The Euler Space

Guerino Mazzola; Yan Pang; William Heinze; Kyriaki Gkoudina; Gian Afrisando Pujakusuma; Jacob Grunklee; Zilu Chen; Tianxue Hu; Yiqing Ma

doi:10.1007/978-3-030-00982-3_6

The Euler Space

Guerino Mazzola, Yan Pang, William Heinze, Kyriaki Gkoudina, Gian Afrisando Pujakusuma, Jacob Grunklee, Zilu Chen, Tianxue Hu, Yiqing Ma

Music (Twin Cities)

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

In this chapter, we will discuss music theories from two mathematical perspectives. In the first part, we will explain what is a tuning and how the Euler Space relates to Western tuning systems. We will use Euler’s theory of tuning to explain three typical tunings: equal temperament tuning, Pythagorean tuning, and just tuning. In the second part, we will use a mathematical torus model ℤ₃ × ℤ₄ and its symmetries to explain counterpoint and its application in the RUBATO^® music software.

Original language	English (US)
Title of host publication	Computational Music Science
Publisher	Springer Nature
Pages	51-61
Number of pages	11
DOIs	https://doi.org/10.1007/978-3-030-00982-3_6
State	Published - 2018

Publication series

Name	Computational Music Science
ISSN (Print)	1868-0305
ISSN (Electronic)	1868-0313

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© 2018, Springer Nature Switzerland AG.

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10.1007/978-3-030-00982-3_6

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abstract = "In this chapter, we will discuss music theories from two mathematical perspectives. In the first part, we will explain what is a tuning and how the Euler Space relates to Western tuning systems. We will use Euler{\textquoteright}s theory of tuning to explain three typical tunings: equal temperament tuning, Pythagorean tuning, and just tuning. In the second part, we will use a mathematical torus model ℤ3 × ℤ4 and its symmetries to explain counterpoint and its application in the RUBATO{\textregistered} music software.",

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AU - Mazzola, Guerino

AU - Pang, Yan

AU - Heinze, William

AU - Gkoudina, Kyriaki

AU - Pujakusuma, Gian Afrisando

AU - Grunklee, Jacob

AU - Chen, Zilu

AU - Hu, Tianxue

AU - Ma, Yiqing

PY - 2018

Y1 - 2018

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AB - In this chapter, we will discuss music theories from two mathematical perspectives. In the first part, we will explain what is a tuning and how the Euler Space relates to Western tuning systems. We will use Euler’s theory of tuning to explain three typical tunings: equal temperament tuning, Pythagorean tuning, and just tuning. In the second part, we will use a mathematical torus model ℤ3 × ℤ4 and its symmetries to explain counterpoint and its application in the RUBATO® music software.

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PB - Springer Nature

ER -

The Euler Space

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