In terms of what we hear, each octave in the harmonic series is divided into increasingly "smaller" and more numerous intervals. ), and we hear these distances as "the same" in all ranges. On the other hand, the octave series is a geometric progression (2×f, 4×f, 8×f, 16×f. But because our ears respond to sound logarithmically, we perceive higher harmonics as "closer together" than lower ones. In terms of frequency (measured in cycles per second, or hertz (Hz)), the difference between consecutive harmonics is therefore constant. The harmonic series is an arithmetic series (2×f, 3×f, 4×f, 5×f. (See inharmonicity and stretched tuning for alterations specific to wire-stringed instruments and certain electric pianos.) However, those alterations are small, and except for precise, highly specialized tuning, it is reasonable to think of the frequencies of the harmonic series as integer multiples of the fundamental frequency. Physical characteristics of the vibrating medium and/or the resonator against which it vibrates often alter these frequencies. Theoretically, these wavelengths produce vibrations at frequencies that are 2, 3, 4, 5, 6, etc. of the length of the string or air column. As the reflected waves interact, frequencies whose wavelengths do not divide evenly into the length of the string or air column are suppressed, and the vibrations that persist are called harmonics. In pitched ( i.e., non-percussion) instruments, these shorter, faster waves are reflected between the two ends of the string or air column. In nearly every musical instrument, the fundamental note is always accompanied by other, higher-frequency tones that are generally called overtones. This frequency determines the musical pitch or note that is created by vibration over the full length of the string or air column. The lowest possible frequency of a harmonic oscillator is called its fundamental frequency. 5 Register and special effects of musical instruments.
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