document_title: Consonance and dissonance

question_text: a group of notes in music that produce a stable or calm sound could be described as

question_tokens: a group of notes in music that produce a stable or calm sound could be described as

text: Consonance and dissonance

text: Consonance[edit]

text: Consonances may include:

text:
Perfect consonances:

unisons and octaves
perfect fourths and perfect fifths

Imperfect consonances:

major thirds and minor sixths
minor thirds and major sixths

text: The definition of consonance has been variously based on experience, frequency, and both physical and psychological considerations (Myers 1904, p. 315). These include:

text:
Frequency ratios: with ratios of lower simple numbers being more consonant than those that are higher (Pythagoras[full citation needed]). Many of these definitions do not require exact integer tunings, only approximation.[vague][citation needed]
Coincidence of partials: with consonance being a greater coincidence of partials (Helmholtz & 1954 [1877],[page needed]). By this definition, consonance is dependent not only on the width of the interval between two notes (i.e., the musical tuning), but also on the combined spectral distribution and thus sound quality (i.e., the timbre) of the notes (see the entry under critical band). Thus, a note and the note one octave higher are highly consonant because the partials of the higher note are also partials of the lower note (Roederer 1995, p. 165). Although Helmholtz's work focused almost exclusively on harmonic timbres and also the tunings, subsequent work has generalized his findings to embrace non-harmonic tunings and timbres (Sethares 1992; Sethares 2005[not in citation given][page needed]; Milne, Sethares, and Plamondon 2007,[page needed]; Milne, Sethares, and Plamondon 2008,[page needed]; Sethares et al. 2009,[page needed]).
Fusion: perception of unity or tonal fusion between two notes (Stumpf 1890, pp. 127–219; Butler and Green 2002, p. 264).

text: "A stable tone combination is a consonance; consonances are points of arrival, rest, and resolution."

text: Dissonance[edit]

text: An unstable tone combination is a dissonance; its tension demands an onward motion to a stable chord. Thus dissonant chords are "active"; traditionally they have been considered harsh and have expressed pain, grief, and conflict.

text: In Western music, dissonance is the quality of sounds that seems unstable and has an aural need to resolve to a stable consonance. Both consonance and dissonance are words applied to harmony, chords, and intervals and, by extension, to melody, tonality, and even rhythm and metre. Although there are physical and neurological facts important to understanding the idea of dissonance, the precise definition of dissonance is culturally conditioned—definitions of and conventions of usage related to dissonance vary greatly among different musical styles, traditions, and cultures. Nevertheless, the basic ideas of dissonance, consonance, and resolution exist in some form in all musical traditions that have a concept of melody, harmony, or tonality.[citation needed] Dissonance being the complement of consonance it may be defined, as above, as non-coincidence of partials, lack of fusion or pattern matching, or as complexity.

text: Additional confusion about the idea of dissonance is created by the fact that musicians and writers sometimes use the word dissonance and related terms in a precise and carefully defined way, more often in an informal way, and very often in a metaphorical sense ("rhythmic dissonance"). For many musicians and composers, the essential ideas of dissonance and resolution are vitally important ones that deeply inform their musical thinking on a number of levels.[citation needed]

text: Despite the fact that words like unpleasant and grating are often used to explain the sound of dissonance, all music with a harmonic or tonal basis—even music perceived as generally harmonious—incorporates some degree of dissonance. The buildup and release of tension (dissonance and resolution), which can occur on every level from the subtle to the crass, is partially responsible for what listeners perceive as beauty, emotion, and expressiveness in music.[citation needed]

text: Musical style[edit]

text: The concept of dissonance does not belong to the domain of harmony as it is presented us by Nature [harmonic series], but is derived from voice leading [guidelines], which is an essential constituent of Art.

text: Understanding a particular musical style's treatment of dissonance—what is considered dissonant and what rules or procedures govern how dissonant intervals, chords, or notes are treated—is key in understanding that particular style. For instance, harmony is generally governed by chords, which are collections of notes defined as tolerably consonant by the style. (There is likely, however, to be a hierarchy of chords, with some considered more consonant and some more dissonant.) Any note that does not fall within the prevailing harmony is considered dissonant. A given style typically pays attention to how its musical structure approaches dissonance (in steps is less jarring, a leap is more jarring), and even more to how they resolve (almost always by step), to how they fit within the meter and rhythm (dissonances on strong beats are more emphatic, those on weaker beats less vital), and to how they lie within the phrase (dissonances tend to resolve at phrase's end).[citation needed]

text: In traditional music[edit]

text: This section does not cite any sources. Please help improve this section by adding citations to reliable sources. Unsourced material may be challenged and removed. (July 2014) (Learn how and when to remove this template message)

text: Sharp dissonant intervals and chords play a prominent role in many traditional musical cultures. Vocal polyphonic traditions from Bulgaria, Serbia, Bosnia-Herzegovina, Albania, Latvia, Georgia, Nuristan, some Vietnamese and Chinese minority singing traditions, Lithuanian sutartinės, some polyphonic traditions from Flores and Melanesia are predominantly based on the use of sharp dissonant intervals and chords. The most prominent dissonance in most of these cultures is the interval of the neutral second (which is between the minor and major seconds). This interval is known to create the maximum sharpness and is known in German ethnomusicology under the term "Schwebungsdiaphonie".

text: Physiological basis[edit]

text: Musical styles are similar to languages, in that certain physical, physiological, and neurological facts create bounds that greatly affect the development of all languages. Nevertheless, different cultures and traditions have incorporated the possibilities and limitations created by these physical and neurological facts into vastly different, living systems of human language. Neither the importance of the underlying facts nor the importance of the culture in assigning a particular meaning to the underlying facts should be understated.[citation needed]

text: For instance, two notes played simultaneously but with slightly different frequencies produce a beating "wah-wah-wah" sound. Musical styles such as traditional European classical music consider this effect objectionable ("out of tune") and go to great lengths to eliminate it. Other musical styles such as Indonesian gamelan consider this sound an attractive part of the musical timbre and go to equally great lengths to create instruments that produce this slight "roughness" (Vassilakis 2005,[page needed]).

text: Sensory dissonance and its two perceptual manifestations (beating and roughness) are both closely related to a sound signal's amplitude fluctuations. Amplitude fluctuations describe variations in the maximum value (amplitude) of sound signals relative to a reference point and are the result of wave interference. The interference principle states that the combined amplitude of two or more vibrations (waves) at any given time may be larger (constructive interference) or smaller (destructive interference) than the amplitude of the individual vibrations (waves), depending on their phase relationship. In the case of two or more waves with different frequencies, their periodically changing phase relationship results in periodic alterations between constructive and destructive interference, giving rise to the phenomenon of amplitude fluctuations.[citation needed]

text: Amplitude fluctuations can be placed in three overlapping perceptual categories related to the rate of fluctuation. Slow amplitude fluctuations (≈≤20 per second) are perceived as loudness fluctuations referred to as beating. As the rate of fluctuation is increased, the loudness appears constant, and the fluctuations are perceived as "fluttering" or roughness. As the amplitude fluctuation rate is increased further, the roughness reaches a maximum strength and then gradually diminishes until it disappears (≈≥75–150 fluctuations per second, depending on the frequency of the interfering tones).

