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A string, tied at A, is kept in tension by W, a suspended weight, and two bridges, B and the movable bridge C, while D is a freely moving wheel, density may be tested by using different strings Monochord Jeans.png
A string, tied at A, is kept in tension by W, a suspended weight, and two bridges, B and the movable bridge C, while D is a freely moving wheel, density may be tested by using different strings

A monochord, also known as sonometer (see below), is an ancient musical and scientific laboratory instrument, involving one (mono) string (Chord). The term monochord is sometimes used as the class-name for any musical stringed instrument having only one string and a stick shaped body, also known as musical bows. According to the Hornbostel–Sachs system, string bows are bar zithers (311.1) while monochords are traditionally board zithers (314). The "harmonical canon", or monochord is, at its least, "merely a string having a board under it of exactly the same length, upon which may be delineated the points at which the string must be stopped to give certain notes," allowing comparison. [2]

Musical instrument History and classification

A musical instrument is an instrument created or adapted to make musical sounds. In principle, any object that produces sound can be considered a musical instrument—it is through purpose that the object becomes a musical instrument. The history of musical instruments dates to the beginnings of human culture. Early musical instruments may have been used for ritual, such as a trumpet to signal success on the hunt, or a drum in a religious ceremony. Cultures eventually developed composition and performance of melodies for entertainment. Musical instruments evolved in step with changing applications.

Chord (music) harmonic set of three or more notes

A chord, in music, is any harmonic set of pitches consisting of multiple notes that are heard as if sounding simultaneously. For many practical and theoretical purposes, arpeggios and broken chords, or sequences of chord tones, may also be considered as chords.

Musical bow simple string musical instrument

The musical bow is a simple string instrument used by a number of South African peoples, which is also found in the Americas via slave trade. It consists of a flexible, usually wooden, stick 1.5 to 10 feet long, and strung end to end with a taut cord, usually metal. It can be played with the hands or a wooden stick or branch. It is uncertain if the musical bow developed from the hunting bow, though the San or Bushmen people of the Kalahari Desert do convert their hunting bows to musical use.


A string is fixed at both ends and stretched over a sound box. One or more movable bridges are then manipulated to demonstrate mathematical relationships among the frequencies produced. "With its single string, movable bridge and graduated rule, the monochord (kanōn [Greek: law]) straddled the gap between notes and numbers, intervals and ratios, sense-perception and mathematical reason." [3] However, "music, mathematics, and astronomy were [also] inexorably linked in the monochord." [4] As a pedagogical tool for demonstrating mathematical relationships between intervals, the monochord remained in use throughout the middle ages. [5]

String (music) musical instrument part, made from metal or plastic

A string is the vibrating element that produces sound in string instruments such as the guitar, harp, piano, and members of the violin family. Strings are lengths of a flexible material that a musical instrument holds under tension so that they can vibrate freely, but controllably. Strings may be "plain", consisting only of a single material, like steel, nylon, or gut, or wound, having a "core" of one material and an overwinding of another. This is to make the string vibrate at the desired pitch, while maintaining a low profile and sufficient flexibility for playability.

Bridge (instrument) device for supporting the strings on a stringed instrument

A bridge is a device that supports the strings on a stringed musical instrument and transmits the vibration of those strings to another structural component of the instrument—typically a soundboard, such as the top of a guitar or violin—which transfers the sound to the surrounding air. Depending on the instrument, the bridge may be made of carved wood, metal or other materials. The bridge supports the strings and holds them over the body of the instrument under tension.

Frequency is the number of occurrences of a repeating event per unit of time. It is also referred to as temporal frequency, which emphasizes the contrast to spatial frequency and angular frequency. The period is the duration of time of one cycle in a repeating event, so the period is the reciprocal of the frequency. For example: if a newborn baby's heart beats at a frequency of 120 times a minute, its period—the time interval between beats—is half a second. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio signals (sound), radio waves, and light.

