American reed organ measurements showed a sinusoidal oscillation with sharp pressure transitions when the reed bends above and below its frame. The fundamental itself is nearly the mechanical resonance frequency of the reed. The overtones of the instrument are harmonics of the fundamental, rather than inharmonic, although a weak inharmonic overtone (6.27f) was reported too. The fundamental frequency comes from a transverse mode, whereas weaker higher transverse and torsional modes were measured too.
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Lamellophones are instruments which have little tines, or "lamellae", which are played by plucking. Unlike stringed instruments or air-column instruments like flutes, the overtones of a plucked lamella are inharmonic, giving the mbira a characteristic sound. The inharmonic overtones are strongest in the attack and die out rather quickly, leaving an almost pure tone. When a tine is plucked, the adjacent tines also create secondary vibrations that increase the harmonic complexity of an individual note.
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William Sethares wrote that just intonation and the western equal tempered scale are related to the harmonic spectra/timbre of many western instruments in an analogous way that the inharmonic timbre of the Thai renat (a xylophone-like instrument) is related to the seven-tone near-equal tempered pelog scale in which they are tuned. Similarly, the inharmonic spectra of Balinese metallophones combined with harmonic instruments such as the stringed rebab or the voice, are related to the five-note near-equal tempered slendro scale commonly found in Indonesian gamelan music .
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Prominent examples of stochastic algorithms are Markov chains and various uses of Gaussian distributions. Stochastic algorithms are often used together with other algorithms in various decision- making processes. Music has also been composed through natural phenomena. These chaotic models create compositions from the harmonic and inharmonic phenomena of nature.
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The fundamental frequency is considered the first harmonic and the first partial. The numbering of the partials and harmonics is then usually the same; the second partial is the second harmonic, etc. But if there are inharmonic partials, the numbering no longer coincides. Overtones are numbered as they appear the fundamental.
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The inharmonic ringing of the instrument's metal resonator is even more prominent in the sounds of brass instruments. Human ears tend to group phase-coherent, harmonically-related frequency components into a single sensation. Rather than perceiving the individual partials–harmonic and inharmonic, of a musical tone, humans perceive them together as a tone color or timbre, and the overall pitch is heard as the fundamental of the harmonic series being experienced. If a sound is heard that is made up of even just a few simultaneous sine tones, and if the intervals among those tones form part of a harmonic series, the brain tends to group this input into a sensation of the pitch of the fundamental of that series, even if the fundamental is not present.
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Some acoustic instruments emit a mix of harmonic and inharmonic partials but still produce an effect on the ear of having a definite fundamental pitch, such as pianos, strings plucked pizzicato, vibraphones, marimbas, and certain pure-sounding bells or chimes. Antique singing bowls are known for producing multiple harmonic partials or multiphonics. Acoustical Society of America – Large grand and small upright pianos by Alexander Galembo and Lola L. Cuddly Hanna Järveläinen et al. 1999. "Audibility of Inharmonicity in String Instrument Sounds, and Implications to Digital Sound Systems" Other oscillators, such as cymbals, drum heads, and other percussion instruments, naturally produce an abundance of inharmonic partials and do not imply any particular pitch, and therefore cannot be used melodically or harmonically in the same way other instruments can.
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He also commented that the cello "startlingly duets with his voice", leading to inharmonic sounds that makes it sound like the instrument "clears its throat during his awkward moments". Reviewers have also commented on the album's "skeletal framework", with "bare melodies rising to the surface, vocal lines encompassing wordless singing" and "constantly shifting textures swirling throughout".
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Gondwana (1980) is a defining musical composition of spectral musicStaines, Joes (2010). The Rough Guide to Classical Music, p.372. . "The locus classicus of early spectral music". for large orchestra composed by Tristan Murail using simulated synthesis to create a harmonic interpolation between an orchestrally synthesized chord derived from a simulated bell sound (inharmonic) and a chord derived from a trombone sound (harmonic).
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Together they form the harmonic series. Overtones which are perfect integer multiples of the fundamental are called harmonics. When an overtone is near to being harmonic, but not exact, it is sometimes called a harmonic partial, although they are often referred to simply as harmonics. Sometimes overtones are created that are not anywhere near a harmonic, and are just called partials or inharmonic overtones.
