Two-dimensional infrared spectroscopy

Two-dimensional infrared spectroscopy (2D IR) is a nonlinear infrared spectroscopy technique that has the ability to correlate vibrational modes in condensed-phase systems. This technique provides information beyond linear infrared spectra, by spreading the vibrational information along multiple axes, yielding a frequency correlation spectrum. A frequency correlation spectrum can offer structural information such as vibrational mode coupling, anharmonicities, along with chemical dynamics such as energy transfer rates and molecular dynamics with femtosecond time resolution. 2DIR experiments have only become possible with the development of ultrafast lasers and the ability to generate femtosecond infrared pulses.
Systems studied.
Among the many systems studied with infrared spectroscopy are water, metal carbonyls, short polypeptides, proteins, perovskite solar cells, and DNA oligomers.
Experimental approaches.
There are two main approaches to two-dimensional spectroscopy, the Fourier-transform method, in which the data is collected in the time-domain and then Fourier-transformed to obtain a frequency-frequency 2D correlation spectrum, and the frequency domain approach in which all the data is collected directly in the frequency domain.
Time domain.
The time-domain approach consists of applying two pump pulses. The first pulse creates a coherence between the vibrational modes of the molecule and the second pulse creates a population, effectively storing information in the molecules. After a determined waiting time, ranging from a zero to a few hundred picoseconds, an interaction with a third pulse again creates a coherence, which, due to an oscillating dipole, radiates an infrared signal. The radiated signal is heterodyned with a reference pulse in order to retrieve frequency and phase information; the signal is usually collected in the frequency domain using a spectrometer yielding detection frequency formula_1. A two-dimensional Fourier-transform along formula_2 then yields a (formula_2, formula_1) correlation spectrum. In all these measurements phase stability among the pulses has to be preserved. Recently, pulse shaping approaches were developed to simplify overcoming this challenge.
Frequency domain.
Similarly, in the frequency-domain approach, a narrowband pump pulse is applied and, after a certain waiting time, then a broadband pulse probes the system. A 2DIR correlation spectrum is obtained by plotting the probe frequency spectrum at each pump frequency.
Spectral interpretation.
After the waiting time in the experiment, it is possible to reach double excited states. This results in the appearance of an overtone peak. The anharmonicity of a vibration can be read from the spectra as the distance between the diagonal peak and the overtone peak. One obvious advantage of 2DIR spectra over
normal linear absorption spectra is that they reveal the coupling between different states. This for example, allows for the determination of the angle between the involved transition dipoles.
The true power of 2DIR spectroscopy is that it allows following dynamical processes such as chemical exchange, motional narrowing, vibrational population transfer, and molecular reorientation on the sub-picosecond time scale. It has for example been used successfully to study hydrogen bond forming and breaking and to determine the transition state geometry of a structural rearrangement in an iron carbonyl compound. Spectral interpretation can be successfully assisted with developed theoretical methods.
Currently, two freely available packages exists for modeling 2D IR spectra. These are the SPECTRON developed by the Mukamel group (University of California, Irvine) and the NISE program developed by the Jansen group (University of Groningen).
Solvent effect.
The consideration of the solvent effect has been shown to be crucial in order to effectively describe the vibrational coupling in solution, since the solvent modify both vibrational frequencies, transition probabilities and couplings. Computer simulations can reveal the spectral signatures arising from solvent degrees of freedom and their change upon water reorganization.


