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Monochord
A monochord, also known as sonometer (see below), is an ancient musical and scientific laboratory instrument, involving one (mono-) string ( chord). The term ''monochord'' is sometimes used as the class-name for any musical stringed instrument having only one string and a stick shaped body, also known as musical bows. According to the Hornbostel–Sachs system, string bows are bar zithers (311.1) while monochords are traditionally board zithers (314). The "harmonical canon", or monochord is, at its least, "merely a string having a board under it of exactly the same length, upon which may be delineated the points at which the string must be stopped to give certain notes," allowing comparison. A string is fixed at both ends and stretched over a sound box. One or more movable bridges are then manipulated to demonstrate mathematical relationships among the frequencies produced. "With its single string, movable bridge and graduated rule, the monochord (''kanōn'' reek: law stradd ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monochord Jeans
A monochord, also known as sonometer (see below), is an ancient musical and scientific laboratory instrument, involving one (mono-) string ( chord). The term ''monochord'' is sometimes used as the class-name for any musical stringed instrument having only one string and a stick shaped body, also known as musical bows. According to the Hornbostel–Sachs system, string bows are bar zithers (311.1) while monochords are traditionally board zithers (314). The "harmonical canon", or monochord is, at its least, "merely a string having a board under it of exactly the same length, upon which may be delineated the points at which the string must be stopped to give certain notes," allowing comparison. A string is fixed at both ends and stretched over a sound box. One or more movable bridges are then manipulated to demonstrate mathematical relationships among the frequencies produced. "With its single string, movable bridge and graduated rule, the monochord (''kanōn'' reek: law straddl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sonometer
A monochord, also known as sonometer (see below), is an ancient musical and scientific laboratory instrument, involving one (mono-) string ( chord). The term ''monochord'' is sometimes used as the class-name for any musical stringed instrument having only one string and a stick shaped body, also known as musical bows. According to the Hornbostel–Sachs system, string bows are bar zithers (311.1) while monochords are traditionally board zithers (314). The "harmonical canon", or monochord is, at its least, "merely a string having a board under it of exactly the same length, upon which may be delineated the points at which the string must be stopped to give certain notes," allowing comparison. A string is fixed at both ends and stretched over a sound box. One or more movable bridges are then manipulated to demonstrate mathematical relationships among the frequencies produced. "With its single string, movable bridge and graduated rule, the monochord (''kanōn'' reek: law stradd ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mersenne's Laws
Mersenne's laws are laws describing the frequency of oscillation of a stretched string or monochord, useful in musical tuning and musical instrument construction. Overview The equation was first proposed by French mathematician and music theorist Marin Mersenne in his 1636 work '' Harmonie universelle''.Mersenne, Marin (1636)''Harmonie universelle'' Cited in, '' Wolfram.com''. Mersenne's laws govern the construction and operation of string instruments, such as pianos and harps, which must accommodate the total tension force required to keep the strings at the proper pitch. Lower strings are thicker, thus having a greater mass per length. They typically have lower tension. Guitars are a familiar exception to this: string tensions are similar, for playability, so lower string pitch is largely achieved with increased mass per length. Higher-pitched strings typically are thinner, have higher tension, and may be shorter. "This result does not differ substantially from Galileo's, yet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fingering (music)
In music, fingering, or on stringed instruments sometimes also called stopping, is the choice of which fingers and hand positions to use when playing certain musical instruments. Fingering typically changes throughout a piece; the challenge of choosing good fingering for a piece is to make the hand movements as comfortable as possible without changing hand position too often. A fingering can be the result of the working process of the composer, who puts it into the manuscript, an editor, who adds it into the printed score, or the performer, who puts his or her own fingering in the score or in performance. A substitute fingering is an alternative to the indicated fingering, not to be confused with finger substitution. Depending on the instrument, not all the fingers may be used. For example, saxophonists do not use the right thumb and string instruments (usually) only use the fingers. Instruments Brass instruments Fingering applies to the rotary and piston valves employed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graduation (instrument)
A graduation is a marking used to indicate points on a visual scale, which can be present on a container, a measuring device, or the axes of a line plot, usually one of many along a line or curve, each in the form of short line segments perpendicular to the line or curve. Often, some of these line segments are longer and marked with a numeral, such as every fifth or tenth graduation. The scale itself can be linear (the graduations are spaced at a constant distance apart) or nonlinear. Linear graduation of a scale occurs mainly (but not exclusively) on straight measuring devices, such as a rule or measuring tape, using units such as inches or millimetres. Graduations can also be spaced at varying spatial intervals, such as when using a logarithmic, for instance on a measuring cup, can vary in scale due to the container's non- cylindrical shape. Graduations along a curve Circular graduations of a scale occur on a circular arc or limb of an instrument. In some cases, non-ci ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Composite Number