Experimental use

1/1, 5/4, 4/3, 3/2, and 2/1 (in C: C, E, F, G, C') Cordado1 English version.png
1/1, 5/4, 4/3, 3/2, and 2/1 (in C: C, E, F, G, C')

The monochord can be used to illustrate the mathematical properties of musical pitch and to illustrate Mersenne's laws regarding string length and tension: "essentially a tool for measuring musical intervals". [4] For example, when a monochord's string is open it vibrates at a particular frequency and produces a pitch. When the length of the string is halved, and plucked, it produces a pitch an octave higher and the string vibrates at twice the frequency of the original (2:1) Loudspeaker.svg   Play  . Half of this length will produce a pitch two octaves higher than the original—four times the initial frequency (4:1)—and so on. Standard diatonic Pythagorean tuning (Ptolemy's Diatonic Ditonic) is easily derived starting from superparticular ratios, (n+1)/n, constructed from the first four counting numbers, the tetractys, measured out on a monochord.[ citation needed ] The mathematics involved include the multiplication table, least common multiples, and prime and composite numbers. [4]

Mathematics Field of study concerning quantity, patterns and change

Mathematics includes the study of such topics as quantity, structure, space, and change.

Pitch (music) perceptual property in music

Pitch is a perceptual property of sounds that allows their ordering on a frequency-related scale, or more commonly, pitch is the quality that makes it possible to judge sounds as "higher" and "lower" in the sense associated with musical melodies. Pitch can be determined only in sounds that have a frequency that is clear and stable enough to distinguish from noise. Pitch is a major auditory attribute of musical tones, along with duration, loudness, and timbre.

Mersennes laws

Mersenne's laws are laws describing the frequency of oscillation of a stretched string or monochord, useful in musical tuning and musical instrument construction. The equation was first proposed by French mathematician and music theorist Marin Mersenne in his 1637 work Traité de l'harmonie universelle. Mersenne's laws govern the construction and operation of string instruments, such as pianos and harps, which must accommodate the total tension force required to keep the strings at the proper pitch. Lower strings are thicker, thus having a greater mass per unit length. They typically have lower tension. Guitars are a familiar exception to this - string tensions are similar, for playability, so lower string pitch is largely achieved with increased mass per length. Higher-pitched strings typically are thinner, have higher tension, and may be shorter. "This result does not differ substantially from Galileo's, yet it is rightly known as Mersenne's law," because Mersenne physically proved their truth through experiments. "Mersenne investigated and refined these relationships by experiment but did not himself originate them". Though his theories are correct, his measurements are not very exact, and his calculations were greatly improved by Joseph Sauveur (1653–1716) through the use of acoustic beats and metronomes.

Several string "monochord" Monocordiopitagoras20060330.png
Several string "monochord"

"As the name implies, only one string is needed to do the experiments; but, since ancient times, several strings were used, all tuned in exact unison, each with a moveable bridge, so that various intervals can be compared to each other [consonance and dissonance]." [4] A "bichord instrument" is one, "having two strings in unison for each note [a course]," such as the mandolin. [6] With two strings one can easily demonstrate how various musical intervals sound. Both open strings are tuned to the same pitch, and then the movable bridge is put in a mathematical position on the second string to demonstrate, for instance, the major third (at 4/5th of the string length) Loudspeaker.svg   Play   or the minor third (at 5/6th of the string length) Loudspeaker.svg   Play  .

Consonance and dissonance categorizations of simultaneous or successive sounds

In music, consonance and dissonance are categorizations of simultaneous or successive sounds. Consonance is associated with sweetness, pleasantness, and acceptability; dissonance is associated with harshness, unpleasantness, or unacceptability.

Course (music) two or more adjacent strings on a musical instrument

A course, on a stringed musical instrument, is two or more adjacent strings that are closely spaced relative to the other strings, and typically played as a single string. The strings in each course are typically tuned in unison or an octave. Course may also refer to a single string normally played on its own on an instrument with other multi-string courses, for example the bass (lowest) string on a nine-string baroque guitar.

Mandolin musical instrument in the lute family (plucked, or strummed)

A mandolin is a stringed musical instrument in the lute family and is usually plucked with a plectrum or "pick". It commonly has four courses of doubled metal strings tuned in unison, although five and six course versions also exist. The courses are normally tuned in a succession of perfect fifths. It is the soprano member of a family that includes the mandola, octave mandolin, mandocello and mandobass.

Many contemporary composers focused on microtonality and just intonation such as Harry Partch, Ivor Darreg, Tony Conrad, Glenn Branca, Bart Hopkin, and Yuri Landman constructed multistring variants of sonometers with movable bridges.

Just intonation

In music, just intonation or pure intonation is the tuning of musical intervals as (small) whole number ratios of frequencies. Any interval tuned in this way is called a just interval. Just intervals and chords are aggregates of harmonic series partials and may be seen as sharing a (lower) implied fundamental. For example, a tone with a frequency of 300 Hz and another with a frequency of 200 Hz are both multiples of 100 Hz. Their interval is, therefore, an aggregate of the second and third partials of the harmonic series of an implied fundamental frequency 100 Hz.

