1.
Octave
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In music, an octave or perfect octave is the interval between one musical pitch and another with half or double its frequency. It is defined by ANSI as the unit of level when the base of the logarithm is two. The octave relationship is a phenomenon that has been referred to as the basic miracle of music. The most important musical scales are written using eight notes. For example, the C major scale is typically written C D E F G A B C, two notes separated by an octave have the same letter name and are of the same pitch class. Three commonly cited examples of melodies featuring the perfect octave as their opening interval are Singin in the Rain, Somewhere Over the Rainbow, the interval between the first and second harmonics of the harmonic series is an octave. The octave has occasionally referred to as a diapason. To emphasize that it is one of the intervals, the octave is designated P8. The octave above or below a note is sometimes abbreviated 8a or 8va, 8va bassa. For example, if one note has a frequency of 440 Hz, the note one octave above is at 880 Hz, the ratio of frequencies of two notes an octave apart is therefore 2,1. Further octaves of a note occur at 2n times the frequency of that note, such as 2,4,8,16, etc. and the reciprocal of that series. For example,55 Hz and 440 Hz are one and two away from 110 Hz because they are 1⁄2 and 4 times the frequency, respectively. After the unison, the octave is the simplest interval in music, the human ear tends to hear both notes as being essentially the same, due to closely related harmonics. Notes separated by a ring together, adding a pleasing sound to music. For this reason, notes an octave apart are given the note name in the Western system of music notation—the name of a note an octave above A is also A. The conceptualization of pitch as having two dimensions, pitch height and pitch class, inherently include octave circularity, thus all C♯s, or all 1s, in any octave are part of the same pitch class. Octave equivalency is a part of most advanced cultures, but is far from universal in primitive. The languages in which the oldest extant written documents on tuning are written, leon Crickmore recently proposed that The octave may not have been thought of as a unit in its own right, but rather by analogy like the first day of a new seven-day week
2.
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
3.
Prime limit
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In music theory, limit or harmonic limit is a way of characterizing the harmony found in a piece or genre of music, or the harmonies that can be made using a particular scale. The term limit was introduced by Harry Partch, who used it to give an upper bound on the complexity of harmony, roughly speaking, the larger the limit number, the more harmonically complex and potentially dissonant will the intervals of the tuning be perceived. A scale belonging to a prime limit has a distinctive hue that makes it aurally distinguishable from scales with other limits. Harry Partch, Ivor Darreg, and Ralph David Hill are among the many microtonalists to suggest that music has been slowly evolving to employ higher and higher harmonics in its constructs, in medieval music, only chords made of octaves and perfect fifths were considered consonant. In the West, triadic harmony arose around the time of the Renaissance, the major and minor thirds of these triads invoke relationships among the first 5 harmonics. Around the turn of the 20th century, tetrads debuted as fundamental building blocks in African-American music, in conventional music theory pedagogy, these seventh chords are usually explained as chains of major and minor thirds. However, they can also be explained as coming directly from harmonics greater than 5, for example, the dominant 7th chord in 12-ET approximates 4,5,6,7, while the major 7th chord approximates 8,10,12,15. In just intonation, intervals between pitches are drawn from the rational numbers, since Partch, two distinct formulations of the limit concept have emerged, odd limit and prime limit. Odd limit and prime limit n do not include the same even when n is an odd prime. For a positive odd number n, the n-odd-limit contains all rational numbers such that the largest odd number that divides either the numerator or denominator is not greater than n. In Genesis of a Music, Harry Partch considered just intonation rationals according to the size of their numerators and denominators, since octaves correspond to factors of 2, the complexity of any interval may be measured simply by the largest odd factor in its ratio. Partchs theoretical prediction of the dissonance of intervals are very similar to those of theorists including Hermann von Helmholtz, William Sethares. An identity is each of the odd numbers below and including the limit in a tuning, for example, the identities included in 5-limit tuning are 1,3, and 5. The number 9, though not a prime, is nevertheless an identity in music, simply because it is an odd number. Partch defines identity as one of the correlatives, major or minor, in a tonality, one of the odd-number ingredients, odentity and udentity are, short for Over-Identity, and, Under-Identity, respectively. An udentity is an identity of an utonality, for a prime number n, the n-prime-limit contains all rational numbers that can be factored using primes no greater than n. In other words, it is the set of rationals with numerator and denominator both n-smooth, given a prime number p, the subset of Q + consisting of those rational numbers x whose prime factorization has the form x = p 1 α1 p 2 α2. P r ≤ p forms a subgroup of and we say that a scale or system of tuning uses p-limit tuning if all interval ratios between pitches lie in this subgroup
4.
Musical temperament
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In musical tuning, a temperament is a tuning system that slightly compromises the pure intervals of just intonation to meet other requirements. Most modern Western musical instruments are tuned in the equal temperament system, tempering is the process of altering the size of an interval by making it narrower or wider than pure. The development of well temperament allowed fixed-pitch instruments to play well in all of the keys. The famous Well-Tempered Clavier by Johann Sebastian Bach takes full advantage of this breakthrough, however, while unpleasant intervals were avoided, the sizes of intervals were still not consistent between keys, and so each key still had its own character. In just intonation, every interval between two pitches corresponds to a whole number ratio between their frequencies, allowing intervals varying from the highest consonance to highly dissonant, for instance,660 Hz /440 Hz constitutes a fifth, and 880 Hz /440 Hz an octave. Such intervals have a stability, or purity to their sound, if, for example, two sound signals with frequencies that vary just by 0. When a musical instrument with harmonic overtones is played, the ear hears a composite waveform that includes a fundamental frequency, the waveform of such a tone is characterized by a shape that is complex compared to a simple waveform, but remains periodic. When two tones depart from exact integer ratios, the shape waveform becomes erratic—a phenomenon that may be described as destabilization, as the composite waveform becomes more erratic, the consonance of the interval also changes. Tempering an interval involves the use of such minor adjustments to enable musical possibilities that are impractical using just intonation. Before Meantone temperament became widely used in the Renaissance, the most commonly used tuning system was Pythagorean tuning, Pythagorean tuning was a system of just intonation that tuned every note in a scale from a progression of pure perfect fifths. This was quite suitable for much of the practice until then. The major third of Pythagorean tuning differed from a just major third by an amount known as syntonic comma, with the correct amount of tempering, the syntonic comma is removed from its major thirds, making them just. This compromise, however, leaves all fifths in this system with a slight beating. Pythagorean tuning also had a problem, which meantone temperament does not solve, which is the problem of modulation. A series of 12 just fifths as in Pythagorean tuning does not return to the pitch, but rather differs by a Pythagorean comma. In meantone temperament, this effect is more pronounced. The use of 53 equal temperament provides a solution for the Pythagorean tuning, when building an instrument, this can be very impractical. Well temperament is the given to a variety of different systems of temperament that were employed to solve this problem, in which some keys are more in tune than others
5.
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
6.
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
7.
Frequency
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Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as frequency, which emphasizes the contrast to spatial frequency. The period is the duration of time of one cycle in a repeating event, for example, if a newborn babys heart beats at a frequency of 120 times a minute, its period—the time interval between beats—is half a second. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as vibrations, audio signals, radio waves. For cyclical processes, such as rotation, oscillations, or waves, in physics and engineering disciplines, such as optics, acoustics, and radio, frequency is usually denoted by a Latin letter f or by the Greek letter ν or ν. For a simple motion, the relation between the frequency and the period T is given by f =1 T. The SI unit of frequency is the hertz, named after the German physicist Heinrich Hertz, a previous name for this unit was cycles per second. The SI unit for period is the second, a traditional unit of measure used with rotating mechanical devices is revolutions per minute, abbreviated r/min or rpm. As a matter of convenience, longer and slower waves, such as ocean surface waves, short and fast waves, like audio and radio, are usually described by their frequency instead of period. Spatial frequency is analogous to temporal frequency, but the axis is replaced by one or more spatial displacement axes. Y = sin = sin d θ d x = k Wavenumber, in the case of more than one spatial dimension, wavenumber is a vector quantity. For periodic waves in nondispersive media, frequency has a relationship to the wavelength. Even in dispersive media, the frequency f of a wave is equal to the phase velocity v of the wave divided by the wavelength λ of the wave. In the special case of electromagnetic waves moving through a vacuum, then v = c, where c is the speed of light in a vacuum, and this expression becomes, f = c λ. When waves from a monochrome source travel from one medium to another, their remains the same—only their wavelength. For example, if 71 events occur within 15 seconds the frequency is, the latter method introduces a random error into the count of between zero and one count, so on average half a count. This is called gating error and causes an error in the calculated frequency of Δf = 1/, or a fractional error of Δf / f = 1/ where Tm is the timing interval. This error decreases with frequency, so it is a problem at low frequencies where the number of counts N is small, an older method of measuring the frequency of rotating or vibrating objects is to use a stroboscope
8.
