![]() The objective is to assemble a sequence of musically useful pitches that correspond to the pitches that musicians use in melodies and the chords that accompany them. Several additional musically useful frequencies can be determined this way. For Pythagoras, that ratio was 3:2-the ratio of the perfect fifth. To determine musical pitches other than "A," it is necessary to apply a ratio other than 2:1, then. ![]() Such is not the case if the melody is transposed by some interval other than an octave. It can be demonstrated that by transposing a melody an octave or more away from its harmonic accompaniment, for instance, the essential tonal relationships are maintained. 660 Hz and 550 Hz are a minor third apart.Ī tone with a frequency of 440 Hz is called the note "A." A tone with a frequency an octave higher (i.e., 880 Hz), or any number of octaves higher, or an octave lower (i.e., 220 Hz), or any number of octaves lower is also called "A." This notion, that any tones an octave apart (or two or more octaves apart, for that matter) have the same note name and have virtually the same melodic and harmonic function, is called the principle of octave equivalence.A major third higher than 440 Hz is 550 Hz.A perfect fifth higher than 440 Hz is 660 Hz.An octave higher than 440 Hz is 880 Hz.16:15 the minor second (aka: "half" step or semitone)īy international agreement (adopted by the International Standards Organization (the ISO) in 1939 in London), the reference frequency for tuning instruments is 440 Hz.9:8 the major second (aka: "whole" step or "whole" tone).The ratios of these pairs of frequencies can be reduced to small, whole-number fractions: Pythagoras and other early music theorists recognized that some intervals are especially useful in music. The basic pitch structure in music theory is an intervala pair of frequencies presented melodically (i.e., successively) or harmonically (i.e., simultaneously). Musical patterns of duration (i.e., rhythm) are best understood in the context of psychological studies of the mechanisms for perceiving time, and will therefore not receive a great deal of attention in this course. Musical patterns of frequency lend themselves particularly well to description from a physics perspective, and will therefore be a significant subject of study in this course. Therefore, most theories of music are preoccupied with these two elements. Musical perception is most sensitive with respect to frequency and duration. With recorded music this can be controlled electronically.Ī theory of music is an effort to describe the characteristic patterns of pitch and rhythm, the use of dynamics, the choices of instruments, and the spatial practices that describe a particular style of music. ![]()
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