Harry Partch composer from the United States

Harry Partch was an American composer, music theorist, and creator of musical instruments. He composed using scales of unequal intervals in just intonation, and was one of the first 20th-century composers in the West to work systematically with microtonal scales. He built custom-made instruments in these tunings on which to play his compositions, and described his theory and practice in his book Genesis of a Music (1947).

Ivor Darreg was an American composer and leading proponent of microtonal or "xenharmonic" music. He also created a series of experimental musical instruments.


Monochords MIM String Instruments.jpg

Parts of a monochord include a tuning peg, nut, string, moveable bridge, fixed bridge, calibration marks, belly or resonating box, and an end pin. [4]

Nut (string instrument) part of a stringed instrument

A nut, on a stringed musical instrument, is a small piece of hard material that supports the strings at the end closest to the headstock or scroll. The nut marks one end of the vibrating length of each open string, sets the spacing of the strings across the neck, and usually holds the strings at the proper height from the fingerboard. Along with the bridge, the nut defines the vibrating lengths of the open strings.

Resonator device or system that exhibits resonance or resonant behavior, that is, it naturally oscillates at some frequencies, called its resonant frequencies, with greater amplitude than at others

A resonator is a device or system that exhibits resonance or resonant behavior, that is, it naturally oscillates at some frequencies, called its resonant frequencies, with greater amplitude than at others. The oscillations in a resonator can be either electromagnetic or mechanical. Resonators are used to either generate waves of specific frequencies or to select specific frequencies from a signal. Musical instruments use acoustic resonators that produce sound waves of specific tones. Another example is quartz crystals used in electronic devices such as radio transmitters and quartz watches to produce oscillations of very precise frequency.

Instruments derived from the monochord (or its moveable bridge) include the guqin, dan bau, koto, vina, hurdy-gurdy, and clavichord ("hence all keyboard instruments"). [4] A monopipe is the wind instrument version of a monochord; a variable open pipe which can produce variable pitches, a sliding cylinder with the numbers of the monochord marked. [7] End correction must be used with this method, to achieve accuracy.

Monochord practitioners

(1617) Fotothek df tg 0006469 Theosophie ^ Philosophie ^ Sonifikation ^ Musik ^ Musikinstrument.jpg
Guido d'Arezzo studying the monochord with Bishop Theobald. Guido d'Arezzo apprenant monocorde Theobald.jpg
Guido d'Arezzo studying the monochord with Bishop Theobald.
Medieval drawing of the philosopher Boethius Boethius.jpeg
Medieval drawing of the philosopher Boethius

The monochord is mentioned in Sumerian writings, and, according to some, was reinvented by Pythagoras (sixth century BCE). [4] Dolge attributes the invention of the moveable bridge to Guido of Arezzo around 1000 CE. [8]

In 1618, Robert Fludd devised a mundane monochord (also celestial or divine monochord) that linked the Ptolemaic universe to musical intervals. "Was it [Mersenne's discoveries through use of the monochord (1637)] physical intuition or a Pythagorean confidence in the importance of small whole numbers? ... It was the latter." [9]

The psalmodicon, a similar instrument but with a chromatic fret board replacing the moveable bridge, was developed in Denmark in the 1820s and became widespread throughout Scandinavia in churches as an alternative to the organ. Scandinavian immigrants also brought it to the United States. It became quite rare by the latter 20th century, but more recently has been revived by folk musicians.

An image of the celestial monochord was used on the 1952 cover of Anthology of American Folk Music by Harry Everett Smith and in the 1977 book The Cosmographical Glass: Renaissance Diagrams of the Universe (p. 133) by S. K. Heninger, Jr., ISBN   978-0-87328-208-6. A reproduction of the monochordum mundanum (mundane monochord) illustration from page 90 of Robert Fludd's "Utriusque Cosmi, Maioris scilicet et Minoris, Metaphysica, Physica, Atque Technica Historia" ("Tomus Primus"), 1617, was used as the cover art for Kepler Quartet's 2011 audio CD, Ben Johnston: String Quartets Nos. 1, 5 & 10 (New World Records Cat. No. 80693), which is classical music that uses pitch ratios extended to higher partials beyond the standard Pythagorean tuning system.

A modern playing technique used in experimental rock as well as contemporary classical music is 3rd bridge. This technique shares the same mechanism as used on the monochord, by dividing the string into two sections with an additional bridge.