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The Audio Dictionary, University of Washington Press. p. 288. Phase shift effects: Uni-Vibe, Electro-Harmonix Small Stone, MXR Phase 90. Ring modulator: A ring modulator produces a resonant, metallic sound by mixing an instrument's audio signal with a carrier wave generated by the device's internal oscillator. The original sound wave is suppressed and replaced by a "ring" of inharmonic higher and lower pitches or "sidebands".
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This powerful method allows, for example, synthesizing a 3-formant voice in a manner similar to FM voice synthesis. DSF allows the synthesis of harmonic and inharmonic, band-limited or unlimited spectra, and can be controlled by an index. As Roads points out, by reducing digital synthesis of complex spectra to a few parameters, DSF can be much more economical.C. Roads 1996, p.260-61.
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The fundamental is obviously a harmonic because it is 1 times itself. A harmonic partial is any real partial component of a complex tone that matches (or nearly matches) an ideal harmonic. An inharmonic partial is any partial that does not match an ideal harmonic. Inharmonicity is a measure of the deviation of a partial from the closest ideal harmonic, typically measured in cents for each partial.
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Many pitched acoustic instruments are designed to have partials that are close to being whole-number ratios with very low inharmonicity; therefore, in music theory, and in instrument design, it is convenient, although not strictly accurate, to speak of the partials in those instruments' sounds as "harmonics", even though they may have some degree of inharmonicity. The piano, one of the most important instruments of western tradition, contains a certain degree of inharmonicity among the frequencies generated by each string. Other pitched instruments, especially certain percussion instruments, such as marimba, vibraphone, tubular bells, timpani, and singing bowls contain mostly inharmonic partials, yet may give the ear a good sense of pitch because of a few strong partials that resemble harmonics. Unpitched, or indefinite- pitched instruments, such as cymbals and tam-tams make sounds (produce spectra) that are rich in inharmonic partials and may give no impression of implying any particular pitch.
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These resonances exhibit positive feedback on the inharmonic effect: if a string vibrates at a frequency just below that of a resonance, the impedance makes it vibrate even lower, and if it vibrates just above a resonance, the impedance makes it vibrate higher. The sounding board has multiple resonant frequencies that are unique to any particular piano. This contributes to the greater variance in the empirically measured Railsback curve in the lower octaves.
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Power Tools for Synthesizer Programming, Hal Leonard. p. 171. Distortion and overdrive: Distortion and overdrive units re- shape or "clip" an audio signal's wave form so that it has flattened peaks, creating "warm" sounds by adding harmonics or "gritty" sounds by adding inharmonic overtones. In tube amplifiers, distortion is created by compressing the instrument's out-going electrical signal in vacuum tubes or "valves". Distortion pedals produce perfectly flattened peaks or "hard" clipping.
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Wind instruments whose air column is open at only one end, such as trumpets and clarinets, also produce partials resembling harmonics. However they only produce partials matching the odd harmonics, at least in theory. The reality of acoustic instruments is such that none of them behaves as perfectly as the somewhat simplified theoretical models would predict. Partials whose frequencies are not integer multiples of the fundamental are referred to as inharmonic partials.
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Roland System-100M modular synthesizer with ring modulator, noise generator, sample & hold, LFO Some of the Minimoog Voyager controls. Note the NOISE/PGM option on the top rotary switches controlling the modulation busses. Noise is used as basic tonal material in electronic music. When pure-frequency sine tones were first synthesised into complex timbres, starting in 1953, combinations using inharmonic relationships (noises) were used far more often than harmonic ones (tones).Stockhausen 1963b, 142 and 144.
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One of Chowning's most famous pieces is called Stria (1977). It was commissioned by IRCAM for the Institute's first major concert series called Perspectives of the 20th Century. His composition was noted for its inharmonic sounds due to his famous FM algorithm and his use of the golden mean (1.618...) in music. Other famous compositions include Turenas (1972), which was one of the first electronic compositions to have the illusion of sounds moving in a 360-degree space .
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Helmholtz agreed with the finding of Ernst Chladni from 1787 that certain sound sources have inharmonic vibration modes. In Helmholtz's time, electronic amplification was unavailable. For synthesis of tones with harmonic partials, Helmholtz built an electrically excited array of tuning forks and acoustic resonance chambers that allowed adjustment of the amplitudes of the partials. Built at least as early as in 1862, these were in turn refined by Rudolph Koenig, who demonstrated his own setup in 1872.
