Senior External Examination

The Senior External Examination is an annually held Queensland examination, serving as a pathway to tertiary study for students who have been away from studies for a long period of time, who left school before attaining their Queensland Certificate of Education (QCE) or had performed poor in their studies and need to improve their selection rank for university. In addition, high-school students can follow the examination to partake in subjects not offered by their schools (such as Korean), but they will usually have to find private tuition. Senior External Examination is recognized by the Queensland Studies Authority (QSA) and the Queensland Tertiary Admissions Centre (QTAC) who together govern high-school subjects and tertiary admission for Queensland.
The Senior External Examination is essentially a condensed form of formal year 11 and 12, allowing those eligible to take the examination for credit toward their QCE. The QCE can be awarded on the basis of only the examination if students complete enough subjects.
In distinguishing formal education from the Senior External Examination, the examination does "not" grant students an overall position (OP) - it uses their results to confer a selection rank only. OPs are generally preferable to university admission as they test not only academic performance but also their performance relative to the school. In 2019, the new system Atar replaced the OPI system for the class of 2020. The first external exams in Queensland will be held at the end of the year. Due to Covid, each year 12 student will have one less assessment for each subject.
Workload.
The subject requirements vary depending on student circumstances. For example, a student who has had no formal year 11&12 education or did not complete the final year of high-school must complete 3-5 subjects, determined by age. It is decided by each of the tertiary institutes' how many subjects are to be studied to be accepted.
Technically, the Senior External Examination is not an educational program but an assessment. There are schools designed for it but enrollment is not compulsory to be eligible. There is no governing of who teaches subjects, and students may have to find private tutors for most of the subject syllabi.
Senior External Examination programs are typically done over the course of a year. In fact, many of the subjects available are not taught at registered schools (such as Modern Greek and Geography) but students may opt for these subjects and learn them by self-directed study or private tutoring.
Availability.
The Senior External Examination is available to adult students who wish to contribute to their QCE. If adults have completed secondary studies without a QCE (e.g. by not completing enough units of study) they can take an examination in the following year, but they're also available to students who have not completed year 11&12. In fact, they have no requirements but most education providers expect the knowledge of a year 10 student.
Subjects offered.
The Senior External Examination offers the following 22 subjects.
There are no examinations for Mathematics C which was a prerequisite for Engineering at many tertiary courses prior to 2010. The Mathematics C prerequisite however has been dropped by most institutions.
Training providers.
Training for the Senior External Examination is non-compulsory. There exist four state schools and one private.
Alternatives.
There are alternative pathways to university than the Senior External Examination. Students may also choose to undertake formal, internal schooling at a high-school, complete enough TAFE courses to be awarded the certificate of education, follow a subject's bridging course or a year of a lower ranked course (typically arts) at a university in the case a certificate of education has been obtained already.
High-schools generally take two years to complete to gain the certificate of education, and are oriented toward teens. There is no such adult high-school equivalent to attaining the certificate in Queensland, though there are in other states, e.g. New South Wales. It may be an option for adults to return to study at a normal secondary school, but there are difficulties with being accepted due to age differences. Many schools frown at adults being on school grounds.
Technical and Further Education (TAFE) also serves as an alternative pathway to university. There are specialized courses for this, including the Adult Tertiary Preparation IV course (ATP) which aims to develop skills in literacy, numeracy and study skills as core components. This does not follow the year 11/12 syllabus, but is independent of it. TAFE subjects generally take longer to complete if they are done entirely for the QCE. It is inadvisable however to use TAFE as a pathway without completing year 12 or equivalent, as many institutions have prerequisites of year 12 studies. It is not possible to gain a Senior Certificate from ATP, however tertiary providers may enrol students with this educational background as they are granted a selection rank for their studies. This can also be taken by school leavers to prepare after a period of being away from study.
Since the Senior External Examination is merely an examination and not a full-time study commitment, it may be possible to do both at one time, thereby gaining more credit.
Completion of a year at a university grants another set of selection ranks, allowing for students to receive higher selection rank based on the performance in those studies. It is possible for students to undertake tertiary study in a less competitive program (e.g., arts) and transfer to a more competitive program with the new rank.


X-ray magnetic circular dichroism

X-ray magnetic circular dichroism (XMCD) is a difference spectrum of two X-ray absorption spectra (XAS) taken in a magnetic field, one taken with left circularly polarized light, and one with right circularly polarized light. By closely analyzing the difference in the XMCD spectrum, information can be obtained on the magnetic properties of the atom, such as its spin and orbital magnetic moment.
In the case of transition metals such as iron, cobalt, and nickel, the absorption spectra for XMCD are usually measured at the L-edge. This corresponds to the process in the iron case: with iron, a 2p electron is excited to a 3d state by an X-ray of about 700 eV. Because the 3d electron states are the origin of the magnetic properties of the elements, the spectra contain information on the magnetic properties.


GRE Mathematics Test

The GRE subject test in mathematics is a standardized test in the United States created by the Educational Testing Service (ETS), and is designed to assess a candidate's potential for graduate or post-graduate study in the field of mathematics. It contains questions from many fields of mathematics; about 50% of the questions come from calculus (including pre-calculus topics, multivariate calculus, and differential equations), 25% come from algebra (including linear algebra, abstract algebra, and number theory), and 25% come from a broad variety of other topics typically encountered in undergraduate mathematics courses, such as point-set topology, probability and statistics, geometry, and real analysis.
Similar to all the GRE subject tests, the GRE Mathematics test is paper-based, as opposed to the GRE general test which is usually computer-based. It contains approximately 66 multiple-choice questions, which are to be answered within 2 hours and 50 minutes. Scores on this exam are required for entrance to most math Ph.D. programs in the United States.
Scores are scaled and then reported as a number between 200 and 990; however, in recent versions of the test, the maximum and minimum reported scores have been 920 and 400, which correspond to the 99th percentile and the 1st percentile, respectively. The mean score for all test takers from July 1, 2011 to June 30, 2014 was 659, with a standard deviation of 137.
Prior to October 2001, a significant percentage of students were achieving perfect scores on the exam, which made it difficult for competitive programs to differentiate between students in the upper percentiles. As a result, the test was reworked and renamed "The Mathematics Subject Test (Rescaled)". According to ETS, "Scores earned on the test after October 2001 should not be compared to scores earned prior to that date."
Tests generally take place three times per year, on one Saturday in each of September, October, and April. Students must register for the exam approximately five weeks before the administration of the exam.


Dorian mode

Dorian mode or Doric mode can refer to three very different but interrelated subjects: one of the Ancient Greek "harmoniai" (characteristic melodic behaviour, or the scale structure associated with it), one of the medieval musical modes, or, most commonly, one of the modern modal diatonic scales, corresponding to the piano keyboard's white notes from D to D, or any transposition of this.
\override Score.TimeSignature #'stencil = ##f
\relative c' {
 \clef treble \time 7/4
 c4^\markup { Modern C Dorian mode } d es f g a bes c2
</score>
Greek Dorian mode.
The Dorian mode (properly "harmonia" or "tonos") is named after the Dorian Greeks. Applied to a whole octave, the Dorian octave species was built upon two tetrachords (four-note segments) separated by a whole tone, running from the "hypate meson" to the "nete diezeugmenon".
In the enharmonic genus, the intervals in each tetrachord are quarter tone–quarter tone–major third.
\override Score.TimeSignature #'stencil = ##f
\relative c' {
 \clef treble \time 4/4
 e4^\markup { Greek Dorian tonos (enharmonic genus) on E } feh geses a b ceh deses e
</score>
In the chromatic genus, they are semitone–semitone–minor third.
\override Score.TimeSignature #'stencil = ##f
\relative c' {
 \clef treble \time 4/4
 e4^\markup { Greek Dorian tonos (chromatic genus) on E } f ges a b c des e
</score>
In the diatonic genus, they are semitone–tone–tone.
\override Score.TimeSignature #'stencil = ##f
\relative c' {
 \clef treble \time 4/4
 e4^\markup { Greek Dorian tonos (diatonic genus) on E } f g a b c d e
</score>
In the diatonic genus, the sequence over the octave is the same as that produced by playing all the white notes of a piano ascending from E to E, a sequence equivalent to the modern Phrygian mode.
Placing the single tone at the bottom of the scale followed by two conjunct tetrachords (that is, the top note of the first tetrachord is also the bottom note of the second), produces the Hypodorian ("below Dorian") octave species: A | B C D E | (E) F G A. Placing the two tetrachords together and the single tone at the top of the scale produces the Mixolydian octave species, a note sequence equivalent to modern Locrian mode.
Medieval Dorian mode.
The early Byzantine church developed a system of eight musical modes (the octoechos), which served as a model for medieval European chant theorists when they developed their own modal classification system starting in the 9th century. The success of the Western synthesis of this system with elements from the fourth book of "De institutione musica" of Boethius, created the false impression that the Byzantine octoechos was inherited directly from ancient Greece.
Originally used to designate one of the traditional "harmoniai" of Greek theory (a term with various meanings, including the sense of an octave consisting of eight tones), the name was appropriated (along with six others) by the 2nd-century theorist Ptolemy to designate his seven "tonoi", or transposition keys. Four centuries later, Boethius interpreted Ptolemy in Latin, still with the meaning of transposition keys, not scales. When chant theory was first being formulated in the 9th century, these seven names plus an eighth, Hypermixolydian (later changed to Hypomixolydian), were again re-appropriated in the anonymous treatise "Alia Musica". A commentary on that treatise, called the "Nova expositio", first gave it a new sense as one of a set of eight diatonic species of the octave, or scales.
In medieval theory, the authentic Dorian mode could include the note B "by licence", in addition to B. The same scalar pattern, but starting a fourth or fifth below the mode final D, and extending a fifth above (or a sixth, terminating on B), was numbered as mode 2 in the medieval system. This was the plagal mode corresponding to the authentic Dorian, and was called the Hypodorian mode. In the untransposed form on D, in both the authentic and plagal forms the note C is often raised to C to form a leading tone, and the variable sixth step is in general B in ascending lines and B in descent.
Modern Dorian mode.
The modern Dorian mode (also called "Russian minor" by Balakirev), by contrast, is a strictly diatonic scale corresponding to the white keys of the piano from D to D (shown below)
\override Score.TimeSignature #'stencil = ##f
\relative c' {
 \clef treble \time 7/4
 d4^\markup { Modern D Dorian mode } e f g a b c d2
</score>
or any transposition of its interval pattern, which has the ascending pattern of whole steps and half steps as follows:
Thus, the Dorian mode is a symmetric scale, since the pattern of whole and half step is the same ascending or descending.
The modern Dorian mode can also be thought of as a scale with a minor third and seventh, a major second and sixth, and a perfect fourth and fifth, notated relative to the major scale as:
It may be considered an "excerpt" of a major scale played from the pitch a whole tone above the major scale's tonic , i.e., a major scale played from its second scale degree up to its second degree again. The resulting scale is, however, "minor" in quality, because, as the D becomes the new tonal centre, the F a minor third above the D becomes the new mediant, or third degree. Thus, when a triad is built upon the tonic, it is a minor triad.
The modern Dorian mode is equivalent to the natural minor scale (or the Aeolian mode) but with a major sixth. The modern Dorian mode resembles the Greek Phrygian "harmonia" in the diatonic genus.
It is also equivalent to the ascending melodic minor scale with a minor seventh.


