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Music And Mathematics
Music theory analyzes the pitch, timing, and structure of music. It uses mathematics to study elements of music such as tempo, chord progression, form, and meter. The attempt to structure and communicate new ways of composing and hearing music has led to musical applications of set theory, abstract algebra and number theory. While music theory has no axiomatic foundation in modern mathematics, the basis of musical sound can be described mathematically (using acoustics) and exhibits "a remarkable array of number properties". History Though ancient Chinese, Indians, Egyptians and Mesopotamians are known to have studied the mathematical principles of sound, the Pythagoreans (in particular Philolaus and Archytas) of ancient Greece were the first researchers known to have investigated the expression of musical scales in terms of numerical ratios, particularly the ratios of small integers. Their central doctrine was that "all nature consists of harmony arising out of numbers". Fro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spectrogram Of Violin
A spectrogram is a visual representation of the spectral density, spectrum of frequencies of a signal as it varies with time. When applied to an audio signal, spectrograms are sometimes called sonographs, voiceprints, or voicegrams. When the data are represented in a 3D plot they may be called ''waterfall displays''. Spectrograms are used extensively in the fields of music, linguistics, sonar, radar, speech processing, seismology, ornithology, and others. Spectrograms of audio can be used to identify spoken words phonetics, phonetically, and to analyse the Animal communication, various calls of animals. A spectrogram can be generated by an optical spectrometer, a bank of band-pass filters, by Fourier transform or by a wavelet transform (in which case it is also known as a scaleogram or scalogram). A spectrogram is usually depicted as a heat map, i.e., as an image with the intensity shown by varying the colour or brightness. Format A common format is a graph with two geomet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Archytas
Archytas (; ; 435/410–360/350 BC) was an Ancient Greek mathematician, music theorist, statesman, and strategist from the ancient city of Taras (Tarentum) in Southern Italy. He was a scientist and philosopher affiliated with the Pythagorean school and famous for being the reputed founder of mathematical mechanics and a friend of Plato. As a Pythagorean, Archytas believed that arithmetic (logistic), rather than geometry, provided the basis for satisfactory proofs, and developed the most famous argument for the infinity of the universe in antiquity. Life Archytas was born in Tarentum, a Greek city in the Italian Peninsula that was part of Magna Graecia, and was the son of Hestiaeus. He was presumably taught by Philolaus, and taught mathematics to Eudoxus of Cnidus and to Eudoxus' student, Menaechmus. Politically and militarily, Archytas appears to have been the dominant figure in Tarentum in his generation, somewhat comparable to Pericles in Athens a half-century earlier. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Repetition (music)
Repetition is important in music, where sounds or sequences are often repeated. It may be called restatement, such as the restatement of a theme (music), theme. While it plays a role in all music, with noise and musical tones lying along a spectrum from irregular to frequency, periodic sounds, it is especially prominent in specific styles. Usage A literal repetition of a musical passage is often indicated by the use of a repeat sign, or the instructions da capo or dal segno. Theodor W. Adorno damned repetition and popular music as psychotic and infantile. In contrast, Richard Middleton (musicologist), Richard Middleton (1990) argues that "while repetition is a feature of ''all'' music, of any sort, a high level of repetition may be a specific mark of 'the popular'" and that this allows an "enabling" of "an inclusive rather than exclusive audience". "There is no universal norm or convention" for the amount or type of repetition; "all music contains repetition – but in di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pulse (music)
In music theory, the pulse is a series of uniformly spaced beats—either audible or implied—that sets the tempo and is the scaffolding for the rhythm. By contrast, rhythm is always audible and can depart from the pulse. So while the rhythm may become too difficult for an untrained listener to fully match, nearly any listener instinctively matches the pulse by simply tapping uniformly, despite rhythmic variations in timing of sounds alongside the pulse.Fitch, W. Tecumseh and Rosenfeld, Andrew J. (2007). Definitions The tempo is the speed of the pulse. If a pulse becomes too fast it would become a drone; one that is too slow would be perceived as unconnected sounds.P. Fraisse, ''Les Structures Rhythmiques'', Erasme Paris 1956, H Woodrow ''Time Perception'' in "A Handbook of Experimental Psychology", ed. S.S. Stevens, Wiley, NY 1951, both quoted at http://www.zeuxilogy.home.ro/media/manifesto.pdf zeuxilogy.home.ro) When the period of any continuous beat is faster than 8–10 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Confucius
Confucius (; pinyin: ; ; ), born Kong Qiu (), was a Chinese philosopher of the Spring and Autumn period who is traditionally considered the paragon of Chinese sages. Much of the shared cultural heritage of the Sinosphere originates in the philosophy and teachings of Confucius. His philosophical teachings, called Confucianism, emphasized personal and governmental morality, harmonious social relationships, righteousness, kindness, sincerity, and a ruler's responsibilities to lead by virtue. Confucius considered himself a transmitter for the values of Ancient China, earlier periods which he claimed had been abandoned in his time. He advocated for filial piety, endorsing strong family loyalty, Ancestor veneration in China, ancestor veneration, the respect of elders by their children and of husbands by their wives. Confucius recommended a robust family unit as the cornerstone for an ideal government. He championed the Silver Rule, or a negative form of the Golden Rule, advising, "Do ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rhythm
Rhythm (from Greek , ''rhythmos'', "any regular recurring motion, symmetry") generally means a " movement marked by the regulated succession of strong and weak elements, or of opposite or different conditions". This general meaning of regular recurrence or pattern in time can apply to a wide variety of cyclical natural phenomena having a periodicity or frequency of anything from microseconds to several seconds (as with the riff in a rock music song); to several minutes or hours, or, at the most extreme, even over many years. The Oxford English Dictionary defines rhythm as ''"The measured flow of words or phrases in verse, forming various patterns of sound as determined by the relation of long and short or stressed and unstressed syllables in a metrical foot or line; an instance of this"''. Rhythm is related to and distinguished from pulse, meter, and beats: In the performance arts, rhythm is the timing of events on a human scale; of musical sounds and silences that occur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic
In physics, acoustics, and telecommunications, a harmonic is a sinusoidal wave with a frequency that is a positive integer multiple of the ''fundamental frequency'' of a periodic signal. The fundamental frequency is also called the ''1st harmonic''; the other harmonics are known as ''higher harmonics''. As all harmonics are periodic at the fundamental frequency, the sum of harmonics is also periodic at that frequency. The set of harmonics forms a '' harmonic series''. The term is employed in various disciplines, including music, physics, acoustics, electronic power transmission, radio technology, and other fields. For example, if the fundamental frequency is 50 Hz, a common AC power supply frequency, the frequencies of the first three higher harmonics are 100 Hz (2nd harmonic), 150 Hz (3rd harmonic), 200 Hz (4th harmonic) and any addition of waves with these frequencies is periodic at 50 Hz. In music, harmonics are used on string instruments and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chinese Musicology
Chinese musicology is the academic study of traditional Chinese music. This discipline has a very long history. Traditional Chinese music can be traced back to around 8,000 years ago during the Neolithic age. The concept of music, called ''yue'' (), stands among the oldest categories of Chinese thought; however, in historical sources, it does not receive clear definition until the writing of the ''Classic of Music'' (lost during the Han dynasty). Different musical traditions have influenced it throughout its history, dating back to the Xia and Shang dynasties. Music scales The first musical scales were derived from the harmonic series (music), harmonic series. On the Guqin (a traditional instrument) all of the dotted positions are equal string length divisions related to the open string like 1/2, 1/3, 2/3, 1/4, 3/4, etc. and are quite easy to recognize on this instrument. The Guqin has a scale of 13 positions all representing a natural harmonic position related to the open string. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indian Music Scale
Swara () or svara is an Indian classical music term that connotes simultaneously a breath, a vowel, a note, the sound of a musical note corresponding to its name, and the successive steps of the octave, or ''saptanka''. More comprehensively, it is the ancient Indian concept of the complete dimension of musical pitch. At its most basic comparison to western music, a ''swara'' is, essentially, a "note" of a given scale. However, that is but a loose interpretation of the word, as a ''swara'' is identified as both a musical note and tone; a "tone" is a precise substitute for sur, relating to "tunefulness". Traditionally, Indian musicians have just seven ''swara''s/notes with short names: sa, re, ga, ma, pa, dha, ni, which they collectively refer to as ''saptank'' or ''saptaka''. This is one of the reasons why ''swara'' is considered a symbolic expression for the number seven. In another loose comparison to western music, ''saptak'' (as an octave or scale) may be interpreted as s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Musical Acoustics
Musical acoustics or music acoustics is a multidisciplinary field that combines knowledge from physics, psychophysics, organology (classification of the instruments), physiology, music theory, ethnomusicology, signal processing and instrument building, among other disciplines. As a branch of acoustics, it is concerned with researching and describing the physics of music – how sounds are employed to make music. Examples of areas of study are the function of musical instruments, the human voice (the physics of speech and singing), computer analysis of melody, and in the clinical use of music in music therapy. The pioneer of music acoustics was Hermann von Helmholtz, a German polymath of the 19th century who was an influential physician, physicist, physiologist, musician, mathematician and philosopher. His book '' On the Sensations of Tone as a Physiological Basis for the Theory of Music'' is a revolutionary compendium of several studies and approaches that provided a complete n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physics
Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." It is one of the most fundamental scientific disciplines. "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plato
Plato ( ; Greek language, Greek: , ; born BC, died 348/347 BC) was an ancient Greek philosopher of the Classical Greece, Classical period who is considered a foundational thinker in Western philosophy and an innovator of the written dialogue and dialectic forms. He influenced all the major areas of theoretical philosophy and practical philosophy, and was the founder of the Platonic Academy, a philosophical school in History of Athens, Athens where Plato taught the doctrines that would later become known as Platonism. Plato's most famous contribution is the theory of forms, theory of forms (or ideas), which aims to solve what is now known as the problem of universals. He was influenced by the pre-Socratic thinkers Pythagoras, Heraclitus, and Parmenides, although much of what is known about them is derived from Plato himself. Along with his teacher Socrates, and his student Aristotle, Plato is a central figure in the history of Western philosophy. Plato's complete ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