text: Assuming the ear performs a frequency analysis on incoming signals, as indicated by Ohm's acoustic law (see Helmholtz 1885; Levelt and Plomp 1964,[page needed]), the above perceptual categories can be related directly to the bandwidth of the hypothetical analysis filters (Zwicker, Flottorp, and Stevens 1957,[page needed]; Zwicker 1961,[page needed]). For example, in the simplest case of amplitude fluctuations resulting from the addition of two sine signals with frequencies f1 and f2, the fluctuation rate is equal to the frequency difference between the two sines |f1-f2|, and the following statements represent the general consensus:

text:
If the fluctuation rate is smaller than the filter bandwidth, then a single tone is perceived either with fluctuating loudness (beating) or with roughness.
If the fluctuation rate is larger than the filter bandwidth, then a complex tone is perceived, to which one or more pitches can be assigned but which, in general, exhibits no beating or roughness.

tag: ol

text: Along with amplitude fluctuation rate, the second most important signal parameter related to the perceptions of beating and roughness is the degree of a signal's amplitude fluctuation, that is, the level difference between peaks and valleys in a signal (Terhardt 1974,[page needed]; Vassilakis 2001,[page needed]). The degree of amplitude fluctuation depends on the relative amplitudes of the components in the signal's spectrum, with interfering tones of equal amplitudes resulting in the highest fluctuation degree and therefore in the highest beating or roughness degree.

text: For fluctuation rates comparable to the auditory filter bandwidth, the degree, rate, and shape of a complex signal's amplitude fluctuations are variables that are manipulated by musicians of various cultures to exploit the beating and roughness sensations, making amplitude fluctuation a significant expressive tool in the production of musical sound. Otherwise, when there is no pronounced beating or roughness, the degree, rate, and shape of a complex signal's amplitude fluctuations remain important, through their interaction with the signal's spectral components. This interaction is manifested perceptually in terms of pitch or timbre variations, linked to the introduction of combination tones (Vassilakis 2001; Vassilakis 2005; Vassilakis 2007).

text: The beating and roughness sensations associated with certain complex signals are therefore usually understood in terms of sine-component interaction within the same frequency band of the hypothesized auditory filter, called critical band.

text:
Two pitches moving from the interval of a Major 2nd to a unison

This file illustrates the roughness and beat oscillations that gradually reduce as the interval moves towards the unison.

Problems playing this file? See media help.

text: Frequency ratios: ratios of higher simple numbers are more dissonant than lower ones (Pythagoras[full citation needed]).

text: In human hearing, the varying effect of simple ratios may be perceived by one of these mechanisms:

text:
Fusion or pattern matching: fundamentals may be perceived through pattern matching of the separately analyzed partials to a best-fit exact-harmonic template (Gerson and Goldstein 1978,[page needed]) or the best-fit subharmonic (Terhardt 1974,[page needed]), or harmonics may be perceptually fused into one entity, with dissonances being those intervals less likely mistaken for unisons, the imperfect intervals, because of the multiple estimates, at perfect intervals, of fundamentals, for one harmonic tone (Terhardt 1974,[page needed]). By these definitions, inharmonic partials of otherwise harmonic spectra are usually processed separately (Hartmann et al., 1990), unless frequency or amplitude modulated coherently with the harmonic partials (McAdams 1983). For some of these definitions, neural firing supplies the data for pattern matching; see directly below (e.g., Moore 1989, pp. 183–87; Srulovicz and Goldstein 1983).
Period length or neural-firing coincidence: with the length of periodic neural firing created by two or more waveforms, higher simple numbers creating longer periods or lesser coincidence of neural firing and thus dissonance (Patterson 1986,[page needed]; Boomsliter and Creel 1961,[page needed]; Meyer 1898,[page needed]; Roederer 1973, pp. 145–49). Purely harmonic tones cause neural firing exactly with the period or some multiple of the pure tone.
Dissonance is more generally defined by the amount of beating between partials (called harmonics or overtones when occurring in harmonic timbres) (Helmholtz & 1954 [1877],[page needed]). Terhardt 1984,[page needed] calls this "sensory dissonance". By this definition, dissonance is dependent not only on the width of the interval between two notes' fundamental frequencies, but also on the widths of the intervals between the two notes' non-fundamental partials. Sensory dissonance (i.e., presence of beating and/or roughness in a sound) is associated with the inner ear's inability to fully resolve spectral components with excitation patterns whose critical bands overlap. If two pure sine waves, without harmonics, are played together, people tend to perceive maximum dissonance when the frequencies are within the critical band for those frequencies, which is as wide as a minor third for low frequencies and as narrow as a minor second for high frequencies (relative to the range of human hearing) (Sethares 2005, p. 43). If harmonic tones with larger intervals are played, the perceived dissonance is due, at least in part, to the presence of intervals between the harmonics of the two notes that fall within the critical band (Roederer 1995, p. 106).

text: Generally, the sonance (i.e., a continuum with pure consonance at one end and pure dissonance at the other) of any given interval can be controlled by adjusting the timbre in which it is played, thereby aligning its partials with the current tuning's notes (or vice versa) (Sethares 2005, p. 1). The sonance of the interval between two notes can be maximized (producing consonance) by maximizing the alignment of the two notes' partials, whereas it can be minimized (producing dissonance) by mis-aligning each otherwise nearly aligned pair of partials by an amount equal to the width of the critical band at the average of the two partials' frequencies (Sethares 2005, p. 1; Sethares 2009,[page needed]).

text: Controlling the sonance of more-or-less non-harmonic timbres in real time is an aspect of dynamic tonality. For example, in Sethares' piece C To Shining C (discussed here), the sonance of intervals is affected both by tuning progressions and timbre progressions.

text: The strongest homophonic (harmonic) cadence, the authentic cadence, dominant to tonic (D-T, V-I or V7-I), is in part created by the dissonant tritone(Benward & Saker 2003, p. 54) created by the seventh, also dissonant, in the dominant seventh chord, which precedes the tonic.

text: Instruments producing non-harmonic overtone series[edit]

text: Musical instruments like bells and xylophones, called Idiophones, are played such that their relatively stiff, non-trivial[clarification needed] mass is excited to vibration by means of a blow. This contrasts with violins, flutes, or drums, where the vibrating medium is a light, supple string, column of air, or membrane. The overtones of the inharmonic series produced by such instruments may differ greatly from that of the rest of the orchestra, and the consonance or dissonance of the harmonic intervals as well (Gouwens 2009, p. 3).