Navajo meridian and baseline

The Navajo meridian, established in 1869, is one of the two principal meridians for Arizona, the other being the Gila and Salt River meridian. Its initial point was stated as latitude 35° 45' north, longitude 108° 32' 45" west from Greenwich, but has been revised as The Navajo meridian and baseline were used to set townships and ranges in a special survey for the original Navajo Reservation, and was set at the eastern boundary of that reservation. The Arizona lands surveyed using the Navajo meridian and baseline were ranges six west to ten west and townships one north to fourteen north, and included Canyon de Chelly National Monument.
While the above-mentioned Arizona lands still reference the Navajo meridian and baseline, in New Mexico the surveys of lands originally surveyed under it were canceled in 1936, and have since been resurveyed using the New Mexico meridian and baseline. In Arizona, only the portions of the Navajo Reservation that are east of the Hopi Reservation were surveyed using the Navajo meridian and baseline.


4997 Ksana

4997 Ksana, provisional designation , is a carbonaceous Palladian asteroid from the outer region of the asteroid belt, approximately 10 kilometers in diameter. It was discovered on 6 October 1986, by Russian astronomer Lyudmila Karachkina at Crimean Astrophysical Observatory on the Crimean peninsula. The asteroid was named for Russian chemist Kseniya Nessler.
Orbit and classification.
"Ksana" is a small member of the Pallas family (), a small asteroid family of carbonaceous B-type asteroids. It orbits the Sun in the outer main-belt at a distance of 1.9–3.8 AU once every 4 years and 10 months (1,778 days). Its orbit has an eccentricity of 0.33 and an inclination of 33° with respect to the ecliptic.
As no precoveries were taken, the asteroid's observation arc begins with its discovery observation in 1986.
Physical characteristics.
On the SMASS taxonomic scheme, "Ksana" is a B-type asteroid, which are primitive, volatile-rich asteroids. This also agrees with the overall spectral type of the Pallas family.
Diameter and albedo.
According to the surveys carried out by the Japanese Akari satellite and NASA's Wide-field Infrared Survey Explorer with its subsequent NEOWISE mission, "Ksana" measures between 7.36 and kilometers in diameter and its surface has an albedo between 0.16 and 0.316.
The "Collaborative Asteroid Lightcurve Link" assumes a standard albedo for carbonaceous asteroids of 0.057 and calculates a larger diameter of 14.64 kilometers with an absolute magnitude of 12.9.
Rotation period.
In February 2007, a rotational lightcurve of "Ksana" was obtained from photometric observations by Italian astronomer Federico Manzini at the SAS observatory in Novara, Italy. It gave it a rotation period of hours with a brightness variation of 0.21 in magnitude ().
Naming.
This minor planet was named by the discoverer for his friend, the Russian chemist Kseniya Andreevna Nessler, who has been an advocate against environmental pollution. The asteroid's name "Ksana" is a variation of Kseniya (Ксения), the equivalent to the romanized Xenia. The official naming citation was published by the Minor Planet Center on 1 September 1993 ().