Phantom power

Phantom power, in the context of professional audio equipment, is DC electric power transmitted through microphone cables to operate microphones that contain active electronic circuitry.
It is best known as a convenient power source for condenser microphones, though many active direct boxes also use it. The technique is also used in other applications where power supply and signal communication take place over the same wires.
Phantom power supplies are often built into mixing consoles, microphone preamplifiers and similar equipment. In addition to powering the circuitry of a microphone, traditional condenser microphones also use phantom power for polarizing the microphone's transducer element.
History.
Phantom powering was first used (and still is used) in copper wire based landline telephone systems since the introduction of the rotary-dial telephone in 1919. One such application in the telephone system was to provide a DC signaling path around transformer connected amplifiers in analogue line transmission systems.
The first known commercially available phantom-powered microphone was the Schoeps model CMT 20, which came out in 1964, built to the specifications of French radio with 9–12 volt DC phantom power; the positive pole of this powering was grounded. Microphone preamplifiers of the Nagra IV-series tape recorders offered this type of powering as an option for many years and Schoeps continued to support "negative phantom" until the CMT series was discontinued in the mid-1970s, but it is obsolete now.
In 1966, Neumann GmbH presented a new type of transistorized microphone to the Norwegian Broadcasting Corporation, NRK. Norwegian Radio had requested phantom-powered operation. Since NRK already had 48-volt power available in their studios for their emergency lighting systems, this voltage was used for powering the new microphones (model KM 84), and is the origin of 48-volt phantom power. This arrangement was later standardized in DIN 45596.
Standards.
The International Electrotechnical Commission Standards Committee's "Multimedia systems - Guide to the recommended characteristics of analogue interfaces to achieve interoperability" (IEC 61938:2018) specifies parameters for microphone phantom power delivery. Three variants are defined by the document: P12, P24 and P48. In addition, two additional variants (P12L and SP48) are mentioned for specialized applications. Most microphones now use the P48 standard (maximum available power is 240 mW). Although 12 and 48-volt systems are still in use, the standard recommends 24-volt supply for new systems.
Technical information.
Phantom powering consists of a phantom circuit where direct current is applied equally through the two signal lines of a balanced audio connector (in modern equipment, both pins 2 and 3 of an XLR connector). The supply voltage is referenced to the ground pin of the connector (pin 1 of an XLR), which normally is connected to the cable shield or a ground wire in the cable or both. When phantom powering was introduced, one of its advantages was that the same type of balanced, shielded microphone cable that studios were already using for dynamic microphones could be used for condenser microphones. This is in contrast to microphones with vacuum-tube circuitry, most of which require special, multi-conductor cables.
With phantom power, the supply voltage is effectively invisible to balanced microphones that do not use it, which includes most dynamic microphones. A balanced signal consists only of the differences in voltage between two signal lines; phantom powering places the same DC voltage on both signal lines of a balanced connection. This is in marked contrast to another, slightly earlier method of powering known as "parallel powering" or "T-powering" (from the German term "Tonaderspeisung"), in which DC was overlaid directly onto the signal in differential mode. Connecting a conventional microphone to an input that had parallel powering enabled could very well damage the microphone.
The IEC 61938 Standard defines 48-volt, 24-volt, and 12-volt phantom powering. The signal conductors are positive, both fed through resistors of equal value (6.81 kΩ for 48 V, 1.2 kΩ for 24 V, and 680 Ω for 12 V), and the shield is ground. The 6.81 kΩ value is not critical, but the resistors must be matched to within 0.1% or better to maintain good common-mode rejection in the circuit. The 24-volt version of phantom powering, proposed quite a few years after the 12 and 48 V versions, was also included in the DIN standard and is in the IEC standard, but it was never widely adopted by equipment manufacturers.
Nearly all modern mixing consoles have a switch for turning phantom power on or off; in most high-end equipment this can be done individually by channel, while on smaller mixers a single master switch may control power delivery to all channels. Phantom power can be blocked in any channel with a 1:1 isolation transformer or blocking capacitors. Phantom powering can cause equipment malfunction or even damage if used with cables or adapters that connect one side of the input to ground, or if certain equipment other than microphones is connected to it.
Instrument amplifiers rarely provide phantom power. To use equipment requiring it with these amplifiers, a separate power supply must be inserted into the line. These are readily available commercially, or alternatively are one of the easier projects for the amateur electronics constructor.
Caveats.
Some microphones offer a choice of internal battery powering or (external) phantom powering. In some such microphones it is advisable to remove the internal batteries when phantom power is being used since batteries may corrode and leak chemicals. Other microphones are specifically designed to switch over to the internal batteries if an external supply fails.
Phantom powering is not always implemented correctly or adequately, even in professional-quality preamps, mixers, and recorders. In part this is because first-generation (late-1960s through mid-1970s) 48-volt phantom-powered condenser microphones had simple circuitry and required only small amounts of operating current (typically less than 1 mA per microphone), so the phantom supply circuits typically built into recorders, mixers, and preamps of that time were designed on the assumption that this current would be adequate. The original DIN 45596 phantom-power specification called for a maximum of 2 mA. This practice has carried forward to the present; many 48-volt phantom power supply circuits, especially in low-cost and portable equipment, simply cannot supply more than 1 or 2 mA total without breaking down. Some circuits also have significant additional resistance in series with the standard pair of supply resistors for each microphone input; this may not affect low-current microphones much, but it can disable microphones that need more current.
Mid-1970s and later condenser microphones designed for 48-volt phantom powering often require much more current (e.g., 2–4 mA for Neumann transformerless microphones, 4–5 mA for the Schoeps CMC ("Colette") series and Josephson microphones, 5–6 mA for most Shure KSM-series microphones, 8 mA for CAD Equiteks and 10 mA for Earthworks). The IEC standard gives 10 mA as the maximum allowed current per microphone. If its required current is not available, a microphone may still put out a signal, but it cannot deliver its intended level of performance. The specific symptoms vary somewhat, but the most common result will be reduction of the maximum sound-pressure level that the microphone can handle without overload (distortion). Some microphones will also show lower sensitivity (output level for a given sound-pressure level).
Most ground lift switches have the unwanted effect of disconnecting phantom power. There must always be a DC current path between pin 1 of the microphone and the negative side of the 48-volt supply, if power is to reach the microphone's electronics. Lifting the ground, which is normally pin 1, breaks this path and disables the phantom power supply.
There is a common belief that connecting a dynamic or ribbon microphone to a phantom-powered input will damage it. There are three possibilities for this damage to occur. If there is a fault in the cable, phantom power may damage some mics by applying a voltage across the output of the microphone. Equipment damage is also possible if a phantom-powered input connected to an unbalanced dynamic microphone or electronic musical instruments. The transient generated when a microphone is hot-plugged into an input with active phantom power can damage the microphone and possibly the preamp circuit of the input because not all pins of the microphone connector make contact at the same time, and there is an instant when current can flow to charge the capacitance of the cable from one side of the phantom-powered input and not the other. This is particularly a problem with long microphone cables. It is considered good practice to disable phantom power to devices that don't require it.
Digital phantom power.
Digital microphones complying with the AES 42 standard may be provided with phantom power at 10 volts, impressed on both audio leads and ground. This supply can furnish up to 250 mA to digital microphones. A keyed variation of the usual XLR connector, the XLD connector, may be used to prevent accidental interchange of analog and digital devices.
Other microphone powering techniques.
T-power, also known as A-B powering or T12, described in DIN 45595, is an alternative to phantom powering that is still widely used in the world of production film sound. Many mixers and recorders intended for that market have a T-power option. Many older Sennheiser and Schoeps microphones use this powering method, although newer recorders and mixers are phasing out this option. Adapter barrels, and dedicated power supplies, are made to accommodate T powered microphones. There is often no audible difference between microphones featuring this method and microphones with P48 powering. In this scheme, 12volts is applied through 180ohm resistors between the microphone's "hot" terminal (XLR pin 2) and the microphone's "cold" terminal (XLR pin 3). This results in a 12-volt potential difference with significant current capability across pins 2 and 3, which would likely cause permanent damage if applied to a dynamic or ribbon microphone.
Plug-in-power (PiP), is the low-current 3–5 V supply provided at the microphone jack of some consumer equipment, such as portable recorders and computer sound cards. It is also defined in IEC 61938. It is unlike phantom power since it is an unbalanced interface with a low voltage (around +5volts) connected to the signal conductor with return through the sleeve; the DC power is in common with the audio signal from the microphone. A capacitor is used to block the DC from subsequent audio frequency circuits. It is often used for powering electret microphones, which will not function without power. It is suitable only for powering microphones specifically designed for use with this type of power supply. Damage may result if these microphones are connected to true (48 V) phantom power through a 3.5 mm to XLR adapter that connects the XLR shield to the 3.5 mm sleeve. Plug-in-power is covered by Japanese standard CP-1203A:2007
A similar line-powering scheme is found in computer sound cards. Both plug-in-power and soundcard power are defined in the second edition of IEC 61938.
These alternative powering schemes are sometimes improperly referred to as "phantom power" and should not be confused with true 48-volt phantom powering described above.
Some condenser microphones can be powered with a 1.5-volt cell contained in a small compartment in the microphone or in an external housing.
Phantom power is sometimes used by workers in avionics to describe the DC bias voltage used to power aviation microphones, which use a lower voltage than professional audio microphones. Phantom power used in this context is 8–16volts DC in series with a 470ohm (nominal) resistor as specified in RTCA Inc. standard DO-214. These microphones evolved from the carbon microphones used in the early days of aviation and the telephone which relied on a DC bias voltage across the carbon microphone element.
Other uses.
"Phantom power" is also used in applications other than microphones:


