1.
Inversion (music)
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In music theory, the word inversion has several meanings. There are inverted chords, inverted melodies, inverted intervals, the concept of inversion also plays a role in musical set theory. An interval is inverted by raising or lowering either of the notes using displacement of the octave so that retain their names. Under inversion, perfect intervals remain perfect, major intervals become minor and vice versa, augmented intervals become diminished, traditional interval names add together to make nine, seconds become sevenths and vice versa, thirds become sixes and vice versa, and fourths become fifths and vice versa. Thus a perfect fourth becomes a fifth, an augmented fourth becomes a diminished fifth, and a simple interval and its inversion. A chords inversion describes the relationship of its bass to the tones in the chord. For instance, a C major triad contains the tones C, E and G, its inversion is determined by which of these tones is the bottom note in the chord. The term inversion is used to categorically refer to the different possibilities. In texts that make this restriction, the position may be used instead to refer to all of the possibilities as a category. A root-position chord Play is sometimes known as the parent chord of its inversions. For example, C is the root of a C major triad and is in the bass when the triad is in position, the 3rd. The following chord is also a C major triad in root position, the rearrangement of the notes above the bass into different octaves and the doubling of notes, is known as voicing. In an inverted chord, the root is not in the bass, the inversions are numbered in the order their bass tones would appear in a closed root position chord. In the second inversion Play, the bass is G—the 5th of the triad—with the root and the 3rd above it, forming a 4th and a 6th above the bass of G, respectively. This inversion can be either consonant or dissonant, and analytical notation sometimes treats it differently depending on the harmonic, for more details, look at Second inversion Third inversions exist only for chords of four or more tones, such as 7th chords. In a third-inversion chord Play, the 7th of the chord is in the bass position, each numeral expresses the interval that results from the voices above it. For example, in root-position triad C-E-G, the intervals above bass note C are a 3rd and a 5th, giving the figures 5-3. If this triad were inverted, the figures 6-3 would apply, due to the intervals of third and sixth appearing above bass note E. Figured bass is similarly applied to 7th chords, certain arbitrary conventions of abbreviation exist in the use of figured bass
Inversion (music)
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Inversion example from Bach's
The Well-Tempered Clavier Play top (
help ·
info) Play bottom (
help ·
info). The melody on the first line starts on A, while the melody on the second line is identical except that it starts on E and when the first melody goes up the second goes down an equal number of diatonic steps, and when the first goes down the second goes up an equal number of steps.
2.
Unison
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UNISON is the second largest trade union in the United Kingdom with almost 1.3 million members. UNISONs current general secretary is Dave Prentis and he was elected on 28 February 2000 and took up the post on 1 January 2001, succeeding Rodney Bickerstaffe who had held the post for five years. Members of UNISON are typically from industries within the public sector, the majority of people joining UNISON are workers within sectors such as local government, education, the National Health Service Registered Nurses, NHS Managers and Clinical Support Workers. The union also admits ancillary staff such as Health Care Assistants and Assistant Practitioners, probation services, police services, utilities, and transport. These Service Groups all have their own national and regional democratic structures within UNISONs constitution, as a trade union, UNISON provides support to members on work related issues, including protection and representation at work, help with pay and conditions of service and legal advice. Each company or organisation will usually be represented by a particular UNISON branch, the stewards receive training in workplace issues and are then able to co-ordinate and represent members both on an individual basis and collectively. Each branch is run by an elected committee of members which holds regular meetings. UNISON own and operate a resort, UNISON Croyde Bay Resort. Members receive a 15% discount as well as have access to a 50% low paid member discount scheme, to encourage all voices to be heard UNISON has self organised groups of Black members, women members, lesbian, gay, bisexual & transgender members, and disabled members. Young members and retired members also have their own sections within the union, membership numbers have remained relatively stable at between 1.2 and 1.4 million in the decade to 2014. The levels of subscription are determined by the National Delegate Conference and are recorded as a Schedule in the union rules, the National Delegate Conference has the power to vary the subscriptions levied after a majority vote, although the subscription rates do not change frequently. Local branches may also, after a majority vote of members and this is in addition to the standard rate, and must be used for local branch purposes. Membership fees vary depending on how members are paid and the level of their current salary. Subscriptions are generally paid by what is known as check-off or DOCAS. This is where the employer deducts the contribution from the salary on behalf of the union. Payment is taken by Direct Debit if the member joins online, if the member requests it. Student members in full-time education have a fixed rate subscription of £10 per year, Members who have had continuous membership for at least two years may opt to pay a one-off fee of £15 upon retirement from paid employment. This allows them to retain the benefits of being a member for life
Unison
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UNISON — the Public Service Union
Unison
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UNISON sign outside their headquarters on Euston Road, London
Unison
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Ants and Bear campaign poster.
Unison
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One in a Million campaign poster.
3.
Semitone
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A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically. It is defined as the interval between two adjacent notes in a 12-tone scale, for example, C is adjacent to C♯, the interval between them is a semitone. In music theory, a distinction is made between a diatonic semitone, or minor second and a semitone or augmented unison. In twelve-tone equal temperament all semitones are equal in size, in other tuning systems, semitone refers to a family of intervals that may vary both in size and name. In quarter-comma meantone, seven of them are diatonic, and 117.1 cents wide, while the five are chromatic. 12-tone scales tuned in just intonation typically define three or four kinds of semitones, for instance, Asymmetric five-limit tuning yields chromatic semitones with ratios 25,24 and 135,128, and diatonic semitones with ratios 16,15 and 27,25. The condition of having semitones is called hemitonia, that of having no semitones is anhemitonia, a musical scale or chord containing semitones is called hemitonic, one without semitones is anhemitonic. The minor second occurs in the scale, between the third and fourth degree, and between the seventh and eighth degree. It is also called the diatonic semitone because it occurs between steps in the diatonic scale, the minor second is abbreviated m2. Its inversion is the major seventh, listen to a minor second in equal temperament. Here, middle C is followed by D♭, which is a tone 100 cents sharper than C, melodically, this interval is very frequently used, and is of particular importance in cadences. In the perfect and deceptive cadences it appears as a resolution of the leading-tone to the tonic, in the plagal cadence, it appears as the falling of the subdominant to the mediant. It also occurs in many forms of the cadence, wherever the tonic falls to the leading-tone. Harmonically, the interval usually occurs as some form of dissonance or a tone that is not part of the functional harmony. It may also appear in inversions of a seventh chord. In unusual situations, the second can add a great deal of character to the music. For instance, Frédéric Chopins Étude Op.25, No.5 opens with a melody accompanied by a line that plays fleeting minor seconds and these are used to humorous and whimsical effect, which contrasts with its more lyrical middle section. This eccentric dissonance has earned the piece its nickname, the wrong note étude and this kind of usage of the minor second appears in many other works of the Romantic period, such as Modest Mussorgskys Ballet of the Unhatched Chicks
Semitone
–
The melodic minor second is an integral part of most cadences of the
Common practice period. Play (
help ·
info)
4.
Interval class
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For example, the interval class between pitch classes 4 and 9 is 5 because 9 −4 =5 is less than 4 −9 = −5 ≡7. See modular arithmetic for more on modulo 12, the largest interval class is 6 since any greater interval n may be reduced to 12 − n. The concept of interval class accounts for octave, enharmonic, consider, for instance, the following passage, (To hear a MIDI realization, click the following,106 KB In the example above, all four labeled pitch-pairs, or dyads, share a common intervallic color. In atonal theory, this similarity is denoted by interval class—ic 5, tonal theory, however, classifies the four intervals differently, interval 1 as perfect fifth,2, perfect twelfth,3, diminished sixth, and 4, perfect fourth. The unordered pitch class interval i may be defined as i = the smaller of i ⟨ a, b ⟩ and i ⟨ b, a ⟩, where i <a, b> is an ordered pitch-class interval. While notating unordered intervals with parentheses, as in the example directly above, is perhaps the standard, some theorists, including Robert Morris, prefer to use braces, pitch interval Similarity relation Morris, Robert. Class Notes for Atonal Music Theory, ISBN 0-300-04536-0 ISBN 0-300-04537-9 Solomons Set Theory Primer
Interval class
Interval class
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Interval class Play (
help ·
info).
5.
Just intonation
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In music, just intonation or pure intonation is any musical tuning in which the frequencies of notes are related by ratios of small whole numbers. Any interval tuned in this way is called a pure or just interval, pure intervals are important in music because they correspond to the vibrational patterns found in physical objects which correlate to human perception. The two notes in any just interval are members of the harmonic series. Frequency ratios involving large integers such as 1024,729 are not generally said to be justly tuned, the Indian classical music system uses just intonation tuning as codified in the Natya Shastra. Various societies perceive pure intervals as pleasing or satisfying consonant and, conversely, however, various societies do not have these associations. Just intonation can be contrasted and compared with equal temperament, which dominates Western instruments of fixed pitch, however, except for doubling of frequencies, no other intervals are exact ratios of small integers. Each just interval differs a different amount from its analogous, equally tempered interval, justly tuned intervals can be written as either ratios, with a colon, or as fractions, with a solidus. For example, two tones, one at 300 hertz, and the other at 200 hertz are both multiples of 100 Hz and as members of the harmonic series built on 100 Hz. Thus 3,2, known as a fifth, may be defined as the musical interval between the second and third harmonics of any fundamental pitch. Just intonation An A-major scale, followed by three major triads, and then a progression of fifths in just intonation, equal temperament An A-major scale, followed by three major triads, and then a progression of fifths in equal temperament. By listening to the file, and then listening to this one, one might be able to hear the beating in this file. Equal temperament and just intonation compared A pair of major thirds, the first in each pair is in equal temperament, the second is in just intonation. Equal temperament and just intonation compared with square waveform A pair of major chords, the first is in equal temperament, the second is in just intonation. The pair of chords is repeated with a transition from equal temperament to just temperament between the two chords, in the equal temperament chords a roughness or beating can be heard at about 4 Hz and about 0.8 Hz. In the just intonation triad, this roughness is absent, the square waveform makes the difference between equal and just temperaments more obvious. Harmonic intervals come naturally to horns, vibrating strings, and in human singing voices. Pythagorean tuning, perhaps the first tuning system to be theorized in the West, is a system in all tones can be found using powers of the ratio 3,2. It is easier to think of this system as a cycle of fifths
Just intonation
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Harmonic series, partials 1–5 numbered Play (
help ·
info).
6.
Cent (music)
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The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each, alexander J. Ellis based the measure on the acoustic logarithms decimal semitone system developed by Gaspard de Prony in the 1830s, at Robert Holford Macdowell Bosanquets suggestion. It has become the method of representing and comparing musical pitches. Like a decibels relation to intensity, a cent is a ratio between two close frequencies, for the ratio to remain constant over the frequency spectrum, the frequency range encompassed by a cent must be proportional to the two frequencies. An equally tempered semitone spans 100 cents by definition, an octave—two notes that have a frequency ratio of 2, 1—spans twelve semitones and therefore 1200 cents.0005777895. For example, in just intonation the major third is represented by the frequency ratio 5,4, applying the formula at the top shows that this is about 386 cents. The equivalent interval on the piano would be 400 cents. The difference,14 cents, is about a seventh of a half step, as x increases from 0 to 1⁄12, the function 2x increases almost linearly from 1.00000 to 1.05946. The exponential cent scale can therefore be accurately approximated as a linear function that is numerically correct at semitones. That is, n cents for n from 0 to 100 may be approximated as 1 +0. 0005946n instead of 2 n⁄1200. The rounded error is zero when n is 0 or 100, and is about 0.72 cents high when n is 50 and this error is well below anything humanly audible, making this piecewise linear approximation adequate for most practical purposes. It is difficult to establish how many cents are perceptible to humans, one author stated that humans can distinguish a difference in pitch of about 5–6 cents. The threshold of what is perceptible, technically known as the just noticeable difference, also varies as a function of the frequency, the amplitude and the timbre. In one study, changes in tone quality reduced student musicians ability to recognize, as out-of-tune and it has also been established that increased tonal context enables listeners to judge pitch more accurately. Free, online web sites for self-testing are available, while intervals of less than a few cents are imperceptible to the human ear in a melodic context, in harmony very small changes can cause large changes in beats and roughness of chords. When listening to pitches with vibrato, there is evidence that humans perceive the mean frequency as the center of the pitch, normal adults are able to recognize pitch differences of as small as 25 cents very reliably. Adults with amusia, however, have trouble recognizing differences of less than 100 cents, iring noticed that the Grad/Werckmeister and the schisma are nearly the same and both may be approximated by 600 steps per octave. Yasser promoted the decitone, centitone, and millitone, for example, Equal tempered perfect fifth =700 cents =175.6 savarts =583.3 millioctaves =350 centitones
Cent (music)
7.
Equal temperament
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An equal temperament is a musical temperament, or a system of tuning, in which the frequency interval between every pair of adjacent notes has the same ratio. In equal temperament tunings, the interval is often found by dividing some larger desired interval, often the octave. That resulting smallest interval, 1⁄12 the width of an octave, is called a semitone or half step, the standard pitch has not always been 440 but has varied and generally risen over the past few hundred years. For example, some music has been written in 19-TET and 31-TET, in Western countries, when people use the term equal temperament without qualification, they usually mean 12-TET. To avoid ambiguity between equal temperaments that divide the octave and ones that divide some other interval, the equal division of the octave. According to this system, 12-TET is called 12-EDO, 31-TET is called 31-EDO. Other instruments, such as wind, keyboard, and fretted instruments, often only approximate equal temperament. Some wind instruments that can easily and spontaneously bend their tone, most notably trombones, use tuning similar to string ensembles, the two figures frequently credited with the achievement of exact calculation of equal temperament are Zhu Zaiyu in 1584 and Simon Stevin in 1585. Kenneth Robinson attributes the invention of equal temperament to Zhu Zaiyu, Zhu Zaiyu is quoted as saying that, in a text dating from 1584, I have founded a new system. I establish one foot as the number from which the others are to be extracted, altogether one has to find the exact figures for the pitch-pipers in twelve operations. Kuttner disagrees and remarks that his claim cannot be considered correct without major qualifications, kuttner proposes that neither Zhu Zaiyu or Simon Stevin achieved equal temperament, and that neither of the two should be treated as inventors. The origin of the Chinese pentatonic scale is traditionally ascribed to the mythical Ling Lun, allegedly his writings discussed the equal division of the scale in the 27th century BC. However, evidence of the origins of writing in this period in China is limited to rudimentary inscriptions on oracle bones, an approximation for equal temperament was described by He Chengtian, a mathematician of Southern and Northern Dynasties around 400 AD. He came out with the earliest recorded approximate numerical sequence in relation to equal temperament in history,900849802758715677638601570536509.5479450, historically, there was a seven-equal temperament or hepta-equal temperament practice in Chinese tradition. Zhu Zaiyu, a prince of the Ming court, spent thirty years on research based on the equal temperament idea originally postulated by his father and he described his new pitch theory in his Fusion of Music and Calendar 乐律融通 published in 1580. An extended account is given by Joseph Needham. Similarly, after 84 divisions the length was divided by a factor of 128,84 =27 =128, according to Gene Cho, Zhu Zaiyu was the first person to solve the equal temperament problem mathematically. Matteo Ricci, a Jesuit in China recorded this work in his personal journal, in 1620, Zhus work was referenced by a European mathematician
Equal temperament
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Prince Zhu Zaiyu constructed 12 string equal temperament tuning instrument, front and back view
Equal temperament
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Simon Stevin's Van de Spiegheling der singconst c. 1605.
Equal temperament
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Figure 1: The
syntonic tuning continuum, which includes many notable "equal temperament" tunings (Milne 2007).
8.
24 equal temperament
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A quarter tone play, is a pitch halfway between the usual notes of a chromatic scale or an interval about half as wide as a semitone, which is half a whole tone. Many composers are known for having written music including quarter tones or the quarter-tone scale —proposed by 19th-century music theorists Heinrich Richter in 1823, george Tucker, Ivan Alexandrovich Wyschnegradsky, and Iannis Xenakis. The term quarter tone can refer to a number of different intervals, for example, some 17th- and 18th-century theorists used the term to describe the distance between a sharp and enharmonically distinct flat in mean-tone temperaments. In the quarter tone scale, also called 24 tone equal temperament, the tone is 50 cents, or a frequency ratio of 24√2 or approximately 1.0293. In this scale the quarter tone is the smallest step, a semitone is thus made of two steps, and three steps make a three-quarter tone play or neutral second, half of a minor third. The 8-TET scale is composed of three-quarter tones, in just intonation the quarter tone can be represented by the septimal quarter tone,36,35, or by the undecimal quarter tone,33,32, approximately half the semitone of 16,15 or 25,24. The ratio of 36,35 is only 1.23 cents narrower than a 24-TET quarter tone and this just ratio is also the difference between a minor third and septimal minor third. Quarter tones and intervals close to also occur in a number of other equally tempered tuning systems. 22-TET contains an interval of 54.55 cents, slightly wider than a quarter-tone, whereas 53-TET has an interval of 45.28 cents, 72-TET also has equally tempered quarter-tones, and indeed contains 3 quarter tone scales, since 72 is divisible by 24. Johnston uses an upward and downward arrow to indicate a note is raised or lowered by a ratio of 33,32, because many musical instruments manufactured today are designed for the 12-tone scale, not all are usable for playing quarter tones. Sometimes special playing techniques must be used, other instruments can be used to play quarter tones when using audio signal processing effects such as pitch shifting. Pairs of conventional instruments tuned a tone apart can be used to play some quarter tone music. Indeed, quarter-tone pianos have been built, which consist essentially of two stacked one above the other in a single case, one tuned a quarter tone higher than the other. Many Persian dastgah and Arabic maqamat contain intervals of three-quarter tone size, the quarter tone scale may be primarily a theoretical construct in Arabic music. Previously, pitches of a mode were chosen from a scale consisting of seventeen tones, the Japanese multi-instrumentalist and experimental musical instrument builder Yuichi Onoue developed a 24-TET quarter tone tuning on his guitar. Several quarter-tone albums have been recorded by Jute Gyte, a one-man avantgarde black metal band from Missouri, the enharmonic genus of the Greek tetrachord consisted of a ditone or an approximate major third, and a semitone, which was divided into two microtones. Intervals matched particularly closely include the second, neutral third. The septimal minor third and septimal major third are approximated rather poorly, overall, 24-TET can be viewed as matching the 11th and 13th harmonics more closely than the 7th
24 equal temperament
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Trumpet with 3 normal valves and a quartering on the extension valve (right).
24 equal temperament
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A
quarter tone clarinet by Fritz Schüller.
9.
Music
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Music is an art form and cultural activity whose medium is sound organized in time. The common elements of music are pitch, rhythm, dynamics, different styles or types of music may emphasize, de-emphasize or omit some of these elements. The word derives from Greek μουσική, Ancient Greek and Indian philosophers defined music as tones ordered horizontally as melodies and vertically as harmonies. Common sayings such as the harmony of the spheres and it is music to my ears point to the notion that music is often ordered and pleasant to listen to. However, 20th-century composer John Cage thought that any sound can be music, saying, for example, There is no noise, the creation, performance, significance, and even the definition of music vary according to culture and social context. There are many types of music, including music, traditional music, art music, music written for religious ceremonies. For example, it can be hard to draw the line between some early 1980s hard rock and heavy metal, within the arts, music may be classified as a performing art, a fine art or as an auditory art. People may make music as a hobby, like a teen playing cello in a youth orchestra, the word derives from Greek μουσική. According to the Online Etymological Dictionary, the music is derived from mid-13c. Musike, from Old French musique and directly from Latin musica the art of music and this is derived from the. Greek mousike of the Muses, from fem. of mousikos pertaining to the Muses, from Mousa Muse. In classical Greece, any art in which the Muses presided, Music is composed and performed for many purposes, ranging from aesthetic pleasure, religious or ceremonial purposes, or as an entertainment product for the marketplace. With the advent of recording, records of popular songs. Some music lovers create mix tapes of their songs, which serve as a self-portrait. An environment consisting solely of what is most ardently loved, amateur musicians can compose or perform music for their own pleasure, and derive their income elsewhere. Professional musicians sometimes work as freelancers or session musicians, seeking contracts and engagements in a variety of settings, There are often many links between amateur and professional musicians. Beginning amateur musicians take lessons with professional musicians, in community settings, advanced amateur musicians perform with professional musicians in a variety of ensembles such as community concert bands and community orchestras. However, there are many cases where a live performance in front of an audience is also recorded and distributed. Live concert recordings are popular in classical music and in popular music forms such as rock, where illegally taped live concerts are prized by music lovers
Music
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A painting on an Ancient Greek vase depicts a music lesson (c. 510 BC).
Music
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Jean-Gabriel Ferlan performing at a 2008 concert at the collège-lycée Saint-François Xavier
Music
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The composer
Michel Richard Delalande, pen in hand.
Music
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Funk places most of its emphasis on rhythm and
groove, with entire songs based around a
vamp on a single chord. Pictured are the influential funk musicians
George Clinton and
Parliament Funkadelic in 2006.
10.
Latin language
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Latin is a classical language belonging to the Italic branch of the Indo-European languages. The Latin alphabet is derived from the Etruscan and Greek alphabets, Latin was originally spoken in Latium, in the Italian Peninsula. Through the power of the Roman Republic, it became the dominant language, Vulgar Latin developed into the Romance languages, such as Italian, Portuguese, Spanish, French, and Romanian. Latin, Italian and French have contributed many words to the English language, Latin and Ancient Greek roots are used in theology, biology, and medicine. By the late Roman Republic, Old Latin had been standardised into Classical Latin, Vulgar Latin was the colloquial form spoken during the same time and attested in inscriptions and the works of comic playwrights like Plautus and Terence. Late Latin is the language from the 3rd century. Later, Early Modern Latin and Modern Latin evolved, Latin was used as the language of international communication, scholarship, and science until well into the 18th century, when it began to be supplanted by vernaculars. Ecclesiastical Latin remains the language of the Holy See and the Roman Rite of the Catholic Church. Today, many students, scholars and members of the Catholic clergy speak Latin fluently and it is taught in primary, secondary and postsecondary educational institutions around the world. The language has been passed down through various forms, some inscriptions have been published in an internationally agreed, monumental, multivolume series, the Corpus Inscriptionum Latinarum. Authors and publishers vary, but the format is about the same, volumes detailing inscriptions with a critical apparatus stating the provenance, the reading and interpretation of these inscriptions is the subject matter of the field of epigraphy. The works of several hundred ancient authors who wrote in Latin have survived in whole or in part and they are in part the subject matter of the field of classics. The Cat in the Hat, and a book of fairy tales, additional resources include phrasebooks and resources for rendering everyday phrases and concepts into Latin, such as Meissners Latin Phrasebook. The Latin influence in English has been significant at all stages of its insular development. From the 16th to the 18th centuries, English writers cobbled together huge numbers of new words from Latin and Greek words, dubbed inkhorn terms, as if they had spilled from a pot of ink. Many of these words were used once by the author and then forgotten, many of the most common polysyllabic English words are of Latin origin through the medium of Old French. Romance words make respectively 59%, 20% and 14% of English, German and those figures can rise dramatically when only non-compound and non-derived words are included. Accordingly, Romance words make roughly 35% of the vocabulary of Dutch, Roman engineering had the same effect on scientific terminology as a whole
Latin language
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Latin inscription, in the
Colosseum
Latin language
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Julius Caesar 's
Commentarii de Bello Gallico is one of the most famous classical Latin texts of the Golden Age of Latin. The unvarnished, journalistic style of this
patrician general has long been taught as a model of the urbane Latin officially spoken and written in the floruit of the
Roman republic.
Latin language
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A multi-volume Latin dictionary in the
University Library of Graz
Latin language
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Latin and Ancient Greek Language - Culture - Linguistics at
Duke University in 2014.
11.
Interval (music)
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In music theory, an interval is the difference between two pitches. 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 and 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, 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 result in an exponential increase of frequency. For this reason, intervals are often measured in cents, a 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 and number, examples include the minor third or perfect fifth. These names describe 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♭. The size of an interval can be represented using two alternative and equivalently valid methods, each appropriate to a different context, frequency ratios or cents, 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, Intervals with small-integer ratios are often called just intervals, or pure intervals. Most commonly, however, musical instruments are tuned using a different tuning system. As a consequence, the size of most equal-tempered intervals cannot be expressed by small-integer ratios, for instance, an equal-tempered fifth has a frequency ratio of 2 7⁄12,1, approximately equal to 1.498,1, or 2.997,2. For a comparison between the size of intervals in different tuning systems, see section Size in different tuning systems, the standard system for comparing interval sizes is with cents. The cent is a unit of measurement. If frequency is expressed in a scale, and along that scale the distance between a given frequency and its double is divided into 1200 equal parts, each of these parts is one cent. In twelve-tone equal temperament, a system in which all semitones have the same size. Hence, in 12-TET the cent can be defined as one hundredth of a semitone
Interval (music)
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Melodic and harmonic intervals. Play (
help ·
info)
12.
Pitch (music)
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Pitch can be determined only in sounds that have a frequency that is clear and stable enough to distinguish from noise. Pitch is a major attribute of musical tones, along with duration, loudness. Pitch may be quantified as a frequency, but pitch is not a purely objective physical property, Pitch is an auditory sensation in which a listener assigns musical tones to relative positions on a musical scale based primarily on their perception of the frequency of vibration. Pitch is closely related to frequency, but the two are not equivalent, frequency is an objective, scientific attribute that can be measured. Pitch is each persons subjective perception of a wave, which cannot be directly measured. However, this not necessarily mean that most people wont agree on which notes are higher and lower. Sound waves themselves do not have pitch, but their oscillations can be measured to obtain a frequency and it takes a sentient mind to map the internal quality of pitch. However, pitches are usually associated with, and thus quantified as frequencies in cycles per second, or hertz, by comparing sounds with pure tones, Complex and aperiodic sound waves can often be assigned a pitch by this method. According to the American National Standards Institute, pitch is the attribute of sound according to which sounds can be ordered on a scale from low to high. That is, high pitch means very rapid oscillation, and low pitch corresponds to slower oscillation, despite that, the idiom relating vertical height to sound pitch is shared by most languages. At least in English, it is just one of many deep conceptual metaphors that involve up/down, the exact etymological history of the musical sense of high and low pitch is still unclear. There is evidence that humans do actually perceive that the source of a sound is slightly higher or lower in vertical space when the frequency is increased or reduced. The pitch of tones can be ambiguous, meaning that two or more different pitches can be perceived, depending upon the observer. In a situation like this, the percept at 200 Hz is commonly referred to as the missing fundamental, Pitch depends to a lesser degree on the sound pressure level of the tone, especially at frequencies below 1,000 Hz and above 2,000 Hz. The pitch of lower tones gets lower as sound pressure increases, for instance, a tone of 200 Hz that is very loud seems one semitone lower in pitch than if it is just barely audible. Above 2,000 Hz, the pitch gets higher as the sound gets louder, theories of pitch perception try to explain how the physical sound and specific physiology of the auditory system work together to yield the experience of pitch. In general, pitch perception theories can be divided into place coding, place theory holds that the perception of pitch is determined by the place of maximum excitation on the basilar membrane. However, a purely place-based theory cannot account for the accuracy of pitch perception in the low, temporal theories offer an alternative that appeals to the temporal structure of action potentials, mostly the phase-locking and mode-locking of action potentials to frequencies in a stimulus
Pitch (music)
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In musical notation, the different vertical positions of notes indicate different pitches. Play top (
help ·
info) & Play bottom (
help ·
info)
13.