Monochord Monochord3.png

A sonometer is a diagnostic instrument used to measure the tension, frequency or density of vibrations. They are used in medical settings to test both hearing and bone density. A sonometer, or audiometer, is used to determine hearing sensitivity, while a clinical bone sonometer measures bone density to help determine such conditions as the risk of osteoporosis.

In audiology, the device is used to test for hearing loss and other disorders of the ear. The audiometer measures the ability to hear sounds at frequencies normally detectable by the human ear. Several test are usually conducted using the audiometer which will then be used to assess hearing ability. Results typically are recorded on a chart known as an audiogram.

A clinical bone sonometer, approved for use in the United States by the Food and Drug Administration in 1998, is a device which tests for the risk of bone fractures associated with osteoporosis. This test, called an ultrasound bone densitometry screening, is not typically used for diagnostic purposes; it is generally used as a risk assessment tool. Testing is often recommended for those whose personal history and lifestyle choices indicate a possible high risk for osteoporosis. Testing is usually conducted by an orthopedist, rheumatologist or neurologist specializing in the treatment of osteoporosis. The patient simply places his or her heel in the sonometer, and it is then scanned using ultrasound to determine bone density. This is a fast and low-cost procedure generally lasting 30 seconds or less. Results typically are available immediately following the procedure. Two score results are possible: a T-score, which compares a patient's scan against that of a young person of the same gender; and a Z-score, which compares the scan against someone of similar age, weight and gender. The T-scores results are used to assess the risk of osteoporosis. A score above -1 indicates a low risk for osteoporosis; below -1 to -2.5 indicates a risk of developing osteoporosis; and a score below -2.5 indicates more intensive testing should be performed and that osteoporosis is likely present. The Z-score reports how much bone the patient has as compared to others his age. If this number is high or low, further testing may be ordered.

See also

Related Research Articles

Guitar fretted string instrument

The guitar is a fretted musical instrument that usually has six strings. It is typically played with both hands by strumming or plucking the strings with either a guitar pick or the finger(s)/fingernails of one hand, while simultaneously fretting with the fingers of the other hand. The sound of the vibrating strings is projected either acoustically, by means of the hollow chamber of the guitar, or through an electrical amplifier and a speaker.

Musical tuning umbrella term for the act of tuning an instrument and a system of pitches

In music, there are two common meanings for tuning:

Piano musical instrument

The piano is an acoustic, stringed musical instrument invented in Italy by Bartolomeo Cristofori around the year 1700, in which the strings are struck by hammers. It is played using a keyboard, which is a row of keys that the performer presses down or strikes with the fingers and thumbs of both hands to cause the hammers to strike the strings.


A harmonic is any member of the harmonic series. The term is employed in various disciplines, including music, physics, acoustics, electronic power transmission, radio technology, and other fields. It is typically applied to repeating signals, such as sinusoidal waves. A harmonic of such a wave is a wave with a frequency that is a positive integer multiple of the frequency of the original wave, known as the fundamental frequency. The original wave is also called the 1st harmonic, the following 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. 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, 150 Hz, 200 Hz and any addition of waves with these frequencies is periodic at 50 Hz.

An nth characteristic mode, for n > 1, will have nodes that are not vibrating. For example, the 3rd characteristic mode will have nodes at L and L, where L is the length of the string. In fact, each nth characteristic mode, for n not a multiple of 3, will not have nodes at these points. These other characteristic modes will be vibrating at the positions L and L. If the player gently touches one of these positions, then these other characteristic modes will be suppressed. The tonal harmonics from these other characteristic modes will then also be suppressed. Consequently, the tonal harmonics from the nth characteristic modes, where n is a multiple of 3, will be made relatively more prominent.


An overtone is any frequency greater than the fundamental frequency 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. These overlapping terms are variously used when discussing the acoustic behavior of musical instruments. 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.

Inharmonicity degree to which the frequencies of overtones depart from whole multiples of the fundamental frequency

In music, inharmonicity is the degree to which the frequencies of overtones depart from whole multiples of the fundamental frequency.

Piano tuning process of tuning a piano

Piano tuning is the act of making minute adjustments to the tensions of the strings of an acoustic piano to properly align the intervals between their tones so that the instrument is 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.

Piano wire

Piano wire, or "music wire", is a specialized type of wire made to become springs or to be used as piano strings. It is made from tempered high-carbon steel, also known as spring steel, which replaced iron as the material starting in 1834.

