A monochord, also known as sonometer (see below), is an ancient

musical Musical is the adjective of music. Musical may also refer to: * Musical theatre, a performance art that combines songs, spoken dialogue, acting and dance * Musical film Musical film is a film genre in which songs by the Character (arts), charac ...

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: * triangle, quadrilateral, pentagon, hexagon, oc ...

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

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 String or strings may refer to: *String (structure), a long flexible structure made from threads twisted together, which is used to tie, bind, or hang other objects Arts, entertainment, and media Films * ''Strings'' (1991 film), a Canadian anim ...

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 railway) without blocking the path underneath. It is constructed for the purpose of providing passage over the obstacle, which is usually somet ...

are then manipulated to demonstrate mathematical relationships among the

frequencies Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...

produced. "With its single string, movable bridge and graduated rule, the monochord (''kanōn'' reek: law straddled the gap between notes and numbers, intervals 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 the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...

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'', pp. 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 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 plucked, it produces a pitch an

octave In music, an octave (: eighth) or perfect octave (sometimes called the diapason) is an interval between two notes, one having twice the frequency of vibration of the other. The octave relationship is a natural phenomenon that has been referr ...

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

tetractys The tetractys (), or tetrad, or the tetractys of the decad is a triangular number, 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 fourt ...

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

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

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. Accordingly it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime numb ...

"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">course_(music).html" ;"title=" course (music)">course" such as the mandolin. With two strings one can easily demonstrate how various musical interval (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 In music theory, a third is a Interval (music), musical interval encompassing three staff positions (see Interval (music)#Number, Interval number for more details), and the major third () is a third spanning four Semitone, half steps or two ...

(at 4/5th of the string length) or the

minor third In music theory, a minor third is a interval (music), musical interval that encompasses three half steps, or semitones. Staff notation represents the minor third as encompassing three staff positions (see: interval (music)#Number, interval numb ...

(at 5/6th of the string length) . Many contemporary composers focused on microtonality and

just intonation In music, just intonation or pure intonation is a musical tuning, tuning system in which the space between notes' frequency, frequencies (called interval (music), intervals) is a natural number, whole number ratio, ratio. Intervals spaced in thi ...

such as Harry Partch, Ivor Darreg,

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 Branca (October 6, 1948 – May 13, 2018) was an American avant-garde music, avant-garde composer, guitarist, and luthier. Known for his use of volume, scordatura, alternative guitar tunings, minimal music, repetition, drone (music), dronin ...

, Bart Hopkin, and Yuri Landman constructed multistring variants of sonometers with movable bridges.

Instruments

Parts of a monochord include a tuning peg, nut, string, moveable bridge, fixed bridge, calibration marks, belly or resonating box, and an end pin. Instruments derived from the monochord (or its moveable bridge) include the guqin, dan bau, koto, vina,

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

, and

clavichord The clavichord is a stringed rectangular keyboard instrument that was used largely in the Late Middle Ages, through the Renaissance music, Renaissance, Baroque music, Baroque and Classical period (music), Classical eras. Historically, it was most ...

("hence all keyboard instruments"). 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. End correction must be used with this method, to achieve accuracy.

Monochord practitioners

The monochord is mentioned in

Sumer Sumer () is the earliest known civilization, located in the historical region of southern Mesopotamia (now south-central Iraq), emerging during the Chalcolithic and Early Bronze Age, early Bronze Ages between the sixth and fifth millennium BC. ...

ian writings, and, according to some, was reinvented by

Pythagoras Pythagoras of Samos (; BC) was an ancient Ionian Greek philosopher, polymath, and the eponymous founder of Pythagoreanism. His political and religious teachings were well known in Magna Graecia and influenced the philosophies of P ...

(sixth century BCE). Dolge attributes the invention of the moveable bridge to

Guido of Arezzo Guido of Arezzo (; – after 1033) was an Italian music theorist and pedagogue of High medieval music. A Benedictine monk, he is regarded as the inventor—or by some, developer—of the modern Staff (music), staff notation that had a massive ...

around 1000 CE. 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, cosmol ...

devised a mundane monochord (also celestial or divine monochord) that linked the Ptolemaic 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, 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 ''Anthology of American Folk Music'' is a three-volume compilation album released in August 1952 by Folkways Records. The album was compiled by experimental filmmaker Harry Smith from his own personal collection of 78 rpm records. It consists ...

'' 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 ...

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 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 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, wit ...

as well as

contemporary classical music Contemporary classical music is Western art music composed close to the present day. At the beginning of the 21st-century classical music, 21st century, it commonly referred to the post-1945 Modernism (music), post-tonal music after the death of ...

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.

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