text: According to John Gouwens (2009, p. 3), the carillon's harmony profile is summarized:

text:
Consonant: minor third, tritone, minor sixth, perfect fourth, perfect fifth, and possibly minor seventh or even major second
Dissonant: major third, major sixth
Variable upon individual instrument: major seventh
Interval inversion does not apply.

text: In history of Western music[edit]

text:
“
When we consider musical works we find that the triad is ever-present and that the interpolated dissonances have no other purpose than to effect the continuous variation of the triad.
”

— Lorenz Mizler 1739 (quoted in Forte 1979, p. 136)

text: Dissonance has been understood and heard differently in different musical traditions, cultures, styles, and time periods. Relaxation and tension have been used as analogy since the time of Aristotle till the present (Kliewer 1975, p. 290).

text: One of the early composers known for use of dissonants was Monteverdi (Kempers and Bakker 1949, p. 14: "His use of dissonants was in contradiction to all known rules; his melodies showed unheard-of intervals; he even neglected the rules of counterpoint, secure in his conviction that the new subjective art form needed a new means of expression"). The use of dissonants was also practiced by Moscheles (Anon. 1826, p. 349: "It however appears, that Mr. Moscheles, according to the most esteemed writers and the rules of composition, is perfectly justified in writing it D flat. The D flat is here a diminished 7th, which, though a dissonant, is not necessarily resolved in all cases") and taught by Chopin (Eigeldinger, Howat, and Shohet 1988, p. 42: "Musical prosody and declamation; phrasing—Here are the chief practical directions as to expression which Chopin often repeated to his pupils: A long note is stronger, as is also a high note. A dissonant is likewise stronger, and equally so a syncopated note. The ending of a phrase, before a comma, or a stop, is always weak. If the melody ascends, one plays crescendo, if it descends, decrescendo. Moreover, notice must be taken of natural accents.)"

text: Antiquity and Middle-Ages[edit]

text: In Ancient Greece, armonia denoted the production of a unified complex, particularly one expressible in numerical ratios. Applied to music, the concept concerned how sounds in a scale or a melody fit together (in this sense, it could also concern the tuning of a scale) (Philip 1966, pp. 123–24). The term symphonos was used by Aristoxenus and others to describe the intervals of the fourth, the fifth, the octave and their doublings; other intervals were said diaphonos. This terminology probably referred to the Pythagorean tuning, where fourths, fifths and octaves (ratios 4:3, 3:2 and 2:1) were directly tunable, while the other degrees (other 3-prime ratios) could only be tuned by combinations of the preceding (Aristoxenus 1902, pp. 188–206 See Tenney 1988, pp. 11–12). Until the advent of polyphony and even later, this remained the basis of the concept of consonance/dissonance (symphonia/diaphonia) in Occidental theory.

text: In the early Middle Ages, the Latin term consonantia translated either armonia or symphonia. Boethius (6th century) characterizes consonance by its sweetness, dissonance by its harshness: "Consonance (consonantia) is the blending (mixtura) of a high sound with a low one, sweetly and uniformly (suauiter uniformiterque) arriving to the ears. Dissonance is the harsh and unhappy percussion (aspera atque iniocunda percussio) of two sounds mixed together (sibimet permixtorum)" (Boethius n.d., f. 13v.). It remains unclear, however, whether this could refer to simultaneous sounds. The case becomes clear, however, with Hucbald of Saint Amand (c900), who writes: "Consonance (consonantia) is the measured and concordant blending (rata et concordabilis permixtio) of two sounds, which will come about only when two simultaneous sounds from different sources combine into a single musical whole (in unam simul modulationem conveniant) […]. There are six of these consonances, three simple and three composite, […] octave, fifth, fourth, and octave-plus-fifth, octave-plus-fourth and double octave" (Hucbald n.d., p. 107; translated in Babb 1978, p. 19).

text: According to Johannes de Garlandia & 13th century:

text:
Perfect consonance: unisons and octaves. (Perfecta dicitur, quando due voces junguntur in eodem tempore, ita quod una, secundum auditum, non percipitur ab alia propter concordantiam, et dicitur equisonantiam, ut in unisono et diapason. — "[Consonance] is said perfect, when two voices are joined at the same time, so that the one, by audition, cannot be distinguished from the other because of the concordance, and it is called equisonance, as in unison and octave.")
Median consonance: fourths and fifths. (Medie autem dicuntur, quando duo voces junguntur in eodem tempore; que neque dicuntur perfecte, neque imperfecte, sed partim conveniunt cum perfectis, et partim cum imperfectis. Et sunt due species, scilicet diapente et diatessaron. — "Consonances are said median, when two voices are joined at the same time, which neither can be said perfect, nor imperfect, but which partly agree with the perfect, and partly with the imperfect. And they are of two species, namely the fifth and the fourth.")
Imperfect consonance: minor and major thirds. (Imperfect consonances are not formally mentioned in the treatise, but the quotation above concerning median consonances does refer to imperfect consonances, and the section on consonances concludes: Sic apparet quod sex sunt species concordantie, scilicet: unisonus, diapason, diapente, diatessaron, semiditonus, ditonus. — "So it appears that there are six species of consonances, that is: unison, octave, fifth, fourth, minor third, major third." The last two appear as imperfect consonances by elimination.)
Imperfect dissonance: major sixth (tone + fifth) and minor seventh (minor third + fifth). (Imperfecte dicuntur, quando due voces junguntur ita, quod secundum auditum vel possunt aliquo modo compati, tamen non concordant. Et sunt due species, scilicet tonus cum diapente et semiditonus cum diapente. — [Dissonances] are said imperfect, when two voices are joined so that by audition although they can to some extent match, nevertheless they do not concord. And there are two species, namely tone plus fifth and minor third plus fifth.")
Median dissonance: tone and minor sixth (semitone + fifth). (Medie dicuntur, quando due voces junguntur ita, quod partim conveniunt cum perfectis, partim cum imperfectis. Et iste sunt due species, scilicet tonus et simitonium cum diapente. — [Dissonances] are said median when two voices are joined so that they partly match the perfect, partly the imperfect. And they are of two species, namely tone and semitone plus fifth.")
Perfect dissonance: semitone, tritone, major seventh (major third + fifth). (Here again, the perfect dissonances can only be deduced by elimination from this phrase: Iste species dissonantie sunt septem, scilicet: semitonium, tritonus, ditonus cum diapente; tonus cum diapente, semiditonus cum diapente; tonus et semitonium cum diapente. — These species of dissonances are seven: semitone, tritone, major third plus fifth; tone plus fifth, minor third plus fifth; tone and semitone plus fifth.")

