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音乐与数学存在着天然的联系。德国哲学家及数学家莱布尼兹说:“音乐,就它的基础来说,是数学的;就它的出现来说,是直觉的。”“音乐是心灵的算术练习,心灵在听音乐时计算着自己而不知。”(汪流等编《艺术特征论》210页)音乐中众多的术语与数学有关,如:一音对一音、二声部歌曲、三声部赋格曲、四重奏、五声音阶、平行六和弦、七连音、八度卡农、九度音程、十度复对位、十一和弦、十二音体系、一百零八分音符……以及为记忆音程性质与五线谱调名的口诀等。律学与数学的关系更加密切。标准音高a′=440次/秒。音程比:纯五度=3/2;全音=9/8;十二平均律半音=(2/1)~(1/12)=1.05946;而log_(10)A/B=
There is a natural connection between music and mathematics. Leibnitz, a German philosopher and mathematician, said: “Music, in its foundations, is mathematical and, in its appearance, intuitive.” “Music is the arithmetic of the mind, the mind is listening to music (Wang et al., Ed., ”Artistic Features", p 210) There are many terms in music related to mathematics, such as a sound of one sound, a sound of two voices, a fugue of three voices, Quartet, pentatonic, parallel six chord, seven-note, octave canon, nine-degree intervals, ten degrees complex, eleven chords, twelve-tone system, one hundred and eight notes ... and for the nature of the memory And tune the name of formulas and other formulas. Law and mathematics are more closely related. Standard pitch a ’= 440 beats / second. Interleave ratio: pure fifth degree = 3/2; full tone = 9/8; twelve average regular semitone = (2/1) ~ (1/12) = 1.05946; and log_ (10) A / B =