Pitch (music)
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Pitch can be determined only in sounds that have a frequency that is clear and stable enough to distinguish from noise. Pitch is a major attribute of musical tones, along with duration, loudness. Pitch may be quantified as a frequency, but pitch is not a purely objective physical property, Pitch is an auditory sensation in which a listener assigns musical tones to relative positions on a musical scale based primarily on their perception of the frequency of vibration. Pitch is closely related to frequency, but the two are not equivalent, frequency is an objective, scientific attribute that can be measured. Pitch is each persons subjective perception of a wave, which cannot be directly measured. However, this not necessarily mean that most people wont agree on which notes are higher and lower. Sound waves themselves do not have pitch, but their oscillations can be measured to obtain a frequency and it takes a sentient mind to map the internal quality of pitch. However, pitches are usually associated with, and thus quantified as frequencies in cycles per second, or hertz, by comparing sounds with pure tones, Complex and aperiodic sound waves can often be assigned a pitch by this method. According to the American National Standards Institute, pitch is the attribute of sound according to which sounds can be ordered on a scale from low to high. That is, high pitch means very rapid oscillation, and low pitch corresponds to slower oscillation, despite that, the idiom relating vertical height to sound pitch is shared by most languages. At least in English, it is just one of many deep conceptual metaphors that involve up/down, the exact etymological history of the musical sense of high and low pitch is still unclear. There is evidence that humans do actually perceive that the source of a sound is slightly higher or lower in vertical space when the frequency is increased or reduced. The pitch of tones can be ambiguous, meaning that two or more different pitches can be perceived, depending upon the observer. In a situation like this, the percept at 200 Hz is commonly referred to as the missing fundamental, Pitch depends to a lesser degree on the sound pressure level of the tone, especially at frequencies below 1,000 Hz and above 2,000 Hz. The pitch of lower tones gets lower as sound pressure increases, for instance, a tone of 200 Hz that is very loud seems one semitone lower in pitch than if it is just barely audible. Above 2,000 Hz, the pitch gets higher as the sound gets louder, theories of pitch perception try to explain how the physical sound and specific physiology of the auditory system work together to yield the experience of pitch. In general, pitch perception theories can be divided into place coding, place theory holds that the perception of pitch is determined by the place of maximum excitation on the basilar membrane. However, a purely place-based theory cannot account for the accuracy of pitch perception in the low, temporal theories offer an alternative that appeals to the temporal structure of action potentials, mostly the phase-locking and mode-locking of action potentials to frequencies in a stimulus
9.
Logarithm
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In mathematics, the logarithm is the inverse operation to exponentiation. That means the logarithm of a number is the exponent to which another fixed number, in simple cases the logarithm counts factors in multiplication. For example, the base 10 logarithm of 1000 is 3, the logarithm of x to base b, denoted logb, is the unique real number y such that by = x. For example, log2 =6, as 64 =26, the logarithm to base 10 is called the common logarithm and has many applications in science and engineering. The natural logarithm has the e as its base, its use is widespread in mathematics and physics. The binary logarithm uses base 2 and is used in computer science. Logarithms were introduced by John Napier in the early 17th century as a means to simplify calculations and they were rapidly adopted by navigators, scientists, engineers, and others to perform computations more easily, using slide rules and logarithm tables. The present-day notion of logarithms comes from Leonhard Euler, who connected them to the function in the 18th century. Logarithmic scales reduce wide-ranging quantities to tiny scopes, for example, the decibel is a unit quantifying signal power log-ratios and amplitude log-ratios. In chemistry, pH is a measure for the acidity of an aqueous solution. Logarithms are commonplace in scientific formulae, and in measurements of the complexity of algorithms and they describe musical intervals, appear in formulas counting prime numbers, inform some models in psychophysics, and can aid in forensic accounting. In the same way as the logarithm reverses exponentiation, the logarithm is the inverse function of the exponential function applied to complex numbers. The discrete logarithm is another variant, it has uses in public-key cryptography, the idea of logarithms is to reverse the operation of exponentiation, that is, raising a number to a power. For example, the power of 2 is 8, because 8 is the product of three factors of 2,23 =2 ×2 ×2 =8. It follows that the logarithm of 8 with respect to base 2 is 3, the third power of some number b is the product of three factors equal to b. More generally, raising b to the power, where n is a natural number, is done by multiplying n factors equal to b. The n-th power of b is written bn, so that b n = b × b × ⋯ × b ⏟ n factors, exponentiation may be extended to by, where b is a positive number and the exponent y is any real number. For example, b−1 is the reciprocal of b, that is, the logarithm of a positive real number x with respect to base b, a positive real number not equal to 1, is the exponent by which b must be raised to yield x
10.
Classical music
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Classical music is art music produced or rooted in the traditions of Western music, including both liturgical and secular music. The central norms of this tradition became codified between 1550 and 1900, which is known as the common-practice period, Western staff notation is used by composers to indicate to the performer the pitches, tempo, meter and rhythms for a piece of music. This can leave less room for such as improvisation and ad libitum ornamentation. The term classical music did not appear until the early 19th century, the earliest reference to classical music recorded by the Oxford English Dictionary is from about 1836. This score typically determines details of rhythm, pitch, and, the written quality of the music has enabled a high level of complexity within them, J. S. The use of written notation also preserves a record of the works, Musical notation enables 2000s-era performers to sing a choral work from the 1300s Renaissance era or a 1700s Baroque concerto with many of the features of the music being reproduced. That said, the score does not provide complete and exact instructions on how to perform a historical work, even if the tempo is written with an Italian instruction, we do not know exactly how fast the piece should be played. Bach was particularly noted for his complex improvisations, during the Classical era, the composer-performer Mozart was noted for his ability to improvise melodies in different styles. During the Classical era, some virtuoso soloists would improvise the cadenza sections of a concerto, during the Romantic era, Beethoven would improvise at the piano. The instruments currently used in most classical music were largely invented before the mid-19th century and they consist of the instruments found in an orchestra or in a concert band, together with several other solo instruments. The symphony orchestra is the most widely known medium for music and includes members of the string, woodwind, brass. The concert band consists of members of the woodwind, brass and it generally has a larger variety and number of woodwind and brass instruments than the orchestra but does not have a string section. However, many bands use a double bass. Many of the used to perform medieval music still exist. Medieval instruments included the flute, the recorder and plucked string instruments like the lute. As well, early versions of the organ, fiddle, Medieval instruments in Europe had most commonly been used singly, often self accompanied with a drone note, or occasionally in parts. From at least as early as the 13th century through the 15th century there was a division of instruments into haut, during the earlier medieval period, the vocal music from the liturgical genre, predominantly Gregorian chant, was monophonic, using a single, unaccompanied vocal melody line. Polyphonic vocal genres, which used multiple independent vocal melodies, began to develop during the medieval era, becoming prevalent by the later 13th
11.
Logarithmic scale
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A logarithmic scale is a nonlinear scale used when there is a large range of quantities. Common uses include the strength, sound loudness, light intensity. It is based on orders of magnitude, rather than a linear scale. In particular our sense of hearing perceives equal ratios of frequencies as equal differences in pitch, the top left graph is linear in the X and Y axis, and the Y-axis ranges from 0 to 10. A base-10 log scale is used for the Y axis of the left graph. The top right graph uses a scale for just the X axis. A slide rule has logarithmic scales, and nomograms often employ logarithmic scales, the geometric mean of two numbers is midway between the numbers. Before the advent of graphics, logarithmic graph paper was a commonly used scientific tool. If both the vertical and horizontal axes of a plot are scaled logarithmically, the plot is referred to as a log–log plot, if only the ordinate or abscissa is scaled logarithmically, the plot is referred to as a semi-logarithmic plot. Bit Byte Decade John Napier Level Logarithm Logarithmic mean Preferred number Dehaene, Stanislas, Izard, Véronique, Spelke, Elizabeth, Pica, distinct intuitions of the number scale in Western and Amazonian indigene cultures. American Association for the Advancement of Science, why using logarithmic scale to display share prices
12.