text: One example of imperfect consonances previously considered dissonances[clarification needed] in Guillaume de Machaut's "Je ne cuit pas qu'onques" (Machaut 1926, p. 13, Ballade 14, "Je ne cuit pas qu'onques a creature", mm. 27–31):

text: According to Margo Schulter (1997a):

text: Stable:

text:
Purely blending: unisons and octaves
Optimally blending: fourths and fifths

text: Unstable:

text:
Relatively blending: minor and major thirds
Relatively tense: major seconds, minor sevenths, and major sixths
Strongly discordant: minor seconds, tritonus, and major sevenths, and often minor sixths

text: It is worth noting that "perfect" and "imperfect" and the notion of being (esse) must be taken in their contemporaneous Latin meanings (perfectum, imperfectum) to understand these terms, such that imperfect is "unfinished" or "incomplete" and thus an imperfect dissonance is "not quite manifestly dissonant" and perfect consonance is "done almost to the point of excess".[citation needed] Also, inversion of intervals (major second in some sense equivalent to minor seventh) and octave reduction (minor ninth in some sense equivalent to minor second) were yet unknown during the Middle Ages.[citation needed]

text: Due to the different tuning systems compared to modern times, the minor seventh and major ninth were "harmonic consonances", meaning that they correctly reproduced the interval ratios of the harmonic series which softened a bad effect (Schulter 1997b).[clarification needed] They were also often filled in by pairs of perfect fourths and perfect fifths respectively, forming resonant (blending) units characteristic of the musics of the time (Schulter 1997c), where "resonance" forms a complementary trine with the categories of consonance and dissonance.[clarification needed] Conversely, the thirds and sixths were tempered severely from pure ratios[clarification needed], and in practice usually treated as dissonances in the sense that they had to resolve to form complete perfect cadences and stable sonorities (Schulter 1997d).

text: The salient differences from modern conception:[citation needed][clarification needed]

text:
parallel fourths and fifths were acceptable and necessary, open fourths and fifths inside octaves were the characteristic stable sonority in 3 or more voices,
minor sevenths and major ninths were fully structural,
tritones—as a deponent[clarification needed] sort of fourth or fifth—were sometimes stacked with perfect fourths and fifths,
thirds and sixths (and tall stacks thereof) were not the sort of intervals upon which stable harmonies were based,
final cadential consonances of fourth, fifths, and octaves need not be the target of "resolution" on a beat-to-beat (or similar) time basis: minor sevenths and major ninths may move to octaves forthwith, or sixths to fifths (or minor sevenths), but the fourths and fifths within might become "dissonant" 5/3, 6/3, or 6/4 chordioids[clarification needed], continuing the succession of non-consonant sonorities for timespans limited only by the next cadence.

text: Renaissance[edit]

text: In Renaissance music, the perfect fourth above the bass was considered a dissonance needing immediate resolution. The regola delle terze e seste ("rule of thirds and sixths") required that imperfect consonances should resolve to a perfect one by a half-step progression in one voice and a whole-step progression in another (Dahlhaus 1990, p. 179). The viewpoint concerning successions of imperfect consonances—perhaps more concerned by a desire to avoid monotony than by their dissonant or consonant character—has been variable. Anonymous XIII (13th century) allowed two or three, Johannes de Garlandia's Optima introductio (13th-14th century) three, four or more, and Anonymous XI (15th century) four or five successive imperfect consonances. Adam von Fulda (Gerbert 1784, 3:353) wrote "Although the ancients formerly would forbid all sequences of more than three or four imperfect consonances, we more modern do not prohibit them."

text: Common practice period[edit]

text: In the common practice period, musical style required preparation for all dissonances, followed by a resolution to a consonance. There was also a distinction between melodic and harmonic dissonance. Dissonant melodic intervals included the tritone and all augmented and diminished intervals. Dissonant harmonic intervals included:

text:
Minor second and major seventh
Augmented fourth and diminished fifth (enharmonically equivalent, tritone)

text: Thus, Western musical history can be seen as progressing from a limited definition of consonance to an ever-wider definition of consonance.[citation needed] Early in history, only intervals low in the overtone series were considered consonant. As time progressed, intervals ever higher on the overtone series were considered as such. The final result of this was the so-called "emancipation of the dissonance" (Schoenberg 1975, pp. 258–64) by some 20th-century composers. Early-20th-century American composer Henry Cowell viewed tone clusters as the use of higher and higher overtones (Cowell 1969, pp. 111–39).

text: Despite the fact that this idea of the historical progression towards the acceptance of ever greater levels of dissonance is somewhat oversimplified and glosses over important developments in the history of Western music, the general idea was attractive to many 20th-century modernist composers and is considered a formative meta-narrative of musical modernism.[citation needed]

text: Composers in the Baroque era were well aware of the expressive potential of dissonance:

text: Bach uses dissonance to communicate religious ideas in his sacred cantatas and Passion settings. At the end of the St Matthew Passion, where the agony of Christ’s betrayal and crucifixion is portrayed, John Eliot Gardiner (2013, 427) hears "a final reminder of this comes in the unexpected and almost excruciating dissonance Bach inserts over the very last chord: the melody instruments insist on B natural—the jarring leading tone—before eventually melting in a C minor cadence."

text: In the opening aria of Cantata BWV 54, Widerstehe doch der Sünde("upon sin oppose resistance"), nearly every strong beat carries a dissonance:

text: Albert Schweizer says that this aria “begins with an alarming chord of the seventh… It is meant to depict the horror of the curse upon sin that is threatened in the text" (Schweizer 1905, 53). Gillies Whittaker (1959, 368) points out that “The thirty-two continuo quavers of the initial four bars support four consonances only, all the rest are dissonances, twelve of them being chords containing five different notes. It is a remarkable picture of desperate and unflinching resistance to the Christian to the fell powers of evil.”

text: According to H.C. Robbins Landon, the opening movement of Haydn’s Symphony No. 82, “a brilliant C major work in the best tradition” contains “dissonances of barbaric strength that are succeeded by delicate passages of Mozartean grace." [1]:

text: Mozart's music contains a number of quite radical experiments in dissonance. The following comes from his Adagio and Fugue in C Minor, K. 546:

text: Mozart’s Quartet in C major, K465 opens with an adagio introduction that gave the work its nickname, the “Dissonance Quartet”:

text: There are several passing dissonances in this adagio passage, for example on the first beat of bar 3. However the most striking effect here is implied, rather than sounded explicitly. The A flat in the first bar is contradicted by the high A natural in the second bar, but these notes do not sound together as a discord. (See also False relation.)

