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Mathematics Of Musical Scales
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, 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 geometric dimensio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Archytas
Archytas (; el, Ἀρχύτας; 435/410–360/350 BC) was an Ancient Greek philosopher, mathematician, music theorist, astronomer, statesman, and strategist. He was a scientist of the Pythagorean school and famous for being the reputed founder of mathematical mechanics, as well as a good friend of Plato. Life and work Archytas was born in Tarentum, Magna Graecia and was the son of Mnesagoras or Hadees. For a while, he was taught by Philolaus, and was a teacher of mathematics to Eudoxus of Cnidus. Archytas and Eudoxus' student was Menaechmus. As a Pythagorean, Archytas believed that only arithmetic, not geometry, could provide a basis for satisfactory proofs. Archytas is believed to be the founder of mathematical mechanics.: ''Vitae philosophorum'' As only described in the writings of Aulus Gellius five centuries after him, he was reputed to have designed and built the first artificial, self-propelled flying device, a bird-shaped model propelled by a jet of what was probably st ... [...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. While it plays a role in all music, with noise and musical tones lying along a spectrum from irregular to periodic sounds,(Moravcsik, 114)(Rajagopal, ) it is especially prominent in specific styles. Repetition 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 criticized repetition and popular music as being psychotic and infantile. In contrast, 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"(Middleton 1990, p. 139). "There is no universal norm or convention" for the amount or type of repetition, "all music contains repetit ... [...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 atop the pulse.Fitch, W. Tecumseh and Rosenfeld, Andrew J. (2007). Definitions The pulse may be audible or implied. The tempo of the piece 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 o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Confucius
Confucius ( ; zh, s=, p=Kǒng Fūzǐ, "Master Kǒng"; or commonly zh, s=, p=Kǒngzǐ, labels=no; – ) was a Chinese philosopher and politician of the Spring and Autumn period who is traditionally considered the paragon of Chinese sages. Confucius's teachings and philosophy underpin East Asian culture and society, remaining influential across China and East Asia to this day. Confucius considered himself a transmitter for the values of earlier periods which he claimed had been abandoned in his time. His philosophical teachings, called Confucianism, emphasized personal and governmental morality, correctness of social relationships, justice, kindness, and sincerity. His followers competed with many other schools during the Hundred Schools of Thought era, only to be suppressed in favor of the Legalists during the Qin dynasty. After the collapse of Qin and the victory of Han over Chu, Confucius's thoughts received official sanction in the new government. During the Tan ... [...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. 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 over time, of the steps of a dance, or the meter of spoken language and poetry. In some performing arts, such as hip hop music, the rhythmic delivery of the lyrics is one of the most important elements of the style. Rhythm may also refer to visual presentation, as "timed mov ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic
A harmonic is a wave with a frequency that is a positive integer multiple of the ''fundamental frequency'', the frequency of the original periodic signal, such as a sinusoidal wave. The original signal 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 wind instrum ... [...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 乐 (yuè), stands among the oldest categories of Chinese thought; however, in the known sources it does not receive a fairly clear definition until the writing of the ''Classic of Music'' (lost during the Han dynasty). Music scales The first musical scales were derived from the 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. The ancient Chinese defined, by mathematical means, a gamut or series of 十二律 (Shí-èr-lǜ), meaning twelve lǜ, from which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indian Music Scale
Svara or swara (Devanagari: स्वर, generally pronounced as ''swar'') is a Sanskrit word that connotes simultaneously a breath, a vowel, the sound of a musical note corresponding to its name, and the successive steps of the octave or ''saptaka''. More comprehensively, it is the ancient Indian concept about the complete dimension of musical pitch. Most of the time a ''svara'' is identified as both musical note and tone, but a tone is a precise substitute for sur, related to tunefulness. Traditionally, Indians have just seven ''svara''s/notes with short names, e.g. saa, re/ri, ga, ma, pa, dha, ni which Indian musicians collectively designate as ''saptak'' or ''saptaka''. It is one of the reasons why ''svara'' is considered a symbolic expression for the number seven. Origins and history Etymology The word ''swara'' or ''svara'' (Sanskrit: स्वर) is derived from the root ''svr'' which means "to sound". To be precise, the ''svara'' is defined in the Sanskrit ''nirukt ... [...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 natural science that studies matter, its 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." Physics is one of the most fundamental scientific disciplines, with its main goal being to understand how the universe behaves. "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 physic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plato
Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was a Greek philosopher born in Athens during the Classical period in Ancient Greece. He founded the Platonist school of thought and the Academy, the first institution of higher learning on the European continent. Along with his teacher, Socrates, and his student, Aristotle, Plato is a central figure in the history of Ancient Greek philosophy and the Western and Middle Eastern philosophies descended from it. He has also shaped religion and spirituality. The so-called neoplatonism of his interpreter Plotinus greatly influenced both Christianity (through Church Fathers such as Augustine) and Islamic philosophy (through e.g. Al-Farabi). In modern times, Friedrich Nietzsche diagnosed Western culture as growing in the shadow of Plato (famously calling Christianity "Platonism for the masses"), while Alfred North Whitehead famously said: "the safest general characterization of the European philosophical tra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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