One- and two-tailed tests

In statistical significance testing, a one-tailed test and a two-tailed test are alternative ways of computing the statistical significance of a parameter inferred from a data set, in terms of a test statistic. A two-tailed test is appropriate if the estimated value is greater or less than a certain range of values, for example, whether a test taker may score above or below a specific range of scores. This method is used for null hypothesis testing and if the estimated value exists in the critical areas, the alternative hypothesis is accepted over the null hypothesis.
A one-tailed test is appropriate if the estimated value may depart from the reference value in only one direction, left or right, but not both. An example can be whether a machine produces more than one-percent defective products. In this situation, if the estimated value exists in one of the one-sided critical areas, depending on the direction of interest (greater than or less than), the alternative hypothesis is accepted over the null hypothesis. Alternative names are one-sided and two-sided tests; the terminology "tail" is used because the extreme portions of distributions, where observations lead to rejection of the null hypothesis, are small and often "tail off" toward zero as in the normal distribution, colored in yellow, or "bell curve", pictured on the right and colored in green.
Applications.
One-tailed tests are used for asymmetric distributions that have a single tail, such as the chi-squared distribution, which are common in measuring goodness-of-fit, or for one side of a distribution that has two tails, such as the normal distribution, which is common in estimating location; this corresponds to specifying a direction. Two-tailed tests are only applicable when there are two tails, such as in the normal distribution, and correspond to considering either direction significant.
In the approach of Ronald Fisher, the null hypothesis H0 will be rejected when the "p"-value of the test statistic is sufficiently extreme (vis-a-vis the test statistic's sampling distribution) and thus judged unlikely to be the result of chance. This is usually done by comparing the resulting p-value with the specified significance level, denoted by formula_1, when computing the statistical significance of a parameter"." In a one-tailed test, "extreme" is decided beforehand as either meaning "sufficiently small" "or" meaning "sufficiently large" – values in the other direction are considered not significant. One may report that the left or right tail probability as the one-tailed p-value, which ultimately corresponds to the direction in which the test statistic deviates from H0. In a two-tailed test, "extreme" means "either sufficiently small or sufficiently large", and values in either direction are considered significant. For a given test statistic, there is a single two-tailed test, and two one-tailed tests, one each for either direction. When provided a significance level formula_1, the critical regions would exist on the two tail ends of the distribution with an area of formula_3 each for a two-tailed test. Alternatively, the critical region would solely exist on the single tail end with an area of formula_1 for a one-tailed test. For a given significance level in a two-tailed test for a test statistic, the corresponding one-tailed tests for the same test statistic will be considered either twice as significant (half the "p"-value) if the data is in the direction specified by the test, or not significant at all ("p"-value above formula_1) if the data is in the direction opposite of the critical region specified by the test.
For example, if flipping a coin, testing whether it is biased "towards" heads is a one-tailed test, and getting data of "all heads" would be seen as highly significant, while getting data of "all tails" would be not significant at all ("p" = 1). By contrast, testing whether it is biased in "either" direction is a two-tailed test, and either "all heads" or "all tails" would both be seen as highly significant data. In medical testing, while one is generally interested in whether a treatment results in outcomes that are "better" than chance, thus suggesting a one-tailed test; a "worse" outcome is also interesting for the scientific field, therefore one should use a two-tailed test that corresponds instead to testing whether the treatment results in outcomes that are "different" from chance, either better or worse. In the archetypal lady tasting tea experiment, Fisher tested whether the lady in question was "better" than chance at distinguishing two types of tea preparation, not whether her ability was "different" from chance, and thus he used a one-tailed test.
Coin flipping example.
In coin flipping, the null hypothesis is a sequence of Bernoulli trials with probability 0.5, yielding a random variable "X" which is 1 for heads and 0 for tails, and a common test statistic is the sample mean (of the number of heads) formula_6 If testing for whether the coin is biased towards heads, a one-tailed test would be used – only large numbers of heads would be significant. In that case a data set of five heads (HHHHH), with sample mean of 1, has a formula_7 chance of occurring, (5 consecutive flips with 2 outcomes - ((1/2)^5 =1/32). This would have formula_8 and would be significant (rejecting the null hypothesis) if the test was analyzed at a significance level of formula_9 (the significance level corresponding to the cutoff bound). However, if testing for whether the coin is biased towards heads or tails, a two-tailed test would be used, and a data set of five heads (sample mean 1) is as extreme as a data set of five tails (sample mean 0). As a result, the "p"-value would be formula_10 and this would not be significant (not rejecting the null hypothesis) if the test was analyzed at a significance level of formula_9.
History.
The "p"-value was introduced by Karl Pearson in the Pearson's chi-squared test, where he defined P (original notation) as the probability that the statistic would be at or above a given level. This is a one-tailed definition, and the chi-squared distribution is asymmetric, only assuming positive or zero values, and has only one tail, the upper one. It measures goodness of fit of data with a theoretical distribution, with zero corresponding to exact agreement with the theoretical distribution; the "p"-value thus measures how likely the fit would be this bad or worse.
The distinction between one-tailed and two-tailed tests was popularized by Ronald Fisher in the influential book Statistical Methods for Research Workers, where he applied it especially to the normal distribution, which is a symmetric distribution with two equal tails. The normal distribution is a common measure of location, rather than goodness-of-fit, and has two tails, corresponding to the estimate of location being above or below the theoretical location (e.g., sample mean compared with theoretical mean). In the case of a symmetric distribution such as the normal distribution, the one-tailed "p"-value is exactly half the two-tailed "p"-value:
Fisher emphasized the importance of measuring the tail – the observed value of the test statistic and all more extreme – rather than simply the probability of specific outcome itself, in his "The Design of Experiments" (1935). He explains this as because a "specific" set of data may be unlikely (in the null hypothesis), but more extreme outcomes likely, so seen in this light, the specific but not extreme unlikely data should not be considered significant.
Specific tests.
If the test statistic follows a Student's "t"-distribution in the null hypothesis – which is common where the underlying variable follows a normal distribution with unknown scaling factor, then the test is referred to as a one-tailed or two-tailed "t"-test. If the test is performed using the actual population mean and variance, rather than an estimate from a sample, it would be called a one-tailed or two-tailed "Z"-test.
The statistical tables for "t" and for "Z" provide critical values for both one- and two-tailed tests. That is, they provide the critical values that cut off an entire region at one or the other end of the sampling distribution as well as the critical values that cut off the regions (of half the size) at both ends of the sampling distribution.


6F (music)


Hurdle model

A hurdle model is a class of statistical models where a random variable is modelled using two parts, the first which is the probability of attaining value 0, and the second part models the probability of the non-zero values. The use of hurdle models are often motivated by an excess of zero's in the data, that is not sufficiently accounted for in more standard statistical models.
In a hurdle model, a random variable "x" is modelled as
where formula_3 is a truncated probability distribution function, truncated at 0.
Hurdle models were introduced by John G. Cragg in 1971, where the non-zero values of "x" were modelled using a normal model, and a probit model was used to model the zeros. The probit part of the model was said to model the presence of "hurdles" that must be overcome for the values of x to attain non-zero values, hence the designation "hurdle model". Hurdle models were later developed for count data, with Poisson, geometric, and negative binomial models for the non-zero counts .
Relationship with zero-inflated models.
Hurdle models differ from zero-inflated models in that zero-inflated models model the zeros using a two-component mixture model. With a mixture model, the probability of the variable being zero is determined by both the main distribution and the mixture weight. Specifically, a zero-inflated model for a random variable "x" is
where formula_6 is the mixture weight that determines the amount of zero-inflation. A zero-inflated model can only increase the probability of formula_7, but this is not a restriction in hurdle models.


Height gauge

A height gauge is a measuring device used for determining the height of objects, and for marking of items to be worked on.
These measuring tools are used in metalworking or metrology to either set or measure vertical distances; the pointer is sharpened to allow it to act as a scriber and assist in marking out work pieces.
Devices similar in concept, with lower resolutions, are used in health care settings (health clinics, surgeries) to find the height of people, in which context they are called stadiometers.
Height gauges may also be used to measure the height of an object by using the underside of the scriber as the datum. The datum may be permanently fixed or the height gauge may have provision to adjust the scale, this is done by sliding the scale vertically along the body of the height gauge by turning a fine feed screw at the top of the gauge; then with the scriber set to the same level as the base, the scale can be matched to it. This adjustment allows different scribers or probes to be used, as well as adjusting for any errors in a damaged or resharpened probe.
In the toolroom, the distinction between a height gauge and a surface gauge is that a height gauge has a measuring head (whether vernier, fine rack and pinion with dial, or linear encoder with digital display), whereas a surface gauge has only a scriber point. Both are typically used on a surface plate and have a heavy base with an accurately flat, smooth underside.