text: An even more famous example from Mozart comes in a magical passage from the slow movement of his popular "Elvira Madigan" Piano Concerto 21, K467, where the subtle, but quite explicit dissonances on the first beats of each bar are enhanced by exquisite orchestration:

text: Philip Radcliffe (1978, 52) speaks of this as “a remarkably poignant passage with surprisingly sharp dissonances." Radcliffe says that the dissonances here "have a vivid foretaste of Schumann and the way they gently melt into the major key is equally prophetic of Schubert." Eric Blom (1935, p. 226) says that this movement must have "made Mozart's hearers sit up by its daring modernities... There is a suppressed feeling of discomfort about it."

text: The finale of Beethoven’s Symphony No. 9 opens with a startling discord, consisting of a B flat inserted into a D minor chord:

text: Roger Scruton (2009, 101) alludes to Wagner’s description of this chord as introducing “a huge Schreckensfanfare—horror fanfare.” When this passage returns later in the same movement (just before the voices enter) the sound is further complicated with the addition of a diminished seventh chord, creating, in Scruton’s words “the most atrocious dissonance that Beethoven ever wrote, a first inversion D minor triad containing all the notes of the D minor harmonic scale”:

text: Robert Schumann’s song ‘Auf Einer Burg’from his cycle Liederkreis Op. 39, climaxes on a striking dissonance in the fourteenth bar. As Nicholas Cook (1987, p. 242) points out, this is “the only chord in the whole song that Schumann marks with an accent.” Cook goes on to stress that what makes this chord so effective is Schumann’s placing of it in its musical context: “in what leads up to it and what comes of it.” Cook explains further how the interweaving of lines in both piano and voice parts in the bars leading up to this chord (bars 9-14) “are set on a kind of collision course; hence the feeling of tension rising steadily to a breaking point.”

text: Richard Wagner made increasing use of dissonance for dramatic effect as his style developed, particularly in his later operas. In the scene known as "Hagen’s Watch" from the first act of Götterdämmerung, according to Scruton (2016, p. 127) the music conveys a sense of "matchless brooding evil", and the excruciating dissonance in bars 9–10 below it constitute "a semitonal wail of desolation".

text: Another example of a cumulative build-up of dissonance from the early 20th century (1910) can be found in the Adagio that opens Gustav Mahler’s unfinished 10th Symphony :

text: Taruskin (2005, 23) parses this chord (in bars 206 and 208) as a “diminished nineteenth… a searingly dissonant dominant harmony containing nine different pitches. Who knows what Guido Adler, for whom the second and Third Symphonies already contained ‘unprecedented cacophonies’, might have called it?”

text: One example of modernist dissonance comes from a work that received its first performance in 1913, three years after the Mahler:

text: The West's progressive embrace of increasingly dissonant intervals occurred almost entirely within the context of harmonic timbres, as produced by vibrating strings and columns of air, on which the West's dominant musical instruments are based. By generalizing Helmholtz's notion of consonance (described above as the "coincidence of partials") to embrace non-harmonic timbres and their related tunings, consonance has recently been "emancipated" from harmonic timbres and their related tunings (Milne, Sethares, and Plamondon 2007,[page needed]; Milne, Sethares, and Plamadon 2008,[page needed]; Sethares et al. 2009,[page needed]). Using electronically controlled pseudo-harmonic timbres, rather than strictly harmonic acoustic timbres, provides tonality with new structural resources such as Dynamic tonality. These new resources provide musicians with an alternative to pursuing the musical uses of ever-higher partials of harmonic timbres and, in some people's minds, may resolve what Arnold Schoenberg described as the "crisis of tonality" (Stein 1953,[page needed]).

text: Neo-classic harmonic consonance theory[edit]

text: George Russell, in his 1953 Lydian Chromatic Concept of Tonal Organization, presents a slightly different view from classical practice, one widely taken up in Jazz. He regards the tritone over the tonic as a rather consonant interval due to its derivation from the Lydian dominant thirteenth chord (Russell 2008, p. 1).

text: In effect, he returns to a Medieval consideration of "harmonic consonance": that intervals when not subject to octave equivalence (at least not by contraction) and correctly reproducing the mathematical ratios of the harmonic series are truly non-dissonant. Thus the harmonic minor seventh, natural major ninth, half-sharp eleventh note (untempered tritone), half-flat thirteenth note, and half-flat fifteenth note must necessarily be consonant. Octave equivalence (minor ninth in some sense equivalent to minor second, etc.) is no longer unquestioned.

text: Note that most of these pitches exist only in a universe of microtones smaller than a halfstep; notice also that we already freely take the flat (minor) seventh note for the just seventh of the harmonic series in chords. Russell extends by approximation the virtual merits of harmonic consonance to the 12TET tuning system of Jazz and the 12-note octave of the piano, granting consonance to the sharp eleventh note (approximating the harmonic eleventh), that accidental being the sole pitch difference between the Major scale and the Lydian mode.

text: (In another sense, that Lydian scale representing the provenance of the tonic chord (with major seventh and sharp fourth) replaces or supplements the Mixolydian scale of the dominant chord (with minor seventh and natural fourth) as the source from which to derive extended tertian harmony.)

text: Dan Haerle, in his 1980 The Jazz Language (Studio 224 1980, p. 4), extends the same idea of harmonic consonance and intact octave displacement to alter Paul Hindemith's Series 2 gradation table from The Craft of Musical Composition (Hindemith & 1937–70, 1:[page needed]). In contradistinction to Hindemith, whose scale of consonance and dissonance is currently the de facto standard, Haerle places the minor ninth as the most dissonant interval of all, more dissonant than the minor second to which it was once considered by all as octave-equivalent. He also promotes the tritone from most-dissonant position to one just a little less consonant than the perfect fourth and perfect fifth.

text: For context: unstated in these theories is that musicians of the Romantic Era had effectively promoted the major ninth and minor seventh to a legitimacy of harmonic consonance as well, in their fabrics of 4-note chords (Tymoczko 2011, p. 106).


document_title: Bed size

question_text: what size is a european king size mattress

root

text: Bed size

text: Table of common sizes[edit]

text: Modern manufacturing conventions have produced many standard mattress and box spring sizes. Beds vary by country of origin as per the table below. These dimensions are for the mattress – actual bed frames are a little larger to accommodate the mattress. Mattress thickness varies considerably.

tag: p

text:
North America

South America

Europe

Oceania

Asia

US and Canada

Brazil

Continental Europe

Scandinavia

UK and Ireland

Australia

New Zealand

China

Japan

Singapore

Thailand

Small singleor Cot

76 cm × 191 cm(30 in × 75 in)

80 cm × 190 cm(31 in × 75 in)

60 cm × 190 cm(24 in × 75 in)

91 cm × 188 cm(36 in × 74 in)

85 cm × 195 cm(33 in × 77 in)