Frequency
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Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as frequency, which emphasizes the contrast to spatial frequency. The period is the duration of time of one cycle in a repeating event, for example, if a newborn babys heart beats at a frequency of 120 times a minute, its period—the time interval between beats—is half a second. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as vibrations, audio signals, radio waves. For cyclical processes, such as rotation, oscillations, or waves, in physics and engineering disciplines, such as optics, acoustics, and radio, frequency is usually denoted by a Latin letter f or by the Greek letter ν or ν. For a simple motion, the relation between the frequency and the period T is given by f =1 T. The SI unit of frequency is the hertz, named after the German physicist Heinrich Hertz, a previous name for this unit was cycles per second. The SI unit for period is the second, a traditional unit of measure used with rotating mechanical devices is revolutions per minute, abbreviated r/min or rpm. As a matter of convenience, longer and slower waves, such as ocean surface waves, short and fast waves, like audio and radio, are usually described by their frequency instead of period. Spatial frequency is analogous to temporal frequency, but the axis is replaced by one or more spatial displacement axes. Y = sin = sin d θ d x = k Wavenumber, in the case of more than one spatial dimension, wavenumber is a vector quantity. For periodic waves in nondispersive media, frequency has a relationship to the wavelength. Even in dispersive media, the frequency f of a wave is equal to the phase velocity v of the wave divided by the wavelength λ of the wave. In the special case of electromagnetic waves moving through a vacuum, then v = c, where c is the speed of light in a vacuum, and this expression becomes, f = c λ. When waves from a monochrome source travel from one medium to another, their remains the same—only their wavelength. For example, if 71 events occur within 15 seconds the frequency is, the latter method introduces a random error into the count of between zero and one count, so on average half a count. This is called gating error and causes an error in the calculated frequency of Δf = 1/, or a fractional error of Δf / f = 1/ where Tm is the timing interval. This error decreases with frequency, so it is a problem at low frequencies where the number of counts N is small, an older method of measuring the frequency of rotating or vibrating objects is to use a stroboscope
Frequency
–
A resonant-reed frequency meter, an obsolete device used from about 1900 to the 1940s for measuring the frequency of alternating current. It consists of a strip of metal with reeds of graduated lengths, vibrated by an
electromagnet. When the unknown frequency is applied to the electromagnet, the reed which is
resonant at that frequency will vibrate with large amplitude, visible next to the scale.
Frequency
–
As time elapses – represented here as a movement from left to right, i.e. horizontally – the five
sinusoidal waves shown vary regularly (i.e. cycle), but at different
rates. The red
wave (top) has the lowest frequency (i.e. varies at the slowest rate) while the purple wave (bottom) has the highest frequency (varies at the fastest rate).
Frequency
Frequency
–
Modern frequency counter
14.
Scale (music)
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In music theory, a scale is any set of musical notes ordered by fundamental frequency or pitch. A scale ordered by increasing pitch is a scale. Some scales contain different pitches when ascending than when descending, for example, the Melodic minor scale. Due to the principle of equivalence, scales are generally considered to span a single octave. A musical scale represents a division of the space into a certain number of scale steps. A measure of the width of each scale step provides a method to classify scales, based on their interval patterns, scales are put into categories including diatonic, chromatic, major, minor, and others. A specific scale is defined by its interval pattern and by a special note. The tonic of a scale is the selected as the beginning of the octave. Typically, the name of the scale specifies both its tonic and its interval pattern, for example, C major indicates a major scale with a C tonic. Scales are typically listed from low to high, most scales are octave-repeating, meaning their pattern of notes is the same in every octave. An octave-repeating scale can be represented as an arrangement of pitch classes. The distance between two notes in a scale is called a scale step. The notes of a scale are numbered by their steps from the root of the scale, for example, in a C major scale the first note is C, the second D, the third E and so on. Two notes can also be numbered in relation to other, C and E create an interval of a third. A single scale can be manifested at many different pitch levels, for example, a C major scale can be started at C4 and ascending an octave to C5, or it could be started at C6, ascending an octave to C7. As long as all the notes can be played, the octave they take on can be altered, the pitch distances or intervals among the notes of a scale tell us more about the sound of the music than does the mere number of tones. The notes of a scale form intervals with each of the notes of the chord in combination. A 5-note scale has 10 of these intervals, a 6-note scale has 15, a 7-note scale has 21
Scale (music)
15.
Pitch class
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In music, a pitch class is a set of all pitches that are a whole number of octaves apart, e. g. the pitch class C consists of the Cs in all octaves. The pitch class C stands for all possible Cs, in whatever octave position, important to musical set theory, a pitch class is, all pitches related to each other by octave, enharmonic equivalence, or both. Psychologists refer to the quality of a pitch as its chroma, a chroma is an attribute of pitches, just like hue is an attribute of color. A pitch class is a set of all pitches that share the same chroma, because octave-related pitches belong to the same class, when an octave is reached, the numbers begin again at zero. Indeed, the mapping from pitch to real numbers defined in this forms the basis of the MIDI Tuning Standard. To represent pitch classes, we need to identify or glue together all pitches belonging to the same pitch class—i. e, all numbers p and p +12. The result is a quotient group that musicians call pitch class space. Points in this space can be labelled using real numbers in the range 0 ≤ x <12. These numbers provide numerical alternatives to the names of elementary music theory,0 = C,1 = C♯/D♭,2 = D,2.5 = D,3 = D♯/E♭. In this system, pitch classes represented by integers are classes of equal temperament. In music, integer notation is the translation of pitch classes and/or interval classes into whole numbers, thus if C =0, then C♯ =1. A♯ =10, B =11, with 10 and 11 substituted by t and e in some sources and this allows the most economical presentation of information regarding post-tonal materials. In the integer model of pitch, all classes and intervals between pitch classes are designated using the numbers 0 through 11. It is not used to music for performance, but is a common analytical and compositional tool when working with chromatic music, including twelve tone, serial. The C above this is not 12, but 0 again, thus arithmetic modulo 12 is used to represent octave equivalence. One advantage of this system is that it ignores the spelling of notes according to their diatonic functionality, there are a few disadvantages with integer notation. First, theorists have used the same integers to indicate elements of different tuning systems. Thus, the numbers 0,1,2,5, are used to notate pitch classes in 6-tone equal temperament
Pitch class
–
All Cs possible on a piano (except C 8, available on grand) Play (
help ·
info).
16.
Over the Rainbow
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Over the Rainbow is a ballad, with music by Harold Arlen and lyrics by Yip Harburg. It was written for the movie The Wizard of Oz and was sung by actress Judy Garland, the song won the Academy Award for Best Original Song and became Garlands signature song, as well as one of the most enduring standards of the 20th century. Dorothys Aunt Em tells her to find yourself a place where you wont get into any trouble and this prompts Dorothy to walk off by herself, musing to Toto, Some place where there isnt any trouble. Do you suppose there is such a place, Toto and its not a place you can get to by a boat, or a train. Behind the moon, beyond the rain, at which point she begins singing. The song is one on the Songs of the Century list compiled by the Recording Industry Association of America. The American Film Institute also ranked Over the Rainbow the greatest movie song of all time on the list of AFIs 100 Years.100 Songs and it was adopted by American troops in Europe in World War II, as a symbol of the United States. Garland performed the song for the troops as part of a 1943 performance, in April 2005, the United States Postal Service issued a commemorative stamp recognizing lyricist Yip Harburgs accomplishments, the stamp features the opening lyric from Over the Rainbow. The song was used as a wakeup call in the STS-88 Space shuttle mission in Flight Day 4. The song was honored with the 2014 Towering Song Award by the Songwriters Hall of Fame and was sung at its dinner on June 12,2014 by Jackie Evancho. In April 2016, The Daily Telegraph listed the song as number 8 on its list of the 100 greatest songs of all time, the Over the Rainbow sequence and the entirety of the Kansas scenes were directed by King Vidor, though he was not credited. At the start of the film, part of the song is played by the MGM orchestra over the opening credits, a reprise of the song was deleted after being filmed. An additional chorus was to be sung by Dorothy while she was locked in a room in the witchs castle, helplessly awaiting death as the witchs hourglass ran out. In that extremely intense and fear-filled rendition, Dorothy weeps her way through it, unable to finish, concluding with a tear-filled, Im frightened, another instrumental version is played in the underscore in the final scene, and over the closing credits. On October 7,1938, Judy Garland first recorded the song on the MGM soundstages, in September 1939, a studio recording of the song, not from the actual film soundtrack, was recorded and released as a single by Decca Records. In March 1940, that recording was included on a Decca 78-RPM four-record studio cast album entitled The Wizard of Oz. It was not until 1956, when MGM released the soundtrack album from the film. The 1956 soundtrack release was timed to coincide with the premiere of the movie
Over the Rainbow
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Judy Garland performing the song in the 1939 feature film,
The Wizard of Oz.
Over the Rainbow
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"Somewhere over the Rainbow/What a Wonderful World"
Over the Rainbow
–
"Over the Rainbow"
Over the Rainbow
17.
Stranger on the Shore
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Stranger on the Shore is a piece for clarinet written by Acker Bilk for his young daughter and originally named Jenny after her. It was subsequently used as the tune of a BBC TV drama serial for young people. It was first released in 1961 in the UK, and then in the US, in May 1969, the crew of Apollo 10 took Stranger on the Shore on their mission to the moon. Gene Cernan, a member of the crew, included the tune on a cassette tape used in the module of the Apollo spacecraft. The B-side was Take My Lips, the single became a phenomenal success, topping the NME singles chart and spending nearly a year on the Record Retailer Top 50. It was the UKs biggest-selling single of 1962, the instrumental single of all time. It has sold 1.16 million copies as of November 2012, in the pre-rock era, Vera Lynns Auf Wiedersehn Sweetheart had reached #1 in 1952, on the shorter Best Sellers In Stores survey. After Telstar, the next British performers to top the U. S. charts were the Beatles, Stranger on the Shore was Billboards #1 single of 1962, and it spent seven weeks atop the Easy Listening chart, which later became known as the Adult Contemporary chart. The tune became the second of three one-hit wonders named pop single of the year by Billboard (the others being 1958s Volare by Domenico Modugno, the song is certified gold by the Recording Industry Association of America. It was played in the movie The Wanderers, Stranger on the Shore was often featured on The Lawrence Welk Show, where Henry Cuesta, the shows clarinetist, usually played the song as his signature tune. In the AMC series Mad Men, Stranger on the Shore is used as a theme song whenever the son Peggy gave up for adoption is mentioned and it is played twice in An Idiot Abroad by Karl Pilkington, and it is Karls favourite piece of instrumental music. In Mr. Hollands Opus The song young Gertrude Lang learns on the clarinet is Stranger on the Shore by Acker Bilk and it is used as the theme tune for That Mitchell and Webb Sound. It was played on the cello during the virtual reality sequence of the Nowhere Man episode A Rough Whimper of Insanity, lyrics of this song at MetroLyrics
Stranger on the Shore
–
"Stranger on the Shore"
18.
Harmonic series (music)
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A harmonic series is the sequence of sounds where the base frequency of each sound is an integer multiple of the lowest base frequency. Pitched musical instruments are based on an approximate harmonic oscillator such as a string or a column of air. At these resonant frequencies, waves travel in both directions along the string or air column, reinforcing and canceling each other to form standing waves, interaction with the surrounding air causes audible sound waves, which travel away from the instrument. Because of the spacing of the resonances, these frequencies are mostly limited to integer multiples, or harmonics, of the lowest frequency. The musical timbre of a tone from such an instrument is determined by the relative strengths of each harmonic. A complex tone can be described as a combination of many simple periodic waves or partials, each with its own frequency of vibration, amplitude, a partial is any of the sine waves of which a complex tone is composed. A harmonic is any member of the series, an ideal set of frequencies that are positive integer multiples of a common fundamental frequency. The fundamental is also considered a harmonic because it is 1 times itself, a harmonic partial is any real partial component of a complex tone that matches an ideal harmonic. An inharmonic partial is any partial that does not match an ideal harmonic, Inharmonicity is a measure of the deviation of a partial from the closest ideal harmonic, typically measured in cents for each partial. Unpitched, or indefinite-pitched instruments, such as cymbals, gongs, or tam-tams make sounds that are rich in inharmonic partials, an overtone is any partial except the lowest partial. The term overtone does not imply harmonicity or inharmonicity and has no special meaning other than to exclude the fundamental. It is the relative strengths of the different overtones that gives an instrument its particular timbre, some electronic instruments, such as synthesizers, can play a pure frequency with no overtones. Synthesizers can also combine pure frequencies into more complex tones, such as to other instruments. Certain flutes and ocarinas are very nearly without overtones, in most pitched musical instruments, the fundamental is accompanied by other, higher-frequency harmonics. Thus shorter-wavelength, higher-frequency waves occur with varying prominence and give each instrument its characteristic tone quality, the fact that a string is fixed at each end means that the longest allowed wavelength on the string is twice the length of the string. Other allowed wavelengths are 1/2, 1/3, 1/4, 1/5, 1/6, theoretically, these shorter wavelengths correspond to vibrations at frequencies that are 2,3,4,5,6, etc. times the fundamental frequency. Physical characteristics of the vibrating medium and/or the resonator it vibrates against often alter these frequencies, the harmonic series is an arithmetic series. In terms of frequency, the difference between consecutive harmonics is therefore constant and equal to the fundamental, but because human ears respond to sound nonlinearly, higher harmonics are perceived as closer together than lower ones
Harmonic series (music)
–
Harmonic series of a string with terms written as
reciprocals (2/1 written as 1/2)
19.
Pythagorean interval
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In musical tuning theory, a Pythagorean interval is a musical interval with frequency ratio equal to a power of two divided by a power of three, or vice versa. For instance, the fifth with ratio 3/2 and the perfect fourth with ratio 4/3 are Pythagorean intervals. All the intervals between the notes of a scale are Pythagorean if they are tuned using the Pythagorean tuning system, however, some Pythagorean intervals are also used in other tuning systems. For instance, the above-mentioned Pythagorean perfect fifth and fourth are also used in just intonation, notice that the terms ditone and semiditone are specific for Pythagorean tuning, while tone and tritone are used generically for all tuning systems. Interestingly, despite its name, a semiditone can hardly be viewed as half of a ditone, the table shows from which notes some of the above listed intervals can be played on an instrument using a repeated-octave 12-tone scale tuned with D-based symmetric Pythagorean tuning. Further details about this table can be found in Size of Pythagorean intervals, the fundamental intervals are the superparticular ratios 2/1, 3/2, and 4/3. 2/1 is the octave or diapason, 3/2 is the perfect fifth, diapente, or sesquialterum. 4/3 is the fourth, diatessaron, or sesquitertium. These three intervals and their equivalents, such as the perfect eleventh and twelfth, are the only absolute consonances of the Pythagorean system. All other intervals have varying degrees of dissonance, ranging from smooth to rough, the difference between the perfect fourth and the perfect fifth is the tone or major second. This has the ratio 9/8, also known as epogdoon and it is the only other superparticular ratio of Pythagorean tuning, two tones make a ditone, a dissonantly wide major third, ratio 81/64. The ditone differs from the just major third by the syntonic comma, likewise, the difference between the tone and the perfect fourth is the semiditone, a narrow minor third, 32/27, which differs from 6/5 by the syntonic comma. These differences are tempered out or eliminated by using compromises in meantone temperament, the difference between the minor third and the tone is the minor semitone or limma of 256/243. The difference between the tone and the limma is the major semitone or apotome of 2187/2048, there is a one-to-one correspondence between interval names and frequency ratios. Generated collection Just intonation List of meantone intervals List of intervals in 5-limit just intonation Shí-èr-lǜ Whole-tone scale Neo-Gothic usage by Margo Schulter
Pythagorean interval
–
Pythagorean perfect fifth on C Play (
help ·
info): C-G (3/2 ÷ 1/1 = 3/2).
20.
Perfect fourth
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In classical music from Western culture, a fourth is a musical interval encompassing four staff positions, and the perfect fourth is a fourth spanning five semitones. For example, the interval from C to the next F is a perfect fourth, as the note F lies five semitones above C. Diminished and augmented fourths span the same number of staff positions, the perfect fourth may be derived from the harmonic series as the interval between the third and fourth harmonics. The term perfect identifies this interval as belonging to the group of perfect intervals, so called because they are neither major nor minor, up until the late 19th century, the perfect fourth was often called by its Greek name, diatessaron. Its most common occurrence is between the fifth and upper root of all major and minor triads and their extensions. A perfect fourth in just intonation corresponds to a ratio of 4,3, or about 498 cents, while in equal temperament a perfect fourth is equal to five semitones. A helpful way to recognize a fourth is to hum the starting of the Bridal Chorus from Wagners Lohengrin. Other examples are the first two notes of the Christmas carol Hark, the Herald Angels Sing or El Cóndor Pasa, and, for a descending perfect fourth, the second and third notes of O Come All Ye Faithful. The perfect fourth is a perfect interval like the unison, octave, and perfect fifth, in common practice harmony, however, it is considered a stylistic dissonance in certain contexts, namely in two-voice textures and whenever it appears above the bass. Conventionally, adjacent strings of the bass and of the bass guitar are a perfect fourth apart when unstopped, as are all pairs. Sets of tom-tom drums are also tuned in perfect fourths. The 4,3 just perfect fourth arises in the C major scale between G and C, play The use of perfect fourths and fifths to sound in parallel with and to thicken the melodic line was prevalent in music prior to the European polyphonic music of the Middle Ages. In the 13th century, the fourth and fifth together were the concordantiae mediae after the unison and octave, in the 15th century the fourth came to be regarded as dissonant on its own, and was first classed as a dissonance by Johannes Tinctoris in his Terminorum musicae diffinitorium. In practice, however, it continued to be used as a consonance when supported by the interval of a third or fifth in a lower voice. Modern acoustic theory supports the medieval interpretation insofar as the intervals of unison, octave, the octave has the ratio of 2,1, for example the interval between a at A440 and a at 880 Hz, giving the ratio 880,440, or 2,1. The fifth has a ratio of 3,2, and its complement has the ratio of 3,4, ancient and medieval music theorists appear to have been familiar with these ratios, see for example their experiments on the Monochord. In early western polyphony, these simpler intervals were generally preferred, however, in its development between the 12th and 16th centuries, In the earliest stages, these simple intervals occur so frequently that they appear to be the favourite sound of composers. Later, the more complex intervals move gradually from the margins to the centre of musical interest
Perfect fourth
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Perfect fourth Play (
help ·
info)
21.
Perfect fifth
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In music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3,2, or very nearly so. In classical music from Western culture, a fifth is the interval from the first to the last of five notes in a diatonic scale. The perfect fifth spans seven semitones, while the diminished fifth spans six, for example, the interval from C to G is a perfect fifth, as the note G lies seven semitones above C. Play The perfect fifth may be derived from the series as the interval between the second and third harmonics. In a diatonic scale, the dominant note is a fifth above the tonic note. The perfect fifth is more consonant, or stable, than any other interval except the unison and it occurs above the root of all major and minor chords and their extensions. Until the late 19th century, it was referred to by one of its Greek names. Its inversion is the perfect fourth, the octave of the fifth is the twelfth. The term perfect identifies the perfect fifth as belonging to the group of perfect intervals, so called because of their simple pitch relationships and their high degree of consonance. However, when using correct enharmonic spelling, the fifth in Pythagorean tuning or meantone temperament is actually not a perfect fifth. The perfect unison has a pitch ratio 1,1, the perfect octave 2,1, the perfect fourth 4,3, within this definition, other intervals may also be called perfect, for example a perfect third or a perfect major sixth. In terms of semitones, these are equivalent to the tritone, the justly tuned pitch ratio of a perfect fifth is 3,2, meaning that the upper note makes three vibrations in the same amount of time that the lower note makes two. The just perfect fifth can be heard when a violin is tuned, if adjacent strings are adjusted to the ratio of 3,2, the result is a smooth and consonant sound. Keyboard instruments such as the piano normally use a version of the perfect fifth. In 12-tone equal temperament, the frequencies of the perfect fifth are in the ratio 7 or approximately 1.498307. An equally tempered fifth, defined as 700 cents, is about two cents narrower than a just perfect fifth, which is approximately 701.955 cents. Kepler explored musical tuning in terms of ratios, and defined a lower imperfect fifth as a 40,27 pitch ratio. His lower perfect fifth ratio of 1.4815 is much more imperfect than the equal temperament tuning of 1.498, the perfect fifth is a basic element in the construction of major and minor triads, and their extensions
Perfect fifth
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Examples of perfect fifth intervals
22.
Musical note
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In music, the term note has three primary meanings, A sign used in musical notation to represent the relative duration and pitch of a sound, A pitched sound itself. Notes are the blocks of much written music, discretizations of musical phenomena that facilitate performance, comprehension. In the former case, one note to refer to a specific musical event, in the latter. Two notes with fundamental frequencies in an equal to any integer power of two are perceived as very similar. Because of that, all notes with these kinds of relations can be grouped under the pitch class. However, within the English-speaking and Dutch-speaking world, pitch classes are represented by the first seven letters of the Latin alphabet. A few European countries, including Germany, adopt an almost identical notation, the eighth note, or octave, is given the same name as the first, but has double its frequency. The name octave is also used to indicate the span between a note and another with double frequency, for example, the now-standard tuning pitch for most Western music,440 Hz, is named a′ or A4. There are two systems to define each note and octave, the Helmholtz pitch notation and the scientific pitch notation. Letter names are modified by the accidentals, a sharp ♯ raises a note by a semitone or half-step, and a flat ♭ lowers it by the same amount. In modern tuning a half step has a ratio of 12√2. The accidentals are written after the name, so, for example, F♯ represents F-sharp, B♭ is B-flat. Additional accidentals are the double-sharp, raising the frequency by two semitones, and double-flat, lowering it by that amount, in musical notation, accidentals are placed before the note symbols. Systematic alterations to the seven lettered pitches in the scale can be indicated by placing the symbols in the key signature, explicitly noted accidentals can be used to override this effect for the remainder of a bar. A special accidental, the natural symbol ♮, is used to indicate an unmodified pitch, effects of key signature and local accidentals do not accumulate. If the key signature indicates G♯, a flat before a G makes it G♭, though often this type of rare accidental is expressed as a natural. Likewise, a sharp sign on a key signature with a single sharp ♯ indicates only a double sharp. Assuming enharmonicity, many accidentals will create equivalences between pitches that are written differently, for instance, raising the note B to B♯ is equal to the note C
Musical note
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Names of some notes without accidentals
Musical note
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The note A or La
23.
Hertz
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The hertz is the unit of frequency in the International System of Units and is defined as one cycle per second. It is named for Heinrich Rudolf Hertz, the first person to provide proof of the existence of electromagnetic waves. Hertz are commonly expressed in SI multiples kilohertz, megahertz, gigahertz, kilo means thousand, mega meaning million, giga meaning billion and tera for trillion. Some of the units most common uses are in the description of waves and musical tones, particularly those used in radio-. It is also used to describe the speeds at which computers, the hertz is equivalent to cycles per second, i. e. 1/second or s −1. In English, hertz is also used as the plural form, as an SI unit, Hz can be prefixed, commonly used multiples are kHz, MHz, GHz and THz. One hertz simply means one cycle per second,100 Hz means one hundred cycles per second, and so on. The unit may be applied to any periodic event—for example, a clock might be said to tick at 1 Hz, the rate of aperiodic or stochastic events occur is expressed in reciprocal second or inverse second in general or, the specific case of radioactive decay, becquerels. Whereas 1 Hz is 1 cycle per second,1 Bq is 1 aperiodic radionuclide event per second, the conversion between a frequency f measured in hertz and an angular velocity ω measured in radians per second is ω =2 π f and f = ω2 π. This SI unit is named after Heinrich Hertz, as with every International System of Units unit named for a person, the first letter of its symbol is upper case. Note that degree Celsius conforms to this rule because the d is lowercase. — Based on The International System of Units, the hertz is named after the German physicist Heinrich Hertz, who made important scientific contributions to the study of electromagnetism. The name was established by the International Electrotechnical Commission in 1930, the term cycles per second was largely replaced by hertz by the 1970s. One hobby magazine, Electronics Illustrated, declared their intention to stick with the traditional kc. Mc. etc. units, sound is a traveling longitudinal wave which is an oscillation of pressure. Humans perceive frequency of waves as pitch. Each musical note corresponds to a frequency which can be measured in hertz. An infants ear is able to perceive frequencies ranging from 20 Hz to 20,000 Hz, the range of ultrasound, infrasound and other physical vibrations such as molecular and atomic vibrations extends from a few femtoHz into the terahertz range and beyond. Electromagnetic radiation is described by its frequency—the number of oscillations of the perpendicular electric and magnetic fields per second—expressed in hertz. Radio frequency radiation is measured in kilohertz, megahertz, or gigahertz
Hertz
–
Details of a
heartbeat as an example of a non-
sinusoidal periodic phenomenon that can be described in terms of hertz. Two complete cycles are illustrated.
Hertz
–
A
sine wave with varying frequency
24.
Twinkle Twinkle Little Star
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Twinkle, Twinkle, Little Star is a popular English lullaby. The lyrics are from an early 19th-century English poem by Jane Taylor, the poem, which is in couplet form, was first published in 1806 in Rhymes for the Nursery, a collection of poems by Taylor and her sister Ann. The English lyrics have five stanzas, although only the first is widely known and it has a Roud Folk Song Index number of 7666. This song is performed in the key of C Major. The song is in the domain, and has many adaptations around the world. Additional variations exist such as from 1896 in Song Stories for the Kindergarten by Mildred J. Hill, an adaptation of the song, named Twinkle, Twinkle, Little Earth, was written by Charles Randolph Grean, Fred Hertz and Leonard Nimoy. It is included on his first 1967 album Leonard Nimoy Presents Mr. Spocks Music From Outer Space, a version using synonyms from Rogets Thesaurus exists. Ah. vous dirai-je, maman Alphabet song Baa, Baa, a European Union, government-funded education project to collect lullabies from across Europe - includes samples in seven languages. SoundBeep Twinkle Twinkle Little Star with two Instrument versions, piano and kalimba, audio segment from BBC Radio 4 Womans Hour
Twinkle Twinkle Little Star
–
"
A-Tisket, A-Tasket "
Twinkle Twinkle Little Star
–
sheet music from Song Stories for the Kindergarten Play (
help ·
info)
Play full chord (help·info), 
.svg)