Dialing scales

Dialing scales are used to lay out the face of a sundial geometrically. They were proposed by Samuel Foster in 1638, and produced by George Serle and Anthony Thompson in 1658 on a ruler. There are two scales: the latitude scale and the hour scale. They can be used to draw all gnomonic dials – and reverse engineer existing dials to discover their original intended location.
History.
Dialing scales were first discussed by Samuel Foster in 1638. P. Pierre Bobynet, a Jesuit drew a scale in his book "L'horographie ingenieuse contenant des Connoissances, & Curiositez Agréables dans la composition des Cadrans", in 1647. It was however George Serles 1657 book, "Dialling Universal", printed by R & W Leybourn that brought them to popular attention. These scales remained virtually unchanged for 250 years. E. C. Middleton, who had been engraving dialling scales from about 1895, supplied dialling scales accompanied by a typewritten instruction book from Birmingham in 1913– these were the scales calculated by Serle. The North American Sundial Society has printed facsimiles of both the Serle and Middleton books.
The Middleton dial appeared without explanation in the 1994 "Encyclopedia de Diderot et Alembert" (French). Further work has done on these rulers by F.W. Cousins, and by Fred W Sawyer from 1997–2009.
Description.
The traditional scales (Foster Serle scales) are drawn on a ruler. The hour scale shows formula_1 and the latitude scale shows formula_2.
The graduation of these rulers is independent of latitude, making them suitable for drawing all dials. The Foster Serle dial is randomly set for a value of 45°, and is more precise for latitudes below 45°. It is thus a special case in an infinite set of rulers.
Usage.
A right-angle is drawn on the dial-face and the latitude scale is laid against the "x"-axis. The target latitude point is marked across on to the dial face. The hour scale is placed from this point to the noon line (conventionally, the zero point is on the noon line). Each of the hour points is copied over to the dial face, and this procedure is repeated, giving the hours both sides of noon. A straight edge is used to connect these points to the origin, thus drawing the hour lines for that location. A vertical line from the target latitude point, and a horizontal line through the noon point will bisect at the three-hour (9am–3pm) marker.
In the northern hemisphere the hours run clockwise. Symmetries about the noon line, the six-hour line and the three-hour marker can be detected – and these can be used to add additional lines.
The style will be at the same angle as the latitude. It can be simply drawn using the Line of Chords scale on the dialling ruler. A set of compasses is extended to the 60° point on the line of chords. A radius is drawn from the substyle. The compasses are set to the target latitude on the line of chords scale. This measurement is transferred along the radius. That angle represents the style height.
They can be used to draw all gnomonic dials – and reverse engineer existing dials to discover their original intended location.


Tontine Coffee House

The Tontine Coffee House was a coffeehouse in Manhattan, New York City, established in early 1793. Situated at 82 Wall Street, on the north-west corner of Water Street, it was built by a group of stockbrokers to serve as a meeting place for trade and correspondence. It was organized as a tontine, a type of investment plan, and funded by the sale of 203 shares of £200 each. The May 17, 1792, creation of the Buttonwood Agreement, which bound its signatories to trade only with each other, effectively gave rise to a new organization of tradespeople.
In its prime, the Tontine was among New York City's busiest centers for the buying and selling of stocks and other wares, for business dealings and discussion, and for political transaction. Having had a dual function as a combination club and a meeting room, the coffee house played host to auctions, banquets, and balls, among others. After hours, gambling and securities dealings were that were then deemed less than honest. The coffee house also provided a place for the registration of ship cargo and the trading of slaves. The Tontine was noted as classless; individuals from all social strata met there and collectively engaged in the many civil and economic affairs. John Lambert, an English traveller, wrote in 1807:
Political demonstrations and violence were not uncommon at the Tontine Coffee House. In the wake of the French Revolution, fistfights between those respectively sympathetic to the British and the French broke out on a daily basis. An anonymous observer wrote:
On one occasion, French Revolutionists and supporters of the Tammany Hall movement scaled the coffee house and placed a French Liberty Cap on the roof. Several New York publications mentioned the particular, those newspapers with pro-Jacobin or pro–Democratic-Republican slants applauded the perpetrators and encouraged the Tontine's proprietors to allow the Cap to remain. In addition, an onlooker named Alexander Anderson describes conflict between Whigs and Torys at the Tontine in a June 11, 1793, diary entry:
In December 1793, New York's "Columbian Gazetteer" complained that "only persons of the same party" would now associate within the Tontine.
Trading at the Tontine Coffee House continued until 1817. The growth of the Tontine's trade proceedings had effected the creation of the New York Stock and Exchange Board (NYSEB) and necessitated a larger venue. The NYSEB is recognised as the precursor to the present-day New York Stock Exchange, the largest stock exchange in the world. The Tontine itself was transformed into a tavern by a John Morse in 1826, and a hotel by Lovejoy & Belcher in 1832. It survived the Great Fire of 1835 and was demolished in the spring of 1855 to make way for a larger Tontine coffee house. The newer building was itself demolished in 1905.


Appearance event ordination

Appearance event ordination or AEO is a scientific method for biochronology through the ordering of the appearance of fossil mammal genera by multivariate analysis, using conjunctional (overlapping) and disconjunctional (nonoverlapping) range distributions in large sets of data.
Process.
AEO is based on faunal overlap and stratigraphic superposition to derive a best-fit sequence of first and last appearance events.
Step 1.
The first step is to translate patterns of overlap and superposition into pairwise first-before-last statements. The wolf species "Canis edwardii" and "Canis armbrusteri" are used as example taxa for the following patterns. Each statement means "C. edwardii", for example, must have first appeared before "C. armbusteri" last appeared. This is true whenever either (1) "C. edwardii" and "C. armbrusteri" have been found together in at least one nontime-averaged fossil collection, or (2) "C. edwardii" is found lower in at least one lithostratigraphic section than "C. armbrusteri".
Step 2.
A multivariate ordination algorithm is applied to derive a first-pass, hypothesized sequence of first and last appearances. The minimal constraint on this sequence is that if there is an observed, real-world "C. edwardii" before "C. armbrusteri" statement for any pair of taxa, the hypothesized event sequence must replicate it. Then, the program shuffles the events using a maximum likelihood criterion. The criterion basically seeks to pull apart as many hypothesized age range overlaps as possible, especially if they involve common taxa. Taxa are defined as "common" if they are known to overlap with a large fraction of the taxa with which they are implied to overlap.
Step 3.
Once the relative event sequence has been established, it is converted into numerical time with a nonlinear interpolation algorithm that compares event sequence positions and geochronological age estimates for collections that have them. The calibration only uses:
NALMA vs. AEO.
The North American land mammal ages procedure uses subjective opinions by published sources and/or authors, citing authors such as Michael O. Woodburne, Robert W. Wilson, and J. David Archibald.
Appearance event ordination uses objective, explicit, recordable, repeatable, and quantitative analyses of faunal and biostratigraphic data to arrive at a conclusion, according to John Alroy.