Intonation, in music, is a musician's realization of pitch accuracy, or the pitch accuracy of a musical instrument. Intonation may be flat, sharp, or both, successively or simultaneously.

Pythagorean interval

In musical tuning theory, a Pythagorean interval is a musical interval with frequency ratio equal to a power of two divided by a power of three, or vice versa. For instance, the perfect fifth with ratio 3/2 (equivalent to 31/21) and the perfect fourth with ratio 4/3 (equivalent to 22/31) are Pythagorean intervals.

Music and mathematics

Music theory has no axiomatic foundation in modern mathematics, yet the basis of musical sound can be described mathematically and exhibits "a remarkable array of number properties". Elements of music such as its form, rhythm and metre, the pitches of its notes and the tempo of its pulse can be related to the measurement of time and frequency, offering ready analogies in geometry.

Musical temperament a tuning system that slightly compromises the pure intervals of just intonation to meet other requirements

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. A temperament is 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." 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.

Werckmeister temperaments are the tuning systems described by Andreas Werckmeister in his writings. The tuning systems are numbered in two different ways: the first refers to the order in which they were presented as "good temperaments" in Werckmeister's 1691 treatise, the second to their labelling on his monochord. The monochord labels start from III since just intonation is labelled I and quarter-comma meantone is labelled II.


The Moodswinger is a twelve-string electric zither with an additional third bridge designed by Yuri Landman. The rod which functions as the third bridge divides the strings into two sections to cause an overtone multiphonic sound. One of the copies of the instrument is part of the collection of the Musical Instrument Museum in Phoenix, Arizona.

3rd bridge

The 3rd bridge is an extended playing technique used on the electric guitar and other string instruments that allows a musician to produce distinctive timbres and overtones that are unavailable on a conventional string instrument with two bridges. The timbre created with this technique is close to that of gamelan instruments like the bonang and similar Indonesian types of pitched gongs.

A third bridge can be devised by inserting a rigid preparation object between the strings and the body or neck of the instrument, effectively diving the string into distinct vibrating segments.

Scale of harmonics

The scale of harmonics is a musical scale based on the noded positions of the natural harmonics existing on a string. This musical scale is present on the guqin, regarded as one of the first string instruments with a musical scale. Most fret positions appearing on Non-Western string instruments (lutes) are equal to positions of this scale. Unexpectedly, these fret positions are actually the corresponding undertones of the overtones from the harmonic series. The distance from the nut to the fret is an integer number lower than the distance from the fret to the bridge.

Interval ratio ratio of the frequencies of the pitches in a musical interval

In music, an interval ratio is a ratio of the frequencies of the pitches in a musical interval. For example, a just perfect fifth is 3:2, 1.5, and may be approximated by an equal tempered perfect fifth which is 27/12. If the A above middle C is 440 Hz, the perfect fifth above it would be E, at (440*1.5=) 660 Hz, while the equal tempered E5 is 659.255 Hz.


  1. Jeans, Sir James (1937/1968). Science & Music, p.62. Dover. ISBN   0-486-61964-8.
  2. Dr. Crotch (October 1, 1861). "On the Derivation of the Scale, Tuning, Temperament, the Monochord, etc.", The Musical Times.
  3. Creese, David (2010). The Monochord in Ancient Greek Harmonic Science, p.vii. Cambridge. ISBN   9780521843249.
  4. 1 2 3 4 5 6 7 Terpstra, Siemen (1993). "An Introduction to the Monochord", Alexandria 2: The Journal of the Western Cosmological Traditions, Volume 2, p.137-9. David Fideler, ed. Red Wheel/Weiser. ISBN   9780933999978.
  5. Its common use is attested to by illustrations such as this one from an 11th century Norman manuscript: "Hybride tenant un monocorde et chantant." Musiconis Database. Université Paris-Sorbonne. Accessed January 5, 2018.
  6. "Bichord",
  7. Barbour, J. Murray (2013). Tuning and Temperament: A Historical Survey, p.xlviii. Dover/Courier. ISBN   9780486317359. Barbour uses quotes around "what might be called a 'monopipe'".
  8. Dolge, Alfred (1911). Pianos and Their Makers Volume 1: A comprehensive history of the development of the piano from the monochord to the concert grand player piano , p.28. Covina. [ISBN unspecified].
  9. Gozza, Paolo; ed. (2013). Number to Sound: The Musical Way to the Scientific Revolution, p.279. Springer. ISBN   9789401595780. Gozza is referring to statements by Sigalia Dostrovsky's "Early Vibration Theory", p.185-187.