Single, Twin,or Bunk

97 cm × 191 cm(38 in × 75 in)[1]

88 cm × 188 cm(35 in × 74 in)

90 cm × 200 cm(35 in × 79 in)

90 cm × 200 cm(35 in × 79 in)

90 cm × 190 cm(35 in × 75 in)

92 cm × 188 cm(36 in × 74 in)

91 cm × 188 cm(36 in × 74 in)

106 cm × 188 cm(42 in × 74 in)

97 cm × 195 cm(38 in × 77 in)

91 cm × 191 cm(36 in × 75 in)

107 cm × 198 cm(42 in × 78 in)

Twin extra long

97 cm × 203 cm(38 in × 80 in)[1]

90 cm × 210 cm(35 in × 83 in)

91 cm × 203 cm(36 in × 80 in)

97 cm × 205 cm(38 in × 81 in)

King singleor Super single

96 cm × 203 cm(38 in × 80 in)

120 cm × 200 cm(47 in × 79 in)

107 cm × 203 cm(42 in × 80 in)

107 cm × 203 cm(42 in × 80 in)

110 cm × 195 cm(43 in × 77 in)

107 cm × 191 cm(42 in × 75 in)

Small doubleor Three-quarter

120 cm × 190 cm(48 in × 75 in)

140 cm × 200 cm(55 in × 79 in)

120 cm × 190 cm(47 in × 75 in)

122 cm × 195 cm(48 in × 77 in)

Full or Double

130 cm × 190 cm(53 in × 75 in)

138 cm × 188 cm(54 in × 74 in)

140 cm × 200 cm(55 in × 79 in)

180 cm × 200 cm(71 in × 79 in)

135 cm × 190 cm(53 in × 75 in)

138 cm × 188 cm(54 in × 74 in)

137 cm × 188 cm(54 in × 74 in)

152 cm × 188 cm(60 in × 74 in)

140 cm × 195 cm(55 in × 77 in)

122 cm × 198 cm(48 in × 78 in)

Double extra long

130 cm × 200 cm(53 in × 80 in)

140 cm × 205 cm(55 in × 81 in)

Queen

150 cm × 200 cm(60 in × 80 in)

158 cm × 198 cm(62 in × 78 in)

152 cm × 203 cm(60 in × 80 in)

152 cm × 203 cm(60 in × 80 in)

182 cm × 188 cm(72 in × 74 in)

154 cm × 195 cm(61 in × 77 in)

152 cm × 191 cm(60 in × 75 in)

152 cm × 198 cm(60 in × 78 in)

Expanded, Super,or Olympic queen

170 cm × 200 cm(66 in × 80 in)

King or Eastern King

190 cm × 200 cm(76 in × 80 in) or500 cm2 (78 in2)

193 cm × 203 cm(76 in × 80 in)

160 cm × 200 cm(63 in × 79 in)

152 cm × 198 cm(60 in × 78 in)

183 cm × 203 cm(72 in × 80 in)

167 cm × 203 cm(66 in × 80 in)

182 cm × 212 cm(72 in × 83 in)

170 cm × 195 cm(67 in × 77 in)

183 cm × 191 cm(72 in × 75 in)

183 cm × 198 cm(72 in × 78 in)

California King,Western King, or King long

180 cm × 210 cm(72 in × 84 in)

180 cm × 210 cm(72 in × 84 in)

200 cm × 200 cm(80 in × 80 in)

170 cm × 205 cm(67 in × 81 in)

Grand King Super King,Athletic King, or Texas King

200 cm × 250 cm(80 in × 98 in)

180 cm × 200 cm(71 in × 79 in)

180 cm × 200 cm(71 in × 79 in)

203 cm × 203 cm(80 in × 80 in)

183 cm × 203 cm(72 in × 80 in)

194 cm × 205 cm(76 in × 81 in)

Large Emperor

213 cm × 213 cm(84 in × 84 in)

Caesor

245 cm × 200 cm(96 in × 79 in)

tag: table

text: Canada and United States[edit]

text: Standard sizes[edit]

text: Standard bed sizes in the US and Canada are:

text: Other sizes[edit]

text: Europe[edit]

text: UK and Ireland[edit]

text:
Most modern beds/mattresses available in the UK and Ireland are sold using metric dimensions,[5]  as required by law.[which?][citation needed]
The names of standard mattress sizes were, however, originally attributed to specific imperial dimensions which remain in common use as a point of reference.

text:
Size

Dimensions

Notes

Small Single

75 cm × 190 cm (30 in × 75 in)[5]

Common UK size for hospitality (zip & link) twin beds as beds can be combined to make a short king bed.[6] Equivalent to previous 2'6" x 6'3"

Single

90 cm × 190 cm (35 in × 75 in)[5]

Also a standard hospitality sized twin bed in Ireland,[citation needed] two mattresses can be zip linked to make a short Superking bed. Equivalent to previous 3' x 6'3"

European single

90 cm × 200 cm (35 in × 79 in)[7]

Small Double

120 cm × 190 cm (47 in × 75 in)[5]

Equivalent to previous 4' x 6'3"

Double

135 cm × 190 cm (53 in × 75 in)[5]

Equivalent to previous 4'6" x 6'3"

European Double

140 cm × 200 cm (55 in × 79 in)[7]

King

150 cm × 200 cm (59 in × 79 in)[5]

Equivalent to previous 5' x 6'6"

European King

160 cm × 200 cm (63 in × 79 in)[7]

Superking

180 cm × 200 cm (71 in × 79 in)[5]

Equivalent to previous 6' x 6'6"

Emperor

200 cm × 202 cm (79 in × 80 in)[5]

Equivalent to previous 6'6 x 6'8"

Large Emperor

215 cm × 217 cm (85 in × 85 in)[5]

Equivalent to previous 7' x 7'

text: It is worth noting that "bed size" in the UK generally refers to mattress size. This is because mattresses have a standard size grading, whereas bed frames do not. While many companies in the UK do offer bespoke bed making services, most mass-produced bed linens,[5] bed frames and mattresses fit only the standard bed sizes above. A Queen size mattress in the UK is often misunderstood to be one of the larger sizes as is the case in many other parts of the world. At 120cm in width, however, it is smaller than a UK double. Another common mistake is to use a mattress size as the required space for the full dimensions of the bed and mattress.

text: France[edit]

text: Single size beds are usually 90 centimetres (35 in) wide by 190 centimetres (75 in) long.

text:
Most common sizes for double beds are:
140 centimetres (55 in) wide by 190 centimetres (75 in) long
160 centimetres (63 in) wide by 200 centimetres (79 in) long
180 centimetres (71 in) wide by 200 centimetres (79 in) long (less common, but increasing popularity).