A440 (pitch standard)
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A440 or A4, which has a frequency of 440 Hz, is the musical note A above middle C and serves as a general tuning standard for musical pitch. Prior to the standardization on 440 Hz, many countries and organizations followed the French standard since the 1860s of 435 Hz, which had also been the Austrian governments 1885 recommendation. Johann Heinrich Scheibler recommended A440 as a standard in 1834 after inventing the tonometer to measure pitch, the American music industry reached an informal standard of 440 Hz in 1926, and some began using it in instrument manufacturing. In 1936 the American Standards Association recommended that the A above middle C be tuned to 440 Hz and this standard was taken up by the International Organization for Standardization in 1955 as ISO16. It is designated A4 in scientific pitch notation because it occurs in the octave that starts with the fourth C key on a standard 88-key piano keyboard, A440 is widely used as concert pitch in the United Kingdom and the United States. In continental Europe the frequency of A4 commonly varies between 440 Hz and 444 Hz, in the period instrument movement, a consensus has arisen around a modern baroque pitch of 415 Hz, baroque for some special church music at 466 Hz, and classical pitch at 430 Hz. A440 is often used as a reference in just intonation regardless of the fundamental note or key. The US time and frequency station WWV broadcasts a 440 Hz signal at two minutes past every hour, with WWVH broadcasting the same tone at the first minute past every hour and this was added in 1936 to aid orchestras in tuning their instruments. History of pitch standards in Western music Concert pitch Pitch Electronic tuner A
13.
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
14.
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
15.
Arab tone system
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Each tone has its own name not repeated in different octaves, unlike systems featuring octave equivalency. The lowest tone is named yakah and is determined by the lowest pitch in the range of the singer, the next higher octave is nawa and the second tuti. By contrast, in the European equally tempered scale the octave is divided into equal divisions. A two octave range starting with yakah arbitrarily on the G below middle C is used, in practice far fewer than twenty-four tones are used in a single performance. The specific notes used in a piece will be part of one of more than seventy modes or maqam rows named after characteristic tones that are rarely the first tone, the rows are heptatonic and constructed from augmented, major, neutral, and minor seconds. Many different but similar ratios are proposed for the ratios of the tones of each row and performance practice. The current tone system is derived from the work of al-Farabi, who used a 25-tone unequal scale, and Mikhail Mishaqah who first presented the 24-tone equal-tempered division
16.
Western world
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The Western world or the West is a term usually referring to different nations, depending on the context, most often including at least part of Europe. There are many accepted definitions about what they all have in common, the Western world is also known as the Occident. The concept of the Western part of the earth has its roots in Greco-Roman civilization in Europe, before the Cold War era, the traditional Western viewpoint identified Western Civilization with the Western Christian countries and culture. Its political usage was changed by the antagonism during the Cold War in the mid-to-late 20th Century. The term originally had a literal geographic meaning, Western culture was influenced by many older great civilizations of the ancient Near East, such as Phoenicia, Minoan Crete, Sumer, Babylonia, and also Ancient Egypt. It originated in the Mediterranean basin and its vicinity, Greece, over time, their associated empires grew first to the east and west to include the rest of Mediterranean and Black Sea coastal areas, conquering and absorbing. Later, they expanded to the north of the Mediterranean Sea to include Western, Central, numerous times, this expansion was accompanied by Christian missionaries, who attempted to proselytize Christianity. There is debate among some as to whether Latin America is in a category of its own, specifically, Western culture may imply, a Biblical Christian cultural influence in spiritual thinking, customs and either ethic or moral traditions, around the Post-Classical Era and after. European cultural influences concerning artistic, musical, folkloric, ethic and oral traditions, the concept of Western culture is generally linked to the classical definition of the Western world. In this definition, Western culture is the set of literary, scientific, political, artistic, much of this set of traditions and knowledge is collected in the Western canon. The term has come to apply to countries whose history is marked by European immigration or settlement, such as the Americas, and Oceania. The geopolitical divisions in Europe that created a concept of East and West originated in the Roman Empire, Roman Catholic Western and Central Europe, as such, maintained a distinct identity particularly as it began to redevelop during the Renaissance. Even following the Protestant Reformation, Protestant Europe continued to see itself as more tied to Roman Catholic Europe than other parts of the civilized world. Use of the term West as a cultural and geopolitical term developed over the course of the Age of Exploration as Europe spread its culture to other parts of the world. Additionally, closer contacts between the West and Asia and other parts of the world in recent times have continued to cloud the use, herodotus considered the Persian Wars of the early 5th century BC a conflict of Europa versus Asia. The terms West and East were not used by any Greek author to describe that conflict, the Great Schism and the Fourth Crusade confirmed this deviation. The Renaissance in the West emerged partly from currents within the Roman Empire, Ancient Rome was a civilization that grew from a city-state founded on the Italian Peninsula about the 9th century BC to a massive empire straddling the Mediterranean Sea. In its 12-century existence, Roman civilization shifted from a monarchy, to a republic, nonetheless, despite its great legacy, a number of factors led to the eventual decline of the Roman Empire
17.
Pseudo-octave
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When used as a basis for an equal temperament, the pseudo-octave may also be called the interval of equivalence, the repeat ratio, and the nonoctave. The stretched octave, for example 2.01,1, sounds out of tune when played with true harmonic overtones, in piano tuning, stretched octaves are commonly encountered, where the inharmonicity caused by string thickness and tension makes it necessary to widen every interval very slightly. Another example is the play on clarinets of the Bohlen–Pierce scale. Stretched octaves are caused by the physics of standing waves in a stretched wire, the pitch of each overtone produced by a piano string is determined by the ratio of the strings restoring force, divided by its mass per unit length. In an ideal string, the only restoring force would be due to the tension in the string. In practice, piano strings are made from steel, which is stiff. Youngs modulus of the steel is what defines the stiffness. The stiffness adds an extra restoring force to each string, the amount of this extra force depends on the amount of bend being induced in the string, higher normal modes bend the string more, inducing more stiffness-related force and sharpening the pitch of the resulting overtone. Electronic tuner Mel scale Octave Types, BillBremmer. com
18.
Wind instrument
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The pitch of the vibration is determined by the length of the tube and by manual modifications of the effective length of the vibrating column of air. In the case of wind instruments, sound is produced by blowing through a reed. Using different air columns for different tones, such as in the pan flute and this method is used on nearly all brass instruments. Changing the length of the air column by lengthening and/or shortening the tube using a sliding mechanism. This method is used on the trombone and the slide whistle, changing the frequency of vibration through opening or closing holes in the side of the tube. This can be done by covering the holes with fingers or pressing a key which then closes the hole and this method is used in nearly all woodwind instruments. Making the column of air vibrate at different harmonics without changing the length of the column of air, almost all wind instruments use the last method, often in combination with one of the others, to extend their register. A more accurate way to determine whether an instrument is brass or woodwind is to examine how the player produces sound, in brass instruments, the players lips vibrate, causing the air within the instrument to vibrate. For example, the saxophone is typically made of brass, but is classified as an instrument because it produces sound with a vibrating reed. In the Hornbostel-Sachs scheme of musical instrument classification, wind instruments are classed as aerophones, sound production in all wind instruments depends on the entry of air into a flow-control valve attached to a resonant chamber. The resonator is typically a long cylindrical or conical tube, open at the far end, a pulse of high pressure from the valve will travel down the tube at the speed of sound. It will be reflected from the end as a return pulse of low pressure. Under suitable conditions, the valve will reflect the pulse back, with increased energy, Reed instruments such as the clarinet or oboe have a flexible reed or reeds at the mouthpiece, forming a pressure-controlled valve. Standing waves inside the tube will be odd multiples of a quarter-wavelength, with a pressure anti-node at the mouthpiece, the reed vibrates at a rate determined by the resonator. For Lip Reed instruments, the controls the tension in their lips so that they vibrate under the influence of the air flow through them. They adjust the vibration so that the lips are most closed, and the air flow is lowest, standing waves inside the tube will be odd multiples of a quarter-wavelength, with a pressure anti-node at the mouthpiece, and a pressure node at the open end. For Air Reed instruments, the thin grazing air sheet flowing across an opening in the pipe interacts with an edge to generate sound. The jet is generated by the player, when blowing through a thin slit, for recorders and flue organ pipes this slit is manufactured by the instrument maker and has a fixed geometry
19.
Keyboard instrument
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A keyboard instrument is a musical instrument played using a keyboard. The most common of these are the piano, organ, and various keyboards, including synthesizers. Other keyboard instruments include celestas, which are struck idiophones operated by a keyboard, and carillons, today, the term keyboard often refers to keyboard-style synthesizers. Another important use of the keyboard is in historical musicology. Particularly in the 18th century, the harpsichord, the clavichord, and the piano were in competition. Hence in a phrase like Mozart excelled as a player the word keyboard is usefully noncommittal. The earliest known keyboard instrument was the Ancient Greek hydraulis, a type of pipe organ, the keys were likely balanced and could be played with a light touch, as is clear from the reference in a Latin poem by Claudian, who says magna levi detrudens murmura tactu. Intent, that is “let him thunder forth as he presses out mighty roarings with a light touch”, from its invention until the fourteenth century, the organ remained the only keyboard instrument. Often, the organ did not feature a keyboard at all, almost every keyboard until the fifteenth century had seven naturals to each octave. The clavichord and the harpsichord appeared during the 14th century—the clavichord probably being earlier, the harpsichord and clavichord were both common until widespread adoption of the piano in the 18th century, after which their popularity decreased. The piano was revolutionary, because a pianist could vary the volume of the sound by varying the vigor with which each key was struck. The pianos full name is gravicèmbalo con piano e forte meaning harpsichord with soft and loud but can be shortened to piano-forte, which means soft-loud in Italian. In its current form, the piano is a product of the late 19th century, in fact, the modern piano is significantly different from even the 19th-century pianos used by Liszt, Chopin, and Brahms. See Piano history and musical performance, keyboard instruments were further developed in the early twentieth century. Early electromechanical instruments, such as the Ondes Martenot, appeared early in the century and this was a very important contribution to the keyboards history. Much effort has gone into creating an instrument that sounds like the piano but lacks its size, the electric piano and electronic piano were early efforts that, while useful instruments in their own right, did not convincingly reproduce the timbre of the piano. Electric and electronic organs were developed during the same period, more recent electronic keyboard designs strive to emulate the sound of specific make and model pianos using digital samples and computer models. Concerns celebrated keyboard players and the various instruments used over the centuries
20.
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
21.
Trombone
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The trombone is a musical instrument in the brass family. Like all brass instruments, sound is produced when the players vibrating lips cause the air column inside the instrument to vibrate, nearly all trombones have a telescoping slide mechanism that varies the length of the instrument to change the pitch. Many modern trombone models also utilize a rotary valve as a means to lower pitch of the instrument, variants such as the valve trombone and superbone have three valves like those on the trumpet. The word trombone derives from Italian tromba and -one, so the name means large trumpet, the trombone has a predominantly cylindrical bore like its valved counterpart the baritone and in contrast to its conical valved counterparts, the euphonium and the horn. The most frequently encountered trombones are the trombone and bass trombone. The most common variant, the tenor, is an instrument pitched in B♭, an octave below the B♭ trumpet. A person who plays the trombone is called a trombonist or trombone player, the trombone is a predominantly cylindrical tube bent into an elongated S shape. Rather than being completely cylindrical from end to end, the tube is a series of tapers with the smallest at the mouthpiece receiver. The design of these affects the intonation of the instrument. As with other instruments, sound is produced by blowing air through pursed lips producing a vibration that creates a standing wave in the instrument. The detachable cup-shaped mouthpiece is similar to that of the baritone horn and it has the venturi, a small constriction of the air column that adds resistance greatly affecting the tone of the instrument, and is inserted into the mouthpiece receiver in the slide section. The slide section consists of a leadpipe, the inner and outer tubes. Modern stays are soldered, while sackbuts were made with loose, the slide, the most distinctive feature of the trombone, allows the player to extend the length of the air column, lowering the pitch. To prevent friction from slowing the action of the slide, additional sleeves were developed during the Renaissance, and this part of the slide must be lubricated frequently. Additional tubing connects the slide to the bell of the instrument through a neckpipe, for example, second position A is not in exactly the same place on the slide as second position E. Many types of trombone also include one or more rotary valves used to increase the length of the instrument by directing the air flow through additional tubing. This allows the instrument to reach notes that are not possible without the valve as well as play other notes in alternate positions. Like the trumpet, the trombone is considered a cylindrical bore instrument since it has sections of tubing, principally in the slide section
22.
Zhu Zaiyu
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Zhu Zaiyu was a prince of the Ming dynasty of China. In 1584, Prince Zhu innovatively described the equal temperament via accurate mathematical calculation, Zhu was born in Qinyang, Henan Province to an aristocratic family, the sixth-generation descendant of the Hongxi Emperor, the fourth emperor of the Ming Dynasty. Zhu inherited the title the Prince of Zheng in 1593, on the emperors order, he was granted a new princely title in 1606, the year he delivered a set of ten musicological treatises to the court, establishing his scholarly merit. His posthumous name was 鄭端靖世子 Zhu wrote on music theory and temperament, music history, dance and dance music, three music theory works in particular are associated with the ideas of equal temperament, the「律學新說」, 「律呂精義」, and 「算學新說」. His work has described as the crowning achievement of two millennia of acoustical experiment and research and he is described as one of the most important historians of his nations music. Zhang Heng Book of Songs Jing Fang Shen Kuo Equal temperament Shí-èr-lǜ Chinese mathematics Chinese musicology
23.
Simon Stevin
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Simon Stevin, sometimes called Stevinus, was a Flemish/Dutch/Netherlandish mathematician, physicist and engineer. He was active in a great areas of science and engineering. Very little is known with certainty about Stevins life and what we know is mostly inferred from other recorded facts, the exact birth date and the date and place of his death are uncertain. It is assumed he was born in Bruges since he enrolled at Leiden University under the name Simon Stevinus Brugensis and his name is usually written as Stevin, but some documents regarding his father use the spelling Stevijn. This is a normal spelling shift in 16th century Dutch and he was born around the year 1548 to unmarried parents, Anthonis Stevin and Catelyne van der Poort. His father is believed to have been a son of a mayor of Veurne. While Simons father was not mentioned in the book of burghers, many other Stevins were later mentioned in the Poorterboeken. Simon Stevins mother Cathelijne was the daughter of a family from Ypres. Her father Hubert was a poorter of Bruges, Simons mother Cathelijne later married Joost Sayon who was involved in the carpet and silk trade and a member of the schuttersgilde Sint-Sebastiaan. Through her marriage Cathelijne became a member of a family of Calvinists and it is believed that Stevin grew up in a relatively affluent environment and enjoyed a good education. He was likely educated at a Latin school in his hometown, Stevin left Bruges in 1571 apparently without a particular destination. Stevin was most likely a Calvinist since a Catholic would likely not have risen to the position of trust he later occupied with Maurice, Prince of Orange and it is assumed that he left Bruges to escape the religious persecution of Protestants by the Spanish rulers. Based on references in his work Wisconstighe Ghedaechtenissen, it has been inferred that he must have moved first to Antwerp where he began his career as a merchants clerk. Some biographers mention that he travelled to Prussia, Poland, Denmark, Norway and Sweden and other parts of Northern Europe and it is possible that he completed these travels over a longer period of time. In 1577 Simon Stevin returned to Bruges and was appointed city clerk by the aldermen of Bruges and he worked in the office of Jan de Brune of the Brugse Vrije, the castellany of Bruges. Why he had returned to Bruges in 1577 is not clear and it may have been related to the political events of that period. Bruges was the scene of religious conflict. Catholics and Calvinists alternately controlled the government of the city and they usually opposed each other but would occasionally collaborate in order to counteract the dictates of King Philip II of Spain
24.
Northern and Southern dynasties
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The Northern and Southern dynasties was a period in the history of China that lasted from 420 to 589, following the tumultuous era of the Sixteen Kingdoms and the Wu Hu states. It is sometimes considered as the part of a longer period known as the Six Dynasties. Though an age of war and political chaos, it was also a time of flourishing arts and culture, advancement in technology. The period saw large-scale migration of Han Chinese to the south of the Yangtze. The period came to an end with the unification of all of China proper by Emperor Wen of the Sui Dynasty, during this period, the process of sinicization accelerated among the non-Chinese arrivals in the north and among the indigenous people in the south. Notable technological advances occurred during this period, the invention of the stirrup during the earlier Jin dynasty helped spur the development of heavy cavalry as a combat standard. Historians also note advances in medicine, astronomy, mathematics, intellectuals of the period include the mathematician and astronomer Zu Chongzhi. After the collapse of a united China under the Han dynasty in 220 due in part to the Yellow Turban. Of these, Cao Wei was the strongest, followed by Eastern Wu and Shu Han, after a 249 coup by Sima Yi, the Sima family essentially controlled Cao Wei and the conquest of Shu by Wei rapidly followed. Following a failed coup by the ruling Cao family against the Sima family, Sima Yan then founded the Jin Dynasty as Emperor Wu of Jin and the conquest of Wu by Jin occurred in 280, ending the Three Kingdoms period and reuniting China. The Jin dynasty was weakened after the War of the Eight Princes from 291-306. During the reigns of Emperor Huai and Emperor Min, the country was put into danger with the uprising of the northern non-Han people collectively known as the Five Barbarians. Invading non-Han armies almost destroyed the dynasty in the Disaster of Yongjia of 311, changan met a similar fate in 316. However, a scion of the house, Sima Rui, Prince of Langya, fled south of the Huai River to salvage what was left in order to sustain the empire. In the north, the Five Barbarians established numerous kingdoms, leading to the period being known as the Sixteen Kingdoms, eventually, the Northern Wei conquered the rest of the northern states in 386. The designation of specific households for military service in the system eventually led to a falling out in their social status. Faced with shortage of numbers, Jin generals were often sent on campaigns to capture non-Chinese people in the south in order to draft them into the military. The Northern dynasties began in 439 when the Northern Wei conquered the Northern Liang to unite northern China and it can be divided into three time periods, Northern Wei, Eastern and Western Weis, Northern Qi and Northern Zhou
25.
Music of China
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Music of China refers to the music of the Chinese people, which may be the music of the Han Chinese as well as other ethnic minorities within mainland China. It also includes music produced by people of Chinese origin in some territories outside mainland China using traditional Chinese instruments or in the Chinese language and it covers a highly diverse range of music from the traditional to the modern. These further developed into forms of music through succeeding dynasties. Chinese music continues to evolve in the times, and more contemporary forms have also emerged. A twelve-tone musical system was created based on the pitches of the pipes, and the first of these pipes produced the yellow bell pitch. Archaeological evidence indicates that music culture developed in China from an early period. During the Zhou Dynasty, a system of court and ceremonial music later termed yayue was established. The word dance similarly also refers to music, and every dance would have have a piece of associated with it. The most important set of music of the period was the Six-dynasty Music Dance performed in rituals in the royal court, correct music according to Zhou concept would involve instruments correlating to the five elements of nature and would bring harmony to nature. Around or before the 7th century BC, a system of pitch generation, Chinese philosophers took varying approaches to music. Some popular forms of music, however, were considered corrupting in the Confucian view, mozi on the other hand condemned music, and argued in Against Music that music is an extravagance and indulgence that serves no useful purpose and may be harmful. According to Mencius, a powerful ruler once asked him whether it was if he preferred popular music to the classics. The answer was that it mattered that the ruler loved his subjects. In ancient China the social status of musicians was much lower than that of painters, though music was seen as central to the harmony, almost every emperor took folk songs seriously, sending officers to collect songs to record the popular culture. One of the Confucianist Classics, Shi Jing 詩經, contained many folk songs dating from 800 BC to about 400 BC, in subsequent dynasties, the development of Chinese music was strongly influenced by the musical traditions of Central Asia. The oldest extant written Chinese music is Youlan or the Solitary Orchid, composed during the 6th or 7th century, but has also been attributed to Confucius. The first major well-documented flowering of Chinese music was for the qin during the Tang Dynasty, through succeeding dynasties over thousands of years, Chinese musicians developed a large assortment of different instruments and playing styles. A wide variety of instruments, such as guzheng and dizi are indigenous, although many popular traditional musical instruments were introduced from Central Asia, such as the erhu
26.
Ming dynasty
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The Ming dynasty was the ruling dynasty of China – then known as the Empire of the Great Ming – for 276 years following the collapse of the Mongol-led Yuan dynasty. The Ming, described by some as one of the greatest eras of orderly government, although the primary capital of Beijing fell in 1644 to a rebellion led by Li Zicheng, regimes loyal to the Ming throne – collectively called the Southern Ming – survived until 1683. He rewarded his supporters and employed them as a counterweight against the Confucian scholar-bureaucrats. One, Zheng He, led seven enormous voyages of exploration into the Indian Ocean as far as Arabia, the rise of new emperors and new factions diminished such extravagances, the capture of the Zhengtong Emperor during the 1449 Tumu Crisis ended them completely. The imperial navy was allowed to fall into disrepair while forced labor constructed the Liaodong palisade, haijin laws intended to protect the coasts from Japanese pirates instead turned many into smugglers and pirates themselves. The growth of Portuguese, Spanish, and Dutch trade created new demand for Chinese products and produced an influx of Japanese. This abundance of specie remonetized the Ming economy, whose money had suffered repeated hyperinflation and was no longer trusted. While traditional Confucians opposed such a prominent role for commerce and the newly rich it created, combined with crop failure, floods, and epidemic, the dynasty collapsed before the rebel leader Li Zicheng, who was defeated by the Manchu-led Eight Banner armies who founded the Qing dynasty. The Mongol-led Yuan dynasty ruled before the establishment of the Ming dynasty, consequently, agriculture and the economy were in shambles, and rebellion broke out among the hundreds of thousands of peasants called upon to work on repairing the dykes of the Yellow River. A number of Han Chinese groups revolted, including the Red Turbans in 1351, the Red Turbans were affiliated with the White Lotus, a Buddhist secret society. Zhu Yuanzhang was a peasant and Buddhist monk who joined the Red Turbans in 1352. In 1356, Zhus rebel force captured the city of Nanjing, with the Yuan dynasty crumbling, competing rebel groups began fighting for control of the country and thus the right to establish a new dynasty. In 1363, Zhu Yuanzhang eliminated his archrival and leader of the rebel Han faction, Chen Youliang, in the Battle of Lake Poyang, arguably the largest naval battle in history. Known for its ambitious use of ships, Zhus force of 200,000 Ming sailors were able to defeat a Han rebel force over triple their size, claimed to be 650. The victory destroyed the last opposing rebel faction, leaving Zhu Yuanzhang in uncontested control of the bountiful Yangtze River Valley, Zhu Yuanzhang took Hongwu, or Vastly Martial, as his era name. Hongwu made an effort to rebuild state infrastructure. He built a 48 km long wall around Nanjing, as well as new palaces, Hongwu organized a military system known as the weisuo, which was similar to the fubing system of the Tang dynasty. With a growing suspicion of his ministers and subjects, Hongwu established the Jinyiwei, some 100,000 people were executed in a series of purges during his rule
27.
Matteo Ricci
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Matteo Ricci, S. J. was an Italian Jesuit priest and one of the founding figures of the Jesuit China missions. His 1602 map of the world in Chinese characters introduced the findings of European exploration to East Asia and he is considered a Servant of God in Roman Catholicism. Ricci arrived at the Portuguese settlement of Macau in 1582 where he began his work in China. Ricci was born October 6,1552, in Macerata, part of the Papal States and he made his classical studies in his native town and studied law at Rome for two years. He entered the Society of Jesus in April 1571 at the Roman College, while there, in addition to philosophy and theology, he also studied mathematics, cosmology, and astronomy under the direction of Father Christopher Clavius. In 1577, he applied for an expedition to the Far East. He sailed from Lisbon, Portugal in March 1578 and arrived in Goa, a Portuguese Colony, Ricci remained there employed in teaching and the ministry until the end of Lent,1582, when he was summoned to Macau to prepare to enter China. Ricci arrived at Macau in the part of August. In August 1582, Ricci arrived at Macau, a Portuguese trading post on the South China Sea. At the time, Christian missionary activity in China was almost completely limited to Macau, paul Jesuit College, and to prepare for the Jesuits mission from Macau into Mainland China. Once in Macau, Ricci studied Chinese language and customs and it was the beginning of a long project that made him one of the first Western scholars to master Chinese script and Classical Chinese. With Ruggieri, he traveled to Guangdongs major cities, Canton, in 1583, Ricci and Ruggieri settled in Zhaoqing, at the invitation of the governor of Zhaoqing, Wang Pan, who had heard of Riccis skill as a mathematician and cartographer. Ricci stayed in Zhaoqing from 1583 to 1589, when he was expelled by a new viceroy and it was in Zhaoqing, in 1584, that Ricci composed the first European-style map of the world in Chinese, now called the Impossible Black Tulip after its rarity. No prints of the 1584 map survive, but six recopied, the manuscript was misplaced in the Jesuit Archives in Rome, rediscovered only in 1934, and published only in 2001. There is now a plaque in Zhaoqing to commemorate Riccis six-year stay there. Expelled from Zhaoqing in 1589, Ricci obtained permission to relocate to Shaoguan in the north of the province, further travels saw Ricci reach Nanjing and Nanchang in 1595. In August 1597, Alessandro Valignano, his superior, appointed him Major Superior of the mission in China, with the rank and powers of a Provincial and he moved to Tongzhou in 1598, and first reached the capital Beijing itself on 7 September 1598. However, because of a Korean/Japanese war at the time, Ricci could not reach the Imperial Palace, after waiting for two months, he left Beijing, first for Nanjing and then Suzhou in Southern Zhili Province
28.
Society of Jesus
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The Society of Jesus Latin, Societas Iesu, S. J. SJ or SI) is a religious congregation of the Catholic Church which originated in Spain. The society is engaged in evangelization and apostolic ministry in 112 nations on six continents, Jesuits work in education, intellectual research, and cultural pursuits. Jesuits also give retreats, minister in hospitals and parishes, and promote social justice, Ignatius of Loyola founded the society after being wounded in battle and experiencing a religious conversion. He composed the Spiritual Exercises to help others follow the teachings of Jesus Christ, ignatiuss plan of the orders organization was approved by Pope Paul III in 1540 by a bull containing the Formula of the Institute. Ignatius was a nobleman who had a background, and the members of the society were supposed to accept orders anywhere in the world. The Society participated in the Counter-Reformation and, later, in the implementation of the Second Vatican Council, the Society of Jesus is consecrated under the patronage of Madonna Della Strada, a title of the Blessed Virgin Mary, and it is led by a Superior General. The Society of Jesus on October 3,2016 announced that Superior General Adolfo Nicolás resignation was officially accepted, on October 14, the 36th General Congregation of the Society of Jesus elected Father Arturo Sosa as its thirty-first Superior General. The headquarters of the society, its General Curia, is in Rome, the historic curia of St. Ignatius is now part of the Collegio del Gesù attached to the Church of the Gesù, the Jesuit Mother Church. In 2013, Jorge Mario Bergoglio became the first Jesuit Pope, the Jesuits today form the largest single religious order of priests and brothers in the Catholic Church. As of 1 January 2015, Jesuits numbered 16,740,11,986 clerics regular,2,733 scholastics,1,268 brothers and 753 novices. In 2012, Mark Raper S. J. wrote, Our numbers have been in decline for the last 40 years—from over 30,000 in the 1960s to fewer than 18,000 today. The steep declines in Europe and North America and consistent decline in Latin America have not been offset by the significant increase in South Asia, the Society is divided into 83 Provinces with six Independent Regions and ten Dependent Regions. On 1 January 2007, members served in 112 nations on six continents with the largest number in India and their average age was 57.3 years,63.4 years for priests,29.9 years for scholastics, and 65.5 years for brothers. The current Superior General of the Jesuits is Arturo Sosa, the Society is characterized by its ministries in the fields of missionary work, human rights, social justice and, most notably, higher education. It operates colleges and universities in countries around the world and is particularly active in the Philippines. In the United States it maintains 28 colleges and universities and 58 high schools and he ensured that his formula was contained in two papal bulls signed by Pope Paul III in 1540 and by Pope Julius III in 1550. The formula expressed the nature, spirituality, community life and apostolate of the new religious order, the meeting is now commemorated in the Martyrium of Saint Denis, Montmartre
29.
Hermann von Helmholtz
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Hermann Ludwig Ferdinand von Helmholtz was a German physician and physicist who made significant contributions in several scientific fields. The largest German association of institutions, the Helmholtz Association, is named after him. In physics, he is known for his theories on the conservation of energy, work in electrodynamics, chemical thermodynamics, Helmholtzs work is influenced by the philosophy of Johann Gottlieb Fichte and Immanuel Kant. He tried to trace their theories in empirical matters like physiology, as a young man, Helmholtz was interested in natural science, but his father wanted him to study medicine at the Charité because there was financial support for medical students. Trained primarily in physiology, Helmholtz wrote on other topics, ranging from theoretical physics, to the age of the Earth. Helmholtzs first academic position was as a teacher of Anatomy at the Academy of Arts in Berlin in 1848 and he then moved to take a post of associate professor of physiology at the Prussian University of Königsberg, where he was appointed in 1849. In 1855 he accepted a professorship of anatomy and physiology at the University of Bonn. He was not particularly happy in Bonn, however, and three later he transferred to the University of Heidelberg, in Baden, where he served as professor of physiology. In 1871 he accepted his final university position, as professor of physics at the University of Berlin and his first important scientific achievement, an 1847 treatise on the conservation of energy, was written in the context of his medical studies and philosophical background. He discovered the principle of conservation of energy while studying muscle metabolism and he tried to demonstrate that no energy is lost in muscle movement, motivated by the implication that there were no vital forces necessary to move a muscle. This was a rejection of the tradition of Naturphilosophie which was at that time a dominant philosophical paradigm in German physiology. He published his theories in his book Über die Erhaltung der Kraft, in the 1850s and 60s, building on the publications of William Thomson, Helmholtz and William Rankine popularized the idea of the heat death of the universe. In fluid dynamics, Helmholtz made several contributions, including Helmholtzs theorems for vortex dynamics in inviscid fluids, Helmholtz was a pioneer in the scientific study of human vision and audition. He coined the term psychophysics, to capture the distinction between the measurement of physical stimuli and their effect on human perception. The physical sound needs to be increased exponentially in order for equal steps to seem linear, Helmholtz paved the way in experimental studies on the relationship between the physical energy and its appreciation, with the goal in mind to develop psychophysical laws. The sensory physiology of Helmholtz was the basis of the work of Wilhelm Wundt, a student of Helmholtz and he, more explicitly than Helmholtz, described his research as a form of empirical philosophy and as a study of the mind as something separate. Helmholtz had, in his early repudiation of Naturphilosophie, stressed the importance of materialism, in 1851, Helmholtz revolutionized the field of ophthalmology with the invention of the ophthalmoscope, an instrument used to examine the inside of the human eye. Helmholtzs interests at that time were focused on the physiology of the senses
30.
Victor-Charles Mahillon
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Victor-Charles Mahillon was a Belgian musician and writer on musical topics. He built, collected, and described more than 1500 musical instruments, the son of Charles Mahillon, he started working at his fathers factory of musical instruments in 1865. In 1869, he started the musical journal LEcho musical, which ran until 1886 and he was the first curator of the instrument collection at the Brussels Royal Music Conservatory from 1879 and contributed many of his own instruments to the collection. He had a deep interest in the science but especially that pertaining to wind instruments. While his work in acoustics was advanced for the time, and has historical interest. His various articles that appeared in the Encyclopædia Britannica, ninth edition, are still of interest, in 1885 he provided instruments to Alfred James Hipkins for use in a series of concerts at the International Inventions Exhibition in London. In 1890 he collaborated with Brian Greene to develop much of the more in-depth classifications of idiophones and his classification of instruments was later adopted by Erich von Hornbostel and Curt Sachs, and is still in use today. 1919, Commander of the Order of Leopold
31.
Aristoxenus
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Aristoxenus of Tarentum was a Greek Peripatetic philosopher, and a pupil of Aristotle. The Elements is the source of our knowledge of ancient Greek music. Aristoxenus was born at Tarentum, and was the son of a musician named Spintharus. This story is, however, contradicted by Aristocles, who asserts that he never mentioned Aristotle, nothing is known of his life after the time of Aristotles departure, apart from a comment in Elementa Harmonica concerning his works. His writings, said to have consisted of four hundred and fifty-three books, were in the style of Aristotle, the only work of his that has come down to us is the three books of the Elements of Harmony, an incomplete musical treatise. Aristoxenus theory had a tendency, in music he held that the notes of the scale are to be judged, not as the Pythagoreans held, by mathematical ratio. Vitruvius in his De architectura paraphrases the writings of Aristoxenus on music, the theory that the soul is a harmony of the four elements composing the body, and therefore mortal, was ascribed to Aristoxenus and Dicaearchus. This theory is comparable to the one offered by Simmias in Platos Phaedo, in his Elements of Harmony, Aristoxenus attempted a complete and systematic exposition of music. In the second book Aristoxenus divides music into seven parts, which he takes to be, the genera, intervals, sounds, systems, tones or modes, mutations, and melopoeia. The remainder of the work is taken up with a discussion of the parts of music according to the order which he had himself prescribed. In his second book he asserted that by the hearing we judge of the magnitude of an interval, however, this should not be construed as meaning that he postulated a simplistic system of harmony resembling that of modern twelve tone theory, and especially not an equally tempered system. As he urges us to consider, fter all, with which of the people who argue about the shades of the genera should one agree. Not everyone looks to the division when tuning the chromatic or the enharmonic. It is sometimes claimed that the nature of Aristoxenus scales and genera deviated sharply from his predecessors, another way of stating this, however perhaps less accurate, is that instead of using discrete ratios to place intervals, he used continuously variable quantities. Aristoxenus himself held that two things must not be overlooked, first, that people have mistakenly supposed us to be saying that a tone can be divided into three equal parts in a melody. They made this mistake because they did not realise that it is one thing to employ the third part of a tone, secondly we accept that from a purely abstract point of view there is no least interval. In book three Aristoxenus goes on to describe twenty eight laws of succession, which are of great interest to those concerned with classical Greek melodic structure. Part of the book of a work on rhythmics and metrics
32.
