A monochord, also known as sonometer (see below), is an ancient musical and scientific laboratory instrument, involving one (

mono- Numeral or number prefixes are prefixes derived from numerals or occasionally other numbers. In English and many other languages, they are used to coin numerous series of words. For example: * unicycle, bicycle, tricycle (1-cycle, 2-cycle, 3-cy ...

) 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 bow The musical bow (bowstring or string bow, a subset of bar zithers) 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 ...

s. According to the

Hornbostel–Sachs Hornbostel–Sachs or Sachs–Hornbostel is a system of musical instrument classification devised by Erich Moritz von Hornbostel and Curt Sachs, and first published in the in 1914. An English translation was published in the '' Galpin Society Jo ...

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. A string is fixed at both ends and stretched over a sound box. One or more movable

bridges A bridge is a structure built to span a physical obstacle (such as a body of water, valley, road, or rail) without blocking the way underneath. It is constructed for the purpose of providing passage over the obstacle, which is usually someth ...

are then manipulated to demonstrate mathematical relationships among the frequencies produced. "With its single string, movable bridge and graduated rule, the monochord (''kanōn'' reek: law straddled the gap between

notes Note, notes, or NOTE may refer to: Music and entertainment * Musical note, a pitched sound (or a symbol for a sound) in music * ''Notes'' (album), a 1987 album by Paul Bley and Paul Motian * ''Notes'', a common (yet unofficial) shortened versio ...

and numbers,

intervals Interval may refer to: Mathematics and physics * Interval (mathematics), a range of numbers ** Partially ordered set#Intervals, its generalization from numbers to arbitrary partially ordered sets * A statistical level of measurement * Interval e ...

and

ratio In mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...

s, sense-perception and mathematical reason." However, "music, mathematics, and

astronomy Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, g ...

were lsoinexorably linked in the monochord."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. . As a pedagogical tool for demonstrating mathematical relationships between intervals, the monochord remained in use throughout the middle ages.

Experimental use

The monochord can be used to illustrate the mathematical properties of musical pitch and to illustrate

Mersenne's 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. Overview The equation was first proposed by French mathematician and music theor ...

regarding string length and tension: "essentially a tool for measuring musical intervals". 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

pluck Pluck or plucking may refer to: Removal * Plucking (hair removal), the removal of hair, fur, or feathers * Feather-plucking, a behavior in birds * Plucking post, as used by birds of prey to dismember their prey * Plucking (glaciation), a proces ...

ed, it produces a pitch an octave higher and the string vibrates at twice the frequency of the original (2:1) . 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 In mathematics, a superparticular ratio, also called a superparticular number or epimoric ratio, is the ratio of two consecutive integer numbers. More particularly, the ratio takes the form: :\frac = 1 + \frac where is a positive integer. Thu ...

ratios, (n+1)/n, constructed from the first four counting numbers, the

tetractys The tetractys ( el, τετρακτύς), or tetrad, or the tetractys of the decad is a triangular figure consisting of ten points arranged in four rows: one, two, three, and four points in each row, which is the geometrical representation of the ...

, measured out on a monochord. The mathematics involved include the

multiplication table In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system. The decimal multiplication table was traditionally taught as an essenti ...

least common multiple In arithmetic and number theory, the least common multiple, lowest common multiple, or smallest common multiple of two integers ''a'' and ''b'', usually denoted by lcm(''a'', ''b''), is the smallest positive integer that is divisible by bo ...

s, and

prime A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

and

composite number A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime, ...

"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 ." A "bichord instrument" is one, "having two strings in unison for each note course.html"_;"title="course_(music).html"_;"title="_course_(music)">course">course_(music).html"_;"title="_course_(music)">course"_such_as_the_

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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) or the minor third (at 5/6th of the string length) . Many contemporary composers focused on microtonality and just intonation such as Harry Partch,

Ivor Darreg Ivor Darreg (May 5, 1917 – February 12, 1994) was an American composer and leading proponent of microtonal or " xenharmonic" music. He also created a series of experimental musical instruments. Biography Darreg, a contemporary of Harry Part ...

Tony Conrad Anthony Schmalz Conrad (March 7, 1940 – April 9, 2016) was an American video artist, experimental filmmaker, musician, composer, sound artist, teacher, and writer. Active in a variety of media since the early 1960s, he was a pioneer of both ...

Glenn Branca Glenn may refer to: Name or surname * Glenn (name) * John Glenn, U.S. astronaut Cultivars * Glenn (mango) * a 6-row barley variety Places In the United States: * Glenn, California * Glenn County, California * Glenn, Georgia, a settleme ...

Bart Hopkin Bart Hopkin is a builder of experimental musical instruments and a writer and publisher on the subject. Hopkin runs the website windworld.com, which provides resources regarding unusual instruments. Hopkin published the magazine ''Experimental Mu ...

, and

Yuri Landman Yuri Landman (born 1 February 1973) is a Dutch inventor of musical instruments and musician who has made several experimental electric string instruments for a number of artists including Lee Ranaldo of Sonic Youth, Liars, Jad Fair of Half Japan ...

constructed multistring variants of sonometers with movable bridges.

Instruments

Parts of a monochord include a

tuning peg A variety of methods are used to tune different stringed instruments. Most change the pitch produced when the string is played by adjusting the tension of the strings. A tuning peg in a pegbox is perhaps the most common system. A peg has a ...

nut Nut often refers to: * Nut (fruit), fruit composed of a hard shell and a seed, or a collective noun for dry and edible fruits or seeds * Nut (hardware), fastener used with a bolt Nut or Nuts may also refer to: Arts, entertainment, and media Co ...

, string, moveable bridge, fixed bridge, calibration marks, belly or resonating box, and an

end pin The endpin is the component of a cello or double bass that makes contact with the floor to support the instrument's weight. It is made of metal, carbon fiber, or, occasionally, wood, and is typically extensible from the bottom of the instrument, s ...

. Instruments derived from the monochord (or its moveable bridge) include the

guqin The ''guqin'' (; ) is a plucked seven-string Chinese musical instrument. It has been played since ancient times, and has traditionally been favoured by scholars and Scholar-bureaucrats, literati as an instrument of great subtlety and refinemen ...

dan bau Dan or DAN may refer to: People * Dan (name), including a list of people with the name ** Dan (king), several kings of Denmark * Dan people, an ethnic group located in West Africa **Dan language, a Mande language spoken primarily in Côte d'Ivoi ...

koto Koto may refer to: * Koto (band), an Italian synth pop group * Koto (instrument), a Japanese musical instrument * Koto (kana), a ligature of two Japanese katakana * Koto (traditional clothing), a traditional dress made by Afro-Surinamese women * K ...

, vina,

hurdy-gurdy The hurdy-gurdy is a string instrument that produces sound by a hand-crank-turned, rosined wheel rubbing against the strings. The wheel functions much like a violin bow, and single notes played on the instrument sound similar to those of a vi ...

, and

clavichord The clavichord is a stringed rectangular keyboard instrument that was used largely in the Late Middle Ages, through the Renaissance, Baroque and Classical eras. Historically, it was mostly used as a practice instrument and as an aid to compositi ...

("hence all keyboard instruments"). A monopipe is the wind instrument version of a monochord; a variable open

pipe Pipe(s), PIPE(S) or piping may refer to: Objects * Pipe (fluid conveyance), a hollow cylinder following certain dimension rules ** Piping, the use of pipes in industry * Smoking pipe ** Tobacco pipe * Half-pipe and quarter pipe, semi-circular ...

which can produce variable pitches, a sliding cylinder with the numbers of the monochord marked.

End correction Whenever a wave forms through a medium/object (organ pipe) with a closed/open end, there is a chance of error in the formation of the wave, i.e. it may not actually start from the opening of the object but instead before the opening, thus resulting ...

must be used with this method, to achieve accuracy.

Monochord practitioners

Fotothek df tg 0006469 Theosophie ^ Philosophie ^ Sonifikation ^ Musik ^ Musikinstrument

Guido d'Arezzo apprenant monocorde Theobald

The monochord is mentioned in Sumerian writings, and, according to some, was reinvented by

Pythagoras Pythagoras of Samos ( grc, Πυθαγόρας ὁ Σάμιος, Pythagóras ho Sámios, Pythagoras the Samian, or simply ; in Ionian Greek; ) was an ancient Ionian Greek philosopher and the eponymous founder of Pythagoreanism. His politi ...

(sixth century BCE). Dolge attributes the invention of the moveable bridge to Guido of Arezzo around 1000 CE.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. . In 1618,

Robert Fludd Robert Fludd, also known as Robertus de Fluctibus (17 January 1574 – 8 September 1637), was a prominent English Paracelsian physician with both scientific and occult interests. He is remembered as an astrologer, mathematician, cosmologis ...

devised a mundane monochord (also celestial or divine monochord) that linked the

Ptolemaic Ptolemaic is the adjective formed from the name Ptolemy, and may refer to: Pertaining to the Ptolemaic dynasty * Ptolemaic dynasty, the Macedonian Greek dynasty that ruled Egypt founded in 305 BC by Ptolemy I Soter * Ptolemaic Kingdom Pertaining ...

universe to musical intervals. "Was it ersenne'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."Gozza, Paolo; ed. (2013). ''Number to Sound: The Musical Way to the Scientific Revolution'', p.279. Springer. . Gozza is referring to statements by Sigalia Dostrovsky's "Early Vibration Theory", p.185-187. The

psalmodicon The psalmodicon (psalmodikon or salmodikon) is a stringed musical instrument; the most common variants have a single string. It was developed in Scandinavia for simplifying music in churches and schools, and as an alternative to the fiddle for ...

, 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 Harry Everett Smith (May 29, 1923 – November 27, 1991) was an American polymath, who was credited variously as an artist, experimental filmmaker, bohemian, mystic, record collector, hoarder, student of anthropology and a Neo-Gnostic bis ...

and in the 1977 book ''The Cosmographical Glass: Renaissance Diagrams of the Universe'' (p. 133) by S. K. Heninger Jr., . 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 New World Records is a record label that was established in 1975 through a Rockefeller Foundation grant to celebrate America's bicentennial (1976) by producing a 100-LP anthology, with American music from many genres.experimental rock Experimental rock, also called avant-rock, is a subgenre of rock music that pushes the boundaries of common composition and performance technique or which experiments with the basic elements of the genre. Artists aim to liberate and innovate, with ...

as well as contemporary classical music is

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 bri ...

. This technique shares the same mechanism as used on the monochord, by dividing the string into two sections with an additional bridge.

Sonometer

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 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 indicates 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.

References

External links