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The sound effect can be achieved without an additional 3rd bridge or extended tail piece. If the player presses on a fret (not behind it, as with standard fretting) and strums the string at the head side, the resonance comes through. Again, on harmonic positions the result is much louder and clearer than on the inharmonic fret positions. The 5th, 7th, 12th and 19th fret generate low-frequency humming overtones with the complementary tone, which is usually played in the regular way.
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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. Additive synthesis most directly generates sound by adding the output of multiple sine wave generators.
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For example, a harmonic sound could be restructured to sound inharmonic, and vice versa. Sound hybridisation or "morphing" has been implemented by additive resynthesis. Additive analysis/resynthesis has been employed in a number of techniques including Sinusoidal Modelling, Spectral Modelling Synthesis (SMS), and the Reassigned Bandwidth-Enhanced Additive Sound Model. Software that implements additive analysis/resynthesis includes: SPEAR,SPEAR Sinusoidal Partial Editing Analysis and Resynthesis for Mac OS X, MacOS 9 and Windows LEMUR, LORIS, SMSTools,SMSTools application for Windows ARSS.
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Markeas is part of the heritage of the Parisian spectral school, that of a "processual" music, a music more attached to sound than to the note, gradually moving from one state of the material to another; a music involving a dialectic between harmonic and inharmonic, between periodicity and aperiodicity. To this compositional approach, Alexandros Markeas adds a theatrical dimension, allowing him to escape from "pure music". His compositions are marked by the use of multimedia techniques. At some time he was a professor of generative improvisation at the Conservatoire de Paris (CNSMD).
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Oscillators and Sound Generators Each of the 12 voices has 2 Oscillators. Each Oscillator has sawtooth, triangle and square/pulse waves, mixable in variable proportions. This feature is similar to the Roland SH-101, whose oscillator had mixable sawtooth, pulse (square) and a sub-oscillator. In Oscillator 1, each waveform can be modified: saw's "spread" parameter adds a second detuned sawtooth, triangle "wrap" progressively clips the waveform adding inharmonic content, and pulse wave has variable pulse width; PWM is also available, and the modulation source can be chosen from LFO1, LFO2 or OSC ENV.
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A septimal minor third is almost exactly two-ninths of an octave, and thus all divisions of the octave into multiples of nine (72 equal temperament being the most notable) have an almost perfect match to this interval. The septimal major sixth, 12/7, is the inverse of this interval. The septimal minor third may be derived in the harmonic series from the seventh harmonic, and as such is in inharmonic ratios with all notes in the regular 12TET scale, with the exception of the fundamental and the octave.
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Marshall began playing openly after his mother died in 1954, but had tuned his first pan long before that. At 14, he got an old ping pong from Tokyo Steelband and tried to retune it, using his harmonica. By 18 he began tuning pans, guided by other tuners such as Carl Greenidge. Mr. Marshall was dissatisfied with what he called ping pong's inferior tone. By 1956, Bertie Marshall had accomplished the most significant development in today’s steelpan tone, revolutionizing the method of tuning, by changing the instrument from the inharmonic style.
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Clinical tests can be divided into two groups: those assessing monaural TFS processing capacities (TFS1 test) and those assessing binaural capacities (binaural pitch, TFS-LF, TFS-AF). TFS1: this test assesses the ability to discriminate between an harmonic complex tone and its frequency-transposed (and thus, inharmonic) version. Binaural pitch: these tests evaluate the ability to detect and discriminate binaural pitch, and melody recognition using different types of binaural pitch. TFS-LF: this test assesses the ability to discriminate low-frequency pure tones that are identical at the two ears from the same tones differing in interaural phase.
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Several composers have begun to make resonance the subject of compositions. Alvin Lucier has used acoustic instruments and sine wave generators to explore the resonance of objects large and small in many of his compositions. The complex inharmonic partials of a swell shaped crescendo and decrescendo on a tamtam or other percussion instrument interact with room resonances in James Tenney's Koan: Having Never Written A Note For Percussion. Pauline Oliveros and Stuart Dempster regularly perform in large reverberant spaces such as the cistern at Fort Worden, WA, which has a reverb with a 45-second decay.