Vincenzo Galilei
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This article refers to the father of Galileo Galilei. For Galileo’s son of the name, see Vincenzo Gamba. He was a figure in the musical life of the late Renaissance. Vincenzo, in his study of pitch and string tension, produced perhaps the first non-linear mathematical description of a phenomenon known to history. It was an extension of a Pythagorean tradition but went beyond it and he was born around 1520 in Santa Maria a Monte, and began studying the lute at an early age. Sometime before 1562 he moved to Pisa, where he married into a noble family, in 1564 Galileo was born, the first of his either six or seven children, another son, Michelagnolo, born in 1575, who also became an accomplished lutenist and composer. Vincenzo was a player of the lute, and early in life attracted the attention of powerful. In 1563 he met Gioseffo Zarlino, the most important music theorist of the century, in Venice. Sometime in the 1570s his interests in music theory, as well as his composition and this describes Baroque practice, especially as he defines rules for resolution of suspensions by a preliminary leap away from, followed by a return to, the expected note of resolution. The use of recitative in opera is widely attributed to Galilei, since he was one of the inventors of monody, Vincenzo Galilei was one of the pioneers in the systematic study of acoustics, mainly in his research in the mathematical formula of stretched strings. Vincenzo made some substantial discoveries in acoustics, particularly involving the physics of vibrating strings and he discovered that while the ratio of an interval is proportional to string lengths it varied with the square root of the tension applied. In the case of strings tuned in a fifth, weights suspended from them needed to be in a ratio of 9,4 to produce the 3,2 perfect fifth. This work was taken further by Marin Mersenne who formulated the current law of vibrating strings, Mersenne was a regular correspondent to many scientists and, after the death of Vincenzo he maintained a regular link to Galileo, and treated him as a prized member of his scientific network. He communicated Galileos ideas for a clock to Christiaan Huygens. Despite being a priest, Mersenne defended Galileo when he came under attack by the church in 1633 and he conducted his own duplicate experiments which improved on their accuracy. Claude Palisca, Vincenzo Galilei, Grove Music Online, ed. L. Macy, Article Vincenzo Galilei, in The New Grove Dictionary of Music and Musicians, ISBN 1-56159-174-2 Gustave Reese, Music in the Renaissance. ISBN 0-393-09530-4 The Concise Edition of Bakers Biographical Dictionary of Musicians, della musica antica, et della moderna Fronimo Dialogo
33.
Galileo Galilei
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Galileo Galilei was an Italian polymath, astronomer, physicist, engineer, philosopher, and mathematician. He played a role in the scientific revolution of the seventeenth century. Galileo also worked in applied science and technology, inventing an improved military compass, Galileos championing of heliocentrism and Copernicanism was controversial during his lifetime, when most subscribed to either geocentrism or the Tychonic system. He met with opposition from astronomers, who doubted heliocentrism because of the absence of a stellar parallax. He was tried by the Inquisition, found vehemently suspect of heresy and he spent the rest of his life under house arrest. He has been called the father of observational astronomy, the father of modern physics, the father of scientific method, and the father of science. Galileo was born in Pisa, Italy, on 15 February 1564, the first of six children of Vincenzo Galilei, a famous lutenist, composer, and music theorist, and Giulia, three of Galileos five siblings survived infancy. The youngest, Michelangelo, also became a noted lutenist and composer although he contributed to financial burdens during Galileos young adulthood, Michelangelo was unable to contribute his fair share of their fathers promised dowries to their brothers-in-law, who would later attempt to seek legal remedies for payments due. Michelangelo would also occasionally have to borrow funds from Galileo to support his musical endeavours and these financial burdens may have contributed to Galileos early fire to develop inventions that would bring him additional income. When Galileo Galilei was eight, his family moved to Florence and he then was educated in the Vallombrosa Abbey, about 30 km southeast of Florence. Galileo Bonaiuti was buried in the church, the Basilica of Santa Croce in Florence. It was common for mid-sixteenth century Tuscan families to name the eldest son after the parents surname, hence, Galileo Galilei was not necessarily named after his ancestor Galileo Bonaiuti. The Italian male given name Galileo derives from the Latin Galilaeus, meaning of Galilee, the biblical roots of Galileos name and surname were to become the subject of a famous pun. In 1614, during the Galileo affair, one of Galileos opponents, in it he made a point of quoting Acts 1,11, Ye men of Galilee, why stand ye gazing up into heaven. Despite being a genuinely pious Roman Catholic, Galileo fathered three children out of wedlock with Marina Gamba and they had two daughters, Virginia and Livia, and a son, Vincenzo. Their only worthy alternative was the religious life, both girls were accepted by the convent of San Matteo in Arcetri and remained there for the rest of their lives. Virginia took the name Maria Celeste upon entering the convent and she died on 2 April 1634, and is buried with Galileo at the Basilica of Santa Croce, Florence. Livia took the name Sister Arcangela and was ill for most of her life, Vincenzo was later legitimised as the legal heir of Galileo and married Sestilia Bocchineri
34.
Fronimo Dialogo
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The Fronimo Dialogo di Vincentio Galilei is an instructional book on playing, composing and intabulating vocal music for the lute. While the title page bears the date 1568, the final page confusingly bears the date 1569. In addition, still in 1569, Girolamo Scotto broke the book into two parts, selling a collection of 30 musical selections from near the end of the book and the Dialogo separately. Unlike other lute instruction manuals of the 16th century, each of the editions of Fronimo contains quite an amount of music. Galilei provided examples in order to illustrate how he believed compositions should be structured, the examples range from a few notes or measures in length up to complete compositions in either mensural notation or lute tablature. In the 1584 edition, for example, there are 48 pieces in tablature form sprinkled throughout the text, the 1568 edition includes a total of 96 complete pieces, many of which are different from those chosen for the 1584 edition. 1568/69 edition 1584 edition Dialogo sopra larte del bene intavolare The Lute Society of America
35.
Ricercar
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A ricercar is a type of late Renaissance and mostly early Baroque instrumental composition. The term means to search out, and many serve a preludial function to search out the key or mode of a following piece. A ricercar may explore the permutations of a motif. For example, Ricercar sopra Benedictus might develop motifs from a motet titled Benedictus, the term is also used to designate an etude or study that explores a technical device in playing an instrument, or singing. In its most common usage, it refers to an early kind of fugue. However the term has a more varied historical usage. In the sixteenth century, the word ricercar could refer to types of compositions. The second type of ricercar, the imitative, contrapuntal type, was to prove the more important historically, marco DallAquila was known for polyphonic ricercars. Examples of both types of ricercars can be found in the works of Girolamo Frescobaldi, e. g. in his Fiori musicali, gödel, Escher, Bach, An Eternal Golden Braid by Douglas Hofstadter, which includes a section entitled Six-part Ricercar. Ricercar, Fugue, Counterpoint in The New Grove Dictionary of Music and Musicians, ISBN 1-56159-174-2 Gustave Reese, Music in the Renaissance. ISBN 0-393-09530-4 Manfred Bukofzer, Music in the Baroque Era, ISBN 0-393-09745-5 Ursula Kirkendale, The Source for Bachs Musical Offering, Journal of the American Musicological Society 33, 99-141. The New Harvard Dictionary of Music, ed, cambridge, Massachusetts, Harvard University Press,1986. ISBN 0-674-61525-5 Arthur J. Ness, Ricercar, Harvard Dictionary of Music, fourth edition, edited by Don Michael Randel, cambridge, Belknap Press for Harvard University Press,2003. The dictionary definition of ricercar at Wiktionary Petrucci Music Library Ricercar Collection
36.
Lute
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The European lute and the modern Near-Eastern oud descend from a common ancestor via diverging evolutionary paths. The lute is used in a variety of instrumental music from the Medieval to the late Baroque eras and was the most important instrument for secular music in the Renaissance. It is also an instrument, especially in vocal works. The player of a lute is called a lutenist, lutanist or lutist, the words lute and oud possibly derive from Arabic al-ʿud. Recent research by Eckhard Neubauer suggests ʿud may in turn be an Arabized version of the Persian name rud and it has equally been suggested the wood in the name may have distinguished the instrument by its wooden soundboard from skin-faced predecessors. Gianfranco Lotti suggests the wood appellation originally carried derogatory connotations because of proscriptions of all music in early Islam. Lutes are made almost entirely of wood, the soundboard is a teardrop-shaped thin flat plate of resonant wood. In all lutes the soundboard has a single decorated sound hole under the strings called the rose. The sound hole is not open, but rather covered with a grille in the form of a vine or a decorative knot. Robert Lundberg, in his book Historical Lute Construction, suggests ancient builders placed bars according to ratios of the scale length. He further suggests the inward bend of the soundboard is an adaptation by ancient builders to afford the lutenists right hand more space between the strings and soundboard. Soundboard thickness varies, but generally hovers between 1.5 and 2 mm, some luthiers tune the belly as they build, removing mass and adapting bracing to produce desirable sonic results. The lute belly is almost never finished, but in cases the luthier may size the top with a very thin coat of shellac or glair to help keep it clean. After joining the top to the sides, a half-binding is usually installed around the edge of the soundboard, the half-binding is approximately half the thickness of the soundboard and is usually made of a contrasting color wood. The rebate for the half-binding must be precise to avoid compromising structural integrity. The back or the shell is assembled from strips of hardwood called ribs. There are braces inside on the soundboard to give it strength, the neck is made of light wood, with a veneer of hardwood to provide durability for the fretboard beneath the strings. Unlike most modern stringed instruments, the fretboard is mounted flush with the top
37.
Francesco Spinacino
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Francesco Spinacino was an Italian lutenist and composer. His surviving output comprises the first two volumes of Ottaviano Petruccis influential series of music publications, Intabolatura de lauto libro primo. These two collections comprise the first known printed music, and his first book was the first ever instrumental music book printed with the movable type system. Spinacino was apparently highly regarded by his contemporaries, as his music was widely copied, there are 81 pieces overall,46 intabulations,27 ricercares, two bassadans and six pieces for lute duet. The ricercares are among the most complex of the period, they have no clearly defined form, particularly notable is Recercare de tutti li toni, which moves through all modes
38.
Gioseffo Zarlino
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Gioseffo Zarlino was an Italian music theorist and composer of the Renaissance. He was possibly the most famous European music theorist between Aristoxenus and Rameau, and made a contribution to the theory of counterpoint as well as to musical tuning. Zarlino was born in Chioggia, near Venice and his early education was with the Franciscans, and he later joined the order himself. In 1536 he was a singer at Chioggia Cathedral, and by 1539 he not only became a deacon, in 1540 he was ordained, and in 1541 went to Venice to study with the famous contrapuntist and maestro di cappella of Saint Marks, Adrian Willaert. In 1565, on the resignation of Cipriano de Rore, Zarlino took over the post of maestro di cappella of St. Marks, one of the most prestigious positions in Italy. While he was a prolific composer, and his motets are polished and display a mastery of canonic counterpoint. Zarlino also described the 1/4-comma meantone and 1/3-comma meantone, considering all three temperaments to be usable and these are the precursors to the 50- 31- and 19-tone equal temperaments, respectively. In his Dimostrationi harmoniche of 1571, he revised the numbering of modes to emphasize C, Zarlino was the first to theorize the primacy of triad over interval as a means of structuring harmony. His exposition of just intonation based on proportions within the Senario and 8 is a departure from the previously established Pythagorean diatonic system as passed on by Boethius, zarlinos writings, primarily published by Francesco Franceschi, spread throughout Europe at the end of the 16th century. Zarlinos compositions are more conservative in idiom than those of many of his contemporaries and his madrigals avoid the homophonic textures commonly used by other composers, remaining polyphonic throughout, in the manner of his motets. His works were published between 1549 and 1567, and include 41 motets, mostly for five and six voices and his 10 motets on the Song of Songs used the text of Isidoro Chiaris translation of the Bible. GCD921406 Zarlino, Modulationes sex vocum, Singer Pur, OEHMS CLASSICS873 Article Gioseffo Zarlino, in The New Grove Dictionary of Music and Musicians, ISBN 1-56159-174-2 Gustave Reese, Music in the Renaissance. ISBN 0-393-09530-4 Gioseffo Zarlino, Istituzioni armoniche, tr. Oliver Strunk, in Source Readings in Music History
39.
Marin Mersenne
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Marin Mersenne, Marin Mersennus or le Père Mersenne was a French theologian, philosopher, mathematician and music theorist, often referred to as the father of acoustics. Mersenne, an ordained priest, had contacts in the scientific world and has been called the center of the world of science. Marin Mersenne was born of peasant parents near Oizé, Maine and he was educated at Le Mans and at the Jesuit College of La Flèche. On 17 July 1611, he joined the Minim Friars, and, after studying theology, between 1614 and 1618, he taught theology and philosophy at Nevers, but he returned to Paris and settled at the convent of LAnnonciade in 1620. There he studied mathematics and music and met with other kindred spirits such as René Descartes, Étienne Pascal, Pierre Petit, Gilles de Roberval and he corresponded with Giovanni Doni, Constantijn Huygens, Galileo Galilei, and other scholars in Italy, England and the Dutch Republic. He was a defender of Galileo, assisting him in translations of some of his mechanical works. For four years, Mersenne devoted himself entirely to philosophic and theological writing and it is sometimes incorrectly stated that he was a Jesuit. He was educated by Jesuits, but he never joined the Society of Jesus and he taught theology and philosophy at Nevers and Paris. He was not afraid to cause disputes among his friends in order to compare their views. In 1635 Mersenne met with Tommaso Campanella, but concluded that he could teach nothing in the sciences but still he has a good memory, Mersenne asked if René Descartes wanted Campanella to come to Holland to meet him, but Descartes declined. He visited Italy fifteen times, in 1640,1641 and 1645, in 1643–1644 Mersenne also corresponded with the German Socinian Marcin Ruar concerning the Copernican ideas of Pierre Gassendi, finding Ruar already a supporter of Gassendis position. Among his correspondents were Descartes, Galilei, Roberval, Pascal, Beeckman and he died September 1 through complications arising from a lung abscess. Some history scientists suggest he died for having drunk a huge quantity of water, along with Descartes. It was written as a commentary on the Book of Genesis, at first sight the book appears to be a collection of treatises on various miscellaneous topics. However Robert Lenoble has shown that the principle of unity in the work is a polemic against magical and divinatory arts, cabalism and he mentions Martin Del Rios Investigations into Magic and criticises Marsilio Ficino for claiming power for images and characters. He condemns astral magic and astrology and the anima mundi, a popular amongst Renaissance neo-platonists. Whilst allowing for an interpretation of the Cabala, he wholeheartedly condemned its magical application—particularly to angelology. He also criticises Pico della Mirandola, Cornelius Agrippa and Francesco Giorgio with Robert Fludd as his main target, Fludd responded with Sophia cum moria certamen, wherein Fludd admits his involvement with the Rosicrucians
40.
Johann Faulhaber
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Johann Faulhaber was a German mathematician. Born in Ulm, Faulhaber was a weaver who later took the role of a surveyor of the city of Ulm. He collaborated with Johannes Kepler and Ludolph van Ceulen, besides his work on the fortifications of cities, Faulhaber built water wheels in his home town and geometrical instruments for the military. Faulhaber made the first publication of Henry Briggss Logarithm in Germany, faulhabers major contribution was in calculating the sums of powers of integers. Jacob Bernoulli makes references to Faulhaber in his Ars Conjectandi, academia Algebrae, darinnen die miraculosische Inventiones, zu den höchsten Cossen weiters continuirt und profitiert werden
41.
Passacaglia
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The passacaglia is a musical form that originated in early seventeenth-century Spain and is still used today by composers. It is usually of a character and is often, but not always, based on a bass-ostinato. The term passacaglia derives from the Spanish pasar and calle and it originated in early 17th century Spain as a strummed interlude between instrumentally accompanied dances or songs. Despite the forms Spanish roots, the first written examples of passacaglias are found in an Italian source dated 1606 and these pieces, as well as others from Italian sources from the beginning of the century, are simple, brief sequences of chords outlining a cadential formula. The passacaglia was redefined in the late 1620s by Italian composer Girolamo Frescobaldi, later composers adopted this model, and by the nineteenth century the word came to mean a series of variations over an ostinato pattern, usually of a serious character. A similar form, the chaconne, was also first developed by Frescobaldi, in early scholarship, attempts to formally differentiate between the historical chaconne and passacaglia were made, but researchers often came to opposite conclusions. One of the best known examples of the passacaglia in Western classical music is the Passacaglia and Fugue in C minor, BWV582, for organ by Johann Sebastian Bach. The French clavecinists, especially Louis Couperin and his nephew François Couperin, Heinrich Ignaz Franz Bibers Passacaglia, the last piece of the monumental Mystery Sonatas, is one of the earliest known compositions for solo violin. The central episode of Claudio Monteverdis madrigal Lamento della Ninfa is a passacaglia on a descending tetrachord, the first two movements of the fourth sonata from Johann Heinrich Schmelzers Sonatæ unarum fidium are passacaglias on a descending tetrachord, but in uncharacteristic major. The fourth movement of Luigi Boccherinis Quintettino No,6, Op.30, is titled Passacalle. Nineteenth-century examples include the C-minor passacaglia for organ by Felix Mendelssohn, the first movement of Hans Hubers Piano Concerto No. 3, Op.113 is a passacaglia, Passacaglias for lute have been composed by figures such as Alessandro Piccinini, G. H. The passacaglia proved an enduring form throughout the century and beyond. Three composers especially identified with the passacaglia are Benjamin Britten, Dmitri Shostakovich, in his operas, Britten often uses a passacaglia to create the climactic moment of the drama. Examples are found in Peter Grimes, Billy Budd, The Turn of the Screw, Death in Venice, Hindemith employed the form to conclude his 1938 ballet, Nobilissima Visione, and it is also found in his early Sonata for viola solo, Op.11, No. 5, as well as in works such as the Fifth String Quartet. Igor Stravinsky used the form for the movement of his Septet. Especially important examples of the form are found in the output of the Second Viennese School, revue Belge de Musicologie / Belgisch Tijdschrift voor Muziekwetenschap 12, 19–34
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