Sproul Observatory

Sproul Observatory was an astronomical observatory owned and operated by Swarthmore College. It was located in Swarthmore, Pennsylvania, United States, and named after William Cameron Sproul, the 27th Governor of Pennsylvania, who graduated from Swarthmore in 1891. The 24" telescope was moved from Sproul Observatory to Bentonville, Arkansas in July 2017
History.
In 1907, William Cameron Sproul communicated to the Board of Managers of Swarthmore College his desire to donate funds for the purchase of equipment for an astronomical observatory. Sproul was a successful businessman who graduated from Swarthmore in 1891 and a trustee to the college. At the time of the gift, he was serving as Pennsylvania State Senator for the 9th District and went on to become the 27th Governor of Pennsylvania.
The telescope was built in 1911 by the John A. Brashear Company in Pittsburgh, Pennsylvania. When the telescope was installed at the observatory in 1913, it was the largest on the East Coast of the United States and one of the largest in the world.
From 1986 to 2004, the computer science department was given office and lab space in the observatory building.
In 2009, Swarthmore College added the Peter van de Kamp Observatory to the newly built Science Center. The new observatory contained a more technologically advanced 24" reflecting telescope and replaced the Sproul Observatory for education and public outreach purposes.
In 2017, the telescope was dismantled and moved to the Eighth Street Market in Bentonville, Arkansas to be restored, upgraded and used for public outreach. The book collection of the Sproul Observatory was donated to an astronomy center in Magdalena, New Mexico.
In 2017, Swarthmore unveiled plans to renovate Sproul Observatory which will transform the observatory into the James Hormel and Michael Nguyen Intercultural Center at Sproul Hall which will bring the Intercultural Center, Interfaith Center, Religious and Spiritual Life Center and the Office of International Student Services in one building.
Planetary discovery controversies.
Under the direction of Peter van de Kamp this observatory made numerous claims of planetary systems and discoveries based on astrometry using the photographic plates made with the refractor telescope. These plates were found to have a systematic error that was misinterpreted as the effect of a planetary system on the parent star. This error was identified as early as 1973 and confirmed by the observatory in the 1980s.


Interval (music)