text: Due to the popularity of imported beds (especially from IKEA), the 200 centimetres (79 in) length is becoming more common.[citation needed]

text: Italy[edit]

text: In Italy, beds are classified by name and use the term Piazza as in "one place" Standard sizes are:[8]

text: Less common:[citation needed]

text: Northern Europe[edit]

text: These sizes are for Germany, Poland, Netherlands, Belgium, Norway, Sweden, Denmark, Iceland, Finland, Estonia, Latvia, and Lithuania. There are some variations between the Nordic countries and the Baltic nations, but these are the most common sizes:

text: Single:

text:
80 cm × 190 cm (31 in × 75 in), traditional standard for bunk beds in Germany
90 cm × 190 cm (35 in × 75 in), traditional standard in Germany
75 cm × 200 cm (30 in × 79 in), standard in Norway[citation needed]
80 cm × 200 cm (31 in × 79 in), common variant in Finland[citation needed]
90 cm × 200 cm (35 in × 79 in), standard single bed in Denmark, Norway, Sweden and Germany.
90 cm × 210 cm (35 in × 83 in)
90 cm × 200 cm (35 in × 79 in), common variant in The Netherlands
90 cm × 220 cm (35 in × 87 in), extra large variant in The Netherlands
100 cm × 200 cm (39 in × 79 in), now very common in Germany
105 cm × 200 cm (41 in × 79 in)
120 cm × 200 cm (47 in × 79 in)[citation needed]

tag: ul

text: Three-Quarter:

text:
120 cm × 200 cm (47 in × 79 in), less common in Scandinavia
140 cm × 200 cm (55 in × 79 in), very common three-quarters in Scandinavia

text: Double:

text:
120 cm × 200 cm (47 in × 79 in), referred to as a "doubter" in the Netherlands, somewhat common for younger people
140 cm × 200 cm (55 in × 79 in)
150 cm × 200 cm (59 in × 79 in), common
160 cm × 200 cm (63 in × 79 in), very common[citation needed], common variant in Finland[citation needed]
180 cm × 200 cm (71 in × 79 in), very common double bed in current Danish, Swedish and Norwegian standards[citation needed]
180 cm × 210 cm (71 in × 83 in)
200 cm × 200 cm (79 in × 79 in) (very wide)

text: Most beds are 200 cm (79 in) cm long. Extra long beds are usually 220 cm (87 in), but they are rare.

text: Portugal[edit]

text: In Portugal the most common sizes for beds are:

text:
Solteiro (single)
80 centimetres (31 in) wide by 190 centimetres (75 in) long (can go up to 105 cm wide by 200 cm long)

text:
Casal (double)
140 centimetres (55 in) wide by 190 centimetres (75 in), 195 or 200 cm long

text:
Queen Size
160 centimetres (63 in) or 180 centimetres (71 in) wide by 190, 195 or 200 cm long

text:
King Size
180 centimetres (71 in) wide by 190, 195 or 200 cm long

text:
Super King Size
200 centimetres (79 in) wide by 200 cm long

text: Spain[edit]

text: In Spain the most common sizes are:

text: 180/190/200 cm long

text: 80/90/105/120/135/150 cm wide, the most common:

text: "Individual" (single) = 90 cm wide

text: "Matrimonio" (marital) = 135/150 cm wide

text: Switzerland[edit]

text: Single:

text:
70 cm × 200 cm (28 in × 79 in), only used for double beds with two separate mattresses
80 cm × 200 cm (31 in × 79 in), only used for double beds with two separate mattresses
90 cm × 200 cm (35 in × 79 in), common single bed
120 cm × 200 cm (47 in × 79 in), uncommon, mainly available as European-style futon beds that are sold with mattress, slats and frame
140 cm × 200 cm (55 in × 79 in), common, especially among young people

text: Double:

text:
160 cm × 200 cm (63 in × 79 in), common
180 cm × 200 cm (71 in × 79 in), common
200 cm × 200 cm (79 in × 79 in), proposed when enough space is available

text: Oceania[edit]

text: Australia[edit]

text: The following bed sizes are available in Australia

text: New Zealand[edit]

text: The following bed sizes are available in New Zealand

text: Africa[edit]

text: South Africa[edit]

text: Comprehensive list of bed sizes in South Africa:

text: XL mattress sizes vary only in length but not in width.

text: Asia[edit]

text: China[edit]

text: In China, the regulation standard has following sizes available:[10]

text:
Length: 1900 mm, 1950 mm, 2000 mm, 2100 mm;
Width: Single: 800 mm, 900 mm, 1000 mm, 1100 mm, 1200 mm;
Width: Double: 1350 mm, 1400 mm, 1500 mm, 1800 mm.

text: In practice, bed sizes are usually categorized by the width. The length is typically two metres, but may vary. The most common sizes are:

text: There are also extra size beds available, but they are less common.

text: Indonesia, Singapore, and Malaysia[edit]

text: The following bed sizes are available in Indonesia, Singapore, and Malaysia:


document_title: Political science

question_text: who began the systematic study of political science

text: Political science

text: Overview[edit]

text: The examples and perspective in this section deal primarily with the United States and do not represent a worldwide view of the subject. You may improve this article, discuss the issue on the talk page, or create a new article, as appropriate. (August 2016) (Learn how and when to remove this template message)

text: Political scientists study matters concerning the allocation and transfer of power in decision making, the roles and systems of governance including governments and international organizations, political behaviour and public policies. They measure the success of governance and specific policies by examining many factors, including stability, justice, material wealth, peace and public health. Some political scientists seek to advance positive (attempt to describe how things are, as opposed to how they should be) theses by analysing politics. Others advance normative theses, by making specific policy recommendations.

text: Political scientists provide the frameworks from which journalists, special interest groups, politicians, and the electorate analyse issues. According to Chaturvedy, "...Political scientists may serve as advisers to specific politicians, or even run for office as politicians themselves. Political scientists can be found working in governments, in political parties or as civil servants. They may be involved with non-governmental organizations (NGOs) or political movements. In a variety of capacities, people educated and trained in political science can add value and expertise to corporations. Private enterprises such as think tanks, research institutes, polling and public relations firms often employ political scientists." [5] In the United States, political scientists known as "Americanists" look at a variety of data including constitutional development, elections, public opinion and public policy such as Social Security reform, foreign policy, US Congressional committees, and the US Supreme Court — to name only a few issues.

text: Because political science is essentially a study of human behaviour, in all aspects of politics, observations in controlled environments are often challenging to reproduce or duplicate, though experimental methods are increasingly common (see experimental political science).[6] Citing this difficulty, former American Political Science Association President Lawrence Lowell once said "We are limited by the impossibility of experiment. Politics is an observational, not an experimental science."[7] Because of this, political scientists have historically observed political elites, institutions, and individual or group behaviour in order to identify patterns, draw generalizations, and build theories of politics.

