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.[1] The correct and accurate harmonic tuning is therefore important in creating a good strike tone.
The main partials sounded by the Erfurt bell (1497) or any harmonically-tuned bell in musical notation. The strike note/prime is E, with hum note, minor third, fifth, octave or nominal, and major third and perfect fifth in the second octave.
When a bell is struck, the energy imparted causes vibration of the bell in a complex manner and a series of tones known as partials or harmonics are generated.
"This atonal strike sound includes many inharmonic partials that die out quickly, giving way to a strike note or strike tone that is dominated by the prominent partials of the bell. Most observers identify the metallic strike note as having a pitch at or near the frequency of the strong second partial (prime or fundamental), but to others its pitch is an octave higher. Finally, as the sound of the bell ebbs, the slowly decaying hum tone (an octave below the prime, see subharmonic) lingers on."[3] "When a bell is properly struck, the first note that prominently attracts the attention of the ear is what is known as the strike note, tap note, or fundamental, this is what we call the note of the bell. The low sound heard after the strike note has lost its intensity is called the hum. There are also present a minor third and perfect fifth in the first octave, and a major third and perfect fifth in the second octave."[4]
Regarding their names: "When struck by its clapper, a bell vibrates in a complex way...In general, each normal mode of vibration contributes one partial to the sound of the bell. These partials are customarily given names such as hum, prime, minor third (or tierce), fifth (or quint), octave (or nominal), upper octave, etc. The strike note of the bell, which is determined by three partials (the octave, upper fifth, and the upper octave), is generally close to the pitch of the prime in a well-tuned bell."[5] Bells with good tone are well-tuned.[6]
"From this it will be seen that (1) the hum note should be a perfect octave below the strike note; (2) the nominal should be a perfect octave above the strike note; (3) the third above the strike note is a minor 3rd and the fifth perfect; (4) that all these notes should be in perfect tune with each other. Above the nominal the major 3rd and perfect 5th can be heard in bells of considerable size; in smaller bells they are so weak as not to be worthy of consideration."[6] However, historical approaches to bell tuning meant that in the past "Very few bells agree with these conditions. Generally the hum note is a sixth or seventh, and in rare cases a ninth below the strike note. The nominal is somewhere about an octave or a ninth above the strike note, and the other notes diverge accordingly. Bells that are swung are more likely to conform to the conditions than those that are struck."[7][8]
Tuning a bell
When the strike note or fundamental of a bell is tuned, its harmonic series must be tuned with it. Bells often contain secondary strike tones which are inharmonic, or unrelated to the harmonic series of the original strike note. "Whether a founder tunes the nominal or the strike note makes little difference, however, because the nominal is one of the main partials that determines the tuning of the strike note,"[9] the nominal, twelfth, and double octave being the most important in regards to strike note, resembling harmonics 2:3:4.
The hum tone, which should be an octave below the strike tone, is the actual first partial: "The strike tone appears to be the fifth partial of a rather unusual series: the ear misjudging it for the octave below, and accepting it as the fundamental of the series. That the strike tone is in some sense aural perception is no longer doubted: the most likely explanation is that it is a perceptual effect, possibly a difference tone created subjectively by the ear from two objectively existing partials."[1]
"It is interesting that the hum tone of a bell is generally not audible at all—the perceived pitch of the bell (called the 'strike tone') is one octave higher than the hum tone, and there is no component in the sound spectrum of the bell corresponding to the strike tone."[10] "The strike note is of great interest to psychoacousticians, because it is a subjective tone created by three strong nearly harmonic partials in the bell sound. The octave or nominal, the twelfth, and the upper octave normally have frequencies nearly in the ratios 2:3:4 [See Table]. The ear assumes these to be partials of a missing fundamental, which it hears as the strike note."[3] In a well-tuned bell the strike note is generally close to the prime.[11]
In chimes, modes 4, 5, and 6 appear to determine the strike tone and have frequencies in the ratios 92:112:132, or 81:121:169, "which are close enough to the ratios 2:3:4 for the ear to consider them nearly harmonic and to use them as a basis for establishing a virtual pitch."[11]Play chime note on Cⓘ
Spectrum of a Winchester Cathedral bell as analyzed by Jonathan Harvey using FFT. "The bell produces a secondary pitch (f') which lies outside that 'inharmonic series though it is clearly audible when the bell is struck, 'to curiously thrilling and disturbing effect.'" Play approximation The strike tone is middle C, the hum tone an octave below.
Downes, Michael (2009). Jonathan Harvey: Song offerings and White as jasmine. Farnham, England: Burlington, VT Ashgate. ISBN978-0-7546-6022-4. OCLC319321762.
A harmonic series is the sequence of harmonics, musical tones, or pure tones whose frequency is an integer multiple of a fundamental frequency.
In music, just intonation or pure intonation is the tuning of musical intervals as whole number ratios of frequencies. An interval tuned in this way is said to be pure, and is called a just interval. Just intervals consist of tones from a single harmonic series of an implied fundamental. For example, in the diagram, if the notes G3 and C4 are tuned as members of the harmonic series of the lowest C, their frequencies will be 3 and 4 times the fundamental frequency. The interval ratio between C4 and G3 is therefore 4:3, a just fourth.
In music, there are two common meanings for tuning:
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.
An overtone is any resonant frequency above the fundamental frequency of a sound. 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.
In music theory, an interval is a difference in pitch between two sounds. An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord.
