Harmonic series (music) in the context of "Major third"

In physics, acoustics, and telecommunications, a harmonic is a sinusoidal wave with a frequency that is a positive integer multiple of the fundamental frequency of a periodic signal. The fundamental frequency is also called the 1st harmonic; the other harmonics are known as higher harmonics. As all harmonics are periodic at the fundamental frequency, the sum of harmonics is also periodic at that frequency. The set of harmonics forms a harmonic series.

The term is employed in various disciplines, including music, physics, acoustics, electronic power transmission, radio technology, and other fields. For example, if the fundamental frequency is 50 Hz, a common AC power supply frequency, the frequencies of the first three higher harmonics are 100 Hz (2nd harmonic), 150 Hz (3rd harmonic), 200 Hz (4th harmonic) and any addition of waves with these frequencies is periodic at 50 Hz.

Pizzicato (/ˌpɪtsɪˈkɑːtoʊ/, Italian: [pittsiˈkaːto]; translated as 'pinched', and sometimes roughly as 'plucked') is a playing technique that involves plucking the strings of a string instrument. The exact technique varies somewhat depending on the type of instrument:

• On bowed string instruments it is a method of playing by plucking the strings with the fingers, rather than using the bow. This produces a very different sound from bowing, short and percussive rather than sustained.
• On keyboard string instruments, such as the piano, pizzicato may be employed (although rarely seen in traditional repertoire, this technique has been normalized in contemporary music, with ample examples by George Crumb, Tōru Takemitsu, Helmut Lachenmann, and others) as one of the variety of techniques involving direct manipulation of the strings known collectively as "string piano".
• On the guitar, it is a muted form of plucking, which bears an audible resemblance to pizzicato on a bowed string instrument with its relatively shorter sustain. It is also known (especially in non-classical guitar) as palm muting.

When a string is struck or plucked, including pizzicato, sound waves are generated that do not belong to a harmonic series as when a string is bowed. This complex timbre is called inharmonicity. The inharmonicity of a string depends on its physical characteristics, such as tension, composition, diameter and length. The inharmonicity disappears when strings are bowed because the bow's stick-slip action is periodic, so it drives all of the resonances of the string at exactly harmonic ratios, even if it has to drive them slightly off their natural frequency.

A vibration in a string is a wave. Initial disturbance (such as plucking or striking) causes a vibrating string to produce a sound with constant frequency, i.e., constant pitch. The nature of this frequency selection process occurs for a stretched string with a finite length, which means that only particular frequencies can survive on this string. If the length, tension, and linear density (e.g., the thickness or material choices) of the string are correctly specified, the sound produced is a musical tone. Vibrating strings are the basis of string instruments such as guitars, cellos, and pianos. For a homogeneous string, the motion is given by the wave equation.

A brass instrument is a musical instrument that produces sound by sympathetic vibration of air in a tubular resonator in sympathy with the vibration of the player's lips. The term labrosone, from Latin elements meaning "lip" and "sound", is also used for the group, since instruments employing this "lip reed" method of sound production can be made from other materials like wood or animal horn, particularly early or traditional instruments such as the cornett, alphorn or shofar.

There are several factors involved in producing different pitches on a brass instrument. Slides, valves, crooks (though they are rarely used today), or keys are used to change vibratory length of tubing, thus changing the available harmonic series, while the player's embouchure, lip tension and air flow serve to select the specific harmonic produced from the available series.

Flanging /ˈflændʒɪŋ/ is an audio effect produced by mixing two identical signals together, one signal delayed by a small and (usually) gradually changing period, usually smaller than 20 milliseconds. This produces a swept comb filter effect: peaks and notches are produced in the resulting frequency spectrum, related to each other in a linear harmonic series. Varying the time delay causes these to sweep up and down the frequency spectrum. A flanger is an effects unit that creates this effect.

Part of the output signal is usually fed back to the input (a re-circulating delay line), producing a resonance effect that further enhances the intensity of the peaks and troughs. The phase of the fed-back signal is sometimes inverted, producing another variation on the flanger sound.

In music, an octave (Latin: octavus: eighth) or perfect octave (sometimes called the diapason) is an interval between two notes, one having twice the frequency of vibration of the other. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems". The interval between the first and second harmonics of the harmonic series is an octave. In Western music notation, notes separated by an octave (or multiple octaves) have the same name and are of the same pitch class.

To emphasize that it is one of the perfect intervals (including unison, perfect fourth, and perfect fifth), the octave is designated P8. Other interval qualities are also possible, though rare. The octave above or below an indicated note is sometimes abbreviated 8 or 8 (Italian: all'ottava), 8 bassa (Italian: all'ottava bassa, sometimes also 8), or simply 8 for the octave in the direction indicated by placing this mark above or below the staff.

An overtone is any resonant frequency above the fundamental frequency of a sound (or of any oscillation). An overtone may or may not be a harmonic. In other words, overtones are all pitches higher than the lowest pitch within an individual sound; the fundamental is the lowest pitch. While the fundamental is usually heard most prominently, overtones are actually present in any pitch except a true sine wave. The relative volume or amplitude of various overtone partials is one of the key identifying features of timbre, or the individual characteristic of a sound.

Using the model of Fourier analysis, the fundamental and the overtones together are called partials. Harmonics, or more precisely, harmonic partials, are partials whose frequencies are numerical integer multiples of the fundamental (including the fundamental, which is 1 times itself). These overlapping terms are variously used when discussing the acoustic behavior of musical instruments. (See etymology below.) The model of Fourier analysis provides for the inclusion of inharmonic partials, which are partials whose frequencies are not whole-number ratios of the fundamental (such as 1.1 or 2.14179).

The fundamental frequency, often referred to simply as the fundamental (abbreviated as f₀ or f₁ ), is defined as the lowest frequency of a periodic waveform. In music, the fundamental is the musical pitch of a note that is perceived as the lowest partial present. In terms of a superposition of sinusoids, the fundamental frequency is the lowest frequency sinusoidal in the sum of harmonically related frequencies, or the frequency of the difference between adjacent frequencies. In some contexts, the fundamental is usually abbreviated as f₀, indicating the lowest frequency counting from zero. In other contexts, it is more common to abbreviate it as f₁, the first harmonic. (The second harmonic is then f₂ = 2⋅f₁, etc.)

According to Benward and Saker's Music: In Theory and Practice: