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Giambattista Benedetti
Giambattista (Gianbattista) Benedetti (August 14, 1530 – January 20, 1590 in) was an Italian mathematician from Venice who was also interested in physics, mechanics, the construction of sundials, and the science of music. Science of motion In his works ''Resolutio omnium Euclidis problematum'' (1553) and ''Demonstratio proportionum motuum localium'' (1554), Benedetti proposed a new doctrine of the speed of bodies in free fall. The accepted Aristotelian doctrine at that time was that the speed of a freely falling body is directly proportional to the total weight of the body and inversely proportional to the density of the medium. Benedetti's view was that the speed depends on just the difference between the specific gravity of the body and that of the medium. As opposed to the Aristotelian theory, his theory predicts that two objects of the same material but of different weights would fall at the same speed, and also that objects of different materials in a vacuum would fal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Venice
Venice ( ; it, Venezia ; vec, Venesia or ) is a city in northeastern Italy and the capital of the Veneto Regions of Italy, region. It is built on a group of 118 small islands that are separated by canals and linked by over 400 bridges. The islands are in the shallow Venetian Lagoon, an enclosed bay lying between the mouths of the Po River, Po and the Piave River, Piave rivers (more exactly between the Brenta (river), Brenta and the Sile (river), Sile). In 2020, around 258,685 people resided in greater Venice or the ''Comune di Venezia'', of whom around 55,000 live in the historical island city of Venice (''centro storico'') and the rest on the mainland (''terraferma''). Together with the cities of Padua, Italy, Padua and Treviso, Italy, Treviso, Venice is included in the Padua-Treviso-Venice Metropolitan Area (PATREVE), which is considered a statistical metropolitan area, with a total population of 2.6 million. The name is derived from the ancient Adri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Consonance And Dissonance
In music, consonance and dissonance are categorizations of simultaneous or successive Sound, sounds. Within the Western tradition, some listeners associate consonance with sweetness, pleasantness, and acceptability, and dissonance with harshness, unpleasantness, or unacceptability, although there is broad acknowledgement that this depends also on familiarity and musical expertise. The terms form a structural dichotomy in which they define each other by mutual exclusion: a consonance is what is not dissonant, and a dissonance is what is not consonant. However, a finer consideration shows that the distinction forms a gradation, from the most consonant to the most dissonant. In casual discourse, as German composer and music theorist Paul Hindemith stressed, "The two concepts have never been completely explained, and for a thousand years the definitions have varied". The term ''sonance'' has been proposed to encompass or refer indistinctly to the terms ''consonance'' and ''dissonance' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taxicab Distance
A taxicab geometry or a Manhattan geometry is a geometry whose usual distance function or metric of Euclidean geometry is replaced by a new metric in which the distance between two points is the sum of the absolute differences of their Cartesian coordinates. The taxicab metric is also known as rectilinear distance, ''L''1 distance, ''L''1 distance or \ell_1 norm (see ''Lp'' space), snake distance, city block distance, Manhattan distance or Manhattan length. The latter names refer to the rectilinear street layout on the island of Manhattan, where the shortest path a taxi travels between two points is the sum of the absolute values of distances that it travels on avenues and on streets. The geometry has been used in regression analysis since the 18th century, and is often referred to as LASSO. The geometric interpretation dates to non-Euclidean geometry of the 19th century and is due to Hermann Minkowski. In \mathbb^2 , the taxicab distance between two points (x_1, y_1) and (x_2, y_ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Tenney
James Tenney (August 10, 1934 – August 24, 2006) was an American composer and music theorist. He made significant early musical contributions to plunderphonics, sound synthesis, algorithmic composition, process music, spectral music, microtonal music, and tuning systems including extended just intonation. His theoretical writings variously concern musical form, texture, timbre, consonance and dissonance, and harmonic perception. Biography James Tenney was born in Silver City, New Mexico, and grew up in Arizona and Colorado. He attended the University of Denver, the Juilliard School of Music, Bennington College (B.A., 1958) and the University of Illinois (M.A., 1961). He studied piano with Eduard Steuermann and composition with Chou Wen-chung, Lionel Nowak, Paul Boepple, Henry Brant, Carl Ruggles, Kenneth Gaburo, John Cage, Harry Partch, and Edgard Varèse. He also studied acoustics, information theory and tape music composition under Lejaren Hiller. In 1961, Tenney completed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interval Strength