In music theory, an interval is a difference in pitch between two sounds.
An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord.
In Western music, intervals are most commonly differences between notes of a diatonic scale. The smallest of these intervals is a semitone. Intervals smaller than a semitone are called microtones. They can be formed using the notes of various kinds of non-diatonic scales. Some of the very smallest ones are called commas, and describe small discrepancies, observed in some tuning systems, between enharmonically equivalent notes such as C and D. Intervals can be arbitrarily small, and even imperceptible to the human ear.
In physical terms, an interval is the ratio between two sonic frequencies. For example, any two notes an octave apart have a frequency ratio of 2:1. This means that successive increments of pitch by the same interval result in an exponential increase of frequency, even though the human ear perceives this as a linear increase in pitch. For this reason, intervals are often measured in cents, a unit derived from the logarithm of the frequency ratio.
In Western music theory, the most common naming scheme for intervals describes two properties of the interval: the quality (perfect, major, minor, augmented, diminished) and number (unison, second, third, etc.). Examples include the minor third or perfect fifth. These names identify not only the difference in semitones between the upper and lower notes but also how the interval is spelled. The importance of spelling stems from the historical practice of differentiating the frequency ratios of enharmonic intervals such as G–G and G–A.
Size.
The size of an interval (also known as its width or height) can be represented using two alternative and equivalently valid methods, each appropriate to a different context: frequency ratios or cents.
Frequency ratios.
The size of an interval between two notes may be measured by the ratio of their frequencies. When a musical instrument is tuned using a just intonation tuning system, the size of the main intervals can be expressed by small-integer ratios, such as 1:1 (unison), 2:1 (octave), 5:3 (major sixth), 3:2 (perfect fifth), 4:3 (perfect fourth), 5:4 (major third), 6:5 (minor third). Intervals with small-integer ratios are often called "just intervals", or "pure intervals".
Most commonly, however, musical instruments are nowadays tuned using a different tuning system, called 12-tone equal temperament. As a consequence, the size of most equal-tempered intervals cannot be expressed by small-integer ratios, although it is very close to the size of the corresponding just intervals. For instance, an equal-tempered fifth has a frequency ratio of 2:1, approximately equal to 1.498:1, or 2.997:2 (very close to 3:2). For a comparison between the size of intervals in different tuning systems, see .
Cents.
The standard system for comparing interval sizes is with cents. The cent is a logarithmic unit of measurement. If frequency is expressed in a logarithmic scale, and along that scale the distance between a given frequency and its double (also called octave) is divided into 1200 equal parts, each of these parts is one cent. In twelve-tone equal temperament (12-TET), a tuning system in which all semitones have the same size, the size of one semitone is exactly 100 cents. Hence, in 12-TET the cent can be also defined as one hundredth of a semitone.
Mathematically, the size in cents of the interval from frequency "f"1 to frequency "f"2 is
Main intervals.
The table shows the most widely used conventional names for the intervals between the notes of a chromatic scale. A perfect unison (also known as perfect prime) is an interval formed by two identical notes. Its size is zero cents. A semitone is any interval between two adjacent notes in a chromatic scale, a whole tone is an interval spanning two semitones (for example, a major second), and a tritone is an interval spanning three tones, or six semitones (for example, an augmented fourth). Rarely, the term ditone is also used to indicate an interval spanning two whole tones (for example, a major third), or more strictly as a synonym of major third.
Intervals with different names may span the same number of semitones, and may even have the same width. For instance, the interval from D to F is a major third, while that from D to G is a diminished fourth. However, they both span 4 semitones. If the instrument is tuned so that the 12 notes of the chromatic scale are equally spaced (as in equal temperament), these intervals also have the same width. Namely, all semitones have a width of 100 cents, and all intervals spanning 4 semitones are 400 cents wide.
The names listed here cannot be determined by counting semitones alone. The rules to determine them are explained below. Other names, determined with different naming conventions, are listed in a separate section. Intervals smaller than one semitone (commas or microtones) and larger than one octave (compound intervals) are introduced below.
Interval number and quality.
In Western music theory, an interval is named according to its "number" (also called "diatonic number") and "quality". For instance, "major third" (or M3) is an interval name, in which the term "major" (M) describes the quality of the interval, and "third" (3) indicates its number.
Number.
The number of an interval is the number of letter names or staff positions (lines and spaces) it encompasses, including the positions of both notes forming the interval. For instance, the interval C–G is a fifth (denoted P5) because the notes from C to the G above it encompass five letter names (C, D, E, F, G) and occupy five consecutive staff positions, including the positions of C and G. The table and the figure above show intervals with numbers ranging from 1 (e.g., P1) to 8 (e.g., P8). Intervals with larger numbers are called compound intervals.
There is a one-to-one correspondence between staff positions and diatonic-scale degrees (the notes of diatonic scale).
This means that interval numbers can be also determined by counting diatonic scale degrees, rather than staff positions, provided that the two notes that form the interval are drawn from a diatonic scale. Namely, C–G is a fifth because in any diatonic scale that contains C and G, the sequence from C to G includes five notes. For instance, in the A-major diatonic scale, the five notes are C–D–E–F–G (see figure). This is not true for all kinds of scales. For instance, in a chromatic scale, the notes from C to G are eight (C–C–D–D–E–F–F–G). This is the reason interval numbers are also called "diatonic numbers", and this convention is called "diatonic numbering".
If one adds any accidentals to the notes that form an interval, by definition the notes do not change their staff positions. As a consequence, any interval has the same interval number as the corresponding natural interval, formed by the same notes without accidentals. For instance, the intervals C–G (spanning 8 semitones) and C–G (spanning 6 semitones) are fifths, like the corresponding natural interval C–G (7 semitones).
Notice that interval numbers represent an inclusive count of encompassed staff positions or note names, not the difference between the endpoints. In other words, one starts counting the lower pitch as one, not zero. For that reason, the interval C–C, a perfect unison, is called a prime (meaning "1"), even though there is no difference between the endpoints. Continuing, the interval C–D is a second, but D is only one staff position, or diatonic-scale degree, above C. Similarly, C–E is a third, but E is only two staff positions above C, and so on. As a consequence, joining two intervals always yields an interval number one less than their sum. For instance, the intervals C–E and E–G are thirds, but joined together they form a fifth (C–G), not a sixth. Similarly, a stack of three thirds, such as C–E, E–G, and G–B, is a seventh (C–B), not a ninth.
This scheme applies to intervals up to an octave (12 semitones). For larger intervals, see below.
Quality.
The name of any interval is further qualified using the terms perfect (P), major (M), minor (m), augmented (A), and diminished (d). This is called its "interval quality". It is possible to have doubly diminished and doubly augmented intervals, but these are quite rare, as they occur only in chromatic contexts. The quality of a compound interval is the quality of the simple interval on which it is based.
Perfect.
Perfect intervals are so-called because they were traditionally considered perfectly consonant,
although in Western classical music the perfect fourth was sometimes regarded as a less than perfect consonance, when its function was contrapuntal. Conversely, minor, major, augmented or diminished intervals are typically considered less consonant, and were traditionally classified as mediocre consonances, imperfect consonances, or dissonances.
Within a diatonic scale all unisons (P1) and octaves (P8) are perfect. Most fourths and fifths are also perfect (P4 and P5), with five and seven semitones respectively. One occurrence of a fourth is augmented (A4) and one fifth is diminished (d5), both spanning six semitones. For instance, in a C-major scale, the A4 is between F and B, and the d5 is between B and F (see table).
By definition, the inversion of a perfect interval is also perfect. Since the inversion does not change the pitch class of the two notes, it hardly affects their level of consonance (matching of their harmonics). Conversely, other kinds of intervals have the opposite quality with respect to their inversion. The inversion of a major interval is a minor interval, the inversion of an augmented interval is a diminished interval.
Major and minor.
As shown in the table, a diatonic scale defines seven intervals for each interval number, each starting from a different note (seven unisons, seven seconds, etc.). The intervals formed by the notes of a diatonic scale are called diatonic. Except for unisons and octaves, the diatonic intervals with a given interval number always occur in two sizes, which differ by one semitone. For example, six of the fifths span seven semitones. The other one spans six semitones. Four of the thirds span three semitones, the others four. If one of the two versions is a perfect interval, the other is called either diminished (i.e. narrowed by one semitone) or augmented (i.e. widened by one semitone). Otherwise, the larger version is called major, the smaller one minor. For instance, since a 7-semitone fifth is a perfect interval (P5), the 6-semitone fifth is called "diminished fifth" (d5). Conversely, since neither kind of third is perfect, the larger one is called "major third" (M3), the smaller one "minor third" (m3).
Within a diatonic scale, unisons and octaves are always qualified as perfect, fourths as either perfect or augmented, fifths as perfect or diminished, and all the other intervals (seconds, thirds, sixths, sevenths) as major or minor.
Augmented and diminished.
