Harmonic in the context of "Interval cycle"

The human voice consists of sound made by a human being using the vocal tract, including talking, singing, laughing, crying, screaming, shouting, humming or yelling. The human voice is specifically a part of human sound production in which the vocal folds (vocal cords) are the primary sound source. (Other sound production mechanisms produced from the same general area of the body involve the production of unvoiced consonants, clicks, whistling and whispering.)

Generally speaking, the mechanism for generating the human voice can be subdivided into three parts; the lungs, the vocal folds within the larynx (voice box), and the articulators. The lungs, the "pump" must produce adequate airflow and air pressure to vibrate vocal folds. The vocal folds (vocal cords) then vibrate to use airflow from the lungs to create audible pulses that form the laryngeal sound source. The muscles of the larynx adjust the length and tension of the vocal folds to 'fine-tune' pitch and tone. The articulators (the parts of the vocal tract above the larynx consisting of tongue, palate, cheek, lips, etc.) articulate and filter the sound emanating from the larynx and to some degree can interact with the laryngeal airflow to strengthen or weaken it as a sound source.

Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are determined by choosing a sequence of fifths which are "pure" or perfect, with ratio ${\displaystyle 3:2}$. This is chosen because it is the next harmonic of a vibrating string, after the octave (which is the ratio ${\displaystyle 2:1}$), and hence is the next most consonant "pure" interval, and the easiest to tune by ear. As Novalis put it, "The musical proportions seem to me to be particularly correct natural proportions." Alternatively, it can be described as the tuning of the syntonic temperament in which the generator is the ratio 3:2 (i.e., the untempered perfect fifth), which is ≈ 702 cents wide.

The system dates back to Ancient Mesopotamia;. (See Music of Mesopotamia § Music theory.) It is named, and has been widely misattributed, to Ancient Greeks, notably Pythagoras (sixth century BC) by modern authors of music theory. Ptolemy, and later Boethius, ascribed the division of the tetrachord by only two intervals, called "semitonium" and "tonus" in Latin (256:243 × 9:8 × 9:8), to Eratosthenes. The so-called "Pythagorean tuning" was used by musicians up to the beginning of the 16th century. "The Pythagorean system would appear to be ideal because of the purity of the fifths, but some consider other intervals, particularly the major third, to be so badly out of tune that major chords [may be considered] a dissonance."

A triangular wave or triangle wave is a non-sinusoidal waveform named for its triangular shape. It is a periodic, piecewise linear, continuous real function.

Like a square wave, the triangle wave contains only odd harmonics. However, the higher harmonics roll off much faster than in a square wave (proportional to the inverse square of the harmonic number as opposed to just the inverse).

An acoustic guitar is a musical instrument in the string family. When a string is plucked, its vibration is transmitted from the bridge, resonating throughout the top of the guitar. It is also transmitted to the side and back of the instrument, resonating through the air in the body, and producing sound from the sound hole. While the original, general term for this stringed instrument is guitar, the retronym 'acoustic guitar' – often used to indicate the steel stringed model – distinguishes it from an electric guitar, which relies on electronic amplification. Typically, a guitar's body is a sound box, of which the top side serves as a sound board that enhances the vibration sounds of the strings. In standard tuning the guitar's six strings are tuned (low to high) E₂ A₂ D₃ G₃ B₃ E₄.

Guitar strings may be plucked individually with a pick (plectrum) or fingertip, or strummed to play chords. Plucking a string causes it to vibrate at a fundamental pitch determined by the string's length, mass, and tension. (Overtones are also present, closely related to harmonics of the fundamental pitch.) The string causes the soundboard and the air enclosed by the sound box to vibrate. As these have their own resonances, they amplify some overtones more strongly than others, affecting the timbre of the resulting sound.

In music, a notehead is the part of a note, usually elliptical in shape, whose placement on the staff indicates the pitch, to which modifications are made that indicate duration. Noteheads may be the same shape but colored completely black or white, indicating the note value (i.e., rhythmic duration). In a whole note, the notehead, shaped differently than shorter notes, is the only component of the note. Shorter note values attach a stem to the notehead, and possibly beams or flags. The longer double whole note can be written with vertical lines surrounding it, two attached noteheads, or a rectangular notehead. An "x" shaped notehead may be used to indicate percussion, percussive effects (ghost notes), or speaking. A square, diamond, or box shaped notehead may be used to indicate a natural or artificial harmonic. A small notehead can be used to indicate a grace note.

Clipping is a form of waveform distortion that occurs when an amplifier is overdriven and attempts to deliver an output voltage or current beyond its maximum capability. Driving an amplifier into clipping may cause it to output power in excess of its power rating.

In the frequency domain, clipping produces strong harmonics in the high-frequency range (as the clipped waveform comes closer to a square wave). The extra high-frequency weighting of the signal could make tweeter damage more likely than if the signal was not clipped.

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:

The harmonic series (also overtone series) is the sequence of harmonics, musical tones, or pure tones whose frequency is an integer multiple of a fundamental frequency.

Pitched musical instruments are often based on an acoustic resonator such as a string or a column of air, which oscillates at numerous modes simultaneously. As waves travel in both directions along the string or air column, they reinforce and cancel one another to form standing waves. Interaction with the surrounding air produces audible sound waves, which travel away from the instrument. These frequencies are generally integer multiples, or harmonics, of the fundamental and such multiples form the harmonic series.

