South African units of measurement

A number of units of measurement were used in South Africa to measure quantities like length, mass, capacity, etc. The Imperial system of measurements was made standard in 1922 and the metric system was adopted in 1970.
System before metric system.
British and old Dutch systems were used.
Length.
The Rhynland rood ("Rijnlandse roede") was a standard Dutch measurement. It was changed in 1859 to the "Cape Foot" due to a drift in standards.
Mass.
One bundle was equal to 0.699 (≈0.7) lbs. [].
Area.
One morgen was equal to .
Capacity.
Several units were used. Some units are provided below:
Dry measures.
These were used to measure rice and salt.
Corn measures.
These were used to measure grain.
Liquid measures.
The country didn't have a unified system of liquid measurement in the 19th century because the Afrikaners used the Dutch gallon and the British used the Imperial gallon. When measuring alcohol, the British system was used only for ale and beer and the Dutch system was used only for wine, brandy and distilled spirits. This was due to specialization in the two colonies, which were not united until 1910. Vintning was more common among the Boer farmers of the Western Cape, who dominated the industry. Meanwhile, the British farmers grew grain that could be brewed into beer. Wine was for export and beer, which was perishable, was for domestic consumption. Each community used their own standard measurement systems to store, sell and ship their wares.
Ale & beer.
The "firkin", "kilderkin", barrel, "hogshead", and "butt" were traditional British measurements of capacity for standard ale and beer containers. They were based on the British ale gallon. (Once there were different measures for ale and beer before the Ale gallon measure became standard for both in 1688; the Ale gallon then became the Imperial gallon in 1824).
Beer bottles in South Africa were different than in other countries.
Wine.
The Dutch East India company used the Cape of Good Hope as a waystation between Europe and the East Indies in the 17th and 18th centuries. Dutch sailors drank the local wine to combat scurvy and exported barrels of it back to Europe. This was followed by the British government's policy of encouraging the wine and brandy industry in South Africa in the early- to mid-19th century through subsidies and low tariffs. (Their recent isolation during Napoleon's Continental System impressed upon them that they would potentially need alternative sources of European commodities in the future.)
The "kanne", "anker", "ahm", and "legger" are obsolete 17th century Dutch measurements of capacity that were used for standard containers of wine and spirits. The standard "Dutch gallon" used was based on that of Amsterdam. They were typically sold in "ankers", half-aums, and "leggers" until 1922, when the Imperial measurement system went into effect.
Gasoline.
Gasoline was formerly sold in Imperial gallons [1 Imp. gal. = 4.55 l], but was switched to litres after the adoption of the metric system.


Rebecca Doerge

Rebecca Whitbeck Doerge is an American researcher in statistical bioinformatics, known for her research on quantitative traits. Formerly the Trent and Judith Anderson Distinguished Professor of Statistics at Purdue University, she is currently the dean of the Mellon College of Science at Carnegie Mellon University, with joint appointments in the departments of biology and statistics.
Education and career.
Doerge was born in Stamford, New York. After graduating in mathematics from the University of Utah in 1986, she earned a master's degree in statistics from Utah in 1988, advised there by Simon Tavaré. She then completed a Ph.D. in statistics from North Carolina State University in 1993. Her dissertation, supervised by Bruce Weir, was "Statistical Methods for Locating Quantitative Trait Loci with Molecular Markers".
After postdoctoral research with Gary Churchill at Cornell University, Doerge joined the Purdue University faculty in 1995. She chaired the Department of Statistics there from 2010 to 2015, and was appointed as Anderson Distinguished Professor in 2011. She moved to Carnegie Mellon to become dean in 2016.
Awards and honors.
Doerge became a fellow of the American Association for the Advancement of Science and of the American Statistical Association in 2007.


4786 Tatianina

4786 Tatianina, provisional designation , is a bright background asteroid and synchronous binary system from the inner regions of the asteroid belt, approximately in diameter. It was discovered on 13 August 1985, by Soviet astronomer Nikolai Chernykh at the Crimean Astrophysical Observatory in Nauchnij, on the Crimean peninsula. It was named after Tatiana Somova, a friend of the discoverer. The E-/Xc-subtype has a short rotation period of 2.9 hours. Its sub-kilometer minor-planet moon was discovered on 20 March 2006 and announced the following month.
Orbit and classification.
"Tatianina" is a non-family asteroid from the main belt's background population. It orbits the Sun in the inner asteroid belt at a distance of 1.9–2.8 AU once every 3 years and 7 months (1,322 days; semi-major axis of 2.36 AU). Its orbit has an eccentricity of 0.19 and an inclination of 7° with respect to the ecliptic.
The asteroid was first observed as at the Algiers Observatory in April 1948. The body's observation arc begins at Nauchnij in May 1970 as , more than 15 years prior to its official discovery observation.
Physical characteristics.
In the SMASS classification, "Tatianina" is a Xc-subtype that transitions from the X-type to the carbonaceous C-type asteroids. It has also been characterized as a bright E-type by the Wide-field Infrared Survey Explorer (WISE).
Rotation period.
Several rotational lightcurves of "Tatianina" have been obtained from photometric observations since 2003 (). Analysis of the best-rated lightcurve from March 2003, during which a satellite was also discovered "(see below)", gave a rotation period of 2.9227 hours with a brightness amplitude of 0.19 and 0.20 magnitude ().
Diameter and albedo.
According to the survey carried out by the NEOWISE mission of NASA's WISE telescope, "Tatianina" measures between 3.282 and 3.475 kilometers in diameter and its surface has an exceptionally high albedo of 0.4763 to 0.514. The "Collaborative Asteroid Lightcurve Link" adopts the revised WISE-data by Petr Pravec, that is an albedo of 0.4763 and rounded diameter of 3.48 kilometers based on an absolute magnitude of 13.718.
Satellite.
During the photometric observations by Donald Pray, Petr Pravec and collaborators in March 2006, it was revealed that "Tatianina" is a synchronous binary asteroid with a minor-planet moon orbiting it every 21.67 hours at an estimated average distance of . The discovery was announced on 11 April 2006. The mutual occultation events suggest the presence of a satellite with an estimated diameter of meters or 19% the size of its primary.
Numbering and naming.
This minor planet was numbered on 28 April 1991. It was named by the discoverer after Tatiana Aleksandrovna Somova, a nursery-school teacher in Saint Petersburg, Russia. The official naming citation was published by the Minor Planet Center on 5 March 1996 ().


Celsius

The degree Celsius is a unit of temperature on the Celsius scale, a temperature scale originally known as the centigrade scale. The degree Celsius (symbol: °C) can refer to a specific temperature on the Celsius scale or a unit to indicate a difference or range between two temperatures. It is named after the Swedish astronomer Anders Celsius (1701–1744), who developed a similar temperature scale. Before being renamed to honor Anders Celsius in 1948, the unit was called "centigrade", from the Latin "centum", which means 100, and "gradus", which means steps.
Since 1743 the Celsius scale has been based on 0 °C for the freezing point of water and 100 °C for the boiling point of water at 1 atm pressure. Prior to 1743 the values were reversed (i.e. the boiling point was 0 degrees and the freezing point was 100 degrees). The 1743 scale reversal was proposed by Jean-Pierre Christin.
By international agreement, between 1954 and 2019 the unit and the Celsius scale were defined by absolute zero and the triple point of Vienna Standard Mean Ocean Water (VSMOW), a precisely defined water standard. This definition also precisely related the Celsius scale to the Kelvin scale, which defines the SI base unit of thermodynamic temperature with symbol K. Absolute zero, the lowest temperature possible, is defined as being exactly 0 K and −273.15 °C. Until 19 May 2019, the temperature of the triple point of water was defined as exactly . This means that a temperature difference of one degree Celsius and that of one kelvin are exactly the same.
On 20 May 2019, the kelvin was redefined so that its value is now determined by the definition of the Boltzmann constant rather than being defined by the triple point of VSMOW. This means that the triple point is now a measured value, not a defined value. The newly-defined exact value of the Boltzmann constant was selected so that the measured value of the VSMOW triple point is exactly the same as the older defined value to within the limits of accuracy of contemporary metrology. The degree Celsius remains exactly equal to the kelvin, and 0 K remains exactly −273.15 °C.
History.
In 1742, Swedish astronomer Anders Celsius (1701–1744) created a temperature scale that was the reverse of the scale now known as "Celsius": 0 represented the boiling point of water, while 100 represented the freezing point of water. In his paper "Observations of two persistent degrees on a thermometer", he recounted his experiments showing that the melting point of ice is essentially unaffected by pressure. He also determined with remarkable precision how the boiling point of water varied as a function of atmospheric pressure. He proposed that the zero point of his temperature scale, being the boiling point, would be calibrated at the mean barometric pressure at mean sea level. This pressure is known as one standard atmosphere. The BIPM's 10th General Conference on Weights and Measures (CGPM) in 1954 defined one standard atmosphere to equal precisely 1,013,250 dynes per square centimeter (101.325 kPa).
In 1743, the Lyonnais physicist Jean-Pierre Christin, permanent secretary of the Academy of Lyon, inverted the celsius scale so that 0 represented the freezing point of water and 100 represented the boiling point of water. Some credit Christin for independently inventing the reverse of Celsius' original scale, while others believe Christin merely reversed Celsius' scale. On 19 May 1743 he published the design of a mercury thermometer, the "Thermometer of Lyon" built by the craftsman Pierre Casati that used this scale.
In 1744, coincident with the death of Anders Celsius, the Swedish botanist Carl Linnaeus (1707–1778) reversed Celsius's scale. His custom-made "linnaeus-thermometer", for use in his greenhouses, was made by Daniel Ekström, Sweden's leading maker of scientific instruments at the time, whose workshop was located in the basement of the Stockholm observatory. As often happened in this age before modern communications, numerous physicists, scientists, and instrument makers are credited with having independently developed this same scale; among them were Pehr Elvius, the secretary of the Royal Swedish Academy of Sciences (which had an instrument workshop) and with whom Linnaeus had been corresponding; , the instrument maker; and Mårten Strömer (1707–1770) who had studied astronomy under Anders Celsius.
The first known Swedish document reporting temperatures in this modern "forward" Celsius scale is the paper "Hortus Upsaliensis" dated 16 December 1745 that Linnaeus wrote to a student of his, Samuel Nauclér. In it, Linnaeus recounted the temperatures inside the orangery at the University of Uppsala Botanical Garden:
Centigrade versus Celsius.
Since the 19th century, the scientific and thermometry communities worldwide have used the phrase "centigrade scale" and temperatures were often reported simply as "degrees" or, when greater specificity was desired, as "degrees centigrade", with the symbol °C.
However, the term "centigrade" was also used in the Spanish and French languages as a unit of angular measurement (1/100 of a right angle), and it had a similar connotation in other languages. The term "centesimal degree" or "gradian" ("grad" or "gon": 100g = 90°, 1g = 0.9°) was used when unambiguous language was required by international standards bodies such as the BIPM. It would more properly now be called "hectograde".
To eliminate confusion between the unit of temperature and the unit of angular measurement, the 9th meeting of the General Conference on Weights and Measures and the Comité International des Poids et Mesures (CIPM) formally adopted "degree Celsius" in 1948 for the degree of temperature, and kept the recognized degree symbol (), rather than adopting the gradian/centesimal degree symbol (g or gon).
For scientific use, "Celsius" is the term usually used, but in English-speaking countries "centigrade" remains in common use, especially in informal contexts. It was not even until February 1985 that the weather forecasts issued by the BBC switched the term from "centigrade" to "Celsius".
Common temperatures.
Some key temperatures relating the Celsius scale to other temperature scales are shown in the table below.
Name and symbol typesetting.
The "degree Celsius" has been the only SI unit whose full unit name contains an uppercase letter since 1967, when the SI base unit for temperature became the kelvin, replacing the capitalized term "degrees Kelvin". The plural form is "degrees Celsius".
The general rule of the International Bureau of Weights and Measures (BIPM) is that the numerical value always precedes the unit, and a space is always used to separate the unit from the number, (not " or "). The only exceptions to this rule are for the unit symbols for degree, minute, and second for plane angle (°, ′, and ″, respectively), for which no space is left between the numerical value and the unit symbol. Other languages, and various publishing houses, may follow different typographical rules.
Unicode character.
Unicode provides the Celsius symbol at code point . However, this is a compatibility character provided for roundtrip compatibility with legacy encodings. It easily allows correct rendering for vertically written East Asian scripts, such as Chinese. The Unicode standard explicitly discourages the use of this character: "In normal use, it is better to represent degrees Celsius "°C" with a sequence of + , rather than . For searching, treat these two sequences as identical."
Temperatures and intervals.
The degree Celsius is subject to the same rules as the kelvin with regard to the use of its unit name and symbol. Thus, besides expressing specific temperatures along its scale (e.g. "Gallium melts at 29.7646 °C" and "The temperature outside is 23 degrees Celsius"), the degree Celsius is also suitable for expressing temperature "intervals": differences between temperatures or their uncertainties (e.g. "The output of the heat exchanger is hotter by 40 degrees Celsius", and "Our standard uncertainty is ±3 °C"). Because of this dual usage, one must not rely upon the unit name or its symbol to denote that a quantity is a temperature interval; it must be unambiguous through context or explicit statement that the quantity is an interval. This is sometimes solved by using the symbol °C (pronounced "degrees Celsius") for a temperature, and C° (pronounced "Celsius degrees") for a temperature interval, although this usage is non-standard. Another way to express the same is , which can be commonly found in literature.
Celsius measurement follows an interval system but not a ratio system; and it follows a relative scale not an absolute scale. For example, an object at 20 °C does not have twice the energy of when it is 10 °C; and 0 °C is not the lowest Celsius value. Thus, degrees Celsius is a useful interval measurement but does not possess the characteristics of ratio measures like weight or distance.
Coexistence of Kelvin and Celsius scales.
In science and in engineering, the Celsius scale and the Kelvin scale are often used in combination in close contexts, e.g. "a measured value was 0.01023 °C with an uncertainty of 70 μK". This practice is permissible because the magnitude of the degree Celsius is equal to that of the kelvin. Notwithstanding the official endorsement provided by decision no. 3 of Resolution 3 of the 13th CGPM, which stated "a temperature interval may also be expressed in degrees Celsius", the practice of simultaneously using both °C and K remains widespread throughout the scientific world as the use of SI-prefixed forms of the degree Celsius (such as "μ°C" or "microdegrees Celsius") to express a temperature interval has not been well adopted.
Melting and boiling points of water.
The melting and boiling points of water are no longer part of the definition of the Celsius scale. In 1948, the definition was changed to use the triple point of water. In 2005 the definition was further refined to use water with precisely defined isotopic composition (VSMOW) for the triple point. In 2019, the definition was changed to use the Boltzmann constant, completely decoupling the definition of the kelvin from the properties of water. Each of these formal definitions left the numerical values of the Celsius scale identical to the prior definition to within the limits of accuracy of the metrology of the time.
When the melting and boiling points of water ceased being part of the definition, they became measured quantities instead. This is also true of the triple point.
In 1948 when the 9th General Conference on Weights and Measures (CGPM) in Resolution 3 first considered using the triple point of water as a defining point, the triple point was so close to being 0.01 °C greater than water's known melting point, it was simply defined as precisely 0.01 °C. However, later measurements showed that the difference between the triple and melting points of VSMOW is actually very slightly (<0.001 °C) greater than 0.01 °C. Thus, the actual melting point of ice is very slightly (less than a thousandth of a degree) below 0 °C. Also, defining water's triple point at 273.16 K precisely defined the magnitude of each 1 °C increment in terms of the absolute thermodynamic temperature scale (referencing absolute zero). Now decoupled from the actual boiling point of water, the value "100 °C" is hotter than 0 °C – in absolute terms – by a factor of "precisely" (approximately 36.61% thermodynamically hotter). When adhering "strictly" to the two-point definition for calibration, the boiling point of VSMOW under one standard atmosphere of pressure was actually 373.1339 K (99.9839 °C). When calibrated to ITS-90 (a calibration standard comprising many definition points and commonly used for high-precision instrumentation), the boiling point of VSMOW was slightly less, about 99.974 °C.
This boiling-point difference of 16.1 millikelvins between the Celsius scale's original definition and the previous one (based on absolute zero and the triple point) has little practical meaning in common daily applications because water's boiling point is very sensitive to variations in barometric pressure. For example, an altitude change of only 28 cm (11 in) causes the boiling point to change by one millikelvin.


EF Standard English Test

The EF Standard English Test is a standardized test of the English language designed for non-native English speakers. It is the product of EF Education First, a global language training company, and a team of language assessment experts including Lyle Bachman, Mari Pearlman, and Ric Luecht. EF compares the EFSET's accuracy to the most widely used high stakes standardized English tests: TOEFL, IELTS, and Cambridge International Examinations.
There are three versions of the EFSET: a 15-minute test ("EFSET Quick English Check"), a 50-minute test which assigns a score on the 6-level Common European Framework of Reference for Languages ("EFSET English Certificate"), and a 2-hour test which assigns a score from 0 to 100 with a TOEFL and IELTS equivalency score in addition to the 6-level CEFR score ("EFSET English Certificate Plus"). All test versions assess receptive skills only (reading and listening comprehension) and do not assess writing or speaking Unlike other standardized English tests, the EFSET uses computerized adaptive testing methods to adjust the difficulty of the test according to the examinee's ability level. The EFSET is not a proctored exam.
Test launch.
EF Education First initially intended to build the EFSET for internal use as a low-cost alternative to third party standardized English tests, with the aim of attaining the same level of accuracy as those tests. Soon, the company realized it could gain branding benefits from releasing a robust, testing tool for any English learner to use. The initial public launch of the EFSET in 2014 was the result of a 3-year process, which included 15 months of formal trials involving 14,500 students.
Scoring.
The EFSET English Certificate Plus is scored on a scale of 0 to 100 with a separate score attributed for reading and listening as well as an overall score. EFSET English Certificate Plus scores are mapped to the 6-level CEFR bands from A1 to C2 as well as to IELTS and TOEFL scores as shown in the table below.


Foundation Insurance Test

The Foundation Insurance Test (FIT) is an insurance qualification in the United Kingdom. The Foundation Insurance Test is considered an entry-level qualification for those beginning insurance careers and is usually taken before advancing to more demanding examinations such as the CII exams. The exam is multiple choice and in 2012 the exam had a pass rate of 78.43%. A nominal pass mark is set at 70% although the actual pass mark may vary.
The test covers several areas of insurance:


260 Huberta

Huberta (minor planet designation: 260 Huberta) is a large asteroid orbiting near the outer edge of the Main belt. It is dark and rich in carbon.
It belongs to the Cybele group of asteroids and may have been trapped in a 4:7 orbital resonance with Jupiter.
It was discovered by Johann Palisa on 3 October 1886 in Vienna and was named after Saint Hubertus.


Microphone stand

A microphone stand is a free-standing mount for a microphone. It allows the microphone to be positioned in the studio, on stage or on location without requiring a person to hold it.
The most basic microphone stand is a "straight stand". It uses a dome-shaped round metal base, or a tripod base, into which is threaded a post for mounting the microphone (most commonly a 5/8-27 threaded hole). This post may be made up of two or more telescoping tubes that fit inside each other, allowing for quick height adjustment. The mechanism for adjusting the height is called the clutch.
There are various versions of the straight stand known as the "desk stand" (short version of straight stand) and heavy duty microphone stand (heavier base and larger tubes) to handle heavy microphones. The tubes used on the straight stand usually have a shiny chrome plating to resist scratching, but may also be finished in a matte black.
A very popular updated version of the straight stand uses the "folding tripod base stand", instead of the round, domed metal base. This folding base allows for easier packing of the stand when moving from location to location and reduces the weight of the stand. However, to compensate for the lack of weight at the base while still maintaining stability, the three "feet" of the tripod must extend out beyond the radius of a round base. The trade-off is that these "feet" may become a trip-hazard on a dark stage.
A number of accessories make microphone stands more useful. Most of these are designed to get the microphone closer to the user without placing the upright portion of the stand directly in front of the performer.
A "boom arm" attaches to the top of the stand so the microphone can move in the horizontal plane. A guitar player, for example, might use this to place the microphone directly in front of his mouth without having the upright portion of the stand in the way of the guitar. It also lets musicians have the microphone closer to the sound source when floor space is at a premium. This can be particularly useful when placing microphones on a drum stand when the microphone stands must compete for space with things like cymbal stands. Boom arms are offered both in fixed length and adjustable (telescoping) lengths.
Another handy device for adjusting microphone placement is a flexible "goose neck" tube. Made of a spiral-wound core of steel, goosenecks are made in various lengths and finishes and provide the ability to make minute changes in microphone position.
Microphones typically attach to the stand via a detachable microphone holder screwed to the end of the boom. (Some microphones screw directly onto the boom.) Commonly used screw threads (from large to small) are:
Various male/female adapters are available to connect dissimilar sizes. Note: A compatible ¼″ 20 tpi UNC is common in photography tripods
Bottomless microphone stand.
A rare type of microphone stand is the "bottomless" microphone stand—essentially a microphone stand with no base, so a singer must hold it throughout a live performance. It is useful as a mobile prop.
Freddie Mercury (the lead singer of Queen), discovered the device by accident: he grabbed a standard microphone stand with such force that it dislodged from its base. For the rest of his career he used a bottomless microphone stand regularly. Robbie Williams as well as heavy metal singers Joey Belladonna of Anthrax and Chuck Billy of Testament also use bottomless microphone stands.


Heptatonic scale

A heptatonic scale is a musical scale that has seven pitches (a.k.a. tones) per octave. Examples include the "major scale" or "minor scale"; e.g., in C major: C D E F G A B C—and in the relative minor, A minor, natural minor: A B C D E F G A; the "melodic minor scale", A B C D E FGA ascending, A G F E D C B A descending; the "harmonic minor scale", A B C D E F GA; and a scale variously known as the "Byzantine", and "Hungarian", scale, C D E F G A B C. Indian classical theory postulates seventy-two seven-tone scale types, collectively called "thaat", whereas others postulate twelve or ten (depending on the theorist) seven-tone scale types.
Several heptatonic scales in Western, Roman, Spanish, Hungarian, and Greek music can be analyzed as juxtapositions of tetrachords. All heptatonic scales have all intervals present in their interval vector analysis, and thus all heptatonic scales are both hemitonic and tritonic. There is a special affinity for heptatonic scales in the Western key signature system.
Diatonic scale.
A diatonic scale is any seven-note scale constructed sequentially using only whole tones and half tones, repeating at the octave, having a tonal center, and comprising only one tritone interval between any two scale members, which ensures that the half tone intervals are as far apart as possible. In Western music, there are seven such scales, and they are commonly known as the modes of the major scale (Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, and Locrian).
Melodic minor scale.
In traditional classical theory, the melodic minor scale has two forms, as noted above, an ascending form and a descending form. Although each of these forms of itself comprises seven pitches, together they comprise nine, which might seem to call into question the scale's status as a heptatonic scale. In certain twentieth-century music, however, it became common systematically to use the ascending form for both ascending and descending passages. Such a use has been notably ascribed to the works of Béla Bartók and to bop and post-bop jazz practice. The traditional descending form of the melodic minor scale is equivalent to the natural minor scale in both pitch collection (which is diatonic) and tonal center.
Harmonic minor scale.
The harmonic minor scale is so called because in tonal music of the common practice period (from approximately 1600 to approximately 1900) chords or harmonies are derived from it more than from the natural minor scale or the melodic minor scale. The augmented second between its sixth degree and its raised seventh degree (the "leading tone"), traditionally considered undesirable in melodic progression, is avoided by placing these pitches in different voices in adjacent chords, as in this progression: F A D, F G B, F A C (ii°b–V7d–iv in C minor). The A in the middle voice does not ascend to B, and the B in the upper voice does not descend to A.
Heptatonia prima and secunda.
The names "heptatonia prima" and "heptatonia secunda" apply to various seven-note scales that can be formed using tones and semitones, but without two semi-tones in succession. (Some are more theoretical.) They are:
Heptatonia prima.
Beginning on keynote C and working up the notes of the 'natural minor' scale (A, B, C, D, E, F, G, A), the seven modes are:
Heptatonia secunda.
While the diatonic modes have two and three tones between each semitone, the heptatonia secunda modes have one and four.
These are sometimes called modes of the melodic ascending minor since that is the most commonly used scale of this type, but other modes can be produced by starting on the different scale notes in turn.
Thus starting on keynote A as above and following the notes of the ascending melodic minor (A, B, C, D, E, F, G) yields these seven modes:
These modes are more awkward to use than those of the diatonic scales due to the four tones in a row yielding augmented intervals on one hand while the one tone between two semitones gives rise to diminished intervals on the other. For example, the last two modes listed above both have 'Locrian' diminished triads built on their tonics, giving them unstable tonality, while the third mode not only has an augmented fourth a la the Lydian mode but also an augmented fifth making the dominant and subdominant essentially unusable.
Heptatonia tertia.
The last group of seven-note tone/semitone scales is "heptatonia tertia", and consists of scales with two adjacent semitones—which amounts to a whole-tone scale, but with an additional note somewhere in its sequence, e.g., B C D E F G A. One such example is the Neapolitan major scale.
Other heptatonic scales.
If the interval of the augmented second is used, many other scales become possible. These include
Gypsy I-II-III-IV-V-VI-VII
Hungarian I-II-III-IV-V-VI-VII
The scales are symmetrical about the tonic and dominant respectively and the names are sometimes used interchangeably.
Phrygian major or dominant harmonic minor I-II-III-IV-V-VI-VII
This differs from the Phrygian in having a major third. It may also be considered built on the dominant of the harmonic minor scale.
Verdi's Scala Enigmatica I-II-III-IV-V-VI-VII i.e. G A B C D E F, which is similar to the heptonia tertia mentioned above, differing only in that the second degree here is flattened.
The harmonic major scale differs from the major scale by having a flat sixth degree: I-II-III-IV-V-VI-VII.
Melakarta.
Melakarta is a South Indian classical method of organizing Raagas based on their unique heptatonic scales. The postulated number of melakarta derives from arithmetical calculation and not from Carnatic practice, which uses far fewer scale forms. Seven-pitch melakarta are considered subsets of a twelve-pitch scale roughly analogous to the Western chromatic scale. The first and fifth melakarta tones, corresponding to the first and eighth chromatic tones, are invariable in inflection, and the fourth melakarta tone, corresponding to the sixth or seventh chromatic tone, is allowed one of two inflections only, a natural () position and a raised () position. The second and third melakarta tones can be picked from the 4 chromatic tones (second through fifth), and similarly for the sixth and seventh. Thus the number of possible forms is equal to twice the square of the number of ways a two-membered subset can be extracted from a four-membered set:
Thaat.
Hindustani heptatonic theory additionally stipulates that the second, third, sixth and seventh degrees of heptatonic scale forms ("septak") are also allowed only two inflections each, in this case, one natural position, and one lowered ("komal") position. Arithmetically this produces 25, or thirty-two, possibilities, but Hindustani theory, in contradistinction to Carnatic theory, excludes scale forms not commonly used.
Chinese Gongche notation.
Gongche notation heptatonic scale gives a do, re, mi, (between fa and fa), sol, la, (between ti and ti) heptatonic scale.


4037 Ikeya


Water detector

A water detector is an electronic device that is designed to detect the presence of water for purposes such as to provide an alert in time to allow the prevention of water leakage. A common design is a small cable or device that lies flat on a floor and relies on the electrical conductivity of water to decrease the resistance across two contacts. The device then sounds an audible alarm together with providing onward signalling in the presence of enough water to bridge the contacts. These are useful in a normally occupied area near any infrastructure that has the potential to leak water, such as HVAC, water pipes, drain pipes, vending machines, dehumidifiers, or water tanks.
Water leak detection.
Water leak detection is an expression more commonly used for larger, integrated systems installed in modern buildings or those containing valuable artifacts, materials or other critical assets where early notification of a potentially damaging leak would be beneficial. In particular, water leak detection has become a necessity in data centers, trading floors, banks, archives and other mission-critical infrastructure.
The water leak detection industry is small and specialized with only a few manufacturers operating worldwide. The original application was in the void created by "computer room" floors in the days of large main-frame computer systems. These use a modular, raised floor based around a structural "floor tile" usually 600 mm square and supported at the corners by pedestals. The void created gave easy access and routing for the mass of power, networking and other interconnecting cables associated with larger computer systems - processors, drives, routers etc. mainframe computers also generated large amounts of heat so a void under the floor could also be used as a plenum to distribute and diffuse chilled air around the computer room. The void therefore was likely to have chilled water pipes running through it along with the drains for condensates associated with refrigeration plant. In addition, designers found the floor void a very convenient place to route other wet services feeding bathrooms, radiators and other facilities.
A leak occurring within a floor void would therefore go unnoticed until the hydrostatic head of pressure meant that the water found its way through to floors below where its dripping through the ceiling would be noted or, and more disconcerting, the water would penetrate the joints and connectors of the power or network cabling and cause system failure from short circuit.
Current digital water leak detection systems can locate multiple water leaks to within 1 meter resolution over a complex network of cables running several kilometers. This functionality reduces the downtime and potential damage caused by inaccurate reporting that was common with older analogue based systems.
Water leak detection systems can be integrated with Building Management Systems using multiple protocols such as Modbus. Using SNMP protocols leak detection systems can inform IT staff in charge of monitoring data center and server rooms.
Integrated multi-zone systems.
The computer room therefore became the early application for systems which would alert the operator to a leaking pipe in sufficient time for remedial action to be taken to prevent a disaster.
As computer rooms could be quite large simple "point of use" detectors were not really appropriate although Point Sensors do have value where simple, single point detection is required in, say, basements and sumps. Most modern leak detection systems developed around the use of a water sensitive cable which can be laid in long lengths and complex patterns around the base of the floor; around the perimeter of rooms; as a "barrier" over which water has to flow; following, tracing or attached directly to lines of water pipes.
General application.
The mainframe computer room has largely been replaced with the Data Centre but the application has remained with almost universal use of "computer-room" style raised floors in nearly all new commercial and office construction. To warrant the installation of leak detection the operator has to perceive the risk in addition to the circumstances but most Mechanical and Electrical Design Engineers will take a view of the risk of damage from a leak in terms of effect on the client's own operations, services and assets and, often as important, those of their adjoining neighbours and those on floors below.
The installation of leak detection systems is therefore becoming more commonplace in most new commercial office construction schemes along with the more obvious targets of museums, galleries and archives.
Leak detection systems must be unobtrusive, effective and robust enough to withstand getting dirty and the moderate physical abuse of other works being carried out under the same floor.
Zoned systems have a reputation for being safe, reliable and not prone to the same types of false alarms which those systems which use cumulative resistance techniques.
Manufacturers such as TTK from France have introduced hi-tech variants like FG-NET touch screen panels with interactive maps on screen. The sensing cables are fitted with micro-controllers patented, that allows unique ability to pin-point faults on every individual sense cable simultaneously.
The leak detection industry is very small and it can be expected that manufacturers will also offer an installation and after sales service.


4737 Kiladze


2754 Efimov

2754 Efimov, provisionally named , is a stony asteroid and binary system from the inner regions of the asteroid belt, approximately 5 kilometers in diameter. It was discovered on 13 August 1966, by Russian astronomer Tamara Smirnova at the Crimean Astrophysical Observatory in Nauchnyj, on the Crimean peninsula. The asteroid was named after Russian aviator Mikhail Efimov.
Orbit and classification.
"Efimov" orbits the Sun in the inner main-belt at a distance of 1.7–2.7 AU once every 3 years and 4 months (1,214 days). Its orbit has an eccentricity of 0.23 and an inclination of 6° with respect to the ecliptic.
Physical characteristics.
In the SMASS classification, "Efimov" is a Sa-type asteroid, which belong to the larger group of S-type asteroids. It is also characterized as a L-type asteroid by PanSTARRS photometric survey.
The "Collaborative Asteroid Lightcurve Link" assumes a standard albedo for stony asteroids of 0.20 and derives a diameter of 4.98 kilometers with an absolute magnitude of 13.92.
Satellite.
"Efimov" is a binary asteroid. In 2006, astronomers discovered a minor-planet moon, designated around "Efimov" using lightcurve observations, with a diameter of 1.29 kilometers and an orbital period of 14 hours and 46 minutes.
Naming.
This minor planet named in memory of Russian aviator Mikhail Nikiforovich Efimov (; 1881–1919), who was the first to realize steep turns and dives.
The approved naming citation was published by the Minor Planet Center on 31 May 1988 ().


3 nm process

In semiconductor manufacturing, the 3 nm process is the next die shrink after the 5-nanometre MOSFET (metal–oxide–semiconductor field-effect transistor) technology node. , Intel, Samsung, and TSMC have all announced plans to put a 3 nm semiconductor node into commercial production. Samsung's process is based on GAAFET (gate-all-around field-effect transistor) technology, a type of multi-gate MOSFET technology, while TSMC's 3nm process will still use FinFET (fin field-effect transistor) technology, despite TSMC developing GAAFET transistors. Specifically, Samsung plans to use its own variant of GAAFET called MBCFET (multi-bridge channel field-effect transistor).
The term "3 nanometer" has no relation to any actual physical feature (such as gate length, metal pitch or gate pitch) of the transistors. It is a commercial or marketing term used by the chip fabrication industry to refer to a new, improved generation of silicon semiconductor chips in terms of increased transistor density, increased speed and reduced power consumption. For example, TSMC has stated that its 3nm FinFET chips will reduce power consumption by 25 to 30 percent at the same speed, increase speed by 10 to 15 percent at the same amount power and increase transistor density by about 33 percent compared to its previous 5nm FinFET chips.
History.
Research and technology demos.
In 1985, a Nippon Telegraph and Telephone (NTT) research team fabricated a MOSFET (NMOS) device with a channel length of 150 nm and gate oxide thickness of 2.5 nm. In 1998, an Advanced Micro Devices (AMD) research team fabricated a MOSFET (NMOS) device with a channel length of 50 nm and oxide thickness of 1.3 nm.
In 2003, a research team at NEC fabricated the first MOSFETs with a channel length of 3 nm, using the PMOS and NMOS processes. In 2006, a team from the Korea Advanced Institute of Science and Technology (KAIST) and the National Nano Fab Center, developed a 3 nm width multi-gate MOSFET, the world's smallest nanoelectronic device, based on gate-all-around (GAAFET) technology.
Commercialization history.
In late 2016, TSMC announced plans to construct a 5 nm–3 nm node semiconductor fabrication plant with a co-commitment investment of around US$15.7 billion.
In 2017, TSMC announced it was to begin construction of the 3 nm semiconductor fabrication plant at the Tainan Science Park in Taiwan. TSMC plans to start volume production of the 3 nm process node in 2023.
In early 2018, IMEC and Cadence stated they had taped out 3 nm test chips, using extreme ultraviolet lithography (EUV) and 193 nm immersion lithography.
In early 2019, Samsung presented plans to manufacture 3 nm GAAFET (gate-all-around field-effect transistors) at the 3 nm node in 2021, using its own MBCFET transistor structure that uses nanosheets instead of nanowires; delivering a 35% performance increase, 50% power reduction and a 45% reduction in area when compared with 7nm. Samsung's semiconductor roadmap also included products at 8, 7, 6, 5, and 4 nm 'nodes'.
In December 2019, Intel announced plans for 3 nm production in 2025.
In January 2020, Samsung announced the production of the world's first 3 nm GAAFET process prototype, and said that it is targeting mass production in 2021.
In August 2020, TSMC announced details of its N3 3 nm process, which is new rather than being an improvement over its N5 5 nm process. Compared with the N5 process, the N3 process should offer a 10–15% (1.10–1.15×) increase in performance, or a 25–35% (1.25–1.35×) decrease in power consumption, with a 1.7× increase in logic density (a scaling factor of 0.58), a 20% increase (0.8 scaling factor) in SRAM cell density, and a 10% increase in analog circuitry density. Since many designs include considerably more SRAM than logic, (a common ratio being 70% SRAM to 30% logic) die shrinks are expected to only be of around 26%. TSMC plans risk production in 2021 with volume production in the second half of 2022.
Beyond 3 nm.
The ITRS uses (as of 2017) the terms "2.1 nm", "1.5 nm", and "1.0 nm" as generic terms for the nodes after 3 nm. "2-nanometre" (2 nm) and "14 angstrom" (14 Å or 1.4 nm) nodes have also been (in 2017) tentatively identified by An Steegen (of IMEC) as future production nodes after 3 nm, with hypothesized introduction dates of around 2024, and beyond 2025 respectively.
In late 2018, TSMC chairman Mark Liu predicted chip scaling would continue to 3 nm and 2 nm nodes; however, as of 2019, other semiconductor specialists were undecided as to whether nodes beyond 3 nm could become viable. TSMC began research on 2 nm in 2019. It has been reported that TSMC is expected to enter 2 nm risk production around 2023 or 2024.
In December 2019, Intel announced plans for 1.4 nm production in 2029.
In May 2021 IBM announced it had produced 2 nm chipmaking technology at their manufacturing research center in Albany and had successfully made a prototype "fingernail-sized" chip with upwards of 50 billion transistors,
which translates to 333 million transistors per square millimeter (assuming a chip area of 150 square millimeters as communicated by IBM). By comparison, TSMC's 3nm chips would contain around 291 million transistors per square millimeter.


Image Forum Festival

Image Forum Festival is Japan's largest art film festival, and the largest dedicated to the screening of new experimental films, both in Japan and around the world. It began in 1987 in Tokyo, and includes space for video installations and live performance. It is now held in Tokyo, Kyoto and Yokohama annually, and often includes other cities across Japan. As well as featuring modern domestic and international films, it includes a selection of historical masterpieces.
The festival is run by Image Forum, a school and cinemathéque that preserves and promotes the production of experimental film, and fosters the next generation of filmmakers. Its affiliate company, Dagurreo Press, Inc. publishes books on filmmaking and video software.
Awards.
Image Forum won the 1988 Japan Movie Pen Club Award.


Hybrid input-output algorithm

Hybrid input-output (HIO) algorithm for phase retrieval is a modification of the error reduction algorithm for retrieving the phases in coherent diffraction imaging. Determining the phases of a diffraction pattern is crucial since the diffraction pattern of an object is its Fourier transform and in order to properly invert transform the diffraction pattern the phases must be known. Only the amplitude however, can be measured from the intensity of the diffraction pattern and can thus be known experimentally. This fact together with some kind of support constraint can be used in order to iteratively calculate the phases. The HIO algorithm uses negative feedback in Fourier space in order to progressively force the solution to conform to the Fourier domain constraints (support). Unlike the error reduction algorithm which alternately applies Fourier and object constraints the HIO "skips" the object domain step and replaces it with negative feedback acting upon the previous solution.
Although it has been shown that the method of error reduction converges to a limit (but usually not to the correct or optimal solution)
there is no limit to how long this process can take. Moreover, the error reduction algorithm will almost certainly find a local minimum instead of the global solution. The HIO differs from error reduction only in one step but this is enough to reduce this problem significantly. Whereas the error reduction approach iteratively improves solutions over time the HIO remodels the previous solution in Fourier space applying negative feedback. By minimizing the mean square error in Fourier space from the previous solution, the HIO provides a better candidate solution for inverse transforming. Although it is both faster and more powerful than error reduction, the HIO algorithm does have a uniqueness problem.
Depending on how strong the negative feedback is there can often be more than one solution for any set of diffraction data. Although a problem, it has been shown that many of these possible solutions stem from the fact that HIO allows for mirror images taken in any plane to arise as solutions. In crystallography, the scientist is seldom interested in the atomic coordinates relative to any other reference than the molecule itself and is therefore more than happy with a solution that is upside-down of flipped from the actual image. A downside is that HIO has a tendency to escape both global and local maxima. This problem also depends on the strength of the feedback parameter, and a good solution to this problem is to switch algorithm when the error reaches its minimum. Other methods of phasing a coherent diffraction pattern include difference map algorithm and "relaxed averaged alternating reflections" or RAAR.


Throat microphone

A throat microphone, also called a laryngophone, is a type of contact microphone that absorbs vibrations directly from the wearer's throat by way of single or dual sensors worn against the neck. The sensors, called transducers, can pick up speech even in extremely noisy or windy environments, such as on a motorcycle or in a nightclub. Other types of microphones do not function well under these conditions because of high levels of background noise. Advanced laryngophones are able to pick up whispers, and therefore perform well in environments where communicating with others at a distance in silence is required, such as during covert military or law enforcement operations. Throat microphones are also very useful when helmets or respiratory protection is required. Many full-face SCBA, CABA, SAR Respirator, Elastomeric Respirator, N95 Respirator PAPR, or re-breather masks do not have a provision for a microphone inside the mask. The throat microphone can be used safely, as it is positioned outside the mask's face seal and as such does not compromise the respiratory protection provided by the mask, nor does it violate mask approvals and certification.
History.
World War I – first throat mics.
Charles Edmond Prince lead the development of throat microphones for the British during World War I for use in the noisy and windy environment of aircraft cockpits. Over a 3 year period from 1915-1918 they went through a series of prototype and production handheld "airplane telephones" before arriving at a hands free throat mic incorporated into a leather flying helmet
World War II – full body suits.
During World War II, German Luftwaffe pilots and panzer crews used throat microphones. Soon after, they were adopted by the Allied air forces—the USAAF with the T-20 and T-30 and the RAF with the Mark II. Later, Soviet pilots relied on LA-3 and LA-5 models.
Scientific studies.
Starting in the 1970s, researchers explored the use of throat microphones in speech therapy,
Current use.
Throat microphones have maintained their presence in the military, law enforcement, and emergency services. Newer single-transducer designs are available that make the throat microphone much more comfortable to wear than earlier units and also better balance transmission quality. Additionally, this next generation of throat microphones provides varying outputs and frequency responses to accommodate a wide variety of professional communication devices such as digital and analog portable radios and Terrestrial Trunked Radio (TETRA) and P25 systems.
Several throat microphones including wireless throat mics now exist for mobile devices. Mobile device apps are starting to allow further customisation for end-user applications. Consumer uses such as for airsoft competitions and motorcycle riding are increasingly more popular. With the advent of COVID-19 and higher rate of face mask usage throat mics for general use is becoming more common to facilitate communications.


Susan Halabi

Susan Halabi is a professor of biostatistics and bioinformatics at Duke University, known for her research on prostate cancer.
As a member of the data safety monitoring board for a study of the anti-prostate cancer effects of abiraterone acetate (Zytiga), she argued that stopping the study early had prevented the study from accurately determining the effectiveness of the drug, and possibly made it appear to be more effective than it actually was. She also took part in a study showing that, when prostate cancer has reached the point of spreading to other parts of the body, the parts that it spreads to can be used to predict the survival rate from the disease.
Halabi earned her Ph.D. in biometry from the University of Texas Health Science Center at Houston in 1994, and joined the Duke faculty in 1996. She up in a family of engineers in Lebanon, where she was one of the first students in the undergraduate biostatistics program at the American University of Beirut. She was named a fellow of the Society for Clinical Trials in 2014, "for her outstanding leadership in cancer clinical trials and prognostic development, ... educational activities, and for dedicated service on national review committees, DSMBs and scientific advisory committees and for the SCT".
She was elected as a Fellow of the American Statistical Association in 2015.


Guitar tunings

Guitar tunings are the assignment of pitches to the open strings of guitars, including acoustic guitars, electric guitars, and classical guitars. Tunings are described by the particular pitches that are made by notes in Western music. By convention, the notes are ordered and arranged from the lowest-pitched string (i.e., the deepest bass sounding note) to the highest-pitched string (i.e.the highest sounding note), or the thickest string to thinnest, or the lowest frequency to the highest. This sometimes confuses beginner guitarists, since the highest-pitched string is referred to as the 1st string, and the lowest-pitched is the 6th string.
Standard tuning defines the string pitches as E, A, D, G, B, and E, from the lowest pitch (low E2) to the highest pitch (high E4). Standard tuning is used by most guitarists, and frequently used tunings can be understood as variations on standard tuning. To aid in memorising these notes, mnemonics are used, for example, Eddy Ate Dynamite, Good Bye Eddy.
The term "guitar tunings" may refer to pitch sets other than standard tuning, also called "nonstandard", "alternative", or "alternate". There are hundreds of these tunings, often with small variants of established tunings. Communities of guitarists who share a common musical tradition often use the same or similar tuning styles.
Standard and alternatives.
Standard.
Standard tuning is the tuning most frequently used on a six-string guitar and musicians assume this tuning by default if a specific alternate (or scordatura) is not mentioned. In scientific pitch notation, the guitar's standard tuning consists of the following notes:
The guitar is a transposing instrument; that is, music for guitars is notated one octave higher than the true pitch. This is to reduce the need for ledger lines in music written for the instrument, and thus simplify the reading of notes when playing the guitar.
Standard tuning provides reasonably simple fingering (fret-hand movement) for playing standard scales and basic chords in all major and minor keys. Separation of the first (high E) and second (B) string, as well as the separation between the third (G), fourth (D), fifth (A), and sixth (low E) strings by a five-semitone interval (a perfect fourth) allows the guitarist to play a chromatic scale with each of the four fingers of the fretting hand controlling one of the first four frets (index finger on fret 1, little finger on fret 4, etc.) only when the hand is in the first position.
The open notes of the second (B) and third (G) strings are separated by four semitones (a major third). This tuning pattern of (low) fourths, one major third, and one fourth was inherited by the guitar from its predecessor instrument, the viol. The irregular major third breaks the fingering patterns of scales and chords, so that guitarists have to memorize multiple chord-shapes for each chord. Scales and chords are simplified by major thirds tuning and all-fourths tuning, which are regular tunings maintaining the same musical interval between consecutive open-string notes.
Alternative.
Alternative ("alternate") tuning refers to any open-string note arrangement other than standard tuning. These offer different kinds of deep or ringing sounds, chord voicings, and fingerings on the guitar. Alternative tunings are common in folk music where the guitar may be called upon to produce a sustained note or chord known as a drone. This often gives folk music its haunting and lamenting ambience due to the atmosphere and mood that the notes make. Alternative tunings change the fingering of common chords when playing the guitar, and this can ease the playing of certain chords while simultaneously increase the difficulty of playing other chords.
Some tunings are used for particular songs, and may be named after the song's title. There are hundreds of these tunings, although many are slight variations of other alternate tunings. Several alternative tunings are used regularly by communities of guitarists who share a common musical tradition, such as American folk or Celtic folk music.
The various alternative tunings have been grouped into the following categories:
Joni Mitchell is known for developing a shorthand descriptive method of noting guitar tuning where the first letter documents the note of the lowest string, and is followed by the relative fret (half-step) offsets required to obtain the pitch of the next (higher) string. This scheme highlights pitch relationships and simplifies the process of comparing different tuning schemes.
String gauges.
String gauge refers to the thickness and diameter of a guitar string, which influences the overall sound and pitch of the guitar depending on the guitar string used. Some alternative tunings are difficult or even impossible to achieve with conventional guitars due to the sets of guitar strings, which have gauges optimized for standard tuning. With conventional sets of guitar strings, some higher tunings increase the string-tension until playing the guitar requires significantly more finger-strength and stamina, or even until a string snaps or the guitar is warped. However, with lower tunings, the sets of guitar strings may be loose and buzz. The tone of the guitar strings is also negatively affected by using unsuitable string gauges on the guitar.
Generally, alternative tunings benefit from re-stringing of the guitar with string gauges purposefully chosen to optimize particular tunings by using lighter strings for higher-pitched notes (to lower the tension of the strings) and heavier strings for lower-pitched notes (to prevent string buzz and vibration).
Dropped tunings.
A dropped tuning is one of the categories of alternative tunings and the process starts with standard tuning and typically lowers the pitch of ("drops") only a single string, almost always the lowest-pitched (E) string on the guitar.
The drop D tuning is common in electric guitar and heavy metal music. The low E string is tuned down one whole step (to D) and the rest of the strings remain in standard tuning. This creates an "open power chord" (three-note fifth) with the low three strings (DAD).
There also exists Double-drop D tuning, in which both E strings are down-tuned a whole step (to D). The rest of the strings keep their original pitch.
Open tunings.
An open tuning allows the guitarist to play a chord by strumming the open strings (no strings fretted).
Open tunings may be "chordal" or "modal". In chordal open tunings, the open chord consists of at least three different pitch classes. In a given key, these are the root note, its 3rd and its 5th, and may include all the strings or a subset. The tuning is named for the base chord when played open, typically a major chord, and all similar chords in the chromatic scale are played by barring all strings across a single fret. Open tunings are common in blues and folk music. These tunings are frequently used in the playing of slide and lap-slide ("Hawaiian") guitars, and Hawaiian slack key music. A musician who is well-known for using open tuning in his music is Ry Cooder, who uses open tunings when playing the slide guitar.
Most modern music uses equal temperament because it facilitates the ability to play the guitar in any key—as compared to just intonation, which favors certain keys, and makes the other keys sound less in tune.
Repetitive open-tunings are used for two classical non-Spanish guitars. For the English guitar, the open chord is C major (C–E–G–C–E–G); for the Russian guitar, which has seven strings, it is G major (D–G–B–D–G–B–D).
When the open strings constitute a minor chord, the open tuning may sometimes be called a "cross-note" tuning.
Major key tunings.
Major open-tunings give a major chord with the open strings.
Open tunings often tune the lowest open note to C, D, or E and they often tune the highest open note to D or E; tuning down the open string from E to D or C avoids the risk of breaking strings, which is associated with tuning up strings.
Open D.
The open D tuning (D–A–D–F–A–D), also called "Vestopol" tuning, is a common open tuning used by European and American/Western guitarists working with alternative tunings. The Allman Brothers instrumental "Little Martha" used an open-D tuning raised one half step, giving an open E♭ tuning with the same intervalic relationships as open D.
Open C.
The English guitar used a repetitive open-C tuning (with distinct open notes C–E–G–C–E–G) that approximated a major-thirds tuning. This tuning is evident in William Ackerman's song "Townsend Shuffle", as well as by John Fahey for his tribute to Mississippi John Hurt.
The C–C–G–C–E–G tuning uses some of the harmonic sequence (overtones) of the note C. This overtone-series tuning was modified by Mick Ralphs, who used a high C note rather than the high G note for "Can't Get Enough" on "Bad Company". Ralphs said, "It needs the open C to have that ring," and "it never really sounds right in standard tuning".
Open G.
Mick Ralphs' open-C tuning was originally an open-G tuning, which listed the initial six overtones of the G note, namely G–G–D–G–B–D; Ralphs used this open-G tuning for "Hey Hey" and while writing the demo of "Can't Get Enough".
Open-G tuning usually refers to D–G–D–G–B–D.
The open G tuning variant G–G–D–G–B–D was used by Joni Mitchell for "Electricity", "For the Roses" and "Hunter (The Good Samaritan)". Truncating this tuning to G–D–G–B–D for his five-string guitar, Keith Richards uses this overtones-tuning on The Rolling Stones's "Honky Tonk Women", "Brown Sugar" and "Start Me Up".
The seven-string Russian guitar uses the open-G tuning D–G–B–D–G–B–D, which contains mostly major and minor thirds.
Creating any kind of open tuning.
Any kind of chordal tuning can be achieved, simply by using the notes in the chord and tuning the strings to those notes. For example, Asus4 has the notes A, D, E. By tuning the strings to only those notes, it creates a chordal Asus4 tuning.
Bass players may omit the last two strings.
Minor or "cross-note" tunings.
Cross-note tunings include a minor third, so giving a minor chord with open strings. Fretting the minor-third string at the first fret produces a major-third, so allowing a one-finger fretting of a major chord. By contrast, it is more difficult to fret a minor chord using an open major-chord tuning.
Bukka White and Skip James are well-known for using cross-note E-minor in their music.
Other open chordal tunings.
Some guitarists choose open tunings that use more complex chords, which gives them more available intervals on the open strings. C6, E6, E7, E6/9 and other such tunings are common among lap-steel players such as Hawaiian slack-key guitarists and country guitarists, and are also sometimes applied to the regular guitar by bottleneck (a slide repurposed from a glass bottle) players striving to emulate these styles. A common C6 tuning, for example, is C–E–G–A–C–E, which provides open major and minor thirds, open major and minor sixths, fifths, and octaves. By contrast, most open major or open minor tunings provide only octaves, fifths, and either a major third/sixth or a minor third/sixth—but not both. Don Helms of Hank Williams band favored C6 tuning; slack-key artist Henry Kaleialoha Allen uses a modified C6/7 (C6 tuning with a B on the bottom); Harmon Davis favored E7 tuning; David Gilmour has used an open G6 tuning.
Modal tunings.
Modal tunings are open tunings in which the open strings of the guitar do not produce a tertian (i.e., major or minor, or variants thereof) chord. The strings may be tuned to exclusively present a single interval (all fourths; all fifths; etc.) or they may be tuned to a non-tertian chord (unresolved suspensions such as E–A–B–E–A–E, for example). Modal open tunings may use only one or two pitch classes across all strings (as, for example, some metal guitarists who tune each string to either E or B, forming "power chords" of ambiguous major/minor tonality).
Popular modal tunings include D Modal (D-G-D-G-B-E) and C Modal (C-G-D-G-B-D).
Lowered (standard).
Derived from standard EADGBE, all the strings are tuned lower by the same interval, thus providing the same chord positions transposed to a lower key. Lower tunings are popular among rock and heavy metal bands. The reason for tuning down below the standard pitch is usually either to accommodate a singer's vocal range or to get a deeper/heavier sound or pitch. Common examples include:
E♭ tuning.
Rock guitarists (such as Jimi Hendrix on the songs Voodoo Child (Slight Return) and Little Wing) occasionally tune all their strings down by one semitone to obtain "E♭ tuning". This makes the strings easier to bend when playing and with standard fingering results in a lower key.
D tuning.
D Tuning, also called One Step Lower, Whole Step Down, Full Step or D Standard, is another alternative. Each string is lowered by a whole tone (two semitones) resulting in D-G-C-F-A-D. It is used mostly by heavy metal bands to achieve a heavier, deeper sound, and by blues guitarists, who use it to accommodate string bending and by 12-string guitar players to reduce the mechanical load on their instrument. Among musicians, Elliott Smith was known to use D tuning as his main tuning for his music. It was also used for several songs on The Velvet Underground's album The Velvet Underground & Nico.
Regular tunings.
In standard tuning, there is an interval of a major third between the second and third strings, and all the other intervals are fourths. The irregularity has a price. Chords cannot be shifted around the fretboard in the standard tuning E–A–D–G–B–E, which requires four chord-shapes for the major chords. There are separate chord-forms for chords having their root note on the third, fourth, fifth, and sixth strings. These are called inversions.
In contrast, regular tunings have equal intervals between the strings, and so they have symmetrical scales all along the fretboard. This makes it simpler to translate chords. For the regular tunings, chords may be moved diagonally around the fretboard. The diagonal movement of chords is especially simple for the regular tunings that are repetitive, in which case chords can be moved vertically: Chords can be moved three strings up (or down) in major-thirds tuning, and chords can be moved two strings up (or down) in augmented-fourths tuning. Regular tunings thus appeal to new guitarists and also to jazz-guitarists, whose improvisation is simplified by regular intervals.
On the other hand, five- and six-string open chords ("cowboy chords") are more difficult to play in a regular tuning than in standard tuning. Instructional literature uses standard tuning. Traditionally a course begins with the hand in first position, that is, with the left-hand covering frets 1–4. Beginning players first learn open chords belonging to the major keys C, G, and D. Guitarists who play mainly open chords in these three major-keys and their relative minor-keys (Am, Em, Bm) may prefer standard tuning over many regular tunings, On the other hand, minor-thirds tuning features many barre chords with repeated notes, properties that appeal to acoustic-guitarists and beginners.
Major thirds and perfect fourths.
Standard tuning mixes a major third (M3) with its perfect fourths. Regular tunings that are based on either major thirds or perfect fourths are used, for example, in jazz.
All fourths tuning E2–A2–D3–G3–C4–F4 keeps the lowest four strings of standard tuning, changing the major third to a perfect fourth. Jazz musician Stanley Jordan stated that all-fourths tuning "simplifies the fingerboard, making it logical".
Major-thirds tuning (M3 tuning) is a regular tuning in which the musical intervals between successive strings are each major thirds, for example E2–G2–C3–E3–G3–C4. Unlike all-fourths and all-fifths tuning, M3 tuning repeats its octave after three strings, which simplifies the learning of chords and improvisation. This repetition provides the guitarist with many possibilities for fingering chords. With six strings, major-thirds tuning has a smaller range than standard tuning; with seven strings, the major-thirds tuning covers the range of standard tuning on six strings.
Major-thirds tunings require less hand-stretching than other tunings, because each M3 tuning packs the octave's twelve notes into four consecutive frets. The major-third intervals let the guitarist play major chords and minor chords with two–three consecutive fingers on two consecutive frets.
Chord inversion is especially simple in major-thirds tuning. The guitarist can invert chords by raising one or two notes on three strings—playing the raised notes with the same finger as the original notes. In contrast, inverting triads in standard and all-fourths tuning requires three fingers on a span of four frets. In standard tuning, the shape of an inversion depends on involvement of the major-third between the 2nd and 3rd strings.
All fifths and "new standard tuning".
All-fifths tuning is a tuning in intervals of perfect fifths like that of a mandolin or a violin; other names include "perfect fifths" and "fifths". It has a wide range. Its implementation has been impossible with nylon strings and has been difficult with conventional steel strings. The high B makes the first string very taut, and consequently a conventionally gauged string easily breaks.
Jazz guitarist Carl Kress used a variation of all-fifths tuning—with the bottom four strings in fifths, and the top two strings in thirds, resulting in B1–F2–C3–G3–B3–D4. This facilitated tenor banjo chord shapes on the bottom four strings and plectrum banjo chord shapes on the top four strings. Contemporary New York jazz-guitarist Marty Grosz uses this tuning.
All-fifths tuning has been approximated by the so-called "New Standard Tuning" (NST) of King Crimson's Robert Fripp, which NST replaces all-fifths' high B4 with a high G4. To build chords, Fripp uses "perfect intervals in fourths, fifths and octaves", so avoiding minor thirds and especially major thirds, which are slightly sharp in equal temperament tuning (in comparison to thirds in just intonation). It is a challenge to adapt conventional guitar-chords to new standard tuning, which is based on all-fifths tuning. Some closely voiced jazz chords become impractical in NST and all-fifths tuning.
Instrumental tunings.
These are tunings in which some or all strings are retuned to emulate the standard tuning of some other instrument, such as a lute, banjo, cittern, mandolin, etc. Many of these tunings overlap other categories, especially open and modal tunings.
Miscellaneous or "special" tunings.
This category includes everything that does not fit into any of the other categories, for example (but not limited to): tunings designated only for a particular piece; non-western intervals and modes; micro- or macro-tones(half sharps/flats, etc.); and "hybrid tunings" combining features of major alternate tuning categories – most commonly an open tuning with the lowest string dropped.


Chi-squared test

A chi-squared test, also written as test, is a statistical hypothesis test that is valid to perform when the test statistic is chi-squared distributed under the null hypothesis, specifically Pearson's chi-squared test and variants thereof. Pearson's chi-squared test is used to determine whether there is a statistically significant difference between the expected frequencies and the observed frequencies in one or more categories of a contingency table.
In the standard applications of this test, the observations are classified into mutually exclusive classes. If the null hypothesis that there are no differences between the classes in the population is true, the test statistic computed from the observations follows a frequency distribution. The purpose of the test is to evaluate how likely the observed frequencies would be assuming the null hypothesis is true.
Test statistics that follow a distribution occur when the observations are independent and normally distributed, which are assumptions often justified under the central limit theorem. There are also tests for testing the null hypothesis of independence of a pair of random variables based on observations of the pairs.
Chi-squared tests often refers to tests for which the distribution of the test statistic approaches the distribution asymptotically, meaning that the sampling distribution (if the null hypothesis is true) of the test statistic approximates a chi-squared distribution more and more closely as sample sizes increase.
History.
In the 19th century, statistical analytical methods were mainly applied in biological data analysis and it was customary for researchers to assume that observations followed a normal distribution, such as Sir George Airy and Professor Merriman, whose works were criticized by Karl Pearson in his 1900 paper.
At the end of the 19th century, Pearson noticed the existence of significant skewness within some biological observations. In order to model the observations regardless of being normal or skewed, Pearson, in a series of articles published from 1893 to 1916, devised the Pearson distribution, a family of continuous probability distributions, which includes the normal distribution and many skewed distributions, and proposed a method of statistical analysis consisting of using the Pearson distribution to model the observation and performing a test of goodness of fit to determine how well the model really fits to the observations.
Pearson's chi-squared test.
In 1900, Pearson published a paper on the test which is considered to be one of the foundations of modern statistics. In this paper, Pearson investigated a test of goodness of fit.
Suppose that observations in a random sample from a population are classified into mutually exclusive classes with respective observed numbers (for ), and a null hypothesis gives the probability that an observation falls into the th class. So we have the expected numbers for all , where
Pearson proposed that, under the circumstance of the null hypothesis being correct, as the limiting distribution of the quantity given below is the distribution.
Pearson dealt first with the case in which the expected numbers are large enough known numbers in all cells assuming every may be taken as normally distributed, and reached the result that, in the limit as becomes large, follows the distribution with degrees of freedom.
However, Pearson next considered the case in which the expected numbers depended on the parameters that had to be estimated from the sample, and suggested that, with the notation of being the true expected numbers and being the estimated expected numbers, the difference
will usually be positive and small enough to be omitted. In a conclusion, Pearson argued that if we regarded as also distributed as distribution with degrees of freedom, the error in this approximation would not affect practical decisions. This conclusion caused some controversy in practical applications and was not settled for 20 years until Fisher's 1922 and 1924 papers.
Other examples of chi-squared tests.
One test statistic that follows a chi-squared distribution exactly is the test that the variance of a normally distributed population has a given value based on a sample variance. Such tests are uncommon in practice because the true variance of the population is usually unknown. However, there are several statistical tests where the chi-squared distribution is approximately valid:
Fisher's exact test.
For an exact test used in place of the 2 x 2 chi-squared test for independence, see Fisher's exact test.
Binomial test.
For an exact test used in place of the 2 x 1 chi-squared test for goodness of fit, see Binomial test.
Yates's correction for continuity.
Using the chi-squared distribution to interpret Pearson's chi-squared statistic requires one to assume that the discrete probability of observed binomial frequencies in the table can be approximated by the continuous chi-squared distribution. This assumption is not quite correct and introduces some error.
To reduce the error in approximation, Frank Yates suggested a correction for continuity that adjusts the formula for Pearson's chi-squared test by subtracting 0.5 from the absolute difference between each observed value and its expected value in a contingency table. This reduces the chi-squared value obtained and thus increases its "p"-value.
Chi-squared test for variance in a normal population.
If a sample of size is taken from a population having a normal distribution, then there is a result (see distribution of the sample variance) which allows a test to be made of whether the variance of the population has a pre-determined value. For example, a manufacturing process might have been in stable condition for a long period, allowing a value for the variance to be determined essentially without error. Suppose that a variant of the process is being tested, giving rise to a small sample of product items whose variation is to be tested. The test statistic in this instance could be set to be the sum of squares about the sample mean, divided by the nominal value for the variance (i.e. the value to be tested as holding). Then has a chi-squared distribution with degrees of freedom. For example, if the sample size is 21, the acceptance region for with a significance level of 5% is between 9.59 and 34.17.
Example chi-squared test for categorical data.
Suppose there is a city of 1,000,000 residents with four neighborhoods: , , , and . A random sample of 650 residents of the city is taken and their occupation is recorded as "white collar", "blue collar", or "no collar". The null hypothesis is that each person's neighborhood of residence is independent of the person's occupational classification. The data are tabulated as:
Let us take the sample living in neighborhood , 150, to estimate what proportion of the whole 1,000,000 live in neighborhood . Similarly we take to estimate what proportion of the 1,000,000 are white-collar workers. By the assumption of independence under the hypothesis we should "expect" the number of white-collar workers in neighborhood to be
Then in that "cell" of the table, we have
The sum of these quantities over all of the cells is the test statistic; in this case, formula_6. Under the null hypothesis, this sum has approximately a chi-squared distribution whose number of degrees of freedom is
If the test statistic is improbably large according to that chi-squared distribution, then one rejects the null hypothesis of independence.
A related issue is a test of homogeneity. Suppose that instead of giving every resident of each of the four neighborhoods an equal chance of inclusion in the sample, we decide in advance how many residents of each neighborhood to include. Then each resident has the same chance of being chosen as do all residents of the same neighborhood, but residents of different neighborhoods would have different probabilities of being chosen if the four sample sizes are not proportional to the populations of the four neighborhoods. In such a case, we would be testing "homogeneity" rather than "independence". The question is whether the proportions of blue-collar, white-collar, and no-collar workers in the four neighborhoods are the same. However, the test is done in the same way.
Applications.
In cryptanalysis, the chi-squared test is used to compare the distribution of plaintext and (possibly) decrypted ciphertext. The lowest value of the test means that the decryption was successful with high probability. This method can be generalized for solving modern cryptographic problems.
In bioinformatics, chi-squared test is used to compare the distribution of certain properties of genes (e.g., genomic content, mutation rate, interaction network clustering, etc.) belonging to different categories (e.g., disease genes, essential genes, genes on a certain chromosome etc.).


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Flack parameter

In X-ray crystallography, the Flack parameter is a factor used to estimate the absolute configuration of a structural model determined by single-crystal structure analysis.
In this approach, one determines the absolute structure of a noncentrosymmetric crystal. The processes used to decide the absolute structure use the anomalous dispersion effect. If atomic scattering factors did not have imaginary parts, the Friedel pairs would have exactly the same amplitudes (i.e., the scattering intensity formula_1 from crystal plane (h k l) is equal to formula_2). However, atomic scattering factors have imaginary parts due to the anomalous dispersion effect, and Friedel's law is broken by this effect.
There are several ways to determine the absolute structure by X-ray crystallography. For example, a comparison of the intensities of Bijvoet pairs or of the R-factors for the two possible structures can suggest the correct absolute structure. One of the more powerful and simple approaches is using the Flack parameter, because this single parameter clearly indicates the absolute structure.
The Flack parameter is calculated during the structural refinement using the equation given below:
where "x" is the Flack parameter, "I" is the square of the scaled observed structure factor and "F" is the calculated structure factor.
By determining "x" for all data, "x" is usually found to be between 0 and 1. If the value is near 0, with a small standard uncertainty, the absolute structure given by the structure refinement is likely correct, and if the value is near 1, then the inverted structure is likely correct. If the value is near 0.5, the crystal may be racemic or twinned. The technique is most effective when the crystal contains both lighter and heavier atoms. Light atoms usually show only a small anomalous dispersion effect. In this case, the Flack parameter can refine to a physically unrealistic value (less than 0 or greater than 1) and has no meaning.
This parameter, introduced by H. D. Flack
became one of a standard set of values being checked for structures with noncentrosymmetric space groups.


Document-based question

In American Advanced Placement exams, a document-based question (DBQ), also known as data-based question, is an essay or series of short-answer questions that is constructed by students using one's own knowledge combined with support from several provided sources. Usually, it is employed on timed history tests.
In the United States.
The document based question was first used for the 1973 AP United States History Exam published by the College Board, created as a joint effort between Development Committee members Reverend Giles Hayes and Stephen Klein. Both were unhappy with student performance on free-response essays, and often found that students were "groping for half-remembered information" and "parroted factual information with little historical analysis or argument" when they wrote their essays. The goal of the Document Based Question was for students to be "less concerned with the recall of previously learned information" and more engaged in deeper historical inquiry. Hayes, in particular, hoped students would "become junior historians and play the role of historians for that hour" as they engaged in the DBQ.
A typical DBQ is a packet of several original sources (anywhere from three to sixteen), labeled by letters (beginning with "Document A" or "Source A") or numbers. Usually all but one or two source(s) are textual, with the other source(s) being graphic (usually a political cartoon, map, or poster if primary and a chart or graph if secondary). In most cases, the sources are selected to provide different perspectives or views on the events or movements being analyzed.
On the Advanced Placement (AP) exams, only primary sources are provided; on the International Baccalaureate (IB) exams, both primary and secondary sources are provided. AP exams also require students to construct and defend a thesis based on one prompt, while IB exams focus on a series of questions, with at least one asking students to assess the "value and limitations" of a source, usually "with reference to the documents' origin or purpose."
The documents contained in the document-based questions are rarely familiar texts (for example, the Emancipation Proclamation and Declaration of Independence are not likely to be on a U.S. history test), though the documents' authors may be major historical figures. The documents vary in length and format.
On some tests students are not permitted to begin responding to the question or questions in the essay packet until after a mandatory reading time ("planning period"), usually around 10 to 15 minutes. During this time, students read the passage and, if desired, make notes or markings. After this period, students are permitted to respond, usually for around 45 minutes to an hour.


PLIDA

PLIDA, or Progetto Lingua Italiana Dante Alighieri (Dante Alighieri Society Diplomas), are language diplomas issued by Dante Alighieri Society certifying the holder's proficiency in Italian language as a foreign language. The diplomas could only be obtained after passing a standardised language test. The Rome Branch of the Dante Alighieri Society is the official centre of examination for the issuing of PLIDA Certification.
Recognition.
The PLIDA certificate is officially recognised by the Ministry of Foreign Affairs, the Ministry of Labour and Welfare and the Ministry of Education, University and Research of Italy.
According to the Decree of the Ministry of the Interior of 4 June 2010, any foreigners should be able to demonstrate proficiency in the Italian language, if they want to obtain the long-term residence permit. Holders of A2 PLIDA certificate could be exempted from the test held by the Prefectures.
With the certificate (B2 or C1 level, depending on university and subject), students can be enrolled into universities or schools without taking the mandatory Italian language examinations.
Eligibility.
PLIDA tests can be taken only by those who are not native speakers of Italian. All candidates can take the test at the level they prefer, and it is not a pre-requisite that they have passed the tests at lower levels.
Test.
The Dante Alighieri Society is the organiser of PLIDA tests, with the academic approval from the Sapienza University of Rome. The Certification test is designed on the principles of the communicative approach, based on real-life tasks so as to test the ability in four areas: listening, reading, writing and speaking. The examination lasts for a minimum of 100 minutes to a maximum of 190 minutes, depending on the level.
There are tests of six levels, A1 to C2, set according to the levels in the Common European Framework of Reference for Languages.
Results.
Tests are marked in terms of a maximum of thirty points. To pass the examination, the candidate has to obtain a minimum of 18/30 in every tested areas, namely, listening, reading, writing and speaking. A candidate who passes at least three of the four areas obtains a credit in the areas passed, and these three credits may be used in the next attempt in the failed area.


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Graphoscope

A graphoscope was a 19th-century device used in parlors in order to enhance the viewing of photographs and text. The graphoscope is supposed to be based on a 1864 patent of Charles John Rowsell.
These novelty items consisted of a single magnifying glass, often in a wooden frame, in an overall construction that could collapse into a compact rectangular form. A photo/card holder was usually also included. A KOMBI camera often had included its design a graphoscope for better film viewing. Many devices combined a Stereoscope and Graphoscope.


Isomeric shift

The isomeric shift (also called isomer shift) is the shift on atomic spectral lines and gamma spectral lines, which occurs as a consequence of replacement of one nuclear isomer by another. It is usually called isomeric shift on atomic spectral lines and Mössbauer isomeric shift respectively. If the spectra also have hyperfine structure the shift refers to the center of gravity of the spectra. The isomeric shift provides important information about the nuclear structure and the physical, chemical or biological environment of atoms. More recently the effect has also been proposed as a tool in the search for the time variation of fundamental constants of nature.
Isomeric shift on atomic spectral lines.
The isomeric shift on atomic spectral lines is the energy or frequency shift in atomic spectra, which occurs when one replaces one nuclear isomer by another. The effect was predicted by Richard M. Weiner in 1956, whose calculations showed that it should be measurable by atomic (optical) spectroscopy (see also). It was observed experimentally for the first time in 1958. The theory of the atomic isomeric shift is also used in the interpretation of the Mössbauer isomeric shift.
Terminology.
The notion of isomer also appears in other fields such as chemistry and meteorology. Therefore, in the first publications devoted to this effect the name "nuclear isomeric shift on spectral lines" was used. Before the discovery of the Mössbauer effect, the isomeric shift referred exclusively to atomic spectra; this explains the absence of the word "atomic" in the initial definition of the effect. Subsequently, the isomeric shift was also observed in gamma spectroscopy through the Mössbauer effect and was called Mössbauer isomeric shift. For further details on the history of the isomeric shift and the terminology used, see.
Isotopic versus isomeric shift on atomic spectral lines.
Atomic spectral lines are due to transitions of electrons between different atomic energy levels "E", followed by emission of photons. Atomic levels are a manifestation of the electromagnetic interaction between electrons and nuclei. The energy levels of two atoms, the nuclei of which are different isotopes of the same element, are shifted one with respect to the other, despite the fact that the electric charges "Z" of the two isotopes are identical. This is so because isotopes differ by the number of neutrons, and therefore the masses and volumes of two isotopes are different; these differences give rise to the isotopic shift on atomic spectral lines.
In the case of two nuclear isomers, the number of protons and the number of neutrons are identical, but the quantum states and in particular the energy levels of the two nuclear isomers differ. This difference induces a difference in the electric charge distributions of two isomers and thus a difference δφ in the corresponding electrostatic nuclear potentials φ, which ultimately leads to a difference Δ"E" in the atomic energy levels. The isomeric shift on atomic spectral lines is then given by
where ψ is the wave function of the electron involved in the transition, "e" its electric charge, and the integration is performed over the electron coordinates.
The isotopic and the isomeric shift are similar in the sense that both are effects in which the finite size of the nucleus manifests itself and both are due to a difference in the electromagnetic interaction energy between the electrons and the nucleus of the atom. The isotopic shift had been known decades before the isomeric shift and provided useful but limited information about atomic nuclei. Unlike the isomeric shift, the isotopic shift was at first discovered in experiment and then interpreted theoretically (see also ). While in the case of the isotopic shift the determination of the interaction energy between electrons and nuclei is a relatively simple electromagnetic problem, for isomers the problem is more involved, since it is the strong interaction, which accounts for the isomeric excitation of the nucleus and thus for the difference of charge distributions of the two isomeric states. This circumstance explains in part why the nuclear isomeric shift was not discovered earlier: the appropriate nuclear theory and in particular the nuclear shell model were developed only in the late 1940s and early 1950s. As to the experimental observation of this shift, it also had to await the development of a new technique, that permitted spectroscopy with isomers, which are metastable nuclei. This too happened only in the 1950s.
While the isomeric shift is sensitive to the internal structure of the nucleus, the isotopic shift is (in a good approximation) not. Therefore, the nuclear physics information that can be obtained from the investigation of the isomeric shift, is superior to what can be obtained from isotopic-shift studies. The measurements through the isomeric shift of e.g. the difference of nuclear radii of the excited and ground state constitute one of the most sensitive tests of nuclear models. Moreover, combined with the Mössbauer effect, the isomeric shift constitutes at present a unique tool in many other fields besides physics.
The nuclear shell model.
According to the nuclear shell model, there exists a class of isomers, for which, in a first approximation, it is sufficient to consider one single nucleon, called the "optical" nucleon, to get an estimate of the difference between the charge distributions of the two isomer states, the rest of the nucleons being "filtered out". This applies in particular for isomers in odd-proton–even-neutron nuclei, with nearly closed shells. Indium-115, for which the effect was calculated, is such an example. The result of the calculation was that the isomeric shift on atomic spectral lines, although rather small, turned out to be two orders of magnitude bigger than a typical natural line width, which constitutes the limit of optical measurability.
The shift measured three years later in Hg-197 was quite close to that calculated for In-115, although in Hg-197, unlike in In-115, the optical nucleon is a neutron instead of a proton, and the electron–free-neutron interaction is much smaller than the electron—free-proton interaction. This is a consequence of the fact that the optical nucleons are not free, but bound particles. Thus the results could be explained within the theory by associating with the odd optical neutron an effective electric charge of "Z"/"A".
The Mössbauer isomeric shift.
The Mössbauer isomeric shift is the shift seen in gamma-ray spectroscopy when one compares two different nuclear isomeric states in two different physical, chemical or biological environments, and is due to the combined effect of the recoil-free Mössbauer transition between the two nuclear isomeric states and the transition between two atomic states in those two environments.
The isomeric shift on atomic spectral lines depends on the electron wave function ψ and on the difference δφ of electrostatic potentials φ of the two isomeric states.
For a given nuclear isomer in two different physical or chemical environments (different physical phases or different chemical combinations), the electron wave functions are also different. Therefore, on top of the isomeric shift on atomic spectral lines, which is due to the difference of the two nuclear isomer states, there will be a shift between the two environments (because of the experimental arrangement, these are called source (s) and absorber (a)). This combined shift is the Mössbauer isomeric shift, and it is described mathematically by the same formalism as the nuclear isomeric shift on atomic spectral lines, except that instead of one electron wave function, that in the source ψs, one deals with the difference between the electron wave function in the source ψs and the electron wave function in the absorber ψa:
The first measurement of the isomeric shift in gamma spectroscopy with the help of the Mössbauer effect was reported in 1960, two years after its first experimental observation in atomic spectroscopy. By measuring this shift, one obtains important and extremely precise information, both about the nuclear isomer states and about the physical, chemical or biological environment of the atoms, represented by the electronic wave functions.
Under its Mössbauer variant, the isomeric shift has found important applications in domains as different as atomic physics, solid-state physics, nuclear physics, chemistry, biology, metallurgy, mineralogy, geology, and lunar research. For further literature, see also.
The nuclear isomeric shift has also been observed in muonic atoms, that is, atoms in which a muon is captured by the excited nucleus and makes a transition from an atomic excited state to the atomic ground state in a time shorter than the lifetime of the excited isomeric nuclear state.