Augmented intervals are wider by one semitone than perfect or major intervals, while having the same interval number (i.e., encompassing the same number of staff positions). Diminished intervals, on the other hand, are narrower by one semitone than perfect or minor intervals of the same interval number. For instance, an augmented third such as C–E spans five semitones, exceeding a major third (C–E) by one semitone, while a diminished third such as C–E spans two semitones, falling short of a minor third (C–E) by one semitone.
The augmented fourth (A4) and the diminished fifth (d5) are the only augmented and diminished intervals that appear in diatonic scales (see table).
Example.
Neither the number, nor the quality of an interval can be determined by counting semitones alone. As explained above, the number of staff positions must be taken into account as well.
For example, as shown in the table below, there are four semitones between A and B, between A and C, between A and D, and between A and E, but
Shorthand notation.
Intervals are often abbreviated with a P for perfect, m for minor, M for major, d for diminished, A for augmented, followed by the interval number. The indications M and P are often omitted. The octave is P8, and a unison is usually referred to simply as "a unison" but can be labeled P1. The tritone, an augmented fourth or diminished fifth is often TT. The interval qualities may be also abbreviated with perf, min, maj, dim, aug. Examples:
Inversion.
A simple interval (i.e., an interval smaller than or equal to an octave) may be inverted by raising the lower pitch an octave or lowering the upper pitch an octave. For example, the fourth from a lower C to a higher F may be inverted to make a fifth, from a lower F to a higher C.
\override Score.TimeSignature
\override Score.SpacingSpanner.strict-note-spacing = ##t
\set Score.proportionalNotationDuration = #(ly:make-moment 1/4)
\new Staff «
 \clef treble \time 4/4
 \new Voice \relative c' {
 \stemUp c2 c' c, c' c, c' c, c'
 \new Voice \relative c' {
 \stemDown c2 c d d e e f f
</score>
There are two rules to determine the number and quality of the inversion of any simple interval:
For example, the interval from C to the E above it is a minor third. By the two rules just given, the interval from E to the C above it must be a major sixth.
Since compound intervals are larger than an octave, "the inversion of any compound interval is always the same as the inversion of the simple interval from which it is compounded."
For intervals identified by their ratio, the inversion is determined by reversing the ratio and multiplying the ratio by 2 until it is greater than 1. For example, the inversion of a 5:4 ratio is an 8:5 ratio.
For intervals identified by an integer number of semitones, the inversion is obtained by subtracting that number from 12.
Since an interval class is the lower number selected among the interval integer and its inversion, interval classes cannot be inverted.
Classification.
Intervals can be described, classified, or compared with each other according to various criteria.
Melodic and harmonic.
An interval can be described as
Diatonic and chromatic.
In general,
The table above depicts the 56 diatonic intervals formed by the notes of the C major scale (a diatonic scale). Notice that these intervals, as well as any other diatonic interval, can be also formed by the notes of a chromatic scale.
The distinction between diatonic and chromatic intervals is controversial, as it is based on the definition of diatonic scale, which is variable in the literature. For example, the interval B–E (a diminished fourth, occurring in the harmonic C-minor scale) is considered diatonic if the harmonic minor scales are considered diatonic as well. Otherwise, it is considered chromatic. For further details, see the main article.
By a commonly used definition of diatonic scale (which excludes the harmonic minor and melodic minor scales), all perfect, major and minor intervals are diatonic. Conversely, no augmented or diminished interval is diatonic, except for the augmented fourth and diminished fifth.
The distinction between diatonic and chromatic intervals may be also sensitive to context. The above-mentioned 56 intervals formed by the C-major scale are sometimes called "diatonic to C major". All other intervals are called "chromatic to C major". For instance, the perfect fifth A–E is chromatic to C major, because A and E are not contained in the C major scale. However, it is diatonic to others, such as the A major scale.
Consonant and dissonant.
Consonance and dissonance are relative terms that refer to the stability, or state of repose, of particular musical effects. Dissonant intervals are those that cause tension and desire to be "resolved" to consonant intervals.
These terms are relative to the usage of different compositional styles.
All of the above analyses refer to vertical (simultaneous) intervals.
Simple and compound.
A simple interval is an interval spanning at most one octave (see Main intervals above). Intervals spanning more than one octave are called compound intervals, as they can be obtained by adding one or more octaves to a simple interval (see below for details).
Steps and skips.
Linear (melodic) intervals may be described as "steps" or "skips". A "step", or "conjunct motion",
is a linear interval between two consecutive notes of a scale. Any larger interval is called a "skip" (also called a "leap"), or "disjunct motion". In the diatonic scale, a step is either a minor second (sometimes also called "half step") or major second (sometimes also called "whole step"), with all intervals of a minor third or larger being skips.
For example, C to D (major second) is a step, whereas C to E (major third) is a skip.
More generally, a step is a smaller or narrower interval in a musical line, and a skip is a wider or larger interval, where the categorization of intervals into steps and skips is determined by the tuning system and the pitch space used.
Melodic motion in which the interval between any two consecutive pitches is no more than a step, or, less strictly, where skips are rare, is called "stepwise" or "conjunct" melodic motion, as opposed to "skipwise" or "disjunct" melodic motions, characterized by frequent skips.
Enharmonic intervals.
Two intervals are considered "enharmonic", or "enharmonically equivalent", if they both contain the same pitches spelled in different ways; that is, if the notes in the two intervals are themselves enharmonically equivalent. Enharmonic intervals span the same number of semitones.
For example, the four intervals listed in the table below are all enharmonically equivalent, because the notes F and G indicate the same pitch, and the same is true for A and B. All these intervals span four semitones.
When played as isolated chords on a piano keyboard, these intervals are indistinguishable to the ear, because they are all played with the same two keys. However, in a musical context, the diatonic function of the notes these intervals incorporate is very different.
The discussion above assumes the use of the prevalent tuning system, 12-tone equal temperament ("12-TET"). But in other historic meantone temperaments, the pitches of pairs of notes such as F and G may not necessarily coincide. These two notes are enharmonic in 12-TET, but may not be so in another tuning system. In such cases, the intervals they form would also not be enharmonic. For example, in quarter-comma meantone, all four intervals shown in the example above would be different.
Minute intervals.
There are also a number of minute intervals not found in the chromatic scale or labeled with a diatonic function, which have names of their own. They may be described as microtones, and some of them can be also classified as commas, as they describe small discrepancies, observed in some tuning systems, between enharmonically equivalent notes. In the following list, the interval sizes in cents are approximate.
Compound intervals.
A compound interval is an interval spanning more than one octave. Conversely, intervals spanning at most one octave are called simple intervals (see Main intervals below).
In general, a compound interval may be defined by a sequence or "stack" of two or more simple intervals of any kind. For instance, a major tenth (two staff positions above one octave), also called "compound major third", spans one octave plus one major third.
Any compound interval can be always decomposed into one or more octaves plus one simple interval. For instance, a major seventeenth can be decomposed into two octaves and one major third, and this is the reason why it is called a compound major third, even when it is built by adding up four fifths.
The diatonic number "DN"c of a compound interval formed from "n" simple intervals with diatonic numbers "DN"1, "DN"2, ..., "DN"n, is determined by:
which can also be written as:
The quality of a compound interval is determined by the quality of the simple interval on which it is based. For instance, a compound major third is a major tenth (1+(8−1)+(3−1) = 10), or a major seventeenth (1+(8−1)+(8−1)+(3−1) = 17), and a compound perfect fifth is a perfect twelfth (1+(8−1)+(5−1) = 12) or a perfect nineteenth (1+(8−1)+(8−1)+(5−1) = 19). Notice that two octaves are a fifteenth, not a sixteenth (1+(8−1)+(8−1) = 15). Similarly, three octaves are a twenty-second (1+3×(8−1) = 22), and so on.
Main compound intervals.
It is also worth mentioning here the major seventeenth (28 semitones)—an interval larger than two octaves that can be considered a multiple of a perfect fifth (7 semitones) as it can be decomposed into four perfect fifths (7 × 4 = 28 semitones), or two octaves plus a major third (12 + 12 + 4 = 28 semitones). Intervals larger than a major seventeenth seldom come up, most often being referred to by their compound names, for example "two octaves plus a fifth" rather than "a 19th".
Intervals in chords.
Chords are sets of three or more notes. They are typically defined as the combination of intervals starting from a common note called the root of the chord. For instance a major triad is a chord containing three notes defined by the root and two intervals (major third and perfect fifth). Sometimes even a single interval (dyad) is considered a chord. Chords are classified based on the quality and number of the intervals that define them.
Chord qualities and interval qualities.
The main chord qualities are major, minor, augmented, diminished, half-diminished, and dominant.
The symbols used for chord quality are similar to those used for interval quality (see above). In addition, + or aug is used for augmented, ° or dim for diminished, for half diminished, and dom for dominant (the symbol − alone is not used for diminished).
Deducing component intervals from chord names and symbols.
The main rules to decode chord "names or symbols" are summarized below. Further details are given at Rules to decode chord names and symbols.