In speech science and phonetics, a formant is the broad spectral maximum that results from an acoustic resonance of the human vocal tract. In acoustics, a formant is usually defined as a broad peak, or local maximum, in the spectrum. For harmonic sounds, with this definition, the formant frequency is sometimes taken as that of the harmonic that is most augmented by a resonance. The difference between these two definitions resides in whether "formants" characterise the production mechanisms of a sound or the produced sound itself. In practice, the frequency of a spectral peak differs slightly from the associated resonance frequency, except when, by luck, harmonics are aligned with the resonance frequency, or when the sound source is mostly non-harmonic, as in whispering and vocal fry.

A room can be said to have formants characteristic of that particular room, due to its resonances, i.e., to the way sound reflects from its walls and objects. Room formants of this nature reinforce themselves by emphasizing specific frequencies and absorbing others, as exploited, for example, by Alvin Lucier in his piece I Am Sitting in a Room. In acoustic digital signal processing, the way a collection of formants (such as a room) affects a signal can be represented by an impulse response.

The strike tone, strike note, or tap note, of a percussion instrument (e.g. bell, chime or gong) when struck, is the dominant note perceived immediately by the human ear. It is also known as the prime or fundamental note. However, an analysis of the bell's frequency spectrum reveals that the fundamental only exists weakly and its dominance is a human perception of a note built up by the complex series of harmonics that are generated. The correct and accurate harmonic tuning is therefore important in creating a good strike tone.

Auditory imagery is a form of mental imagery that is used to organize and analyze sounds when there is no external auditory stimulus present. This form of imagery is broken up into a couple of auditory modalities such as verbal imagery or musical imagery. This modality of mental imagery differs from other sensory images such as motor imagery or visual imagery. The vividness and detail of auditory imagery can vary from person to person depending on their background and condition of their brain. Through all of the research developed to understand auditory imagery behavioral neuroscientists have found that the auditory images developed in subjects' minds are generated in real time and consist of fairly precise information about quantifiable auditory properties as well as melodic and harmonic relationships. These studies have been able to recently gain confirmation and recognition due to the arrival of Positron emission tomography and fMRI scans that can confirm a physiological and psychological correlation.

Harmonic analysis is a branch of mathematics concerned with investigating the connections between a function and its representation in frequency. The frequency representation is found by using the Fourier transform for functions on unbounded domains such as the full real line or by Fourier series for functions on bounded domains, especially periodic functions on finite intervals. Generalizing these transforms to other domains is generally called Fourier analysis, although the term is sometimes used interchangeably with harmonic analysis. Harmonic analysis has become a vast subject with applications in areas as diverse as number theory, representation theory, signal processing, quantum mechanics, tidal analysis, spectral analysis, and neuroscience.

The term "harmonics" originated from the Ancient Greek word harmonikos, meaning "skilled in music". In physical eigenvalue problems, it began to mean waves whose frequencies are integer multiples of one another, as are the frequencies of the harmonics of music notes. Still, the term has been generalized beyond its original meaning.

A pipe is a tubular wind instrument in general, or various specific wind instruments. The word is an onomatopoeia, and comes from the tone which can resemble that of a bird chirping .

With just three holes, a pipe's range is obtained by overblowing to sound at least the second or the third harmonic partials.

The fingerboard (also known as a fretboard on fretted instruments) is an important component of most stringed instruments. It is a thin, long strip of material, usually wood, that is laminated to the front of the neck of an instrument. The strings run over the fingerboard, between the nut and bridge. To play the instrument, a musician presses strings down to the fingerboard to change the vibrating length, changing the pitch. This is called stopping the strings. Depending on the instrument and the style of music, the musician may pluck, strum or bow one or more strings with the hand that is not fretting the notes. On some instruments, notes can be sounded by the fretting hand alone, such as with hammer ons, an electric guitar technique.

The word "fingerboard" in other languages sometimes occurs in musical directions. In particular, the direction sul tasto (Ital., also sulla tastiera, Fr. sur la touche, G. am Griffbrett) for bowed string instruments to play with the bow above the fingerboard. This reduces the prominence of upper harmonics, giving a more ethereal tone.

Additive synthesis is a sound synthesis technique that creates timbre by adding sine waves together.

The timbre of musical instruments can be considered in the light of Fourier theory to consist of multiple harmonic or inharmonic partials or overtones. Each partial is a sine wave of different frequency and amplitude that swells and decays over time due to modulation from an ADSR envelope or low frequency oscillator.

Frequency modulation synthesis (or FM synthesis) is a form of sound synthesis whereby the frequency of a waveform is changed by modulating its frequency with a modulator. The (instantaneous) frequency of an oscillator is altered in accordance with the amplitude of a modulating signal.

FM synthesis can create both harmonic and inharmonic sounds. To synthesize harmonic sounds, the modulating signal must have a harmonic relationship to the original carrier signal. As the amount of frequency modulation increases, the sound grows progressively complex. Through the use of modulators with frequencies that are non-integer multiples of the carrier signal (i.e. inharmonic), inharmonic bell-like and percussive spectra can be created.

Sympathetic resonance or sympathetic vibration is a harmonic phenomenon wherein a passive string or vibratory body responds to external vibrations to which it has a harmonic likeness. The classic example is demonstrated with two similarly-tuned tuning forks. When one fork is struck and held near the other, vibrations are induced in the unstruck fork, even though there is no physical contact between them. In similar fashion, strings will respond to the vibrations of a tuning fork when sufficient harmonic relations exist between them. The effect is most noticeable when the two bodies are tuned in unison or an octave apart (corresponding to the first and second harmonics, integer multiples of the inducing frequency), as there is the greatest similarity in vibrational frequency. Sympathetic resonance is an example of injection locking occurring between coupled oscillators, in this case coupled through vibrating air. In musical instruments, sympathetic resonance can produce both desirable and undesirable effects.

According to The New Grove Dictionary of Music and Musicians: