1.
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
2.
Diminished third
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In classical music from Western culture, a diminished third is the musical interval produced by narrowing a minor third by a chromatic semitone. For instance, the interval from A to C is a third, three semitones wide, and both the intervals from A♯ to C, and from A to C♭ are diminished thirds. Being diminished, it is considered a dissonant interval, in equal temperament a diminished third is enharmonic with the major second, both having a value of 200 cents. However, in tunings with fifths flatter than the 700 cents of equal temperament. In 19 equal temperament it is in fact equivalent to an augmented second. In 31 equal temperament it has a typical value of 232.3 cents. In a twelve-note keyboard tuned in a meantone tuning from E♭ to G♯, in superpythagorean tunings, the diminished third is narrower than the major second. In 22 equal temperament, the third is ~109 cents while the chromatic semitone is ~163 cents. Thus, 22-ET is a system in which both semitones are not in fact semitones, but the third is a semitone. For example, a German sixth chord E♭-G-B♭-C♯-E♭ exhibits a diminished third between C♯ and E♭ which complements the augmented sixth between E♭ and C♯, the just diminished third arises in the extended C major scale between F♯ and A♭, Play and between B and D♭
3.
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
4.
Minor seventh
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In the music of Western culture, a seventh is a musical interval encompassing seven staff positions, and the minor seventh is one of two commonly occurring sevenths. It is qualified as minor because it is the smaller of the two, the minor seventh spans ten semitones, the major seventh eleven, minor seventh intervals are rarely featured in melodies but occur more often than major sevenths. The best-known example, in due to its frequent use in theory classes, is found between the first two words of the phrase Theres a place for us in the song Somewhere in West Side Story. Another well-known example occurs between the first two notes of the introduction to the theme music from Star Trek, The Original Series theme. The most common occurrence of the seventh is built on the root of the prevailing keys dominant triad. Consonance and dissonance are relative, depending on context, the seventh being defined as a dissonance requiring resolution to a consonance. In just intonation there is both a 16,9 small just minor seventh, also called Pythagorean small minor seventh, an interval close in frequency is the harmonic seventh. Minor seventh chord Musical tuning List of meantone intervals
5.
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
6.
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
7.
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
8.
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
9.
Quarter tone
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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
10.
Western culture
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The term also applies beyond Europe, to countries and cultures whose histories are strongly connected to Europe by immigration, colonization, or influence. For example, Western Culture includes countries in the Americas and Australasia, whose language, before the Cold War era, the traditional Western viewpoint identified Western Civilization with the Western Christian countries and culture. Ancient Greece is considered the birthplace of Western culture, with the worlds first democratic system of government and major advances in philosophy, science, Greece was followed by Rome, which made key contributions in law, government, engineering and political organization. European culture developed with a range of philosophy, medieval scholasticism, and mysticism. Rational thinking developed through an age of change and formation, with the experiments of the Enlightenment. More often an ideology is what will be used to categorize it as a Western society. There is some disagreement about what nations should or should not be included in the category, many parts of the Eastern Roman Empire are considered Western today but were Eastern in the past. Since the context is highly biased and context-dependent, there is no agreed definition what the West is and it is difficult to determine which individuals fit into which category and the East–West contrast is sometimes criticized as relativistic and arbitrary. Globalism has spread Western ideas so widely that almost all cultures are, to some extent. Stereotyped views of the West have been labeled Occidentalism, paralleling Orientalism—the term for the 19th-century stereotyped views of the East, as Europe discovered the wider world, old concepts adapted. The area that had formerly considered the Orient became the Near East, as the interests of the European powers interfered with Meiji Japan and Qing China for the first time. Thus, the Sino-Japanese War in 1894–1895 occurred in the Far East, the Greeks contrasted themselves to their Eastern neighbors, such as the Trojans in Iliad, setting an example for later contrasts between east and west. In the Middle Ages, the Near East provided a contrast to the West, concepts of what is the West arose out of legacies of the Western Roman Empire and the Eastern Roman Empire. Later, ideas of the west were formed by the concepts of Latin Christendom, Western culture is neither homogeneous nor unchanging. As with all cultures, it has evolved and gradually changed over time. Nevertheless, it is possible to follow the evolution and history of the West, and appreciate its similarities and differences, its borrowings from, and contributions to, other cultures of humanity. Nevertheless, the Greeks felt they were the most civilized and saw themselves as something between the wild barbarians of most of Europe and the soft, slavish Middle-Easterners. In the meantime, however, Greece, under Alexander, had become a capital of the East, the Celts also created some significant literature in the ancient world whenever they were given the opportunity
11.
Music theory
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Music theory is the study of the practices and possibilities of music. The term is used in three ways in music, though all three are interrelated. The first is what is otherwise called rudiments, currently taught as the elements of notation, of key signatures, of time signatures, of rhythmic notation, Theory in this sense is treated as the necessary preliminary to the study of harmony, counterpoint, and form. The second is the study of writings about music from ancient times onwards, Music theory is frequently concerned with describing how musicians and composers make music, including tuning systems and composition methods among other topics. However, this medieval discipline became the basis for tuning systems in later centuries, Music theory as a practical discipline encompasses the methods and concepts composers and other musicians use in creating music. The development, preservation, and transmission of music theory in this sense may be found in oral and written music-making traditions, musical instruments, and other artifacts. In ancient and living cultures around the world, the deep and long roots of music theory are clearly visible in instruments, oral traditions, and current music making. Many cultures, at least as far back as ancient Mesopotamia and ancient China, have also considered music theory in more formal ways such as written treatises, in modern academia, music theory is a subfield of musicology, the wider study of musical cultures and history. Etymologically, music theory is an act of contemplation of music, from the Greek θεωρία, a looking at, viewing, contemplation, speculation, theory, also a sight, a person who researches, teaches, or writes articles about music theory is a music theorist. University study, typically to the M. A. or Ph. D level, is required to teach as a music theorist in a US or Canadian university. Methods of analysis include mathematics, graphic analysis, and especially analysis enabled by Western music notation, comparative, descriptive, statistical, and other methods are also used. See for instance Paleolithic flutes, Gǔdí, and Anasazi flute, several surviving Sumerian and Akkadian clay tablets include musical information of a theoretical nature, mainly lists of intervals and tunings. The scholar Sam Mirelman reports that the earliest of these dates from before 1500 BCE. Further, All the Mesopotamian texts are united by the use of a terminology for music that, much of Chinese music history and theory remains unclear. The earliest texts about Chinese music theory are inscribed on the stone and they include more than 2800 words describing theories and practices of music pitches of the time. The bells produce two intertwined pentatonic scales three tones apart with additional pitches completing the chromatic scale, Chinese theory starts from numbers, the main musical numbers being twelve, five and eight. Twelve refers to the number of pitches on which the scales can be constructed, the Lüshi chunqiu from about 239 BCE recalls the legend of Ling Lun. On order of the Yellow Emperor, Ling Lun collected twelve bamboo lengths with thick, blowing on one of these like a pipe, he found its sound agreeable and named it huangzhong, the Yellow Bell
12.
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
13.
Staff (music)
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Appropriate music symbols, depending on the intended effect, are placed on the staff according to their corresponding pitch or function. Musical notes are placed by pitch, percussion notes are placed by instrument, the absolute pitch of each line of a non-percussive staff is indicated by the placement of a clef symbol at the appropriate vertical position on the left-hand side of the staff. For example, the treble clef, also known as the G clef, is placed on the second line, the lines and spaces are numbered from bottom to top, the bottom line is the first line and the top line is the fifth line. The musical staff is analogous to a graph of pitch with respect to time. Pitches of notes are given by their position on the staff. A time signature to the right of the clef indicates the relationship between timing counts and note symbols, while bar lines group notes on the staff into measures, staff is more common in American English, stave in British English. The plural is staves in either case, stave is, in fact, the vertical position of the notehead on the staff indicates which note to play, higher-pitched notes are marked higher on the staff. The notehead can be placed with the center of its notehead intersecting a line, notes outside the range of the staff are placed on or between ledger lines—lines the width of the note they need to hold—added above or below the staff. Exactly which staff positions represent which notes is determined by a clef placed at the beginning of the staff, the clef identifies a particular line as a specific note, and all other notes are determined relative to that line. For example, the treble clef puts the G above middle C on the second line, the interval between adjacent staff positions is one step in the diatonic scale. Once fixed by a clef, the represented by the positions on the staff can be modified by the key signature. A clefless staff may be used to represent a set of percussion sounds, a single vertical line drawn to the left of multiple staves creates a system, indicating that the music on all the staves is to be played simultaneously. A bracket is a vertical line joining staves, to show groupings of instruments that function as a unit. A brace is used to join multiple staves that represent a single instrument, such as a piano, organ, harp, or marimba. Sometimes, a bracket is used to show instruments grouped in pairs, such as the first and second oboes, or the first. In some cases, a brace is used for this instead of a bracket. When more than one system appears on a page, often two parallel diagonal strokes are placed on the left side of the score to separate them. Four-part SATB vocal settings, especially in hymnals, use a notation on a two-staff system with soprano and alto voices sharing the upper staff
14.
Musical notation
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Types and methods of notation have varied between cultures and throughout history, and much information about ancient music notation is fragmentary. Although many ancient cultures used symbols to represent melodies and rhythms, none of them were particularly comprehensive, the seeds of what would eventually become modern western notation were sown in medieval Europe, starting with the Catholic churchs goal for ecclesiastical uniformity. The church began notating plainchant melodies so that the same chants could be used throughout the church, Music notation developed in the Renaissance and Baroque music eras. The introduction of figured bass notation in the Baroque era marked the beginning of the first compositions based around chord progressions, in the classical period and the Romantic music era, notation continued to develop as new musical instrument technologies were developed. Music notation has been adapted to many kinds of music, including music, popular music. The earliest form of notation can be found in a cuneiform tablet that was created at Nippur, in Sumer. The tablet represents fragmentary instructions for performing music, that the music was composed in harmonies of thirds, a tablet from about 1250 BC shows a more developed form of notation. Although the interpretation of the system is still controversial, it is clear that the notation indicates the names of strings on a lyre. Although they are fragmentary, these represent the earliest notated melodies found anywhere in the world. The notation consists of symbols placed above text syllables, an example of a complete composition is the Seikilos epitaph, which has been variously dated between the 2nd century BC to the 1st century AD. Three hymns by Mesomedes of Crete exist in manuscript, the Delphic Hymns, dated to the 2nd century BC, also use this notation, but they are not completely preserved. Ancient Greek notation appears to have out of use around the time of the Decline of the Roman Empire. Byzantine music has survived as music for court ceremonies, including vocal religious music. It is not known if it is based on the monodic modal singing, unlike Western notation Byzantine neumes always indicate modal steps in relation to a clef or modal key. These step symbols themselves, or better phonic neumes, resemble brush strokes and are colloquially called gántzoi in Modern Greek, Notes as pitch classes or modal keys are represented in written form only between these neumes. In modern notation they simply serve as a reminder and modal and tempo directions have been added. In Papadic notation medial signatures usually meant a change into another echos. With exception of vú and zō they do correspond to Western solmization syllables as re, mi, fa, sol, la, si
15.
Diminished second
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In modern Western tonal music theory, a diminished second is the interval produced by narrowing a minor second by one chromatic semitone. It is enharmonically equivalent to a perfect unison, thus, it is the interval between notes on two adjacent staff positions, or having adjacent note letters, altered in such a way that they have no pitch difference in twelve-tone equal temperament. An example is the interval from a B to the C♭ immediately above, in particular, it may be regarded as the difference between a diatonic and chromatic semitone. For instance, the interval from B to C is a semitone, the interval from B to B♯ is a chromatic semitone, and their difference. Being diminished, it is considered a dissonant interval and this makes it a highly variable quantity between tuning systems. Hence for example C♯ is narrower than D♭ by a diminished second interval, in 12-tone equal temperament, the diminished second is identical to the unison, because both semitones have the same size. In 19-tone equal temperament, on the hand, it is identical to the chromatic semitone and is a respectable 63.16 cents wide. It shows a similar size in third-comma meantone, where it coincides with the greater diesis, the most commonly used meantone temperaments fall between these extremes, giving it an intermediate size. In Pythagorean tuning, however, the interval actually shows a descending direction, i. e. a ratio below unison, such is also the case in twelfth-comma meantone, although that diminished second is only a twelfth of the Pythagorean one. The table below summarizes the definitions of the second in the main tuning systems. In the column labeled Difference between semitones, m2 is the second, A1 is the augmented unison, and S1, S2, S3. Notice that for 5-limit tuning, 1/6-, 1/4-, and 1/3-comma meantone, List of musical intervals List of pitch intervals List of meantone intervals Comma
16.
Augmented second
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For instance, the interval from C to D is a major second, two semitones wide, and the interval from C to D♯ is an augmented second, spanning three semitones. Augmented seconds occur in many scales, most important the harmonic minor and they also occur in the various Gypsy scales. In harmonic minor scales, the second occurs between the sixth and seventh scale degrees. For example, in the scale of A harmonic minor, the notes F, an augmented second is enharmonically equivalent to a minor third in equal temperament, but is not the same interval in other meantone tunings. In any tuning close to quarter-comma meantone it will be close to the 7,6 ratio of the minor third. Hence the distinction is not, as thought and even taught, a purely formal and contextual one. The 75,64 just augmented second arises in the C harmonic minor scale between A♭ and B
17.
Degree (music)
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In music theory, a scale degree refers to the position of a particular note on a scale relative to the tonic, the first and main note of the scale from which each octave is assumed to begin. The term is useful for indicating the size of intervals and chords, scale degrees can be applied to any musical scale, however, the concept is most commonly applied to scales in which a tonic is specified by definition, such as the 7-tone diatonic scales. It is possible to assign a scale degree to the 12-tone chromatic scale, the expression scale step is sometimes used synonymously with scale degree, but it may alternatively refer to the distance between between two successive scale degrees. The terms whole step and half step are used as interval names. The number of degrees and the distance between them together define the scale they are in. These names are derived from a scheme where the note is the center
18.
Major scale
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The major scale or Ionian scale is one of the most commonly used musical scales, especially in Western music. It is one of the diatonic scales, like many musical scales it is made up of seven notes, the eighth duplicates the first at double its frequency so that it is called a higher octave of the same note. In Carnatic music, it is known as Dheerasankarabharanam, and in Hindustani classical music it is known as Bilaval, a major scale is a diatonic scale. The sequence of intervals between the notes of a scale is, whole, whole, half, whole, whole, whole, half where whole stands for a whole tone. A major scale may be seen as two tetrachords separated by a whole tone. Each tetrachord consists of two whole tones followed by a semitone, whole, whole, half, seven sharps or flats make major keys that may be more conveniently spelled with five flats or sharps. The term major scale is used in the names of some other scales whose first, third. The harmonic major scale has a minor sixth and it differs from the harmonic minor scale only by raising the third degree. The melodic major scale is the mode of the jazz minor scale. It is the Ionian scale with a sixth and minor seventh. The combined scale that goes as Ionian ascending and as melodic major descending is also called melodic major, the double harmonic major scale has a minor second and a minor sixth. It is the mode of the Hungarian minor scale. Ionian mode Major and minor Listen to and download harmonised Major scale piano MP3s The major scale for guitar in one position, with derivation
19.
Tonic (music)
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The triad formed on the tonic note, the tonic chord, is thus the most significant chord in these styles of music. More generally, the tonic is the pitch upon which all other pitches of a piece are hierarchically referenced, scales are named after their tonics, thus the tonic of the scale of C is the note C. Simple folk music and traditional songs may begin and end on the tonic note, in very much conventionally tonal music, harmonic analysis will reveal a broad prevalence of the primary harmonies, tonic, dominant, and subdominant, and especially the first two of these. The tonic is often confused with the root, which is the note of a chord. The root of a chord is different from the tonic, because different types of chords have root notes. It is also represented with the Roman numeral I, two parallel keys have the same tonic. For example, in both C major and C minor, the tonic is C, however, relative keys have different tonics. For example, C major and A minor share a key signature that feature no sharps or flats, thus a pitch center may function referentially or contextually in an atonal context, often acting as axis or line of symmetry in an interval cycle. Pitch centricity was coined by Arthur Berger in his Problems of Pitch Organization in Stravinsky
20.
Supertonic
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In music or music theory, the supertonic is the second degree or note of a diatonic scale, one step above the tonic. It is sung as re in solfege, if in major or minor, through the lowering of the second scale degree, the chord is major then it is a Neapolitan 6th chord, N6 or ♭II6. The supertonic may be raised as part of the diminished seventh chord. One variant of the seventh chord is the supertonic diminished seventh with the raised supertonic. Pre-dominant chords are chords which distinguish chord V as a goal of motion they create gravity and harmonic motion towards dominant harmony, and form a fundamental aspect of western tonal music. The supertonic chord is known as a pre-dominant chord, as it is one of the chords which has a natural tendency to gravitate towards chord V. The supertonic chord lies a fifth above chord V, descending fifths are a strong basis for harmonic motion. It is preferable to avoid chord two in root position in the minor mode due to the quality of its diminished intervals. This is less of a if the chord contains a chordal seventh, indeed. Supertonic seventh chords are such intense pre-dominant chords because they outline the leading note contained in chord V with a dissonance, supertonic also refers to a relationship of musical keys. For example, relative to the key of C major, the key of D major is the supertonic, modulation to the supertonic is relatively common, though in classical music it is more common to modulate to the dominant or other keys. In German theory derived from Hugo Riemann, the supertonic is considered the subdominant parallel, Sp/T in major though sP/T in minor
21.
Musical keyboard
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A musical keyboard is the set of adjacent depressible levers or keys on a musical instrument. Depressing a key on the causes the instrument to produce sounds, either by mechanically striking a string or tine, plucking a string, causing air to flow through a pipe. On electric and electronic keyboards, depressing a key connects a circuit, since the most commonly encountered keyboard instrument is the piano, the keyboard layout is often referred to as the piano keyboard. The twelve notes of the Western musical scale are laid out with the lowest note on the left, because these keys were traditionally covered in ivory they are often called the white notes or white keys. The keys for the remaining five notes—which are not part of the C major scale— are raised, because these keys receive less wear, they are often made of black colored wood and called the black notes or black keys. The pattern repeats at the interval of an octave, the arrangement of longer keys for C major with intervening, shorter keys for the intermediate semitones dates to the 15th century. The break was between middle C and C-sharp, or outside of Iberia between B and C, broken keyboards reappeared in 1842 with the harmonium, the split occurring at E4/F4. The reverse-colored keys on Hammond organs such as the B3, C3, the chromatic compass of keyboard instruments has tended to increase. Harpsichords often extended over five octaves in the 18th century, while most pianos manufactured since about 1870 have 88 keys, some modern pianos have even more notes. While modern synthesizer keyboards commonly have either 61,76 or 88 keys, organs normally have 61 keys per manual, though some spinet models have 44 or 49. An organ pedalboard is a keyboard with long pedals that are played by the organists feet, pedalboards vary in size from 12 to 32 notes. In a typical layout, black note keys have uniform width. In the larger gaps between the keys, the width of the natural notes C, D and E differ slightly from the width of keys F, G, A and B. This allows close to uniform spacing of 12 keys per octave while maintaining uniformity of seven natural keys per octave, over the last three hundred years, the octave span distance found on historical keyboard instruments has ranged from as little as 125 mm to as much as 170 mm. Several reduced-size standards have been proposed and marketed, a 15/16 size and the 7/8 DS Standard keyboard developed by Christopher Donison in the 1970s and developed and marketed by Steinbuhler & Company. There have been variations in the design of the keyboard to address technical and musical issues, thus, an octave would have eight white keys and only four black keys. During the sixteenth century, when instruments were tuned in meantone temperament, some harpsichords were constructed with the G♯. The broken octave, a variation of the short octave
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Fret
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A fret is a raised element on the neck of a stringed instrument. Frets usually extend across the width of the neck. On most modern western fretted instruments, frets are metal strips inserted into the fingerboard, on some historical instruments and non-European instruments, frets are made of pieces of string tied around the neck. Frets divide the neck into fixed segments at intervals related to a musical framework, on instruments such as guitars, each fret represents one semitone in the standard western system, in which one octave is divided into twelve semitones. Fret is often used as a verb, meaning simply to press down the string behind a fret, fretting often refers to the frets and/or their system of placement. Pressing the string against the fret reduces the length of the string to that between the bridge and the next fret between the fretting finger and the bridge. This is damped if the string were stopped with the fingertip on a fretless fingerboard. Frets make it easier for a player to achieve an acceptable standard of intonation. Furthermore, a fretted fingerboard makes it easier to play chords accurately, a disadvantage of frets is that they restrict pitches to the temperament defined by the fret positions. A player may still influence intonation, however, by pulling the string to the side to increase string tension and this technique is often used by electric guitarists of all genres, and is an important part of sitar playing. On instruments with frets that are thicker off the fingerboard, string tension, sometimes a player can pull the string toward the bridge or nut, thus lowering or raising the string tension and pitch. However, except for instruments that accommodate extensive string pulling, like the sitar, since the intonation of most modern western fretted instruments is equal tempered, the ratio of the distances of two consecutive frets to the bridge is 212, or approximately 1.059463. Theoretically, the twelfth fret should divide the string in two exact halves, to compensate for the increase in string tension when the string is pressed against the frets, the bridge position is adjusted slightly so the 12th fret plays exactly in tune. Fan frets (also fanned frets, slanted frets, or multi-scale, Frets are generally perpendicular to the instruments neck centerline, on a fanned fretboard, the frets are angled with only one center fret perpendicular to the neck’s centerline. This gives the strings more length and the higher strings shorter length. The idea is to more accurate tuning and deeper bass. Some think that fanned frets might be more ergonomic, fanned frets first appeared on the 16th century Orpharion, a variant of the cittern, tuned like a lute. John Starrett revived the idea in the seventies on his innovative instrument
23.
Melody
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A melody, also tune, voice, or line, is a linear succession of musical tones that the listener perceives as a single entity. In its most literal sense, a melody is a combination of pitch and rhythm, while more figuratively and it may be considered the foreground to the background accompaniment. A line or part need not be a foreground melody, melodies often consist of one or more musical phrases or motifs, and are usually repeated throughout a composition in various forms. Melodies may also be described by their melodic motion or the pitches or the intervals between pitches, pitch range, tension and release, continuity and coherence, cadence, the true goal of music—its proper enterprise—is melody. All the parts of harmony have as their purpose only beautiful melody. Therefore, the question of which is the significant, melody or harmony, is futile. Beyond doubt, the means is subordinate to the end, given the many and varied elements and styles of melody many extant explanations confine us to specific stylistic models, and they are too exclusive. Paul Narveson claimed in 1984 that more than three-quarters of melodic topics had not been explored thoroughly, melodies in the 20th century utilized a greater variety of pitch resources than ha been the custom in any other historical period of Western music. While the diatonic scale was used, the chromatic scale became widely employed. Composers also allotted a structural role to the dimensions that previously had been almost exclusively reserved for pitch. Kliewer states, The essential elements of any melody are duration, pitch, and quality, texture, for example, Jazz musicians use the term lead or head to refer to the main melody, which is used as a starting point for improvisation. Rock music, melodic music, and other forms of popular music, indian classical music relies heavily on melody and rhythm, and not so much on harmony, as the music contains no chord changes. Balinese gamelan music often uses complicated variations and alterations of a melody played simultaneously. In western classical music, composers often introduce an initial melody, or theme, classical music often has several melodic layers, called polyphony, such as those in a fugue, a type of counterpoint. Often, melodies are constructed from motifs or short melodic fragments, richard Wagner popularized the concept of a leitmotif, a motif or melody associated with a certain idea, person or place. Appropriation Hocket Parsons code, a notation used to identify a piece of music through melodic motion—the motion of the pitch up. Harvard Dictionary of Music, 2nd ed. p. 517–19, the Art of Melody, p. xix–xxx. A Textbook of Melody, A course in functional melodic analysis, a History Of Melody, Barrie and Rockliff, London
24.
Steps and skips
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In music, a step, or conjunct motion, is the difference in pitch between two consecutive notes of a musical scale. In other words, it is the interval between two consecutive scale degrees, any larger interval is called a skip, or disjunct motion. In the diatonic scale, a step is either a second or a major second. For example, C to D is a step, whereas C to E is a skip, renaissance melodies are generally characterized by conjunct motion, with only occasional leaps of more than a fifth and then rarely anything but a sixth or octave. In contrast, melody in the 20th century varied greatly including the diatonic idiom of the 18th century, the variety of idioms from the 19th century, some of these later idioms included many or predominately leaps. Coltrane changes Giant Steps Linear progression Transposition
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Interval ratio
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In music, an interval ratio is a ratio of the frequencies of the pitches in a musical interval. For example, a just perfect fifth is 3,2,1.5, if the A above middle C is 440 Hz, the perfect fifth above it would be E, at 660 Hz, while the equal tempered E5 is 659.255 Hz. Ratios have a relationship to string length, for example stopping a string at two-thirds its length produces a pitch one. Intervals may be ranked by relative consonance and dissonance, as such ratios with lower integers are generally more consonant than intervals with higher integers. For example,2,1,4,3,9,8,65536,59049, consonance and dissonance may more subtly be defined by limit, wherein the ratios whose limit, which includes its integer multiples, is lower are generally more consonant. For example, the 3-limit 128,81 and the 7-limit 14,9, despite having larger integers 128,81 is less dissonant than 14,9, as according to limit theory. For ease of comparison intervals may also be measured in cents, for example, the just perfect fifth is 701.955 cents while the equal tempered perfect fifth is 700 cents. Frequency ratios are used to describe intervals in both Western and non-Western music. 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. To most people, just intervals sound consonant, i. e. pleasant, although the size of equally tuned intervals is typically similar to that of just intervals, in most cases it cannot be expressed by small-integer ratios. For instance, a tempered perfect fifth has a frequency ratio of about 1.4983,1. For a comparison between the size of intervals in different tuning systems, see section Size in different tuning systems
26.
Syntonic comma
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The comma is referred to as a comma of Didymus because it is the amount by which Didymus corrected the Pythagorean major third to a just major third. Namely,81,64 ÷5,4 =81,80, the difference between four justly tuned perfect fifths, and two octaves plus a justly tuned major third. A just perfect fifth has a size of 3,2, a just major third has a size of 5,4, and one of them plus two octaves is equal to 5,1. The difference between these is the syntonic comma, namely,81,16 ÷5,1 =81,80. The difference between one octave plus a justly tuned minor third, and three justly tuned perfect fourths, namely,12,5 ÷64,27 =81,80. The difference between the two kinds of major second which occur in 5-limit tuning, major tone and minor tone, namely,9,8 ÷10,9 =81,80. The difference between a Pythagorean major sixth and a justly tuned or pure major sixth, namely,27,16 ÷5,3 =81,80. On a piano keyboard a stack of four fifths is exactly equal to two octaves plus a major third, in other words, starting from a C, both combinations of intervals will end up at E. Using justly tuned octaves, fifths, and thirds, however, the ratio between their frequencies, as explained above, is a syntonic comma. Pythagorean tuning uses justly tuned fifths as well, but uses the complex ratio of 81,64 for major thirds. Quarter-comma meantone uses justly tuned major thirds, but flattens each of the fifths by a quarter of a syntonic comma and this is one of the reasons why 12-tone equal temperament is currently the preferred system for tuning most musical instruments. Mathematically, by Størmers theorem,81,80 is the closest superparticular ratio possible with regular numbers as numerator and denominator. A superparticular ratio is one whose numerator is 1 greater than its denominator, such as 5,4, and a number is one whose prime factors are limited to 2,3. Thus, although smaller intervals can be described within 5-limit tunings, the syntonic comma has a crucial role in the history of music. It is the amount by which some of the notes produced in Pythagorean tuning were flattened or sharpened to produce just minor and major thirds, in Pythagorean tuning, the only highly consonant intervals were the perfect fifth and its inversion, the perfect fourth. The Pythagorean major third and minor third were dissonant, and this prevented musicians from using triads and chords, in late Middle Ages, musicians realized that by slightly tempering the pitch of some notes, the Pythagorean thirds could be made consonant. For instance, if the frequency of E is decreased by a comma, C-E. But the fifth C-G stays consonant, since only E has been flattened, since then, other tuning systems were developed, and the syntonic comma was used as a reference value to temper the perfect fifths in an entire family of them
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15 equal temperament
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In music,15 equal temperament, called 15-TET, 15-EDO, or 15-ET, is a tempered scale derived by dividing the octave into 15 equal steps. Each step represents a ratio of 15√2, or 80 cents. Because 15 factors into 3 times 5, it can be seen as being made up of three scales of 5 equal divisions of the octave, each of which resembles the Slendro scale in Indonesian gamelan,15 equal temperament is not a meantone system. Guitars have been constructed for 15-ET tuning, the American musician Wendy Carlos used 15-ET as one of two scales in the track Afterlife from the album Tales of Heaven and Hell. Easley Blackwood, Jr. has written and recorded a suite for 15-ET guitar, Blackwood believes that 15 equal temperament, is likely to bring about a considerable enrichment of both classical and popular repertoire in a variety of styles. Here are the sizes of some common intervals in 15-ET, 15-ET matches the 7th and 11th harmonics well, but only matches the 3rd and 5th harmonics roughly. The perfect fifth is more out of tune than in 12-ET, 19-ET, or 22-ET, and the third in 15-ET is the same as the major third in 12-ET. Unlike 12-ET and 19-ET, 15-ET matches the 11,8 and 16,11 ratios, 15-ET also has a neutral second and septimal whole tone. To construct a third, one must stack two intervals of different sizes, whereas one can divide both the minor third and perfect fourth into two equal intervals. Ivor Darreg, 15-TONE SCALE SYSTEM, Sonic-Arts. org, brewt, Fifteen note equal temperament tutorial
28.
Consonance and dissonance
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In music, consonance and dissonance form a structural dichotomy in which the terms define each other by mutual exclusion, a consonance is what is not dissonant, and reciprocally. However, a finer consideration shows that the forms a gradation. Consonance is associated with sweetness, pleasantness and acceptability and dissonance with harshness, unpleasantness, as Hindemith stressed, The two concepts have never been completely explained, and for a thousand years the definitions have varied. The opposition can be made in different contexts, In acoustics or psychophysiology, in modern times, it usually is based on the perception of harmonic partials of the sounds considered, to such an extent that the distinction really holds only in the case of harmonic sounds. In music, even if the opposition often is founded on the preceding, objective distinction, it often is subjective, conventional, cultural. A major second would be considered dissonant if it occurred in a J. S, Bach prelude from the 1700s, however, the same interval may sound consonant in the context of a Claude Debussy piece from the early 1900s or an atonal contemporary piece. For this reason, consonance and dissonance have been considered particularly in the case of Western polyphonic music, most historical definitions of consonance and dissonance since about the 16th century have stressed their pleasant/unpleasant, or agreeable/disagreeable character. In addition, the oppositions pleasant/unpleasant or agreeable/disagreeable evidence a confusion between the concepts of dissonance and of noise and these include, Frequency ratios, with ratios of lower simple numbers being more consonant than those that are higher. Many of these definitions do not require exact integer tunings, only approximation, coincidence of partials, with consonance being a greater coincidence of partials. By this definition, consonance is dependent not only on the width of the interval between two notes, but also on the spectral distribution and thus sound quality of the notes. Thus, a note and the note one octave higher are highly consonant because the partials of the note are also partials of the lower note. Although Helmholtzs work focused almost exclusively on harmonic timbres and also the tunings, subsequent work has generalized his findings to embrace non-harmonic tunings, fusion, perception of unity or tonal fusion between two notes. A stable tone combination is a consonance, consonances are points of arrival, rest, 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, 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. Nevertheless, the ideas of dissonance, consonance, and resolution exist in some form in all musical traditions that have a concept of melody, harmony. 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. For many musicians and composers, the ideas of dissonance
29.
Diatonic scale
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This pattern ensures that, in a diatonic scale spanning more than one octave, all the half steps are maximally separated from each other. The word diatonic comes from the Greek διατονικός, meaning progressing through tones, the seven pitches of any diatonic scale can be obtained using a chain of six perfect fifths. Musical keyboards are designed to play notes, and hence diatonic scales. A diatonic scale can be described as two tetrachords separated by a whole tone. The term diatonic originally referred to the genus, one of the three genera of the ancient Greeks. In musical set theory, Allen Forte classifies diatonic scales as set form 7–35 and this article does not concern alternative seven-note diatonic scales such as the harmonic minor or the melodic minor. Western music from the Middle Ages until the late 19th century is based on the diatonic scale, there is one claim that the 45, 000-year-old Divje Babe Flute uses a diatonic scale, but there is no proof or consensus it is even a musical instrument. There is evidence that the Sumerians and Babylonians used some version of the diatonic scale and this derives from surviving inscriptions that contain a tuning system and musical composition. Despite the conjectural nature of reconstructions of the known as the Hurrian songs from the surviving score. The scales corresponding to the medieval Church modes were diatonic, one of these, the one starting on B, has no pure fifth above its reference note, it is probably for this reason that it was not used. Of the six remaining scales, two were described as corresponding to two others with a B♭ instead of a B♮, A–B–C–D–E–F–G–A was described as D–E–F–G–A–B♭C–D and C–D–E–F–G–A–B–C as F–G–A–B♭–C–D–E–F, as a result, medieval theory described the Church modes as corresponding to four diatonic scales only. Heinrich Glarean considered that the modal scales including a B♭ had to be the result of a transposition, by the beginning of the Baroque period, the notion of musical key was established, describing additional possible transpositions of the diatonic scale. Major and minor scales came to dominate until at least the start of the 20th century, some Church modes survived into the early 18th century, as well as appearing occasionally in classical and 20th-century music, and later in modal jazz. Glareans six natural scales could be transposed not only to include one flat in the signature, of these six scales, three are major scales, three are minor. To these may be added the seventh diatonic scale, with a fifth above the reference note. Transposing each of seven scales on the twelve degrees of the chromatic scale results in a total of eighty-four diatonic scales. The modern musical keyboard originated as a keyboard with only lower keys. The major scale, for instance, can be represented as T–T–S–T–T–T–S or 2–2–1–2–2–2–1 The major scale or Ionian scale is one of the diatonic scales and it is made up of seven distinct notes, plus an eighth that duplicates the first an octave higher
30.
20th-century music
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During the 20th century there was a vast increase in the variety of music that people had access to. The 20th-century orchestra was far more flexible than its predecessors and used a wider variety of instruments. In Beethovens and Felix Mendelssohns time in the 19th century, the orchestra was composed of a standard core of instruments which was very rarely modified. The 20th century saw dramatic innovations in musical forms and styles, composers and songwriters experimented with new musical styles, such as genre fusions. As well, composers and musicians used new electric, electronic, in the 1980s, some styles of music, such as electronic dance music genres such as house music were created largely with synthesizers and drum machines. Faster modes of such as jet flight allowed musicians and fans to travel more widely to perform or hear shows. Busoni, Stravinsky, Schoenberg, and Schreker were already recognized before 1914 as modernists, composers such as Ravel, Milhaud, and Gershwin combined classical and jazz idioms. Late-Romantic and modernist nationalism was also in British, American. Composers such as Ralph Vaughan Williams, Aaron Copland, Carlos Chávez, in the middle of the century composers such as Harry Partch and Ben Johnston explored just intonation. There were three schools of neoclassicism, associated with Igor Stravinsky, Paul Hindemith, and Arnold Schoenberg. Similar sympathies in the half of the century are generally subsumed under the heading postmodernism. A compositional tradition arose in the mid-20th century—particularly in North America—called experimental music and its most famous and influential exponent was John Cage. According to Cage, an action is one the outcome of which is not foreseen. Minimalist music, involving a simplification of materials and intensive repetition of motives began in the late 1950s with the composers Terry Riley, Steve Reich, later, minimalism was adapted to a more traditional symphonic setting by composers including Reich, Glass, and John Adams. For more examples see List of 20th-century classical composers, contemporary classical music can be understood as belonging to the period that started in the mid-1970s to early 1990s, which includes modernist, postmodern, neoromantic, and pluralist music. However, the term may also be employed in a sense to refer to all post-1945 musical forms. Many composers working in the early 21st century were prominent figures in the 20th century, some younger composers such as Oliver Knussen, Thomas Adès, and Michael Daugherty did not rise to prominence until late in the 20th century. For more examples see List of 21st-century classical composers, in the early twentieth century, electronic devices were invented that were capable of generating sound electronically, without an initial mechanical source of vibration
31.
Arabic music
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Arabic music or Arab music is the music of the Arab world. Arab music, while independent and flourishing in the 2010s, has a history of interaction with many other regional musical styles and genres. It is an amalgam of the music of the Arab people in the Arabian Peninsula, as was the case in other artistic and scientific fields, Arabs translated Greek texts and works of music and developed the musical theory of the Greeks. Pre-Islamic Arab music was similar to that of Ancient Middle Eastern music, most historians agree that there existed distinct forms of music in the Arabian peninsula in the pre-Islamic period between the 5th and 7th century AD. Arab poets of that time—called shuara al-Jahiliyah or Jahili poets, meaning the poets of the period of ignorance—used to recite poems with a high notes and it was believed that Jinns revealed poems to poets and music to musicians. The choir at the served as a pedagogic facility where the educated poets would recite their poems. The compositions were simple and every singer would sing in a single maqam, among the notable songs of the period were the huda, the nasb, sanad, and rukbani. Both compositions and improvisations in traditional Arabic music are based on the maqam system, maqams can be realized with either vocal or instrumental music, and do not include a rhythmic component. Al-Kindi was the first great theoretician of Arabic music and he proposed adding a fifth string to the oud and discussed the cosmological connotations of music. He built upon the achievements of the Greek musicians in using the alphabetical annotation for one eighth and he published fifteen treatises on music theory, but only five have survived. In one of his treatises the word musiqa was used for the first time in Arabic, abulfaraj wrote a book about music. Kitab al-Aghani is a collection of poems and songs that runs to over 20 volumes in modern editions. Al-Farabi wrote a book on music titled Kitab al-Musiqi al-Kabir. His pure Arabian tone system is used in Arabic music. Al-Ghazali wrote a treatise on music in Persia which declared, Ecstasy means the state comes from listening to music. In 1252, Safi al-Din developed a form of musical notation. A similar geometric representation would not appear in the Western world until 1987, by the 11th century, Islamic Iberia had become a center for the manufacture of instruments. These goods spread gradually throughout France, influencing French troubadours, the English words lute, rebec, and naker are derived from Arabic oud, rabab, and naqareh
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Music of Turkey
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Much of its modern popular music can trace its roots to the emergence in the early 1930s drive for Westernization. With the assimilation of immigrants from various regions the diversity of musical genres, Turkey has also seen documented folk music and recorded popular music produced in the ethnic styles of Greek, Armenian, Albanian, Polish, Azeri and Jewish communities, among others. Many Turkish cities and towns have vibrant local music scenes which, in turn, despite this however, western-style pop music lost popularity to arabesque in the late 70s and 80s, with even its greatest proponents Ajda Pekkan and Sezen Aksu falling in status. It became popular again by the beginning of the 1990s, as a result of an opening economy, with the support of Aksu, the resurging popularity of pop music gave rise to several international Turkish pop stars such as Tarkan and Sertab Erener. Ottoman court music has a large and varied system of modes or scales known as makams, a number of notation systems were used for transcribing classical music, the most dominant being the Hamparsum notation in use until the gradual introduction of western notation. Turkish classical music is taught in conservatories and social clubs, the most respected of which is Istanbuls Üsküdar Musiki Cemiyeti, a full fasıl concert would include four different instrumental forms and three vocal forms, including a light classical song, şarkı. A strictly classical fasıl remains is the same throughout, from the introductory taksim. Composers and Performers Other famous proponents of this genre include Sufi Dede Efendi, Prince Cantemir, Baba Hamparsum, Kemani Tatyos Efendi, Sultan Selim III, the most popular modern Turkish classical singer is Münir Nurettin Selçuk, who was the first to establish a lead singer position. Other performers include Bülent Ersoy, Zeki Müren, Müzeyyen Senar, from the makams of the royal courts to the melodies of the royal harems, a type of dance music emerged that was different from the oyun havası of fasıl music. In the Ottoman Empire, the harem was that part of a house set apart for the women of the family and it was a place in which non-family males were not allowed. Eunuchs guarded the sultans harems, which were large, including several hundred women who were wives and concubines. There, female dancers and musicians entertained the women living in the harem, belly dance was performed by women for women. This female dancer, known as a rakkase, hardly ever appeared in public and this type of harem music was taken out of the sultans private living quarters and to the public by male street entertainers and hired dancers of the Ottoman Empire, the male rakkas. These dancers performed publicly for wedding celebrations, feasts, festivals, modern oriental dance in Turkey is derived from this tradition of the Ottoman rakkas. However, Çiftetelli is now a form of music, with names of songs that describe their local origins. Dancers are also known for their use of finger cymbals as instruments. Romani are known throughout Turkey for their musicianship and their urban music brought echoes of classical Turkish music to the public via the meyhane or taverna. This type of music with food and alcoholic beverages is often associated with the underclass of Turkish society
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Balkans
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The Balkan Peninsula, or the Balkans, is a peninsula and a cultural area in Eastern and Southeastern Europe with various and disputed borders. The region takes its name from the Balkan Mountains that stretch from the Serbia-Bulgaria border to the Black Sea, the highest point of the Balkans is Mount Musala 2,925 metres in the Rila mountain range. In Turkish, Balkan means a chain of wooded mountains, the name is still preserved in Central Asia with the Balkan Daglary and the Balkan Province of Turkmenistan. A less popular hypothesis regarding its etymology is that it derived from the Persian Balā-Khāna, from Antiquity through the Middle Ages, the Balkan Mountains had been called by the local Thracian name Haemus. According to Greek mythology, the Thracian king Haemus was turned into a mountain by Zeus as a punishment, a reverse name scheme has also been suggested. D. Dechev considers that Haemus is derived from a Thracian word *saimon, a third possibility is that Haemus derives from the Greek word haema meaning blood. The myth relates to a fight between Zeus and the monster/titan Typhon, Zeus injured Typhon with a thunder bolt and Typhons blood fell on the mountains, from which they got their name. The earliest mention of the name appears in an early 14th-century Arab map, the Ottomans first mention it in a document dated from 1565. There has been no other documented usage of the word to refer to the region before that, there is also a claim about an earlier Bulgar Turkic origin of the word popular in Bulgaria, however it is only an unscholarly assertion. The word was used by the Ottomans in Rumelia in its meaning of mountain, as in Kod̲j̲a-Balkan, Čatal-Balkan, and Ungurus-Balkani̊. The concept of the Balkans was created by the German geographer August Zeune in 1808, during the 1820s, Balkan became the preferred although not yet exclusive term alongside Haemus among British travelers. Among Russian travelers not so burdened by classical toponymy, Balkan was the preferred term, zeunes goal was to have a geographical parallel term to the Italic and Iberian Peninsula, and seemingly nothing more. The gradually acquired political connotations are newer and, to a large extent, after the dissolution of Yugoslavia beginning in June 1991, the term Balkans again received a negative meaning, especially in Croatia and Slovenia, even in casual usage. A European Union initiative of 1999 is called the Stability Pact for South Eastern Europe, and its northern boundary is often given as the Danube, Sava and Kupa Rivers. The Balkan Peninsula has an area of about 470,000 km2. It is more or less identical to the known as Southeastern Europe. As of 1920 until World War II, Italy included Istria, the current territory of Italy includes only the small area around Trieste inside the Balkan Peninsula. However, the regions of Trieste and Istria are not usually considered part of the Balkans by Italian geographers, the Western Balkans is a neologism coined to describe the countries of ex-Yugoslavia and Albania
34.
Diatonic and chromatic
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They are very often used as a pair, especially when applied to contrasting features of the common practice music of the period 1600–1900. These terms may mean different things in different contexts, very often, diatonic refers to musical elements derived from the modes and transpositions of the white note scale C–D–E–F–G–A–B. In some usages it includes all forms of scale that are in common use in Western music. Chromatic most often refers to structures derived from the chromatic scale, in ancient Greece there were three standard tunings of a lyre. These three tunings were called diatonic, chromatic, and enharmonic, and the sequences of four notes that they produced were called tetrachords, a diatonic tetrachord comprised, in descending order, two whole tones and a semitone, such as A G F E. In the chromatic tetrachord the second string of the lyre was lowered from G to G♭, in the enharmonic tetrachord the tuning had two quarter tone intervals at the bottom, A G F E. For all three tetrachords, only the two strings varied in their pitch. The term cromatico was occasionally used in the Medieval and Renaissance periods to refer to the coloration of certain notes, in works of the Ars Nova from the 14th century, this was used to indicate a temporary change in metre from triple to duple, or vice versa. This usage became common in the 15th century as open white noteheads became the standard notational form for minims. These uses for the word have no relationship to the meaning of chromatic. The term chromatic began to approach its modern usage in the 16th century, Medieval theorists defined scales in terms of the Greek tetrachords. The gamut was the series of pitches from which all the Medieval scales notionally derive, the origin of the word gamut is explained at the article Hexachord, here the word is used in one of the available senses, the all-encompassing gamut as described by Guido dArezzo. The intervals from one note to the next in this Medieval gamut are all tones or semitones, recurring in a pattern with five tones. The semitones are separated as much as they can be, between alternating groups of three tones and two tones, here are the intervals for a string of ascending notes from the gamut. This would include the major scale, and the minor scale. There are specific applications in the music of the Common Practice Period, most, but not all writers, accept the natural minor as diatonic. Among such theorists there is no agreed general term that encompasses the major, inclusive usage Some writers consistently include the melodic and harmonic minor scales as diatonic also. For this group, every scale standardly used in common practice music, mixed usage Still other writers mix these two meanings of diatonic, and this can lead to confusions and misconceptions
35.
Pentatonic scale
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A pentatonic scale is a musical scale or mode with five notes per octave in contrast to a heptatonic scale such as the major scale and minor scale. Pentatonic scales are common and are found all over the world. They are divided into those with semitones and those without, examples of its use include Chopins Etude in G-flat major, op. 5, the Black Key etude, in the major pentatonic, musicology commonly classifies pentatonic scales as either hemitonic or anhemitonic. Hemitonic scales contain one or more semitones and anhemitonic scales do not contain semitones, for example, in Japanese music the anhemitonic yo scale is contrasted with the hemitonic in scale. Hemitonic pentatonic scales are also called ditonic scales, because the largest interval in them is the ditone and this should not be confused with the identical term also used by musicologists to describe a scale including only two notes. Anhemitonic pentatonic scales can be constructed in many ways, the major pentatonic scale may be thought of as a gapped or incomplete major scale. However, the scale has a unique character and is complete in terms of tonality. Another construction works backward, It omits two pitches from a diatonic scale, if one were to begin with a C major scale, for example, one might omit the fourth and the seventh scale degrees, F and B. The remaining notes then makes up the major scale, C, D, E, G. Omitting the third and seventh degrees of the C major scale obtains the notes for another transpositionally equivalent anhemitonic pentatonic scale, omitting the first and fourth degrees of the C major scale gives a third anhemitonic pentatonic scale, G, A, B, D, E. The black keys on a piano keyboard comprise a G-flat major pentatonic scale, G-flat, A-flat, B-flat, D-flat, and E-flat and it may also be considered a gapped blues scale. The C minor pentatonic is C, E-flat, F, G, the A minor pentatonic, the relative minor of C, comprises the same tones as the C major pentatonic, starting on A, giving A, C, D, E, G. This minor pentatonic contains all three tones of an A minor triad, because of their simplicity, pentatonic scales are often used to introduce beginners to music. The five pentatonic scales found by running up the keys on the piano are. This may be derived by proceeding with the principle that gives the Pythagorean diatonic and chromatic scales. Considering the anhemitonic scale as a subset of a just diatonic scale, assigning precise frequency proportions to the pentatonic scales of most cultures is problematic as tuning may be variable. Composer Lou Harrison has been one of the most recent proponents, Harrison and William Colvig tuned the slendro scale of the gamelan Si Betty to overtones 16,19,21,24,28
36.
C (musical note)
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In terms of musical pitch, C or Do is the first note of the fixed-Do solfège scale. When the A440 pitch standard is used to tune a musical instrument, Middle C is designated C4 in scientific pitch notation because of the notes position as the fourth C key from left on a standard 88-key piano keyboard. Another system known as scientific pitch assigns a frequency of 256 Hz but, while numerically convenient, other note-octave systems, including those used by some makers of digital music keyboards, may refer to Middle C differently. In MIDI, Middle C is note number 60, the C4 designation is the most commonly recognized in auditory science, and in musical studies it is often used in place of the Helmholtz designation c. While the expression Middle C is generally clear across instruments and clefs, C4 may be called Low C by someone playing a Western concert flute, which has a higher and narrower playing range than the piano, while C5 would be Middle C. This technically inaccurate practice has led some pedagogues to encourage standardizing on C4 as the definitive Middle C in instructional materials across all instruments, in vocal music, the term Soprano C, sometimes called High C or Top C, is the C two octaves above Middle C. It is so named because it is considered the defining note of the voice type. It is C6 in scientific notation and c in Helmholtz notation. The term Tenor C is sometimes used in music to refer to C5. In organ music, the term Tenor C can refer to an organ builders term for small C or C3, in stoplists it usually means that a rank is not full compass, omitting the bottom octave. For the frequency of each note on a piano, see piano key frequencies. Pythagorean,701.955 ×12 =8423.46 =23.46 = B♯+++ ET,700 ×12 =8400 =0 = B♯ = C1200 ×7 =8400 =0 = C This difference,23.46 cents, is known as the Pythagorean comma. Piano key frequencies A440 C major C minor Root
37.
Musical tuning
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In music, there are two common meanings for tuning, Tuning practice, the act of tuning an instrument or voice. Tuning systems, the systems of pitches used to tune an instrument. Tuning is the process of adjusting the pitch of one or many tones from musical instruments to establish typical intervals between these tones, Tuning is usually based on a fixed reference, such as A =440 Hz. Out of tune refers to a pitch/tone that is too high or too low in relation to a given reference pitch. While an instrument might be in relative to its own range of notes. Some instruments become out of tune with damage or time and must be readjusted or repaired, different methods of sound production require different methods of adjustment, Tuning to a pitch with ones voice is called matching pitch and is the most basic skill learned in ear training. Turning pegs to increase or decrease the tension on strings so as to control the pitch, instruments such as the harp, piano, and harpsichord require a wrench to turn the tuning pegs, while others such as the violin can be tuned manually. Modifying the length or width of the tube of an instrument, brass instrument, pipe, bell. The sounds of instruments such as cymbals are inharmonic—they have irregular overtones not conforming to the harmonic series. Tuning may be done aurally by sounding two pitches and adjusting one of them to match or relate to the other, a tuning fork or electronic tuning device may be used as a reference pitch, though in ensemble rehearsals often a piano is used. Symphony orchestras and concert bands tend to tune to an A or a B♭, respectively, interference beats are used to objectively measure the accuracy of tuning. As the two approach a harmonic relationship, the frequency of beating decreases. When tuning a unison or octave it is desired to reduce the beating frequency until it cannot be detected, for other intervals, this is dependent on the tuning system being used. Harmonics may be used to facilitate tuning of strings that are not themselves tuned to the unison, for example, lightly touching the highest string of a cello at the middle while bowing produces the same pitch as doing the same a third of the way down its second-highest string. The resulting unison is more easily and quickly judged than the quality of the fifth between the fundamentals of the two strings. In music, the open string refers to the fundamental note of the unstopped. The strings of a guitar are tuned to fourths, as are the strings of the bass guitar. Violin, viola, and cello strings are tuned to fifths, however, non-standard tunings exist to change the sound of the instrument or create other playing options
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Five-limit tuning
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Powers of 2 represent intervallic movements by octaves. Powers of 3 represent movements by intervals of perfect fifths, powers of 5 represent intervals of major thirds. Thus, 5-limit tunings are constructed entirely from extensions of three basic purely-tuned intervals, hence, 5-limit tuning is considered a method for obtaining just intonation. If octaves are ignored, it can be seen as a 2-dimensional lattice of pitch classes extending indefinitely in two directions, however, most tuning systems designed for acoustic instruments restrict the total number of pitches for practical reasons. It is also typical to have the number of pitches in each octave. In that case, the system can also be thought of as an octave-repeating scale of a certain number of pitches per octave. For example, if we have a 5-limit tuning system where the note is C256, then fC =256 Hz. There are several ways to define E above this C. Using thirds, one may go up one factor 5 and down two factors 2, reaching a frequency ratio of 5/4, or using fifths one may go up four factors of 3 and down six factors of 2, reaching 81/64. The prominent notes of a scale are tuned so that their frequencies form ratios of relatively small integers. Here the row headed Natural expresses all these ratios using a common list of natural numbers. In other words, the lowest occurrence of this one-octave scale shape within the series is as a subset of 8 of the 25 harmonics found in the octave from harmonics 24 to 48 inclusive. The three major thirds are correct, and three of the thirds are as expected, but D to F is a semiditone or Pythagorean minor third. As a consequence, we obtain a scale in which EGB and ACE are just minor triads, but the DFA triad doesnt have the minor shape or sound we might expect, being. Furthermore, the BDF triad is not the diminished triad that we would get by stacking two 6,5 minor thirds, being instead, Another way to do it is as follows. The three major thirds are still 5,4, and three of the thirds are still 6,5 with the fourth being 32,27. FAC and CEG still form just major triads, but GBD is now, there are other possibilities such as raising A instead of lowering D, but each adjustment breaks something else. It is evidently not possible to get all seven diatonic triads in the configuration for major, for minor and that demonstrates the need for increasing the numbers of pitches to execute the desired harmonies in tune
39.
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
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Major second
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In Western music theory, a major second is a second spanning two semitones. A second is an interval encompassing two adjacent staff positions. For example, the interval from C to D is a major second, diminished, minor and augmented seconds are notated on adjacent staff positions as well, but consist of a different number of semitones. The major second is the interval that occurs between the first and second degrees of a scale, the tonic and the supertonic. On a musical keyboard, a second is the interval between two keys separated by one key, counting white and black keys alike. On a guitar string, it is the interval separated by two frets, in moveable-do solfège, it is the interval between do and re. It is considered a step, as opposed to larger intervals called skips. Intervals composed of two semitones, such as the second and the diminished third, are also called tones, whole tones. One source says step is chiefly US. The preferred usage has been argued since the 19th century, Mr. M. in teaching the Diatonic scale calls a tone a step, and a semitone a half step, now, who ever heard of a step in music, or in sound. The largest ones are called major tones or greater tones, the smallest are called minor tones or lesser tones and their size differs by exactly one syntonic comma. Some equal temperaments, such as 15-ET and 22-ET, also distinguish between a greater and a lesser tone, the major second was historically considered one of the most dissonant intervals of the diatonic scale, although much 20th-century music saw it reimagined as a consonance. It is common in different musical systems, including Arabic music, Turkish music and music of the Balkans. It occurs in both diatonic and pentatonic scales, listen to a major second in equal temperament. Here, middle C is followed by D, which is a tone 200 cents sharper than C, the difference in size between a major tone and a minor tone is equal to one syntonic comma. The major tone is the 9,8 interval play, and it is an approximation thereof in other tuning systems, the major tone may be derived from the harmonic series as the interval between the eighth and ninth harmonics. The minor tone may be derived from the series as the interval between the ninth and tenth harmonics. The 10,9 minor tone arises in the C major scale between D and e and G and A, and is a sharper dissonance than 9,8
41.
53 equal temperament
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In music,53 equal temperament, called 53-TET, 53-EDO, or 53-ET, is the tempered scale derived by dividing the octave into 53 equal steps. Play Each step represents a ratio of 21/53, or 22.6415 cents. 53-TET is a tuning of equal temperament in which the tempered fifth is 701.89 cents wide. Theoretical interest in this division goes back to antiquity, ching Fang, a Chinese music theorist, observed that a series of 53 just fifths is very nearly equal to 31 octaves. He calculated this difference with six-digit accuracy to be 177147 /176776, later the same observation was made by the mathematician and music theorist Nicholas Mercator, who calculated this value precisely as, which is known as Mercators comma. Mercators comma is of small value to begin with, but 53 equal temperament flattens each fifth by only 1/53 of that comma. Thus,53 equal temperament is for all practical purposes equivalent to an extended Pythagorean tuning and this property of 53-TET may have been known earlier, Isaac Newtons unpublished manuscripts suggest that he had been aware of it as early as 1664–65. Because a distance of 31 steps in this scale is almost precisely equal to a just perfect fifth, however, 53-TET contains additional intervals that are very close to just intonation. For instance, the interval of 17 steps is also a major third, 53-TET is very good as an approximation to any interval in 5-limit just intonation. The matches to the just intervals involving the 7th harmonic are slightly less close, the 11th harmonic and intervals involving it are less closely matched, as illustrated with the undecimal neutral seconds and thirds in the table below. The 53-ET tuning equates to the unison, or tempers out, the intervals 32805/32768, known as the schisma, because it tempers these out, 53-ET can be used for both schismatic temperament, tempering out the schisma, and Hanson temperament, tempering out the kleisma. The interval of 7/4 is 4.8 cents sharp in 53-ET, and using it for 7-limit harmony means that the septimal kleisma, attempting to use standard notation, seven letter notes plus sharps or flats, can quickly become confusing. This is unlike the case with 19-ET and 31-ET where there is little ambiguity, by not being meantone, it adds some problems that require more attention. Specifically, the third is different from a ditone, two tones, each of which is two fifths minus an octave. Likewise, the third is different from a semiditone. The fact that the comma is not tempered out means that notes. Instead, the triads are chords like C-F♭-G, where the major third is a diminished fourth. Likewise, the triads are chords like C-D♯-G
42.