text: Like all social sciences, political science faces the difficulty of observing human actors that can only be partially observed and who have the capacity for making conscious choices unlike other subjects such as non-human organisms in biology or inanimate objects as in physics. Despite the complexities, contemporary political science has progressed by adopting a variety of methods and theoretical approaches to understanding politics and methodological pluralism is a defining feature of contemporary political science.

text: The advent of political science as a university discipline was marked by the creation of university departments and chairs with the title of political science arising in the late 19th century. In fact, the designation "political scientist" is typically for those with a doctorate in the field, but can also apply to those with a master's in the subject.[8] Integrating political studies of the past into a unified discipline is ongoing, and the history of political science has provided a rich field for the growth of both normative and positive political science, with each part of the discipline sharing some historical predecessors. The American Political Science Association was founded in 1903 and the American Political Science Review was founded in 1906 in an effort to distinguish the study of politics from economics and other social phenomena. To date, the [9]American Political Science Review is the leading journal in Political Science research.

text: Behavioral revolution and new institutionalism[edit]

text: In the 1950s and the 1960s, a behavioural revolution stressing the systematic and rigorously scientific study of individual and group behaviour swept the discipline. A focus on studying political behaviour, rather than institutions or interpretation of legal texts, characterized early behavioural political science, including work by Robert Dahl, Philip Converse, and in the collaboration between sociologist Paul Lazarsfeld and public opinion scholar Bernard Berelson.

text: The late 1960s and early 1970s witnessed a take off in the use of deductive, game theoretic formal modelling techniques aimed at generating a more analytical corpus of knowledge in the discipline. This period saw a surge of research that borrowed theory and methods from economics to study political institutions, such as the United States Congress, as well as political behaviour, such as voting. William H. Riker and his colleagues and students at the University of Rochester were the main proponents of this shift.

text: Despite considerable research progress in the discipline based on all the kinds of scholarship discussed above, it has been observed that progress toward systematic theory has been modest and uneven.[10]

text: Anticipating of crises[edit]

text: The theory of political transitions,[11] and the methods of their analysis and anticipating of crises,[12] form an important part of political science. Several general indicators of crises and methods were proposed for anticipating critical transitions.[13] Among them, a statistical indicator of crisis, simultaneous increase of variance and correlations in large groups, was proposed for crises anticipation and successfully used in various areas.[14] Its applicability for early diagnosis of political crises was demonstrated by the analysis of the prolonged stress period preceding the 2014 Ukrainian economic and political crisis. There was a simultaneous increase in the total correlation between the 19 major public fears in the Ukrainian society (by about 64%) and also in their statistical dispersion (by 29%) during the pre-crisis years.[15] A feature shared by certain major revolutions is that they were not predicted. The theory of apparent inevitability of crises and revolutions was also developed.[16]

text: Political science in the Soviet Union[edit]

text: In the Soviet Union, political studies were carried out under the guise of some other disciplines like theory of state and law, area studies, international relations, studies of labor movement, "critique of bourgeois theories", etc. Soviet scholars were represented at the International Political Science Association (IPSA) since 1955 (since 1960 by the Soviet Association of Political and State Studies).

text: In 1979, the 11th World Congress of IPSA took place in Moscow. Until the late years of the Soviet Union, political science as a field was subjected to tight control of the Communist Party of the Soviet Union and was thus subjected to distrust. Anti-communists accused political scientists of being "false" scientists and of having served the old regime.[17]

text: After the fall of the Soviet Union, two of the major institutions dealing with political science, the Institute of Contemporary Social Theories and the Institute of International Affairs, were disbanded, and most of their members were left without jobs. These institutes were victims of the first wave of anticommunist opinion and ideological attacks. Today, the Russian Political Science Association unites professional political scientists from all around Russia.

text: Recent developments[edit]

text: In 2000, the Perestroika Movement in political science was introduced as a reaction against what supporters of the movement called the mathematicization of political science. Those who identified with the movement argued for a plurality of methodologies and approaches in political science and for more relevance of the discipline to those outside of it.[18]

text: Evolutionary psychology theories argue that humans have evolved a highly developed set of psychological mechanisms for dealing with politics. However, these mechanisms evolved for dealing with the small group politics that characterized the ancestral environment and not the much larger political structures in today's world. This is argued to explain many important features and systematic cognitive biases of current politics.[19]

text: Political science education[edit]

text: Political science, possibly like the social sciences as a whole, "as a discipline lives on the fault line between the 'two cultures' in the academy, the sciences and the humanities."[20] Thus, in some American colleges where there is no separate School or College of Arts and Sciences per se, political science may be a separate department housed as part of a division or school of Humanities or Liberal Arts.[21] Whereas classical political philosophy is primarily defined by a concern for Hellenic and Enlightenment thought, political scientists are also marked by a great concern for "modernity" and the contemporary nation state, along with the study of classical thought, and as such share a greater deal of terminology with sociologists (e.g. structure and agency).

text: Most United States colleges and universities offer B.A. programs in political science. M.A. or M.A.T. and Ph.D. or Ed.D. programs are common at larger universities. The term political science is more popular in North America than elsewhere; other institutions, especially those outside the United States, see political science as part of a broader discipline of political studies, politics, or government. While political science implies use of the scientific method, political studies implies a broader approach, although the naming of degree courses does not necessarily reflect their content.[22] Separate degree granting programs in international relations and public policy are not uncommon at both the undergraduate and graduate levels. Master's level programs in political science are common when political scientists engage in public administration.[23]

text: The national honor society for college and university students of government and politics in the United States is Pi Sigma Alpha.

text: Cognate fields[edit]

text: Most political scientists work broadly in one or more of the following five areas:

text:
Comparative politics, including area studies
International relations
Political philosophy or political theory
Public administration
Public law

text: Some political science departments also classify methodology as well as scholarship on the domestic politics of a particular country as distinct fields. In the United States, American politics is often treated as a separate subfield.

text: In contrast to this traditional classification, some academic departments organize scholarship into thematic categories, including political philosophy, political behaviour (including public opinion, collective action, and identity), and political institutions (including legislatures and international organizations). Political science conferences and journals often emphasize scholarship in more specific categories. The American Political Science Association, for example, has 42 organized sections that address various methods and topics of political inquiry.[24]

text: History[edit]

text: As a social science, contemporary political science started to take shape in the latter half of the 19th century. At that time it began to separate itself from political philosophy, which traces its roots back to the works of Chanakya, Aristotle and Plato which were written nearly 2,500 years ago. The term "political science" was not always distinguished from political philosophy, and the modern discipline has a clear set of antecedents including also moral philosophy, political economy, political theology, history, and other fields concerned with normative determinations of what ought to be and with deducing the characteristics and functions of the ideal state.