In music, inharmonicity is the degree to which the frequencies of overtones depart from whole multiples of the fundamental frequency.
A combination tone is a psychoacoustic phenomenon of an additional tone or tones that are artificially perceived when two real tones are sounded at the same time. Their discovery is credited to the violinist Giuseppe Tartini and so they are also called Tartini tones.
A pseudo-octave, pseudooctave, or paradoxical octave in music is an interval whose frequency ratio is not 2:1, that of the octave, but is perceived or treated as equivalent to this ratio, and whose pitches are considered equivalent to each other as with octave equivalency.
A bell is a directly struck idiophone percussion instrument. Most bells have the shape of a hollow cup that when struck vibrates in a single strong strike tone, with its sides forming an efficient resonator. The strike may be made by an internal "clapper" or "uvula", an external hammer, or—in small bells—by a small loose sphere enclosed within the body of the bell.
Piano tuning is the process of adjusting the tension of the strings of an acoustic piano so that the musical intervals between strings are in tune. The meaning of the term 'in tune', in the context of piano tuning, is not simply a particular fixed set of pitches. Fine piano tuning requires an assessment of the vibration interaction among notes, which is different for every piano, thus in practice requiring slightly different pitches from any theoretical standard. Pianos are usually tuned to a modified version of the system called equal temperament.
Musical acoustics or music acoustics is a multidisciplinary field that combines knowledge from physics, psychophysics, organology, physiology, music theory, ethnomusicology, signal processing and instrument building, among other disciplines. As a branch of acoustics, it is concerned with researching and describing the physics of music – how sounds are employed to make music. Examples of areas of study are the function of musical instruments, the human voice, computer analysis of melody, and in the clinical use of music in music therapy.
In music, consonance and dissonance are categorizations of simultaneous or successive sounds. Within the Western tradition, some listeners associate consonance with sweetness, pleasantness, and acceptability, and dissonance with harshness, unpleasantness, or unacceptability, although there is broad acknowledgement that this depends also on familiarity and musical expertise. The terms form a structural dichotomy in which they define each other by mutual exclusion: a consonance is what is not dissonant, and a dissonance is what is not consonant. However, a finer consideration shows that the distinction forms a gradation, from the most consonant to the most dissonant. In casual discourse, as German composer and music theorist Paul Hindemith stressed, "The two concepts have never been completely explained, and for a thousand years the definitions have varied". The term sonance has been proposed to encompass or refer indistinctly to the terms consonance and dissonance.
Stretched tuning is a detail of musical tuning, applied to wire-stringed musical instruments, older, non-digital electric pianos, and some sample-based synthesizers based on these instruments, to accommodate the natural inharmonicity of their vibrating elements. In stretched tuning, two notes an octave apart, whose fundamental frequencies theoretically have an exact 2:1 ratio, are tuned slightly farther apart. "For a stretched tuning the octave is greater than a factor of 2; for a compressed tuning the octave is smaller than a factor of 2."
A Parsifal bell is a stringed musical instrument designed as a substitute for the church bells that are called for in the score of Richard Wagner's opera Parsifal.
In music, an electronic tuner is a device that detects and displays the pitch of musical notes played on a musical instrument. "Pitch" is the perceived fundamental frequency of a musical note, which is typically measured in Hertz. Simple tuners indicate—typically with an analog needle or dial, LEDs, or an LCD screen—whether a pitch is lower, higher, or equal to the desired pitch. Since the early 2010s, software applications can turn a smartphone, tablet, or personal computer into a tuner. More complex and expensive tuners indicate pitch more precisely. Tuners vary in size from units that fit in a pocket to 19" rack-mount units. Instrument technicians and piano tuners typically use more expensive, accurate tuners.
In music, the septimal minor third, also called the subminor third or septimal subminor third, is the musical interval exactly or approximately equal to a 7/6 ratio of frequencies. In terms of cents, it is 267 cents, a quartertone of size 36/35 flatter than a just minor third of 6/5. In 24-tone equal temperament five quarter tones approximate the septimal minor third at 250 cents. A septimal minor third is almost exactly two-ninths of an octave, and thus all divisions of the octave into multiples of nine have an almost perfect match to this interval. The septimal major sixth, 12/7, is the inverse of this interval.
In musical tuning, a temperament is a tuning system that slightly compromises the pure intervals of just intonation to meet other requirements. Most modern Western musical instruments are tuned in the equal temperament system. Tempering is the process of altering the size of an interval by making it narrower or wider than pure. "Any plan that describes the adjustments to the sizes of some or all of the twelve fifth intervals in the circle of fifths so that they accommodate pure octaves and produce certain sizes of major thirds is called a temperament." Temperament is especially important for keyboard instruments, which typically allow a player to play only the pitches assigned to the various keys, and lack any way to alter pitch of a note in performance. Historically, the use of just intonation, Pythagorean tuning and meantone temperament meant that such instruments could sound "in tune" in one key, or some keys, but would then have more dissonance in other keys.
In music, the undertone series or subharmonic series is a sequence of notes that results from inverting the intervals of the overtone series. While overtones naturally occur with the physical production of music on instruments, undertones must be produced in unusual ways. While the overtone series is based upon arithmetic multiplication of frequencies, resulting in a harmonic series, the undertone series is based on arithmetic division.
Dynamic tonality is a paradigm for tuning and timbre which generalizes the special relationship between just intonation, and the harmonic series to apply to a wider set of pseudo-just tunings and related pseudo-harmonic timbres.
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