Pythagorean tuning
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Pythagorean tuning is a tuning of the syntonic temperament in which the generator is the ratio 3,2, which is 702 cents wide. Hence, it is a system of tuning in which the frequency ratios of all intervals are based on the ratio 3,2. This ratio, also known as the perfect fifth, is chosen because it is one of the most consonant and easiest to tune by ear. As Novalis put it, The musical proportions seem to me to be particularly correct natural proportions, the so-called Pythagorean tuning was used by musicians up to the beginning of the 16th century. The Pythagorean system would appear to be ideal because of the purity of the fifths, Pythagorean tuning is based on a stack of intervals called perfect fifths, each tuned in the ratio 3,2, the next simplest ratio after 2,1. Since notes differing in frequency by a factor of 2 are given the same name, the purpose of this adjustment is to move the 12 notes within a smaller range of frequency, namely within the interval between the base note D and the D above it. This interval is called the basic octave. For instance, the A is tuned such that its frequency equals 3,2 times the frequency of D—if D is tuned to a frequency of 288 Hz, then A is tuned to 432 Hz. Similarly, the E above A is tuned such that its frequency equals 3,2 times the frequency of A, or 9,4 times the frequency of D—with A at 432 Hz, this puts E at 648 Hz. Since this E is outside the basic octave, it is usual to halve its frequency to move it within the basic octave. Therefore, E is tuned to 324 Hz, a 9,8 above D, the B at 3,2 above that E is tuned to the ratio 27,16 and so on. This frequency is doubled to bring it into the basic octave. When extending this tuning however, a problem arises, no stack of 3,2 intervals will fit exactly into any stack of 2,1 intervals. For instance a stack such as this, obtained by adding one note to the stack shown above A♭–E♭–B♭–F–C–G–D–A–E–B–F♯–C♯–G♯ will be similar. More exactly, it will be about a quarter of a semitone larger, thus, A♭ and G♯, when brought into the basic octave, will not coincide as expected. This discrepancy, of about 23.46 cents, or nearly one quarter of a semitone, is known as a Pythagorean comma, to get around this problem, Pythagorean tuning constructs only twelve notes as above, with eleven fifths between them. For example, one may use only the 12 notes from E♭ to G♯. This, as shown above, the remaining interval is left badly out-of-tune, meaning that any music which combines those two notes is unplayable in this tuning. A very out-of-tune interval such as one is known as a wolf interval
43.
Meantone temperament
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Meantone temperament is a musical temperament, which is a system of musical tuning. Quarter-comma meantone is the best known type of meantone temperament, Meantone can receive the following equivalent definitions, The meantone is the mean between the major whole tone and the minor whole tone, i. e. the geometric mean of 9,8 and 10,9. The meantone is the mean of the just major third, i. e. the square root of 5,4, all meantone temperaments are linear temperaments, distinguished by the width of its generator in cents, as shown in the central column of Figure 1. Historically notable meantone temperaments, discussed below, occupy a portion of this tuning continuum. In Figure 1, the tuning ranges of 5-limit, 7-limit, and 11-limit tunings are shown. This last ratio was termed R by American composer, pianist and theoretician Easley Blackwood, if we multiply by 1200, we have the size of fifth in cents. In these terms, some historically notable meantone tunings are listed below, the relationship between the first two columns is exact, while that between them and the third is closely approximate. Equal temperaments useful as meantone tunings include 19-ET, 50-ET, 31-ET, 43-ET, the farther the tuning gets away from quarter-comma meantone, however, the less related the tuning is to harmonic timbres, which can be overcome by tempering the timbre to match the tuning. A whole number of just perfect fifths will never add up to a number of octaves. If a stacked-up whole number of perfect fifths is to close with the octave, then one of the fifths must have a different width than all of the others. For example, to make the 12-note chromatic scale in Pythagorean tuning close at the octave, one fifth must be out of tune by the Pythagorean comma, wolf intervals are an artifact of keyboard design. This can be shown most easily using a keyboard, such as that shown in Figure 2. On an isomorphic keyboard, any musical interval has the same shape wherever it appears. On the keyboard shown in Figure 2, from any given note, there are no wolf intervals within the note-span of this keyboard. The problem is at the edge, on the note E♯, the note thats a perfect fifth higher than E♯ is B♯, which is not included on the keyboard shown. Because there is no B♯ button, when playing an E♯ power chord, one must choose some other note, such as C, even edge conditions produce wolf intervals only if the isomorphic keyboard has fewer buttons per octave than the tuning has enharmonically-distinct notes. When the perfect fifth is exactly 700 cents wide then the tuning is identical to the familiar 12-tone equal temperament and this appears in the table above when R =2,1. Because of the forced on meantone tunings by the one-dimensional piano-style keyboard, well temperaments
44.
19 equal temperament
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In music,19 equal temperament, called 19-TET, 19-EDO, or 19-ET, is the tempered scale derived by dividing the octave into 19 equal steps. Each step represents a ratio of 19√2, or 63.16 cents. 19-edo is the tuning of the temperament in which the tempered perfect fifth is equal to 694.737 cents. Division of the octave into 19 equal-width steps arose naturally out of Renaissance music theory, the greater diesis, the ratio of four minor thirds to an octave was almost exactly a nineteenth of an octave. Interest in such a system goes back to the 16th century. Costeley understood and desired the circulating aspect of this tuning, in 1577, music theorist Francisco de Salinas in effect proposed it. Salinas discussed 1⁄3-comma meantone, in which the fifth is of size 694.786 cents, the fifth of 19-edo is 694.737, which is less than a twentieth of a cent narrower, imperceptible and less than tuning error. Salinas suggested tuning nineteen tones to the octave to this tuning, in the 19th century, mathematician and music theorist Wesley Woolhouse proposed it as a more practical alternative to meantone temperaments he regarded as better, such as 50-edo. The composer Joel Mandelbaum wrote his Ph. D. thesis on the properties of the 19-edo tuning, Mandelbaum and Joseph Yasser have written music with 19-edo. Easley Blackwood has stated that 19-edo makes possible a substantial enrichment of the tonal repertoire, here are the sizes of some common intervals and comparison with the ratios arising in the harmonic series, the difference column measures in cents the distance from an exact fit to these ratios. For reference, the difference from the fifth in the widely used 12 equal temperament is 1.955 cents. Beta scale Elaine Walker Levy, Kenneth J. Costeleys Chromatic Chanson, Annales Musicologues, Moyen-Age et Renaissance, Tome III, howe, Hubert S. Jr. 19-Tone Theory and Applications, Aaron Copland School of Music at Queens College. Sethares, William A. Tunings for 19 Tone Equal Tempered Guitar, Experimental Musical Instruments, Vol. VI, hair, Bailey, Morrison, Pearson and Parncutt, Rehearsing Microtonal Music, Grappling with Performance and Intonational Problems, Microtonalism. ZiaSpace. com - 19tet downloadable mp3s by Elaine Walker of Zia, the Music of Jeff Harrington, Parnasse. com. Jeff Harrington is a composer who has several pieces for piano in the 19-TET tuning. Chris Vaisvil, GR-20 Hexaphonic 19-ET Guitar Improvisation Arto Juhani Heino, Artone 19 Guitar Design, naming the 19 note scale Parvatic
45.
31 equal temperament
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In music,31 equal temperament, 31-ET, which can also be abbreviated 31-TET, 31-EDO, also known as tricesimoprimal, is the tempered scale derived by dividing the octave into 31 equal-sized steps. Play Each step represents a ratio of 31√2, or 38.71 cents. 31-ET is a good approximation of quarter-comma meantone temperament. More generally, it is a diatonic tuning in which the tempered perfect fifth is equal to 696.77 cents. In 1666, Lemme Rossi first proposed an equal temperament of this order, shortly thereafter, having discovered it independently, scientist Christiaan Huygens wrote about it also. Huygens not only realized this, he went farther and noted that 31-ET provides an excellent approximation of septimal, the composer Joel Mandelbaum used this tuning system specifically because of its good matches to the 7th and 11th partials in the harmonic series. The tuning has poor matches to both the 9,8 and 10,9 intervals, however, it has a match for the average of the two. Practically it is close to quarter-comma meantone. This tuning can be considered a meantone temperament, many chords of 31-ET are discussed in the article on septimal meantone temperament. Chords not discussed there include the neutral thirds triad, which might be written C–E–G, C–D–G or C–F–G, and the Orwell tetrad, usual chords like the major chord is rendered nicely in 31-ET because the third and the fifth are very well approximated. Also, it is possible to play chords and supermajor chords. It is also possible to render nicely the harmonic seventh chord, for example on C with C–E–G–A♯. The seventh here is different from stacking a fifth and a minor third and this difference cannot be made in 12-ET
Play (help·info)). A second is a musical interval encompassing two adjacent staff positions (see Interval number for more details). For example, the interval from C to D is a major second, as the note D lies two semitones above C, and the two notes are notated on adjacent staff positions. Diminished, minor and augmented seconds are notated on adjacent staff positions as well, but consist of a different number of semitones (zero, one, and three).
