The aesthetic and ideal research pf the harmonics in the Hellenistie Age of Ancient Greek

Research Project

Project/Area Number	13610054
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Single-year Grants
Section	一般
Research Field	美学(含芸術諸学)
Research Institution	AKITA UNIVERSITY
Principal Investigator	YAMAMOTO Tatsuro AKITA UNIVERSITY Faculty of Education and Human Studies, Professor, 教育文化学部, 教授 (30006572)
Project Period (FY)	2001 – 2002
Project Status	Completed (Fiscal Year 2002)
Budget Amount *help	¥1,400,000 (Direct Cost: ¥1,400,000) Fiscal Year 2002: ¥500,000 (Direct Cost: ¥500,000) Fiscal Year 2001: ¥900,000 (Direct Cost: ¥900,000)
Keywords	harmonia / interval / octave / the fourth / the fifth / tetrachord / conjunction and disjunction / toros / 転位 / エートス / 音階(音組織) / オクターブ種 / 大完全音階 / 調和音程(協和音) / オクターヴ種 / 旋法 / 調(性)、キー
Research Abstract	Concentratedly (vol.I&II) I examined the Harmonics of Ptolemy, who was the peak of Ancient astronomy which is one part of applied mathematics in the ancient period. So he was very much engaged in the harmonics, which was also one part of applied mathematics. He is the Greek who was active in the middle of the 2nd century and supposed to belong to the post-Pythagorean. The characteristic point of his idea is that he looked on the interval as the ratio of two notes which constructed the interval. Ptolemy pushed up this Pythagorean idea to the extreme. Ptolemy criticized Aristoxenus from this point of view, but he became intimated with him by criticizing him. As the result Ptolemy unified the Pythagorean mathematical method and Aristotelean conceptual method. Ptolemy's Harmonic is distinguished for the subtle and mighty logic and suitable "problematization". He solved the problem of Toros, Which had been discussed in vain since the classical period through Aristoxenus.