The table shows the intervals contained in some of the main chords (component intervals), and some of the symbols used to denote them. The interval qualities or numbers in boldface font can be deduced from chord name or symbol by applying rule 1. In symbol examples, C is used as chord root.
Size of intervals used in different tuning systems.
In this table, the interval widths used in four different tuning systems are compared. To facilitate comparison, just intervals as provided by 5-limit tuning (see symmetric scale n.1) are shown in bold font, and the values in cents are rounded to integers. Notice that in each of the non-equal tuning systems, by definition the width of "each" type of interval (including the semitone) changes depending on the note that starts the interval. This is the art of just intonation. In equal temperament, the intervals are never precisely in tune with each other. This is the price of using equidistant intervals in a 12-tone scale. For simplicity, for some types of interval the table shows only one value (the most often observed one).
In -comma meantone, by definition 11 perfect fifths have a size of approximately 697 cents (700 − "ε" cents, where "ε" ≈ 3.42 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 about 738 cents (700 + 11"ε", the wolf fifth or diminished sixth); 8 major thirds have size about 386 cents (400 − 4"ε"), 4 have size about 427 cents (400 + 8"ε", actually diminished fourths), and their average size is 400 cents. 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 -comma meantone fifth and the average fifth). A more detailed analysis is provided at -comma meantone Size of intervals. Note that -comma meantone was designed to produce just major thirds, but only 8 of them are just (5:4, about 386 cents).
The Pythagorean tuning is characterized by smaller differences because they are multiples of a smaller "ε" ("ε" ≈ 1.96 cents, the difference between the Pythagorean fifth and the average fifth). Notice that here the fifth is wider than 700 cents, while in most meantone temperaments, including -comma meantone, it is tempered to a size smaller than 700. A more detailed analysis is provided at Pythagorean tuning#Size of intervals.
The 5-limit tuning system uses just tones and semitones as building blocks, rather than a stack of perfect fifths, and this leads to even more varied intervals throughout the scale (each kind of interval has three or four different sizes). A more detailed analysis is provided at 5-limit tuning#Size of intervals. Note that 5-limit tuning was designed to maximize the number of just intervals, but even in this system some intervals are not just (e.g., 3 fifths, 5 major thirds and 6 minor thirds are not just; also, 3 major and 3 minor thirds are wolf intervals).
The above-mentioned symmetric scale 1, defined in the 5-limit tuning system, is not the only method to obtain just intonation. It is possible to construct juster intervals or just intervals closer to the equal-tempered equivalents, but most of the ones listed above have been used historically in equivalent contexts. In particular, the asymmetric version of the 5-limit tuning scale provides a juster value for the minor seventh (9:5, rather than 16:9). Moreover, the tritone (augmented fourth or diminished fifth), could have other just ratios; for instance, 7:5 (about 583 cents) or 17:12 (about 603 cents) are possible alternatives for the augmented fourth (the latter is fairly common, as it is closer to the equal-tempered value of 600 cents). The 7:4 interval (about 969 cents), also known as the harmonic seventh, has been a contentious issue throughout the history of music theory; it is 31 cents flatter than an equal-tempered minor seventh. For further details about reference ratios, see 5-limit tuning#The justest ratios.
In the diatonic system, every interval has one or more "enharmonic equivalents", such as augmented second for minor third.
Interval root.
Although intervals are usually designated in relation to their lower note, David Cope and Hindemith both suggest the concept of interval root. To determine an interval's root, one locates its nearest approximation in the harmonic series. The root of a perfect fourth, then, is its "top" note because it is an octave of the fundamental in the hypothetical harmonic series. The bottom note of every odd diatonically numbered intervals are the roots, as are the tops of all even numbered intervals. The root of a collection of intervals or a chord is thus determined by the interval root of its strongest interval.
As to its usefulness, Cope provides the example of the final tonic chord of some popular music being traditionally analyzable as a "submediant six-five chord" (added sixth chords by popular terminology), or a first inversion seventh chord (possibly the dominant of the mediant V/iii). According to the interval root of the strongest interval of the chord (in first inversion, CEGA), the perfect fifth (C–G), is the bottom C, the tonic.
Interval cycles.
Interval cycles, "unfold [i.e., repeat] a single recurrent interval in a series that closes with a return to the initial pitch class", and are notated by George Perle using the letter "C", for cycle, with an interval-class integer to distinguish the interval. Thus the diminished-seventh chord would be C3 and the augmented triad would be C4. A superscript may be added to distinguish between transpositions, using 0–11 to indicate the lowest pitch class in the cycle.
Alternative interval naming conventions.
As shown below, some of the above-mentioned intervals have alternative names, and some of them take a specific alternative name in Pythagorean tuning, five-limit tuning, or meantone temperament tuning systems such as quarter-comma meantone. All the intervals with prefix "sesqui-" are justly tuned, and their frequency ratio, shown in the table, is a superparticular number (or epimoric ratio). The same is true for the octave.
Typically, a comma is a diminished second, but this is not always true (for more details, see Alternative definitions of comma). For instance, in Pythagorean tuning the diminished second is a descending interval (524288:531441, or about −23.5 cents), and the Pythagorean comma is its opposite (531441:524288, or about 23.5 cents). 5-limit tuning defines four kinds of comma, three of which meet the definition of diminished second, and hence are listed in the table below. The fourth one, called syntonic comma (81:80) can neither be regarded as a diminished second, nor as its opposite. See Diminished seconds in 5-limit tuning for further details.
Additionally, some cultures around the world have their own names for intervals found in their music. For instance, 22 kinds of intervals, called shrutis, are canonically defined in Indian classical music.
Latin nomenclature.
Up to the end of the 18th century, Latin was used as an official language throughout Europe for scientific and music textbooks. In music, many English terms are derived from Latin. For instance, semitone is from Latin "".
The prefix semi- is typically used herein to mean "shorter", rather than "half". Namely, a semitonus, semiditonus, semidiatessaron, semidiapente, semihexachordum, semiheptachordum, or semidiapason, is shorter by one semitone than the corresponding whole interval. For instance, a semiditonus (3 semitones, or about 300 cents) is not half of a ditonus (4 semitones, or about 400 cents), but a ditonus shortened by one semitone. Moreover, in Pythagorean tuning (the most commonly used tuning system up to the 16th century), a semitritonus (d5) is smaller than a tritonus (A4) by one Pythagorean comma (about a quarter of a semitone).
Pitch-class intervals.
In post-tonal or atonal theory, originally developed for equal-tempered European classical music written using the twelve-tone technique or serialism, integer notation is often used, most prominently in musical set theory. In this system, intervals are named according to the number of half steps, from 0 to 11, the largest interval class being 6.
In atonal or musical set theory, there are numerous types of intervals, the first being the ordered pitch interval, the distance between two pitches upward or downward. For instance, the interval from C upward to G is 7, and the interval from G downward to C is −7. One can also measure the distance between two pitches without taking into account direction with the unordered pitch interval, somewhat similar to the interval of tonal theory.
The interval between pitch classes may be measured with ordered and unordered pitch-class intervals. The ordered one, also called directed interval, may be considered the measure upwards, which, since we are dealing with pitch classes, depends on whichever pitch is chosen as 0. For unordered pitch-class intervals, see interval class.
Generic and specific intervals.
In diatonic set theory, specific and generic intervals are distinguished. Specific intervals are the interval class or number of semitones between scale steps or collection members, and generic intervals are the number of diatonic scale steps (or staff positions) between notes of a collection or scale.
Notice that staff positions, when used to determine the conventional interval number (second, third, fourth, etc.), are counted including the position of the lower note of the interval, while generic interval numbers are counted excluding that position. Thus, generic interval numbers are smaller by 1, with respect to the conventional interval numbers.
Generalizations and non-pitch uses.
The term "interval" can also be generalized to other music elements besides pitch. David Lewin's "Generalized Musical Intervals and Transformations" uses interval as a generic measure of distance between time points, timbres, or more abstract musical phenomena.
For example, an interval between two bell-like sounds, which have no pitch salience, is still perceptible. When two tones have similar acoustic spectra (sets of partials), the interval is just the distance of the shift of a tone spectrum along the frequency axis, so linking to pitches as reference points is not necessary. The same principle naturally applies to pitched tones (with similar harmonic spectra), which means that intervals can be perceived "directly" without pitch recognition. This explains in particular the predominance of interval hearing over absolute pitch hearing.


5344 Ryabov


3DMark

3DMark is a computer benchmarking tool created and developed by UL, (formerly Futuremark), to determine the performance of a computer's 3D graphic rendering and CPU workload processing capabilities. Running 3DMark produces a 3DMark score, with higher numbers indicating better performance. The 3DMark measurement unit is intended to give a normalized mean for comparing different PC hardware configurations (mostly graphics processing units and central processing units), which proponents such as gamers and overclocking enthusiasts assert is indicative of end-user performance capabilities.
Many versions of 3DMark have been released since 1998. Scores cannot be compared across versions as each test is based on a specific version of the DirectX API.


3886 Shcherbakovia