Quarter-comma meantone

Quarter-comma meantone, or -comma meantone, was the most common meantone temperament in the sixteenth and seventeenth centuries, and was sometimes used later. In this system the perfect fifth is flattened by one quarter of a syntonic comma (81:80), with respect to its just intonation used in Pythagorean tuning (frequency ratio 3:2); the result is formula_1, or a fifth of formula_2 cents. (The 12th power of that value is 125, whereas 7 octaves is 128, and so falls formula_3 cents short.) This fifth is then iterated to generate the diatonic scale and other notes of the temperament. The purpose is to obtain justly intoned major thirds (with a frequency ratio equal to 5:4). It was described by Pietro Aron in his "Toscanello de la Musica" of 1523, by saying the major thirds should be tuned to be "sonorous and just, as united as possible." Later theorists Gioseffo Zarlino and Francisco de Salinas described the tuning with mathematical exactitude.
Construction.
In a meantone tuning, we have different chromatic and diatonic semitones; the chromatic semitone is the difference between C and C#, and the diatonic semitone the difference between C and Db. In Pythagorean tuning, the diatonic semitone is often called the Pythagorean limma and the chromatic semitone Pythagorean apotome, but in Pythagorean tuning the apotome is larger, whereas in 1/4-comma meantone the limma is larger. Put another way, in Pythagorean tuning we have that C# is higher than Db, whereas in 1/4-comma meantone we have C# is lower than Db.
In any meantone or Pythagorean tuning, a whole tone is composed of one semitone of each kind, a major third is two whole tones and therefore consists of two semitones of each kind, a perfect fifth of meantone contains four diatonic and three chromatic semitones, and an octave seven diatonic and five chromatic semitones, it follows that:
Thus, in Pythagorean tuning, where sequences of just fifths (frequency ratio 3:2) and octaves are used to produce the other intervals, a whole tone is
and a major third is
An interval of a seventeenth, consisting of sixteen diatonic and twelve chromatic semitones, such as the interval from D4 to F6, can be equivalently obtained using either
This large interval of a seventeenth contains staff positions. In Pythagorean tuning, the size of a seventeenth is defined using a stack of four justly tuned fifths (frequency ratio 3:2):
In quarter-comma meantone temperament, where a just major third (5:4) is required, a slightly narrower seventeenth is obtained by stacking two octaves and a major third:
By definition, however, a seventeenth of the same size (5:1) must be obtained, even in quarter-comma meantone, by stacking four fifths. Since justly tuned fifths, such as those used in Pythagorean tuning, produce a slightly wider seventeenth, in quarter-comma meantone the fifths must be slightly flattened to meet this requirement. Letting "x" be the frequency ratio of the flattened fifth, it is desired that four fifths have a ratio of 5:1,
which implies that a fifth is
a whole tone, built by moving two fifths up and one octave down, is
and a diatonic semitone, built by moving three octaves up and five fifths down, is
Notice that, in quarter-comma meantone, the seventeenth is times narrower than in Pythagorean tuning. This difference in size, equal to about 21.506 cents, is called the syntonic comma. This implies that the fifth is a quarter of a syntonic comma narrower than the justly tuned Pythagorean fifth. Namely, this system tunes the fifths in the ratio of
which is expressed in the logarithmic cents scale as
which is slightly smaller (or flatter) than the ratio of a justly tuned fifth:
which is expressed in the logarithmic cents scale as
The difference between these two sizes is a quarter of a syntonic comma:
In sum, this system tunes the major thirds to the just ratio of 5:4 (so, for instance, if A4 is tuned to 440 Hz, C5 is tuned to 550 Hz), most of the whole tones (namely the major seconds) in the ratio :2, and most of the semitones (namely the diatonic semitones or minor seconds) in the ratio 8:5. This is achieved by tuning the seventeenth a syntonic comma flatter than the Pythagorean seventeenth, which implies tuning the fifth a quarter of a syntonic comma flatter than the just ratio of 3:2. It is this that gives the system its name of "quarter-comma meantone".
12-tone scale.
The whole chromatic scale (a subset of which is the diatonic scale), can be constructed by starting from a given "base note", and increasing or decreasing its frequency by one or more fifths. This method is identical to Pythagorean tuning, except for the size of the fifth, which is tempered as explained above. The construction table below illustrates how the pitches of the notes are obtained with respect to D (the "base note"), in a D-based scale (see Pythagorean tuning for a more detailed explanation).
For each note in the basic octave, the table provides the conventional name of the interval from D (the base note), the formula to compute its frequency ratio, and the approximate values for its frequency ratio and size in cents.
In the formulas, "x" = = 5 is the size of the tempered perfect fifth, and the ratios "x":1 or 1:"x" represent an ascending or descending tempered perfect fifth (i.e. an increase or decrease in frequency by "x"), while 2:1 or 1:2 represent an ascending or descending octave.
As in Pythagorean tuning, this method generates 13 pitches, but A and G have almost the same frequency, and to build a 12-tone scale A is typically discarded (although the choice between these two notes is completely arbitrary).
C-based construction tables.
The table above shows a D-based stack of fifths (i.e. a stack in which all ratios are expressed relative to D, and D has a ratio of 1/1). Since it is centered at D, the base note, this stack can be called "D-based symmetric":
With the perfect fifth taken as , the ends of this scale are 125 in frequency ratio apart, causing a gap of 125/128 (about two-fifths of a semitone) between its ends if they are normalized to the same octave. If the last step (here, G♯) is replaced by a copy of A♭ but in the same octave as G♯, that will increase the interval C♯–G♯ to a discord called a wolf fifth.
Except for the size of the fifth, this is identical to the stack traditionally used in Pythagorean tuning. Some authors prefer showing a C-based stack of fifths, ranging from A to G. Since C is not at its center, this stack is called "C-based asymmetric":
Since the boundaries of this stack (A and G) are identical to those of the D-based symmetric stack, the note names of the 12 tone scale produced by this stack are also identical. The only difference is that the construction table shows intervals from C, rather than from D. Notice that 144 intervals can be formed from a 12 tone scale (see table below), which include intervals from C, D, and any other note. However, the construction table shows only 12 of them, in this case those starting from C. This is at the same time the main advantage and main disadvantage of the C-based asymmetric stack, as the intervals from C are commonly used, but since C is not at the center of this stack, they unfortunately include an augmented fifth (i.e. the interval from C to G), instead of a minor sixth (from C to A). This augmented fifth is an extremely dissonant wolf interval, as it deviates by 41.1 cents (a diesis of ratio 128:125, almost twice a syntonic comma) from the corresponding pure interval of 8:5 or 813.7 cents.
On the contrary, the intervals from D shown in the table above, since D is at the center of the stack, do not include wolf intervals and include a pure m6 (from D to B), instead of an impure augmented fifth. Notice that in the above-mentioned set of 144 intervals pure minor sixths are more frequently observed than impure augmented fifths (see table below), and this is one of the reasons why it is not desirable to show an impure augmented fifth in the construction table. A "C-based symmetric" stack might be also used, to avoid the above-mentioned drawback:
In this stack, G and F have a similar frequency, and G is typically discarded. Also, the note between C and D is called D rather than C, and the note between G and A is called A rather than G. The C-based symmetric stack is rarely used, possibly because it produces the wolf fifth in the unusual position of F–D instead of G–E, where musicians using Pythagorean tuning expected it).
Justly intonated quarter-comma meantone.
A just intonation version of the quarter-comma meantone temperament may be constructed in the same way as Johann Kirnberger's rational version of 12-TET. The value of 5 · 35 is very close to 4, which is why a 7-limit interval 6144:6125 (which is the difference between the 5-limit diesis 128:125 and the septimal diesis 49:48), equal to 5.362 cents, appears very close to the quarter-comma () of 5.377 cents. So the perfect fifth has the ratio of 6125:4096, which is the difference between three just major thirds and two septimal major seconds; four such fifths exceed the ratio of 5:1 by the tiny interval of 0.058 cents. The wolf fifth there appears to be 49:32, the difference between the septimal minor seventh and the septimal major second.
Greater and lesser semitones.
As discussed above, in the quarter-comma meantone temperament,
The tones in the diatonic scale can be divided into pairs of semitones. However, since "S"2 is not equal to "T", each tone must be composed of a pair of unequal semitones, "S", and "X":
Hence,
Notice that "S" is 117.1 cents, and "X" is 76.0 cents. Thus, "S" is the greater semitone, and "X" is the lesser one. "S" is commonly called the diatonic semitone (or minor second), while "X" is called the chromatic semitone (or augmented unison).
The sizes of "S" and "X" can be compared to the just intonated ratio 18:17 which is 99.0 cents. "S" deviates from it by +18.2 cents, and "X" by −22.9 cents. These two deviations are comparable to the syntonic comma (21.5 cents), which this system is designed to tune out from the Pythagorean major third. However, since even the just intonated ratio 18:17 sounds markedly dissonant, these deviations are considered acceptable in a semitone.
In quarter-comma meantone, the minor second is considered acceptable while the augmented unison sounds dissonant and should be avoided.
Size of intervals.
The table above shows only intervals from D. However, intervals can be formed by starting from each of the above listed 12 notes. Thus, twelve intervals can be defined for each interval type (twelve unisons, twelve semitones, twelve intervals composed of 2 semitones, twelve intervals composed of 3 semitones, etc.).
As explained above, one of the twelve fifths (the wolf fifth) has a different size with respect to the other eleven. For a similar reason, each of the other interval types, except for the unisons and the octaves, has two different sizes in quarter-comma meantone. This is the price paid for seeking just intonation. The table below shows their approximate size in cents. Interval names are given in their standard shortened form. For instance, the size of the interval from D to A, which is a perfect fifth (P5), can be found in the seventh column of the row labeled D. Strictly just (or "pure") intervals are shown in bold font. Wolf intervals are highlighted in red.
Surprisingly, although this tuning system was designed to produce pure major thirds, only eight of them are pure (5:4 or about 386.3 cents).
The reason why the interval sizes vary throughout the scale is that the pitches forming the scale are unevenly spaced. Namely, as mentioned above, the frequencies defined by construction for the twelve notes determine two different kinds of semitones (i.e. intervals between adjacent notes):
Conversely, in an equally tempered chromatic scale, by definition the twelve pitches are equally spaced, all semitones having a size of exactly
As a consequence all intervals of any given type have the same size (e.g., all major thirds have the same size, all fifths have the same size, etc.). The price paid, in this case, is that none of them is justly tuned and perfectly consonant, except, of course, for the unison and the octave.
For a comparison with other tuning systems, see also this table.
By definition, in quarter-comma meantone 11 perfect fifths (P5 in the table) have a size of approximately 696.6 cents (700 − "ε" cents, where "ε" ≈ 3.422 cents); since the average size of the 12 fifths must equal exactly 700 cents (as in equal temperament), the other one must have a size of 700 + 11"ε" cents, which is about 737.6 cents (the wolf fifth). Notice that, as shown in the table, the latter interval, although enharmonically equivalent to a fifth, is more properly called a diminished sixth (d6). Similarly,
In short, similar differences in width are observed for all interval types, except for unisons and octaves, and they are all multiples of ε, the difference between the quarter-comma meantone fifth and the average fifth.
Notice that, as an obvious consequence, each augmented or diminished interval is exactly 12"ε" cents (≈ 41.1 cents) wider or narrower than its enharmonic equivalent. For instance, the diminished sixth (or wolf fifth) is 12"ε" cents wider than each perfect fifth, and each augmented second is 12"ε" cents narrower than each minor third. This interval of size 12"ε" is known as a diesis, or diminished second. This implies that "ε" can be also defined as one twelfth of a diesis.
Triads in the chromatic scale.
The major triad can be defined by a pair of intervals from the root note: a major third (interval spanning 4 semitones) and a perfect fifth (7 semitones). The minor triad can likewise be defined by a minor third (3 semitones) and a perfect fifth (7 semitones).
As shown above, a chromatic scale has twelve intervals spanning seven semitones. Eleven of these are perfect fifths, while the twelfth is a diminished sixth. Since they span the same number of semitones, perfect fifths and diminished sixths are considered to be enharmonically equivalent. In an equally-tuned chromatic scale, perfect fifths and diminished sixths have exactly the same size. The same is true for all the enharmonically equivalent intervals spanning 4 semitones (major thirds and diminished fourths), or 3 semitones (minor thirds and augmented seconds). However, in the meantone temperament this is not true. In this tuning system, enharmonically equivalent intervals may have different sizes, and some intervals may markedly deviate from their justly tuned ideal ratios. As explained in the previous section, if the deviation is too large, then the given interval is not usable, either by itself or in a chord.
The following table focuses only on the above-mentioned three interval types, used to form major and minor triads. Each row shows three intervals of different types but which have the same root note. Each interval is specified by a pair of notes. To the right of each interval is listed the formula for the interval ratio. The intervals diminished fourth, diminished sixth and augmented second may be regarded as wolf intervals, and have been marked in red. "S" and "X" denote the ratio of the two abovementioned kinds of semitones (minor second and augmented unison).
First, look at the last two columns on the right. All the 7-semitone intervals except one have a ratio of
which deviates by −5.4 cents from the just 3:2 of 702.0 cents. Five cents is small and acceptable. On the other hand, the diminished sixth from G to E has a ratio of
which deviates by +35.7 cents from the just perfect fifth. Thirty-five cents is beyond the acceptable range.
Now look at the two columns in the middle. Eight of the twelve 4-semitone intervals have a ratio of
which is exactly a just 5:4. On the other hand, the four diminished fourths with roots at C, F, G and B have a ratio of
which deviates by +41.1 cents from the just major third. Again, this sounds badly out of tune.
Major triads are formed out of both major thirds and perfect fifths. If either of the two intervals is substituted by a wolf interval (d6 instead of P5, or d4 instead of M3), then the triad is not acceptable. Therefore, major triads with root notes of C, F, G and B are not used in meantone scales whose fundamental note is C.
Now look at the first two columns on the left. Nine of the twelve 3-semitone intervals have a ratio of
which deviates by −5.4 cents from the just 6:5 of 315.6 cents. Five cents is acceptable. On the other hand, the three augmented seconds whose roots are E, F and B have a ratio of
which deviates by −46.4 cents from the just minor third. It is a close match, however, for the 7:6 septimal minor third of 266.9 cents, deviating by +2.3 cents. These augmented seconds, though sufficiently consonant by themselves, will sound "exotic" or atypical when played together with a perfect fifth.
Minor triads are formed out of both minor thirds and fifths. If either of the two intervals are substituted by an enharmonically equivalent interval (d6 instead of P5, or A2 instead of m3), then the triad will not sound good. Therefore, minor triads with root notes of E, F, G and B are not used in the meantone scale defined above.
Alternative construction.
As discussed above, in the quarter-comma meantone temperament,
It can be verified through calculation that most whole tones (namely, the major seconds) are composed of one greater and one lesser semitone:
Similarly, a fifth is typically composed of three tones and one greater semitone:
which is equivalent to four greater and three lesser semitones:
Diatonic scale.
A diatonic scale can be constructed by starting from the fundamental note and multiplying it either by "T" to move up by a tone or by "S" to move up by a semitone.
 C D E F G A B C'
 "T T S T T T S"
The resulting interval sizes with respect to the base note C are shown in the following table:
Chromatic scale.
Construction of a quarter-comma meantone chromatic scale can proceed by stacking a series of 12 semitones, each of which may be either diatonic ("S") or chromatic ("X").
 C C D E E F F G G A B B C'
 "X S S X S X S X S S X S"
Notice that this scale is an extension of the diatonic scale shown in the previous table. Only five notes have been added: C, E, F, G and B (a pentatonic scale).
As explained above, an identical scale was originally defined and produced by using a sequence of tempered fifths, ranging from E (five fifths below D) to G (six fifths above D), rather than a sequence of semitones. This more conventional approach, similar to the "D-based" Pythagorean tuning system, explains the reason why the X and S semitones are arranged in the particular and apparently arbitrary sequence shown above.
The interval sizes with respect to the base note C are presented in the following table. The frequency ratios are computed as shown by the formulas. Delta is the difference in cents between meantone and 12-TET. -c is the difference in quarter-commas between meantone and Pythagorean tuning.
Comparison with 31 equal temperament.
The perfect fifth of quarter-comma meantone, expressed as a fraction of an octave, is log2 5. This number is irrational and in fact transcendental; hence a chain of meantone fifths, like a chain of pure 3:2 fifths, never closes (i.e. never equals a chain of octaves). However, the continued fraction approximations to this irrational fraction number allow us to find equal divisions of the octave which do close; the denominators of these are 1, 2, 5, 7, 12, 19, 31, 174, 205, 789 ... From this we find that 31 quarter-comma meantone fifths come close to closing, and conversely 31 equal temperament represents a good approximation to quarter-comma meantone. See also schisma.


Planet-hosting stars

This article describes the correlations between stars' characteristics and the characteristics of the planets that orbit them, and other connections between stars and their planets.
Proportion of stars with planets.
Most stars have planets but exactly what proportion of stars have planets is uncertain because not all planets can yet be detected. The radial-velocity method and the transit method (which between them are responsible for the vast majority of detections) are most sensitive to large planets in small orbits. Thus many known exoplanets are "hot Jupiters": planets of Jovian mass or larger in very small orbits with periods of only a few days. A 2005 survey of radial-velocity-detected planets found that about 1.2% of Sun-like stars have a hot jupiter, where "Sun-like star" refers to any main-sequence star of spectral classes late-F, G, or early-K without a close stellar companion. This 1.2% is more than double the frequency of hot jupiters detected by the Kepler spacecraft, which may be because the Kepler field of view covers a different region of the Milky Way where the metallicity of stars is different.
It is further estimated that 3% to 4.5% of Sun-like stars possess a giant planet with an orbital period of 100 days or less, where "giant planet" means a planet of at least 30 Earth masses.
It is known that small planets (of roughly Earth-like mass or somewhat larger) are more common than giant planets. It also appears that there are more planets in large orbits than in small orbits. Based on this, it is estimated that perhaps 20% of Sun-like stars have at least one giant planet whereas at least 40% may have planets of lower mass.
A 2012 study of gravitational microlensing data collected between 2002 and 2007 concludes the proportion of stars with planets is much higher and estimates an average of 1.6 planets orbiting between 0.5–10 AU per star in the Milky Way, the authors of this study conclude that "stars are orbited by planets as a rule, rather than the exception".
In November 2013 it was announced that 22±8% of Sun-like stars have an Earth-sized planet in the habitable zone.
Whatever the proportion of stars with planets, the total number of exoplanets must be very large. Because the Milky Way has at least 200 billion stars, it must also contain tens or hundreds of billions of planets.
Type of star, spectral classification.
Most known exoplanets orbit stars roughly similar to the Sun, that is, main-sequence stars of spectral categories F, G, or K. One reason is that planet-search programs have tended to concentrate on such stars. In addition, statistical analyses indicate that lower-mass stars (red dwarfs, of spectral category M) are less likely to have planets massive enough to be detected by the radial-velocity method. Nevertheless, many planets around red dwarfs have been discovered by the Kepler spacecraft by the transit method, which can detect smaller planets.
Stars of spectral category A typically rotate very quickly, which makes it very difficult to measure the small Doppler shifts induced by orbiting planets because the spectral lines are very broad. However, this type of massive star eventually evolves into a cooler red giant that rotates more slowly and thus can be measured using the radial-velocity method.
A few tens of planets have been found around red giants.
Observations using the Spitzer Space Telescope indicate that extremely massive stars of spectral category O, which are much hotter than the Sun, produce a photo-evaporation effect that inhibits planetary formation.
When the O-type star goes supernova any planets that had formed would become free-floating due to the loss of stellar mass unless the natal kick of the resulting remnant pushes it in the same direction as an escaping planet.
Fallback disks of matter that failed to escape orbit during a supernova may form planets around neutron stars and black holes.
Doppler surveys around a wide variety of stars indicate about 1 in 6 stars having twice the mass of the Sun are orbited by one or more Jupiter-sized planets, vs. 1 in 16 for Sun-like stars and only 1 in 50 for red dwarfs. On the other hand, microlensing surveys indicate that long-period Neptune-mass planets are found around 1 in 3 red dwarfs.
Kepler Space Telescope observations of planets with up to one year periods show that occurrence rates of Earth- to Neptune-sized planets (1 to 4 Earth radii) around M, K, G, and F stars are successively higher towards cooler, less massive stars.
At the low-mass end of star-formation are sub-stellar objects that don't fuse hydrogen: the brown dwarfs and sub-brown dwarfs, of spectral classification L,T and Y. Planets and protoplanetary disks have been discovered around brown dwarfs, and disks have been found around sub-brown dwarfs (e.g. OTS 44).
Rogue planets ejected from their system could retain a system of satellites.
Metallicity.
Ordinary stars are composed mainly of the light elements hydrogen and helium. They also contain a small proportion of heavier elements, and this fraction is referred to as a star's metallicity (even if the elements are not metals in the traditional sense), denoted [m/H] and expressed on a logarithmic scale where zero is the Sun's metallicity.
A 2012 study of the Kepler spacecraft data found that smaller planets, with radii smaller than Neptune's were found around stars with metallicities in the range −0.6 < [m/H] < +0.5 (about four times less than that of the Sun to three times more), whereas larger planets were found mostly around stars with metallicities at the higher end of this range (at solar metallicity and above). In this study small planets occurred about three times as frequently as large planets around stars of metallicity greater than that of the Sun, but they occurred around six times as frequently for stars of metallicity less than that of the Sun. The lack of gas giants around low-metallicity stars could be because the metallicity of protoplanetary disks affects how quickly planetary cores can form and whether they accrete a gaseous envelope before the gas dissipates. However, Kepler can only observe planets very close to their star and the detected gas giants probably migrated from further out, so a decreased efficiency of migration in low-metallicity disks could also partly explain these findings.
A 2014 study found that not only giant planets, but planets of all sizes have an increased occurrence rate around metal-rich stars compared to metal-poor stars, although the larger the planet, the greater this increase as the metallicity increases. The study divided planets into three groups based on radius: gas giants, gas dwarfs, and terrestrial planets with the dividing lines at 1.7 and 3.9 Earth radii. For these three groups the planet occurrence rates are 9.30, 2.03, and 1.72 times higher for metal-rich stars than for metal-poor stars, respectively. There is a bias against detecting smaller planets because metal-rich stars tend to be larger, making it more difficult to detect smaller planets, which means that these increases in occurrence rates are lower limits.
It has also been shown that Sun-like stars with planets are much more likely to be deficient in lithium, although this correlation is not seen at all in other types of stars. However, this claimed relationship has become a point of contention in the planetary astrophysics community, being frequently denied but also supported.
Multiple stars.
Stellar multiplicity increases with stellar mass: the likelihood of stars being in multiple systems is about 25% for red dwarfs, about 45% for Sun-like stars, and rises to about 80% for the most massive stars. Of the multiple stars about 75% are binaries and the rest are higher-order multiplicities.
More than one hundred planets have been discovered orbiting one member of a binary star system (e.g. 55 Cancri, possibly Alpha Centauri Bb), and several circumbinary planets have been discovered which orbit around both members of a binary star (e.g. PSR B1620-26 b, Kepler-16b). A few dozen planets in triple star systems are known (e.g. 16 Cygni Bb) and two in quadruple systems Kepler 64 and 30 Arietis.
The Kepler results indicate circumbinary planetary systems are relatively common (as of October 2013 the spacecraft had found seven circumbinary planets out of roughly 1000 eclipsing binaries searched). One puzzling finding is that although half of the binaries have an orbital period of 2.7 days or less, none of the binaries with circumbinary planets have a period less than 7.4 days. Another surprising Kepler finding is circumbinary planets tend to orbit their stars close to the critical instability radius (theoretical calculations indicate the minimum stable separation is roughly two to three times the size of the stars' separation).
In 2014, from statistical studies of searches for companion stars, it was inferred that around half of exoplanet host stars have a companion star, usually within 100AU. This means that many exoplanet host stars that were thought to be single are binaries, so in many cases it is not known which of the stars a planet actually orbits, and the published parameters of transiting planets could be significantly incorrect because the "planet radius" and "distance from star" are derived from the stellar parameters. Follow-up studies with imaging (such as speckle imaging) are needed to find or rule out companions (and radial velocity techniques would be required to detect binaries really close together) and this has not yet been done for most exoplanet host stars. Examples of known binary stars where it is not known which of the stars a planet orbits are Kepler-132 and Kepler-296, although a 2015 study found that the Kepler-296 planets were likely orbiting the brighter star.
Open clusters.
Most stars form in open clusters, but very few planets have been found in open clusters and this led to the hypothesis that the open-cluster environment hinders planet formation. However, a 2011 study concluded that there have been an insufficient number of surveys of clusters to make such a hypothesis.
The lack of surveys was because there are relatively few suitable open clusters in the Milky Way.
Recent discoveries of both giant planets and low-mass planets in open clusters are consistent with there being similar planet occurrence rates in open clusters as around field stars.
The open cluster NGC 6811 contains two known planetary systems Kepler-66 and Kepler-67.


Tertian

In music theory, tertian (, "of or concerning thirds") describes any piece, chord, counterpoint etc. constructed from the intervals of (major and minor) thirds. An interval such as that between the notes A and C encompasses 3 semitone intervals (A-B-B-C) and is termed a minor third while one such as that between C and E encompasses 4 semitones (C-D-D-E-E) and is called a major third. Tertian harmony (also called tertiary harmony) principally uses chords based on thirds; the term is typically used to contrast with quartal and quintal harmony which uses chords based on fourths or fifths.
A common triad chord can be regarded as consisting of a "stack" of two thirds. There are four permutations: A major third stacked on a major third creates an augmented triad. A minor third on top of a major third manifests a major triad. A major third on top of a minor third produces a minor triad. Finally, a minor third stacked on a minor third constitutes a diminished triad.
A musical scale may also be analysed as a succession of thirds.
The meantone temperament, a system of tuning that emphasises pure thirds, may be called "tertian".
Chords built from sixths may also be referred to as tertian because sixths are equivalent to thirds when inverted, and vice versa: any sixth can be taken as the inversion of a third. For instance the interval C-A is a major sixth that, when inverted, gives the interval A-C, which is a minor third.
Tertian root movements have been used innovatively in chord progressions as an alternative to root motion in fifths, as for example in the "thirds cycle" used in John Coltrane's Coltrane changes, as influenced by Nicolas Slonimsky's "Thesaurus of Scales and Melodic Patterns".


Motion-capture acting

Motion-capture acting, also called performance-capture acting and often abbreviated as Mo-Cap or P-Cap, is a type of acting in which an actor wears markers or sensors on a skintight bodysuit or directly on the skin. Several cameras from different angles record the actor's movements simultaneously, recording the three-dimensional position of the sensors without recording the rest of the actor. Sampling is done many times each second, aided by advances in computer technology. The resulting database of 3D points permits a filmmaker or video game creator to create a digital character and place them in an entirely new setting.
This type of acting is seen as a growth area, with predictions that there will be more work in future for actors. Some talent agents represent motion-capture actors in addition to their live-action actors. Motion-capture acting can be difficult work. For example, one actor was "placed in a tiny booth, had dots placed all over his face that captured his movements, and had to sit perfectly still". As it is a new type of acting work, one report suggested that actors wishing to break into this line of work should go to acting class and become experts in skills such as gunplay, sword fighting, hand-to-hand combat, dancing, running, jumping, gymnastics, and general body movement.
Numerous sources identify English actor Andy Serkis as the "king of motion-capture acting" based on his portrayal of digital characters in films such as "King Kong", "The Lord of the Rings", and "Planet of the Apes". According to one report, the first use of motion-capture acting for a video game was for the 2007 PlayStation 3 release "Heavenly Sword", which starred Serkis. In an August 2011 interview, Serkis said, "Performance-capture technology is really the only way that we could bring these characters to life. It's the way that Gollum was brought to life, and King Kong, and the Naʼvi in "Avatar" and so on [...] it's really another way of capturing an actor's performance. That's all it is, digital make-up."
There have been battles within the entertainment industry about recognition for motion-capture actors. The Alliance of Motion Picture and Television Producers does not consider motion-capture acting to be the same type of work as live-action acting, which means that motion-capture actors are often paid less. The actors' union SAG-AFTRA has lobbied the industry for better employment terms and conditions for motion-capture actors, arguing that the work should be included in standard labor contracts. As of 2020, major award ceremonies still have no motion-capture acting category.


Creep-testing machine

A creep-testing machine measures the alteration of a material after it has undergone stresses.
Engineers use Creep machines to determine the stability and behaviour of a material when put through ordinary stresses. They determine how much strain (load) an object can handle under pressure, so engineers and researchers are able to determine what materials to use.
The device generates a creep time-dependent curve by calculating the steady rate of creep in reference to the time it takes for the material to change.
Creep.
Creep is the tendency of a material to change form over time after facing high temperature and stress. Creep increases with temperature and it is more common when a material is exposed to high temperatures for a long time or at the melting point of the material.
Creep machines are used to understand the creep of materials and determine which type can do the job better, which is important when making and designing materials for everyday uses. They most commonly test the creep of alloys and plastics for the understanding of their properties and advantages of one material's use over another.
Background.
The first creep testing machines were created in 1948 in Britain to test materials for aircraft to see how they would stand in high altitudes, temperature and pressure. The machines were first developed to further calculate and understand the steady rate of creep in materials.
Design.
Researchers look to test objects with a creep machine to understand the process of metallurgy and the physical mechanical properties of a metal, test the development of alloys, receive data from the loads that are derived and to find out whether a sample or material is within the boundary of what they are testing. The basic design of a creep machine is the furnace, loading device and support structure.
The main type of creep testing machine is a constant load creep testing machine. The constant load creep machine consists of a loading platform, foundation, fixture devices and furnace. The fixture devices are the grips and pull rods.
Applications.
Creep machines are most commonly used in experiments to determine how efficient and stable a material is. The machine is used by students and companies to create a creep curve on how much pressure and stress a material can handle. The machine is able to calculate the stress rate, time and pressure.
Creep testing has three different applications in the industry:
Graphing of creep.
Creep is dependent on time so the curve that the machine generates is a time vs. strain graph. The slope of a creep curve is the creep rate dε/dt The trend of the curve is an upward slope. The graphs are important to learn the trends of the alloys or materials used and by the production of the creep-time graph, it is easier to determine the better material for a specific application.
Stages of creep.
There are three stages of creep:
By examining the three stages above, scientists are able to determine the temperature and interval in which an object will be disturbed once exposed to the load. Some materials have a very small secondary creep state and may go straight from the primary creep to the tertiary creep state. This is dependent on the properties of the material that is being tested. This is important to note because going straight to the tertiary state causes the material to break faster from its form.
A linear graph denotes that the material under stress is gradually deforming, and this would be harder to track at what level of stress an object can handle. This would also mean that the material would not have distinct stages, which would make an object's breaking point less predictable. This is a disadvantage to scientists and engineers when trying to determine the level of creep the object can handle.


UK Metric Association

The UK Metric Association, or UKMA, is an advocacy group in the United Kingdom that argues for Metrication in the United Kingdom and advocates the use of the metric system among the general public in the UK. UKMA argues that the continued use of two incompatible systems of measurement causes misunderstanding, confusion and mistakes, undermines consumer protection, wastes time during children's education, results in additional costs, and is against the national interest.
History.
UKMA was founded by Chris Keenan in 1999 and formally associated in 2002 as an independent, non-party political, single-issue organisation. Later, an e-mail forum was started for supporters of metrication. In 2005, a website called ThinkMetric to help and encourage the general public to think in metric units was launched. In 2006, a blog called MetricViews was launched.
The current secretary of UKMA is Derek Pollard. Political patrons include Lord Kinnock (Lab), Dr Nick Palmer (Lab) and Ian Taylor (Con).
Strategies.
One of UKMA's strategies, aimed at getting their message to a wider audience including journalists and researchers, is to use "Wikipedia" as a conduit for their information. In an article in their December 2008 newsletter, members were urged to "correct any inaccuracies" in "Wikipedia" articles. It told about the "bias and inaccuracy" in metrication related articles, including Metrication in the United Kingdom, and highlighted the importance of "keeping an eye on them [metrication articles], visiting them regularly and checking that nobody has reversed any changes that you have made."
Publications.
UKMA has released four major reports, aimed at stimulating discussion in Britain about completing the transition to international standard units:
In 2009, UKMA published an update to Signs Ahead", which reflects the changes that have happened since the publication of the Metric Signs Ahead report. In the same year, UKMA published a traffic signs leaflet called Signs 2.0", which recommends changes to UK road signs to improve clarity, legibility and safety by using universally understood symbols and units of measurement.
Opposition.
The aims of UKMA contrast with those of the British Weights and Measures Association (BWMA), which campaigns against compulsory Metrication in the United Kingdom and advocates the continued use of imperial measures.


Lithobraking

Lithobraking is a landing technique used by uncrewed space vehicles to safely reach the surface of a celestial body while reducing landing speed by impact with the body's surface. The word was probably coined as a whimsical adaptation of aerobraking, which is the process of slowing a space vehicle by the use of aerodynamic drag in a planet's atmosphere. "Lithos" is a Greek word meaning "rock" or "stone," similarly used in words such as lithosphere or lithography.
Successful lithobraking requires either reducing the velocity of the lander prior to impact or protecting the probe with sufficient cushioning to withstand an impact with the surface undamaged. The velocity of a lander can be reduced using retrorockets or parachutes, and it can be protected from the force of impact by cushioning air bags or shock absorbers. The first successful lithobraking was achieved by the Soviet Luna 9 probe resulting in the first soft landing on the Moon using a combination of retrorockets and gas-filled cushioning bags.
When landing on bodies with an atmosphere, lithobraking can be combined with aerobraking instead of relying on retrorockets and air-bags. For bodies with a significant yet insufficiently thick atmosphere (e.g., Mars) all of these may be used together. The Mars Pathfinder and Mars Exploration Rover programs have used this approach successfully. The Russian Mars 96 mission would have attempted a similar landing had it not been lost in Earth's atmosphere shortly after launch. For bodies such as Venus with an exceptionally thick atmosphere, the combination of lithobraking and aerobraking can be sufficient. The Soviet Venera landers descended using parachutes high in the atmosphere before falling freely through the dense lower atmosphere until finally dissipating their remaining velocity (between approximately 7.5 and 8 m/s) on impact.
In the absence of a thick atmosphere, lithobraking is difficult due to the extremely high orbital velocities of most bodies. However, the orbital velocity of small moons (e.g., Phobos), asteroids, and comets can be sufficiently small for this strategy to be feasible. For example, Rosetta lander, Philae, passively landed on the comet 67P/Churyumov–Gerasimenko after separating from the orbiter, dissipating energy only through impact with the surface of comet. The MASCOT lander from Hayabusa2 landed on asteroid 162173 Ryugu in a similar manner. Rather than risking a large monolithic lander in a lithobraking maneuver, a proposed alternative is to instead attempt lithobraking with a swarm of much smaller landers at the same time. If there are many opportunities for a successful landing, then the chance of success on any single landing does not need to be high.
Instead of attempting to slowly dissipate the incoming velocity, it can be used to enable the probe to penetrate the surface.
This can be tried on bodies with low gravitation, such as comets and asteroids, or on planets with atmospheres (by using only small parachutes, or no parachutes at all). Several such missions have been launched, including penetrators on the two Phobos probe landers targeted for Mars' moon Phobos and ones for Mars itself on Mars 96 and Deep Space 2, but so far none have succeeded. The cancelled LUNAR-A probe would have carried penetrators to the Moon.
Certain concepts involve the spacecraft in an orbit tangent to the surface of the body in question, and "docking" with a magnetically levitated (maglev) train, and the train then slowing. This qualifies as lithobraking, as the reaction mass is the planet itself. This technique requires extremely precise guidance and control, in addition to a large infrastructure, and is thus not yet a viable option – although it may be in the future. An advantage to this method is that it can also launch spacecraft without needing propellant.
Lithobraking is also used as a humorous euphemism for the result of a spacecraft crashing into the surface of a body with no measures to ensure its survival, either by accident or with intent. For instance, the term has been used to describe the impact of MESSENGER into Mercury after the spacecraft ran out of fuel. This usage is popular among fans of the game "Kerbal Space Program", where unintentional use of lithobraking is a common gameplay experience, and is referenced in the "Kerbal Space Program 2" announcement trailer, where the tagline is "Lithobraking near you in 2020."


Augmented sixth chord

In music theory, an augmented sixth chord contains the interval of an augmented sixth, usually above its bass tone. This chord has its origins in the Renaissance, was further developed in the Baroque, and became a distinctive part of the musical style of the Classical and Romantic periods.
Conventionally used with a predominant function (resolving to the dominant), the three more common types of augmented sixth chords are usually called the "Italian sixth", the "French sixth", and the "German sixth".
Augmented sixth interval.
The augmented sixth interval is typically between the sixth degree of the minor scale, , and the raised fourth degree, . With standard voice leading, the chord is followed directly or indirectly by some form of the dominant chord, in which both and have resolved to the fifth scale degree, . This tendency to resolve outwards to is why the interval is spelled as an augmented sixth, rather than enharmonically as a minor seventh ( and ).
Although augmented sixth chords are more common in the minor mode, they are also used in the major mode by borrowing of the parallel minor scale.
Types.
There are three main types of augmented sixth chords, commonly known as the "Italian sixth", the "French sixth", and the "German sixth".
 \override Score.TimeSignature #'stencil = ##f
 \new PianoStaff «
 \new Staff «
 \relative c' {
 \clef treble \key c \major \time 4/4
 \textLengthOn
 »
 \new Staff «
 \relative c' {
 \clef bass \key c \major \time 4/4
 <aes c>1 \bar "||"
 <aes c> \bar "||"
 <aes c> \bar "||"
 »
</score>
Though each is named after a European nationality, theorists disagree on their precise origins and have struggled for centuries to define their roots, and fit them into conventional harmonic theory. According to Kostka and Payne, the other two terms are similar to the "Italian sixth", which, "has no historical authenticity-[being] simply a convenient and traditional label."
Italian sixth.
The Italian sixth (It+6 or It6 or iv6) is derived from iv6 with an altered fourth scale degree, . This is the only augmented sixth chord comprising just three distinct notes; in four-part writing, the tonic pitch is doubled.
 \new PianoStaff «
 \new Staff «
 \relative c' {
 \clef treble \key c \major \time 4/4
 <c fis>1 <d g>
 »
 \new Staff «
 \relative c' {
 \clef bass \key c \major \time 4/4
 <aes c>1_\markup { \concat { "It" \raise #1 \small "+6" \hspace #4.3 "V" } }
 <g b> \bar "||"
 »
</score>
The Italian sixth is enharmonically equivalent to an incomplete dominant seventh. VI7=V7: A, C, (E,) G.
French sixth.
The French sixth (Fr+6 or Fr) is similar to the Italian, but with an additional tone, . The notes of the French sixth chord are all contained within the same whole tone scale, lending a sonority common to French music in the 19th century (especially associated with Impressionist music).
 \new PianoStaff «
 \new Staff «
 \relative c' {
 \clef treble \key c \major \time 4/4
 <d fis>1 <d g>
 »
 \new Staff «
 \relative c' {
 \clef bass \key c \major \time 4/4
 <aes c>1_\markup { \concat { "Fr" \raise #1 \small "+6" \hspace #3.7 "V" } }
 <g b> \bar "||"
 »
</score>
This chord has the same notes as a dominant seventh flat five chord and is in fact the second inversion of II75.
German sixth.
The German sixth (Ger+6 or Ger) is also like the Italian, but with an added tone, .
 \new PianoStaff «
 \new Staff «
 \relative c' {
 \clef treble \key c \major \time 4/4
 <es fis>1 <d g>
 »
 \new Staff «
 \relative c' {
 \clef bass \key c \major \time 4/4
 <g b> \bar "||"
 »
</score>
In Classical music, however, it appears in much the same places as the other variants, though perhaps less often because of the contrapuntal difficulties outlined below. It appears frequently in the works of Beethoven, and in ragtime music. The German sixth chord is enharmonically equivalent to a dominant seventh chord though it functions differently.
Avoiding parallel fifths.
It is more difficult to avoid parallel fifths when resolving a German sixth chord to the dominant chord. These parallel fifths, referred to as "Mozart fifths", were occasionally accepted by common practice composers. There are two ways they can be avoided:
Other types.
Other variants of augmented sixth chords can be found in the repertoire, and are sometimes given whimsical geographical names. For example: 4–6–7–2; (F–A–B–D) is called by one source an "Australian sixth", and 7–1–3–5 (B–C–E–G#), sometimes called the "Japanese sixth" Such anomalies usually have alternative interpretations.
Function.
Standard function.
From the Baroque to the Romantic periods, augmented sixth chords had the same harmonic function: as a chromatically altered predominant chord (typically, an alteration of ii, IV, vi7 or their parallel equivalents in the minor mode) leading to a dominant chord. This movement to the dominant is heightened by the semitonal resolution to from above and below (from and ); essentially, these two notes act as leading-tones.
This characteristic has led many analysts to compare the voice leading of augmented sixth chords to the secondary dominant V of V because of the presence of , the leading-tone of V, in both chords. In the major mode, the chromatic voice leading is more pronounced because of the presence of two chromatically altered notes, and , rather than just .
In most occasions, the augmented-sixth chords precede either the dominant, or the tonic in second inversion. The augmented sixths can be treated as chromatically altered passing chords.
Other functions.
In the late Romantic period and other musical traditions, especially jazz, other harmonic possibilities of augmented sixth variants and sonorities outside its function as a predominant were explored, exploiting their particular properties. An example of this is through the "reinterpretation" of the harmonic function of a chord: since a chord could simultaneously have more than one enharmonic spelling with different functions (i.e., both predominant as a German sixth and dominant as a dominant seventh), its function could be reinterpreted mid-phrase. This heightens both chromaticism by making possible the tonicization of remotely related keys, and possible dissonances with the juxtaposition of remotely related keys.
Tchaikovsky considered the augmented sixth chords to be altered dominant chords. He described the augmented sixth chords to be inversions of the diminished triad and of dominant and diminished seventh chords with a lowered second degree (), and accordingly resolving into the tonic. He notes that, "some theorists insist upon [augmented sixth chord's] resolution not into the tonic but into the dominant triad, and regard them as being erected not on the altered 2nd degree, but on the altered 6th degree in major and on the natural 6th degree in minor", yet calls this view, "fallacious", insisting that a, "chord of the augmented sixth on the 6th degree is nothing else than a modulatory degression into the key of the dominant".
The example below shows the last nine measures from Schubert's Piano Sonata in A major, D. 959. In m. 352, an Italian sixth chord built on scale degree functions as a substitute for the dominant.
 #(set-global-staff-size 18)
 \new PianoStaff «
 \new Staff «
 \set Score.currentBarNumber = #349
 \bar ""
 \new Voice \relative c' {
 \clef bass \key a \major \time 4/4
 a8 r \ottava #1 <cis e a> \ottava #0 r r2\fermata
 bes8 r \ottava #1 <d gis! d'> \ottava #0 r r2\fermata \break
 R1
 r2 4 r
 1
 \new Voice \relative c {
 \clef bass \key a \major \time 4/4
 \once \stemDown <cis e>4\pp
 »
 \new Staff «
 \relative c, {
 \clef bass \key a \major \time 4/4
 \omit TupletNumber \tuplet 3/2 { a8 \sustainOn cis e } \tuplet 3/2 { a cis e } r2
 \clef treble r4 8 r r2\fermata
 \clef bass \tuplet 3/2 { bes,,8 d f } \tuplet 3/2 { bes d f } r2
 \clef treble r4 <bes' d gis!>8 r r2\fermata
 \clef bass \tuplet 3/2 { a,,8 cis e } \tuplet 3/2 { a cis e } r2
 R1
 a4 r r
 1 \bar "|."
 »
</score>
Inversions.
Augmented sixth chords are occasionally used with a different chord member in the bass. Since there is no consensus among theorists that they are in root position in their normal form, the word "inversion" isn't necessarily accurate, but is found in some textbooks, nonetheless. Sometimes, "inverted" augmented sixth chords occur as a product of voice leading.
Rousseau considered that the chord could not be inverted. Seventeenth century instances of the augmented sixth with the sharp note in the bass are generally limited to German sources.
The excerpt below is from J.S. Bach's Mass in B minor. At the end of the second measure, the augmented sixth is inverted to create a diminished third or tenth between the bass and the soprano (C–E); these two voices resolve inward to an octave.
 #(set-global-staff-size 16)
 \set Score.proportionalNotationDuration = #(ly:make-moment 1/8)
« \new StaffGroup «
 \new Staff «
 \set Staff.midiInstrument = #"voice oohs"
 \relative c' {
 \clef treble \key g \major \time 3/2
 fis1 f2 e1 \breathe es2 d2^( c4 b) c2 b1.\fermata \bar "|."
 \new Staff «
 \set Staff.midiInstrument = #"voice oohs"
 \clef treble \key g \major \time 3/2
 \new Voice \relative c' {
 c2 b1~ b2 \breathe c bes a1 a2 g1.\fermata
 \new Staff «
 \set Staff.midiInstrument = #"voice oohs"
 \clef "treble_8" \key g \major \time 3/2
 \new Voice \relative c {
 fis1^( gis2~ gis) a \breathe g! g1 fis2 d1.\fermata
 \new Staff «
 \set Staff.midiInstrument = #"voice oohs"
 \clef bass \key g \major \time 3/2
 \new Voice \relative c {
 dis2( d) d cis \breathe c cis d1 d2 g,1.\fermata
 \addlyrics { pul -- tus est et se -- pul -- tus est. } »
 { \new PianoStaff «
 \new Staff «
 \set Staff.midiInstrument = #"piano"
 \clef treble \key g \major \time 3/2
 \new Voice \relative c' {
 R1. R1. R1. R1.\fermata
 \new Staff «
 \set Staff.midiInstrument = #"piano"
 \clef bass \key g \major \time 3/2
 \new Voice \relative c, {
 <dis dis'>4-.( <dis dis'>-. <d d'>-. <d d'>-. <d d'>-. <d d'>-.)
 <cis cis'>-.( <cis cis'>-. <c c'>-. <c c'>-. <cis cis'>-. <cis cis'>-.)
 <d d'>-.( <d d'>-. <d, d'>-. <d d'>-.^\ppp <d d'>-. <d d'>-.)
 <g g'>1.\fermata
</score>
Related chords.
In music theory, the double-diminished triad is an archaic concept and term referring to a triad, or three note chord, which, already being minor, has its root raised a semitone, making it "doubly diminished". However, this may be used as the derivation of the augmented sixth chord. For example, F–A–C is a minor triad, so F–A–C is a doubly diminished triad. This is enharmonically equivalent to G–A–C, an incomplete dominant seventh A, missing its fifth), which is a tritone substitute that resolves to G. Its inversion, A–C–F, is the Italian sixth chord that resolves to G.
Classical harmonic theory would notate the tritone substitute as an augmented sixth chord on 2. The augmented sixth chord can either be (i) an It+6 enharmonically equivalent to a dominant seventh chord (with a missing fifth); (ii) a Ger+6 equivalent to a dominant seventh chord with (with a fifth); or (iii) a Fr+6 equivalent to the Lydian dominant (with a missing fifth), all of which serve in a classical context as a substitute for the secondary dominant of V.
 \relative c' {
 \time 4/4
 <des f aes ces>1^\markup { "Tritone sub" }
 <c e g c> \bar "||"
 <des f b>^\markup { "(i) Italian" }
 <c e c'> \bar "||"
 <des f aes b>^\markup { "(ii) German" }
 <c e g c> \bar "||"
 <des f g b>^\markup { "(iii) French" }
 <c e g c> \bar "||"
</score>
All variants of augmented sixth chords are closely related to the applied dominant V7 of II. Both Italian and German variants are enharmonically identical to dominant seventh chords. For example, in the key of C, the German sixth chord could be reinterpreted as the applied dominant of D.
 \override Score.TimeSignature #'stencil = ##f
 \new PianoStaff «
 \new Staff «
 \relative c' {
 \clef treble \key c \major \time 4/4
 <es ges>1
 <c fis>
 <es fis>
 »
 \new Staff «
 \relative c' {
 \clef bass \key c \major \time 4/4
 <aes c>1_\markup { \center-align { \concat { "V" \raise #1 \small "7" "/♭II" } } } \bar "||"
 <aes c>1_\markup { \concat { "It" \raise #1 \small "+6" } } \bar "||"
 <aes c>1_\markup { \concat { "Ger" \raise #1 \small "+6" } } \bar "||"
 »
</score>
Simon Sechter explains the chord of the French sixth chord as being a chromatically altered version of a seventh chord on the second degree of the scale, . The German sixth is explained as a chromatically altered ninth chord on the same root but with the root omitted.
 \override Score.TimeSignature #'stencil = ##f
 \new PianoStaff «
 \new Staff «
 \relative c' {
 \clef treble \key c \major \time 4/4
 \textLengthOn
 <fis c'>1^\markup { "French" }
 <fis c' es>^\markup { "German" }
 »
 \new Staff «
 \relative c {
 \clef bass \key c \major \time 4/4
 <d aes'>1 \bar "||"
 <\parenthesize d aes'>1 \bar "||"
 »
</score>
The tendency of the interval of the augmented sixth to resolve outwards is therefore explained by the fact that the A, being a dissonant note, a diminished fifth above the root (D), and flatted, must fall, whilst the F – being chromatically raised – must rise.
Relationship between the different types.
The following "curious chromatic sequence", graphed by Dmitri Tymoczko as a four-dimensional tesseract, outlines the relationships between the augmented sixth chords in 12TET tuning:
Minor seventh as virtual augmented sixth chord.
The minor seventh chord may also have its interval of minor seventh (between the root and seventh degree (i.e.: C–B in C–E–G–B) rewritten as an augmented sixth (C–E–G–A). Rearranging and transposing, this gives A–C–E–F, a virtual minor version of the German sixth chord. Again like the typical +6, this enharmonic interpretation gives a resolution irregular for the minor seventh but normal for the augmented sixth, where the two voices at the enharmonic major second converge to a unison or diverge to an octave.
Half-diminished seventh as virtual augmented sixth chord.
The half-diminished seventh chord is the inversion of the German sixth chord (it is its inversion as a set, rather than as a chord). Its interval of minor seventh (between root and seventh degree (i.e.: C–B in C–E–G–B) can be written as an augmented sixth (C–E–G–A). Rearranging and transposing, this gives A–C–D–F, a virtual minor version of the French sixth chord. Like the typical +6, this enharmonic interpretation gives a resolution irregular for the half-diminished seventh but normal for the augmented sixth, where the two voices at the enharmonic major second converge to a unison or diverge to an octave.
Tristan chord.
Richard Wagner's Tristan chord, the first vertical sonority in his opera, "Tristan und Isolde", can be interpreted as a half-diminished seventh that transitions to a French sixth in the key of A minor (F–A–B–D, in red below). The upper voice continues upward with a long appoggiatura (G to A). Note that the D resolves down to D instead of up to E:
 \new PianoStaff «
 \new Staff «
 \new Voice \relative c" {
 \clef treble \key a \minor \time 6/8
 \voiceOne \partial8 r8 R2. gis4.->(~ gis4 \once \override NoteHead.color = #red a8 ais8-> b4~ b8) r r
 \new Voice \relative c' {
 \override DynamicLineSpanner.staff-padding = #4.5
 \once \override DynamicText.X-offset = #-5
 \voiceTwo \partial8 a\pp( f'4.~\< f4 e8 \once \override NoteHead.color = #red dis2.)(\> d!4.)~\p d8 r r
 »
 \new Staff «
 \relative c {
 \clef bass \key a \minor \time 6/8
 \partial8 r8 R2. \once \override NoteHead.color = #red <f b>2.(_\markup { \concat { "Fr" \raise #1 \small "+6" \hspace #8 "V" \raise #1 \small "7" } } <e gis>4.)~ <e gis>8 r r
 »
</score>


History of Cinema (2008 film)

History of Cinema is a 2008 Iranian Irish experimental short film directed by Rouzbeh Rashidi. The film is an experimental derivation from the concept of cinema, expressing this perception through images and sound. The 33 minute film reflects the notion of seventh art with complete personal and free interpretation.
Production.
Rashidi shot the film with webcam and mobile phone cameras between 2002 and 2004. Each segment of the film was shot and edited separately, and compiled them together in 2008 for the final version. Rashidi used archival footage from the early films of cinema and integrated them with the rest of material in order to create the sense of history. The film is heavily saturated, grainy and full of distorted images. The soundscape designed by Rashidi was added into the film with chosen music.
Reception.
History of Cinema premiered at the Global Cinema Festival 2009 in India.
Lucca Film Festival 2010 - (An)Other Irish Cinema Category


Ellen Hamaker

Ellen Louise "E.L." Hamaker (born February 13, 1974) is a Dutch-American psychologist, and statistician. Since 2018 she has been a full professor at Utrecht University, holding the chair Longitudinal Data Analysis at the Department of Methodology and Statistics. Her work focuses on the development of statistical models for the analysis of intensive longitudinal data in psychology, mainly within the frameworks of structural equation modeling and time series analysis.
Biography.
Education.
Hamaker received a bachelor's and master's degree in psychology from Utrecht University, in 1997 and 1999 respectively. She earned her PhD in psychological methods in 2004 at the University of Amsterdam, under the supervision of Peter Molenaar and Conor Dolan, for her thesis: "Time series analysis and the individual as the unit of psychological research"
Academic career.
In 2005 Hamaker became a postdoctoral fellow at the Department of Psychology, University of Virginia. Hamaker returned to the Netherlands in 2006, being appointed assistant professor at the Department of Methodology and Statistics, Utrecht University. She was promoted to associate professor in 2011, before being promoted to full professor with the chair Longitudinal Data Analysis in 2018. Since 2014 she has also been a research fellow at the Research Group of Quantitative Psychology and Individual Differences, KU Leuven, in Belgium.
Research focus.
Hamaker's early research focused on the application of time series techniques within psychology, to study process that unfold within individuals over time. Increased availability of data collected using the experience sampling method in psychology led to increased interest in this methodology in applied psychological research. Most notable of her papers is her critique of the cross-lagged panel model, in which she proposes to better account for stable trait-like differences between individuals through the use of multilevel models with random intercepts. She is also an advocate of within-person thinking in social sciences, pointing out that conclusions based on cross-sectional data do not necessarily generalize to the processes within a particular person.
Since 2015 Hamaker has collaborated frequently with Bengt O. Muthén and Tihomir Asparouhov in the development of the Dynamic Structural Equation Modeling, a module that allows for Bayesian Time Series analysis in the software package Mplus.
Hamaker has stated that the overarching goal of her research is to establish a connection between innovative statistical techniques and applied psychological research.
Achievements and awards.
Throughout her academic career, Hamaker has served as associate editor of "Multivariate Behavioral Research". In 2019 she was appointed a fellow of the Association for Psychological Science.
Personal life.
Hamaker is the granddaughter of Dutch scientist Hugo Christiaan Hamaker, noted for his contributions to physics (the Hamaker constant) and statistics.


Radar chart

A radar chart is a graphical method of displaying multivariate data in the form of a two-dimensional chart of three or more quantitative variables represented on axes starting from the same point. The relative position and angle of the axes is typically uninformative, but various heuristics, such as algorithms that plot data as the maximal total area, can be applied to sort the variables (axes) into relative positions that reveal distinct correlations, trade-offs, and a multitude of other comparative measures.
The radar chart is also known as web chart, spider chart, spider web chart, star chart, star plot, cobweb chart, irregular polygon, polar chart, or Kiviat diagram. It is equivalent to a parallel coordinates plot, with the axes arranged radially.
Overview.
The radar chart is a chart and/or plot that consists of a sequence of equi-angular spokes, called radii, with each spoke representing one of the variables. The data length of a spoke is proportional to the magnitude of the variable for the data point relative to the maximum magnitude of the variable across all data points. A line is drawn connecting the data values for each spoke. This gives the plot a star-like appearance and the origin of one of the popular names for this plot. The star plot can be used to answer the following questions:
Radar charts are a useful way to display multivariate observations with an arbitrary number of variables. Each star represents a single observation. Typically, radar charts are generated in a multi-plot format with many stars on each page and each star representing one observation. The star plot was first used by Georg von Mayr in 1877. Radar charts differ from glyph plots in that all variables are used to construct the plotted star figure. There is no separation into foreground and background variables. Instead, the star-shaped figures are usually arranged in a rectangular array on the page. It is somewhat easier to see patterns in the data if the observations are arranged in some non-arbitrary order (if the variables are assigned to the rays of the star in some meaningful order).
Applications.
One application of radar charts is the control of quality improvement to display the performance metrics of any ongoing program.
They are also used in sports to chart players' strengths and weaknesses, where they are usually called radar charts.
Limitations.
Radar charts are primarily suited for strikingly showing "outliers" and "commonality", or when one chart is greater in every variable than another, and primarily used for ordinal measurements – where each variable corresponds to "better" in some respect, and all variables on the same scale.
Conversely, radar charts have been criticized as poorly suited for making trade-off decisions – when one chart is greater than another on some variables, but less on others.
Further, it is hard to visually compare lengths of different spokes, because radial distances are hard to judge, though concentric circles help as grid lines. Instead, one may use a simple line graph, particularly for time series.
Radar charts can distort data to some extent, especially when areas are filled in, because the area contained becomes proportional to the square of the linear measures. For example, in a chart with 5 variables that range from 1 to 100, the area contained by the polygon bounded by 5 points when all measures are 90, is more than 10% larger than the same for a chart with all values of 82.
Artificial structure.
Radar charts impose several structures on data, which are often artificial:
For example, the alternating data 9, 1, 9, 1, 9, 1 yields a spiking radar chart (which goes in and out), while reordering the data as 9, 9, 9, 1, 1, 1 instead yields two distinct wedges (sectors).
In some cases there is a natural structure, and radar charts can be well-suited. For example, for diagrams of data that vary over a 24-hour cycle, the hourly data is naturally related to its neighbor, and has a cyclic structure, so it can naturally be displayed as a radar chart.
One set of guidelines on the use of radar charts (or rather the closely related "polar area graph") is:
Data set size.
Radar charts are helpful for small-to-moderate-sized multivariate data sets. Their primary weakness is that their effectiveness is limited to data sets with less than a few hundred points. After that, they tend to be overwhelming.
Example.
The chart on the right contains the star plots of 15 cars. The variable list for the sample star plot is:
We can look at these plots individually or we can use them to identify clusters of cars with similar features. For example, we can look at the star plot of the Cadillac Seville (the last one on the image) and see that it is one of the most expensive cars, gets below average (but not among the worst) gas mileage, has an average repair record, and has average-to-above-average roominess and size. We can then compare the Cadillac models (the last three plots) with the AMC models (the first three plots). This comparison shows distinct patterns. The AMC models tend to be inexpensive, have below average gas mileage, and are small in both height and weight and in roominess. The Cadillac models are expensive, have poor gas mileage, and are large in both size and roominess.
Alternatives.
Most simply, one may use a simple line graph, particularly for time series.
For graphical qualitative comparison of 2-dimensional tabular data in several variables, a common alternative are Harvey balls, which are used extensively by "Consumer Reports". Comparison in Harvey balls (and radar charts) may be significantly aided by ordering the variables algorithmically to add order.
An excellent way for visualising structures within multivariate data is offered by principal component analysis (PCA).
Another alternative is to use small, inline bar charts, which may be compared to sparklines.
Although radar and polar charts are often described as the same chart types, some sources make a difference between them and even consider the radar chart to be a polar chart's variation that does not display data in terms of polar coordinate.


Vibrational spectroscopy of linear molecules

To determine the vibrational spectroscopy of linear molecules, the rotation and vibration of linear molecules are taken into account to predict which vibrational (normal) modes are active in the infrared spectrum and the Raman spectrum.
Degrees of freedom.
The location of a molecule in a 3-dimensional space can be described by the total number of coordinates. Each atom is assigned a set of "x", "y", and "z" coordinates and can move in all three directions. Degrees of freedom is the total number of variables used to define the motion of a molecule completely. For "N" atoms in a molecule moving in 3-D space, there are 3"N" total motions because each atom has 3"N" degrees of freedom.
Vibrational modes.
"N" atoms in a molecule have 3"N" degrees of freedom which constitute translations, rotations, and vibrations. For non-linear molecules, there are 3 degrees of freedom for translational (motion along the x, y, and z directions) and 3 degrees of freedom for rotational motion (rotations in Rx, Ry, and Rz directions) for each atom. Linear molecules are defined as possessing bond angles of 180°, so there are 3 degrees of freedom for translational motion but only 2 degrees of freedom for rotational motion because the rotation about its molecular axis leaves the molecule unchanged. When subtracting the translational and rotational degrees of freedom, the degrees of vibrational modes is determined.
Number of degrees of vibrational freedom for nonlinear molecules: 3"N"-6
Number of degrees of vibrational freedom for linear molecules: 3"N"-5
Symmetry of vibrational modes.
All 3"N" degrees of freedom have symmetry relationships consistent with the irreducible representations of the molecule's point group. A linear molecule is characterized as possessing a bond angle of 180° with either a C∞v or D∞h symmetry point group. Each point group has a character table that represents all of the possible symmetry of that molecule. Specifically for linear molecules, the two character tables are shown below:
However, these two character tables have infinite number of irreducible representations, so it is necessary to lower the symmetry to a subgroup that has related representations whose characters are the same for the shared operations in the two groups. A property that transforms as one representation in a group will transform as its correlated representation in a subgroup. Therefore, C∞v will be correlated to C2v and D∞h to D2h. The correlation table for each is shown below:
Once the point group of the linear molecule is determined and the correlated symmetry is identified, all symmetry element operations associated to that correlated symmetry's point group are performed for each atom to deduce the reducible representation of the 3"N" Cartsian displacement vectors. From the right side of the character table, the non-vibrational degrees of freedom, rotational (Rx and Ry) and translational (x, y, and z), are subtracted: Γvib = Γ3N - Γrot - Γtrans. This yields the Γvib, which is used to find the correct normal modes from the original symmetry, which is either C∞v or D∞h, using the correlation table above. Then, each vibrational mode can be identified as either IR or Raman active.
Vibrational spectroscopy.
A vibration will be active in the IR if there is a change in the dipole moment of the molecule and if it has the same symmetry as one of the x, y, z coordinates. To determine which modes are IR active, the irreducible representation corresponding to x, y, and z are checked with the reducible representation of Γvib. An IR mode is active if the same irreducible representation is present in both.
Furthermore, a vibration will be Raman active if there is a change in the polarizability of the molecule and if it has the same symmetry as one of the direct products of the x, y, z coordinates. To determine which modes are Raman active, the irreducible representation corresponding to xy, xz, yz, x2, y2, and z2 are checked with the reducible representation of Γvib. A Raman mode is active if the same irreducible representation is present in both.
Example.
Carbon Dioxide, CO2
1. Assign point group: D∞h
2. Determine group-subgroup point group: D2h
3. Find the number of normal (vibrational) modes or degrees of freedom using the equation: 3n - 5 = 3(3) - 5 = 4
4. Derive reducible representation Γ3N:
5. Decompose the reducible representation into irreducible components:
Γ3N = Ag + B2g + B3g + 2B1u + 2B2u + 2B3u
6. Solve for the irreducible representation corresponding to the normal modes with the subgroup character table:
Γ3N = Ag + B2g + B3g + 2B1u + 2B2u + 2B3u
Γrot = B2g + B3g
Γtrans = B1u + B2u + B3u
Γvib = Γ3N - Γrot - Γtrans
Γvib = Ag + B1u + B2u + B3u
7. Use the correlation table to find the normal modes for the original point group:
"v1" = Ag = Σ
"v2" = B1u = Σ
"v3" = B2u = Πu
"v4" = B3u = Πu
8. Label whether the modes are either IR active or Raman active:
"v1" = Raman active
"v2" = IR active
"v3" = IR active
"v4" = IR active


First Terrace Records

First Terrace Records is an independent record label founded in 2016 by Alex Ives & Joseph Summers.
First Terrace release music covering ambient, electronica, experimental, drone, jazz, modern composition & sound art. First Terrace have released music from artists such as Specimens, K. Leimer and the very well received Peter Broderick project "The Beacon Sound Choir - 'Sunday Songs"' also featuring Machinefabriek.
Label philosophy.
The name of the label and logo are inspired by Dante's "Divine Comedy" & the first level in Purgatorio. Depicting the souls of the proud bent over by the weight of huge stones on their backs in the face of sculptures expressing humility, the opposite virtue to pride which serves as an ethos for the label to remain humble.
The original First Terrace logo was sketched by co-founder Alex Ives and is present on only one record, Specimens - 'Sculptures' LP. Following this a refined version was used on all releases up until 2020 when the label introduced a new version of the logo which is present to this day. Consistent throughout all versions of the logo are the legs (of the proud) which symbolise holding up the weight of pride & thus a reminder to remain humble in your work.
Artists.
List of artists First Terrace Records have released records for:
See also.
List of record labels


930 Westphalia

930 Westphalia ("prov. designation": "or" ) is a very dark background asteroid and a slow rotator from the inner regions of the asteroid belt, that measures approximately in diameter. It was discovered on 10 March 1920, by German astronomer Walter Baade at the Bergedorf Observatory in Hamburg. The carbonaceous C-type asteroid (Ch) has an exceptionally long rotation period of 100.7 hours and is likely spherical in shape. It was named after Westphalia, a region in northwestern Germany.
Orbit and classification.
"Westphalia" is a non-family asteroid of the main belt's background population when applying the hierarchical clustering method to its proper orbital elements. It orbits the Sun in the inner asteroid belt at a distance of 2.1–2.8 AU once every 3 years and 9 months (1,384 days; semi-major axis of 2.43 AU). Its orbit has an eccentricity of 0.14 and an inclination of 15° with respect to the ecliptic. The asteroid was first observed as () at the Simeiz Observatory on 24 February 1916. The body's observation arc begins with its official discovery observation at Bergedorf Observatory on 10 March 1920.
Naming.
This minor planet was named after the region of Westphalia in northwestern Germany, bordering the Netherlands and the Rhine river. It is the birthplace of the discoverer Walter Baade (1893–1960). The was mentioned in "The Names of the Minor Planets" by Paul Herget in 1955 ().
Physical characteristics.
In the Bus–Binzel SMASS classification, "Westphalia" is a hydrated carbonaceous C-type asteroid (Ch).
Rotation period.
In April 2015, a rotational lightcurve of "Westphalia" was obtained from photometric observations by Eduardo Manuel Álvarez at the Los Algarrobos Observatory in Uruguay. Lightcurve analysis gave a rotation period of hours with a brightness amplitude of magnitude, indicative of a spherical, non-elongated shape (). This was the first time a period could be determined for this asteroid, and, as the observer noted, there were only 18 tree-digit asteroids left for which no such measurement had yet been made. With a period above 100 hours, "Westphalia" is a slow rotator. While the slowest rotators have periods above 1000 hours, the vast majority of asteroids have periods between 2.2 and 20 hours.
Diameter and albedo.
According to the survey carried out by the NEOWISE mission of NASA's Wide-field Infrared Survey Explorer (WISE), the Infrared Astronomical Satellite IRAS, and the Japanese Akari satellite, "Westphalia" measures (), () and () kilometers in diameter and its surface has a very low albedo of (), () and (), respectively.
The "Collaborative Asteroid Lightcurve Link" derives an albedo of 0.0438 and a diameter of 36.53 km based on an absolute magnitude of 11.2. Further published mean-diameters and albedos by the WISE team in ascending order include (), (), (), (), () and () and albedos of (), (), (), (), () and ().