By Π₯Π°ΠΌΠ°Π½Π°ΠΊΠ° ΠΠ°ΡΠ°ΡΠΎΡΠΈ , β¦
Π₯Π°ΠΌΠ°Π½Π°ΠΊΠ° ΠΠ°ΡΠ°ΡΠΎΡΠΈ, Π₯ΠΈΡΠ°ΡΠ° ΠΠ΅ΠΉΠ΄ΠΆΠΈ, Π’ΠΎΠ΄Π·Ρ Π‘Π°ΡΠΎΡΠΈ, 2024
Π ΠΊΠ½ΠΈΠ³Π΅ ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½Π° Π½ΠΎΠ²Π°Ρ ΠΊΠΎΠ½ΡΠ΅ΠΏΡΠΈΡ ΠΌΡΠ·ΡΠΊΠΎΠ²Π΅Π΄Π΅Π½ΠΈΡ, ΡΠ°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°ΡΡΠ°Ρ ΠΌΡΠ·ΡΠΊΡ ΠΊΠ°ΠΊ Π²ΡΡΠΈΡΠ»ΠΈΡΠ΅Π»ΡΠ½ΡΡ ΡΡΡΡΠΊΡΡΡΡ, ΡΡΠΈΡΡΠ²Π°ΡΡΡΡ ΠΎΡΠΎΠ±Π΅Π½Π½ΠΎΡΡΠΈ ΡΠ΅Π»ΠΎΠ²Π΅ΡΠ΅ΡΠΊΠΎΠ³ΠΎ Π²ΠΎΡΠΏΡΠΈΡΡΠΈΡ. ΠΠ²ΡΠΎΡΡ ΠΈΡΡΠ»Π΅Π΄ΡΡΡ, ΠΎΠ±Π»Π°Π΄Π°Π΅Ρ Π»ΠΈ ΠΌΡΠ·ΡΠΊΠ° ΡΠ΅ΠΌΠ°Π½ΡΠΈΠΊΠΎΠΉ ΠΈ ΠΌΠΎΠΆΠ½ΠΎ Π»ΠΈ ΡΠ°ΡΠΊΡΡΡΡ Π΅Ρ ΡΠΌΡΡΠ» ΡΠ΅ΡΠ΅Π· ΡΠΈΠΌΠ²ΠΎΠ»Ρ ΠΈ ΡΠ·ΡΠΊ. Π Π°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°ΡΡΡΡ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ Π³Π°ΡΠΌΠΎΠ½ΠΈΠΈ, ΡΠ²ΡΠ·Π°Π½Π½ΡΠ΅ Ρ ΡΠ°ΡΡΠΎΡΠ½ΡΠΌΠΈ ΠΏΡΠΎΠΏΠΎΡΡΠΈΡΠΌΠΈ, ΠΈ ΠΌΠ΅ΡΠΎΠ΄ ΠΠ΅ΡΠΊΠ»ΠΈ Ρ ΠΏΠΎΠ·ΠΈΡΠΈΠΈ ΡΠΈΠΌΠ²ΠΎΠ»ΠΈΡΠ΅ΡΠΊΠΈΡ Π²ΡΡΠΈΡΠ»Π΅Π½ΠΈΠΉ.
Masatoshi Hamanaka, Keiji Hirata, Satoshi Tojo, 2024
This book introduces a new concept in musicology, viewing music as a computational structure that considers human perception. The authors investigate whether music possesses semantics and if its meaning can be revealed through symbols and language. Mathematical definitions of harmony related to frequency proportions and the Berkeley method from the perspective of symbolic computation are examined.