In music theory, an interval is a difference in pitch between two sounds. An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord. In Western music, intervals are most commonly differences between notes of a diatonic scale. Intervals between successive notes of a scale are also known as scale steps. The smallest of these intervals is a semitone. Intervals smaller than a semitone are called microtones. They can be formed using the notes of various kinds of non-diatonic scales. Some of the very smallest ones are called commas, and describe small discrepancies, observed in some tuning systems, between enharmonically equivalent notes such as C and D. Intervals can be arbitrarily small, and even imperceptible to the human ear. In physical terms, an interval is the ratio between two sonic freque ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Cope
David Cope (born May 17, 1941 in San Francisco, California) is an American author, composer, scientist, and former professor of music at the University of California, Santa Cruz (UCSC). His primary area of research involves artificial intelligence and music; he writes programs and algorithms that can analyse existing music and create new compositions in the style of the original input music. He taught a summer workshop in algorithmic computer music that was open to the public (but not free) as well as a general education course entitled Artificial Intelligence and Music for enrolled UCSC students. Cope is also co-founder and CTO Emeritus of Recombinant Inc., a music technology company. Inventions Cope is the inventor of US Patent #7696426 "Recombinant music composition algorithm and method of using the same". Composition His EMI (Experiments in Musical Intelligence) software has produced works in the style of various composers, some of which have been commercially recorded—ra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Overtone
An overtone is any resonant frequency above the fundamental frequency of a sound. (An overtone may or may not be a harmonic) In other words, overtones are all pitches higher than the lowest pitch within an individual sound; the fundamental is the lowest pitch. While the fundamental is usually heard most prominently, overtones are actually present in any pitch except a true sine wave. The relative volume or amplitude of various overtone partials is one of the key identifying features of timbre, or the individual characteristic of a sound. Using the model of Fourier analysis, the fundamental and the overtones together are called partials. Harmonics, or more precisely, harmonic partials, are partials whose frequencies are numerical integer multiples of the fundamental (including the fundamental, which is 1 times itself). These overlapping terms are variously used when discussing the acoustic behavior of musical instruments. Alexander J. Ellis (translating Hermann von Helmholtz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sensations Of Tone
''On the Sensations of Tone as a Physiological Basis for the Theory of Music'' (German ), commonly referred to as ''Sensations of Tone'', is a foundational work on music acoustics and the perception of sound by Hermann von Helmholtz. The first German edition was published in 1863. The English translation by Alexander J. Ellis was first published in 1875 (the first English edition was from the 1870 third German edition; the second English edition from the 1877 fourth German edition was published in 1885; the 1895 and 1912 third and fourth English editions were reprints of the second edition). The editions translated into English contain detailed commentary and notes (titled "Additions by the Translator") by Ellis. Helmholtz declared that he started working on his book in 1854, which concluded in 1862. Helmholtz started publishing on acoustics in 1852. His last article on acoustics was in 1878, reviewing the book by Lord Rayleigh (Theory of Sound). Therefore, Helmholtz published ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hermann Von Helmholtz
Hermann Ludwig Ferdinand von Helmholtz (31 August 1821 – 8 September 1894) was a German physicist and physician who made significant contributions in several scientific fields, particularly hydrodynamic stability. The Helmholtz Association, the largest German association of research institutions, is named in his honor. In the fields of physiology and psychology, Helmholtz is known for his mathematics concerning the eye, theories of vision, ideas on the visual perception of space, color vision research, the sensation of tone, perceptions of sound, and empiricism in the physiology of perception. In physics, he is known for his theories on the conservation of energy, work in electrodynamics, chemical thermodynamics, and on a mechanical foundation of thermodynamics. As a philosopher, he is known for his philosophy of science, ideas on the relation between the laws of perception and the laws of nature, the science of aesthetics, and ideas on the civilizing power of science. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marin Mersenne
Marin Mersenne, OM (also known as Marinus Mersennus or ''le Père'' Mersenne; ; 8 September 1588 – 1 September 1648) was a French polymath whose works touched a wide variety of fields. He is perhaps best known today among mathematicians for Mersenne prime numbers, those which can be written in the form for some integer . He also developed Mersenne's laws, which describe the harmonics of a vibrating string (such as may be found on guitars and pianos), and his seminal work on music theory, ''Harmonie universelle'', for which he is referred to as the "father of acoustics". Mersenne, an ordained Catholic priest, had many contacts in the scientific world and has been called "the center of the world of science and mathematics during the first half of the 1600s" and, because of his ability to make connections between people and ideas, "the post-box of Europe". He was also a member of the Minim religious order and wrote and lectured on theology and philosophy. Life Mersenne was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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