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When octaves are stretched, they are tuned, not to the lowest coincidental overtone (second partial) of the note below, but to a higher one (often the 4th partial). This widens all intervals equally, thereby maintaining intervallic and tonal consistency. All western music, but western classical literature in particular, requires this deviation from the theoretical equal temperament because the music is rarely played within a single octave. A pianist constantly plays notes spread over three and four octaves, so it is critical that the mid and upper range of the treble be stretched to conform to the inharmonic overtones of the lower registers.
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Modern western ears easily tolerate fast beating in non-just intervals (seconds and sevenths, thirds and sixths), but not in perfect octaves or fifths. Happily for pianists, the string stretch that accommodates inharmonicity on a concert grand also nearly exactly mitigates the accumulation of dissonance in the perfect fifth. Other factors, physical and psychoacoustic, affect the tuner's ability to achieve a temperament. Among physical factors are inharmonic effects due to soundboard resonance in the bass strings, poorly manufactured strings, or peculiarities that can cause "false beats" (false because they are unrelated to the manipulation of beats during tuning).
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Most instruments produce harmonic sounds, but many instruments produce partials and inharmonic tones, such as cymbals and other indefinite-pitched instruments. When the tuning note in an orchestra or concert band is played, the sound is a combination of 440 Hz, 880 Hz, 1320 Hz, 1760 Hz and so on. Each instrument in the orchestra or concert band produces a different combination of these frequencies, as well as harmonics and overtones. The sound waves of the different frequencies overlap and combine, and the balance of these amplitudes is a major factor in the characteristic sound of each instrument.
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181 and Whittall 1999, p.27. #"as a quasi-tonal procedure" ["hierarchies analogous to (but distinct from) the traditional western tonal system."] #"as an attempt to transfer serial processes to electronic music" #"as a 'prolongation' of the initial inharmonic series" #"'as different perspectives on an object that is always present'" per Michael Clarke According to Curtis Roads, "Three compositions produced in the 1980s stand as good examples of compositional manipulation of analysis data: Mortuos Plango, Vivos Voco (1981) by Jonathan Harvey, Désintegrations (1983, Salabert Trajectoires) by Tristan Murail, and Digital Moonscapes (1985, CBS/Sony) by Wendy Carlos."Roads, Curtis (1996).
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The opening chords present all the pitch materials of the piece. They are of two kinds: (1) "resonant" chords made by superposing two major, minor, augmented, diminished triads (sometimes with an added seventh or ninth), to form basically "harmonic" structures, and (2) "anti-resonant" or "noisy" chords based on chromatic relationships and containing a large number of seconds and fourths, giving them a more "inharmonic" character . These chords are progressively horizontalised, creating "a syntactic flux between structurally opposite and intermediate constituents" . The resulting opposition between chords and fast, single-voice chromatic figures resembles the compositional alternation of clusters and melodic gestures in Karlheinz Stockhausen's Klavierstück X .
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In general, the harder the surface of the resonator, the more selective it will be, and the softer the surface, the more universal it will become. "[A] hard resonator will respond only when the vibrator contains an overtone that is exactly in tune with the resonator, while a soft resonator permits a wide range of fundamentals to pass through un-dampened but adds its own frequency as on overtone, harmonic or inharmonic as the case may be." Hardness carried to the extreme will result in a penetrating tone with a few very strong high partials. Softness carried to the extreme will result in a mushy, non-directional tone of little character.
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A spectrogram of a violin playing a note and then a perfect fifth above it with the shared partials highlighted by the white dashes (harmonic spectra) Harmonic spectrum (containing only harmonic overtones) Inharmonic spectrum of a bell (dashed gray lines indicate harmonic overtones) Spectral music uses the acoustic properties of sound – or sound spectra – as a basis for composition. Defined in technical language, spectral music is an acoustic musical practice where compositional decisions are often informed by sonographic representations and mathematical analysis of sound spectra, or by mathematically generated spectra. The spectral approach focuses on manipulating the spectral features, interconnecting them, and transforming them. In this formulation, computer-based sound analysis and representations of audio signals are treated as being analogous to a timbral representation of sound.
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