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime, or the unit 1, so the composite numbers are exactly the numbers that are not prime and not a unit. For example, the integer 14 is a composite number because it is the product of the two smaller integers 2 × 7. Likewise, the integers 2 and 3 are not composite numbers because each of them can only be divided by one and itself. The composite numbers up to 150 are: :4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 102, 104, 105, 106, 108, 110, 111, 112, 114, 115, 116, 117, 118, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Number
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, or , involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order. The property of being prime is called primality. A simple but slow method of checking the primality of a given number n, called trial division, tests whether n is a multiple of any integer between 2 and \sqrt. Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error, and the AKS primality test, which alway ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Least Common Multiple
In arithmetic and number theory, the least common multiple, lowest common multiple, or smallest common multiple of two integers ''a'' and ''b'', usually denoted by lcm(''a'', ''b''), is the smallest positive integer that is divisible by both ''a'' and ''b''. Since division of integers by zero is undefined, this definition has meaning only if ''a'' and ''b'' are both different from zero. However, some authors define lcm(''a'',0) as 0 for all ''a'', since 0 is the only common multiple of ''a'' and 0. The lcm is the "lowest common denominator" (lcd) that can be used before fractions can be added, subtracted or compared. The least common multiple of more than two integers ''a'', ''b'', ''c'', . . . , usually denoted by lcm(''a'', ''b'', ''c'', . . .), is also well defined: It is the smallest positive integer that is divisible by each of ''a'', ''b'', ''c'', . . . Overview A multiple of a number is the product of that number and an integer. For example, 10 is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiplication Table
In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system. The decimal multiplication table was traditionally taught as an essential part of elementary arithmetic around the world, as it lays the foundation for arithmetic operations with base-ten numbers. Many educators believe it is necessary to memorize the table up to 9 × 9. History In pre-modern time The oldest known multiplication tables were used by the Babylonians about 4000 years ago. However, they used a base of 60. The oldest known tables using a base of 10 are the Chinese decimal multiplication table on bamboo strips dating to about 305 BC, during China's Warring States period. The multiplication table is sometimes attributed to the ancient Greek mathematician Pythagoras (570–495 BC). It is also called the Table of Pythagoras in many languages (for example French, Italian and Russian), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tetractys
The tetractys ( el, τετρακτύς), or tetrad, or the tetractys of the decad is a triangular figure consisting of ten points arranged in four rows: one, two, three, and four points in each row, which is the geometrical representation of the fourth triangular number. As a mystical symbol, it was very important to the secret worship of Pythagoreanism. There were four seasons, and the number was also associated with planetary motions and music. Pythagorean symbol # The first four numbers symbolize the ''musica universalis'' and the Cosmos as: ## (1) Unity ( Monad) ## (2) Dyad – Power – Limit/Unlimited (peras/apeiron) ## (3) Harmony (Triad) ## (4) Kosmos (Tetrad) # The four rows add up to ten, which was unity of a higher order (The Dekad). # The Tetractys symbolizes the four classical elements— air, fire, water, and earth. # The Tetractys represented the organization of space: ## the first row represented zero dimensions (a point) ## the second row represented one dimen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Superparticular
In mathematics, a superparticular ratio, also called a superparticular number or epimoric ratio, is the ratio of two consecutive integer numbers. More particularly, the ratio takes the form: :\frac = 1 + \frac where is a positive integer. Thus: Superparticular ratios were written about by Nicomachus in his treatise ''Introduction to Arithmetic''. Although these numbers have applications in modern pure mathematics, the areas of study that most frequently refer to the superparticular ratios by this name are music theory and the history of mathematics. Mathematical properties As Leonhard Euler observed, the superparticular numbers (including also the multiply superparticular ratios, numbers formed by adding an integer other than one to a unit fraction) are exactly the rational numbers whose continued fraction terminates after two terms. The numbers whose continued fraction terminates in one term are the integers, while the remaining numbers, with three or more terms in their c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Astronomy
Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, galaxies, and comets. Relevant phenomena include supernova explosions, gamma ray bursts, quasars, blazars, pulsars, and cosmic microwave background radiation. More generally, astronomy studies everything that originates beyond Earth's atmosphere. Cosmology is a branch of astronomy that studies the universe as a whole. Astronomy is one of the oldest natural sciences. The early civilizations in recorded history made methodical observations of the night sky. These include the Babylonians, Greeks, Indians, Egyptians, Chinese, Maya, and many ancient indigenous peoples of the Americas. In the past, astronomy included disciplines as diverse as astrometry, celestial navigation, observational astronomy, and the making of calendars. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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