1

This paper deals with the introduction of "geometric harmony", a discipline that explicitly addresses the spectral characteristics of musical gamut. The framework of Western music, from Renaissance to the present, represents sound in terms of "pitch"-as is evident from its five-line staff notation system-and employs the fundamental frequency as its representative value, 440 Hz, etc. In this paper, by taking the timbres of specific individual instruments as elements and examining the Wasserstein distance between two voices, and Wasserstein deviations between three or more voices, we demonstrate that it is possible to expand the system whilst retaining the entire framework of conventional music theory. At the same time, as an example of practical utility in ensemble playing, we provide a detailed account of the two-voices affinity of the "Throat G" on clarinet, a note known for its fragility in ensemble contexts.

cs.SD↗

arXiv2026

Information-Geometric Superposed Vowel Evaluation: Part 1. Moraic Syllabary (Japanese)

This paper explains the principles and provides examples of a new method for distinguishing between FAKE human speech synthesized by generative AI and natural speech. Since synthetic speech is generated based on information from a limited set of training spectra, the variety of vowels - which are key to identifying individuals - is limited. In contrast, natural speech exhibits a more diverse distribution of vowel spectra due to the flexibility of the human articulatory organ. In this paper, using Japanese - a Syllabary limited to five vowel phonemes, each of which corresponds one-to-one with a specific sound - as an example, we outline a method for distinguishing between synthetic and natural speech reading the same text by analyzing the spectral distributions. If we normalize the spectra of speech sounds and regard them as probability density functions for the frequency bands received by the hair cells of the human cochlea, and evaluate the distance between spectra using the Wasserstein metric, the Wasserstein distances between the vowels of synthetic speech are short. By preserving this distance and performing a topological mapping using persistent homology, the spectral probability density functions of synthetic and natural speech can be decomposed into clusters.

cs.SD↗

arXiv2003

Parametrizations of infinite biconvex sets in affine root systems

We investigate in detail relationships between the set ${\mathfrak B}^\infty$ of all infinite ``biconvex'' sets in the positive root system $Δ_+$ of an arbitrary untwisted affine Lie algebra ${\mathfrak g}$ and the set ${\mathcal W}^\infty$ of all infinite ``reduced word'' of the Weyl group of ${\mathfrak g}$. The study is applied to the classification of ``convex orders'' on $Δ_+$ (cf. \cite{kI}), which are indispensable to construct ``convex bases'' of Poincaré-Birkhoff-Witt type of the upper triangular subalgebra $U_q^+$ of the quantized universal enveloping algebra $U_q({\mathfrak g})$. We construct a set $\boldsymbol{\mathcal P}$ by using data of the underlying finite-dimensional simple Lie algebra, and bijective mappings $\nabla\colon\boldsymbol{\mathcal P}\to{\mathfrak B}^\infty$ and $χ\colon\boldsymbol{\mathcal P}\to W^\infty$ such that $\nabla=\varPhi^\infty\circχ$, where $W^\infty$ is an quotient set of ${\mathcal W}^\infty$ and $\varPhi^\infty\colon W^\infty\to{\mathfrak B}^\infty$ is a natural injective mapping.

math.QA↗

arXiv2000

The classification of convex orders on affine root systems

We classify all total orders having a certain convex property on the positive root system of an arbitrary untwisted affine Lie algebra ${\frak g}$. Such total orders are called convex orders and are used to construct convex bases of Poincaré-Birkhoff-Witt type of the upper triangular subalgebra $U_q^+$ of the quantized enveloping algebra $U_q({\frak g})$.

math.QA↗