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Interval Ratio
In music, an interval ratio is a ratio of the frequencies of the pitches in a musical interval. For example, a just perfect fifth (for example C to G) is 3:2 (), 1.5, and may be approximated by an equal tempered perfect fifth () which is 27/12 (about 1.498). If the A above middle C is 440 Hz, the perfect fifth above it would be E, at (440*1.5=) 660 Hz, while the equal tempered E5 is 659.255 Hz. Ratios, rather than direct frequency measurements, allow musicians to work with relative pitch measurements applicable to many instruments in an intuitive manner, whereas one rarely has the frequencies of fixed pitched instruments memorized and rarely has the capabilities to measure the changes of adjustable pitch instruments (electronic tuner). Ratios have an inverse relationship to string length, for example stopping a string at two-thirds (2:3) its length produces a pitch one and one-half (3:2) that of the open string (not to be confused with inversion). Intervals may be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Major Second On C
Major (Commandant (rank), commandant in certain jurisdictions) is a military rank of commissioned officer status, with corresponding ranks existing in many military forces throughout the world. When used unhyphenated and in conjunction with no other indicators, major is one rank above Captain (land), captain, and one rank below lieutenant colonel. It is considered the most junior of the field officer ranks. Background Majors are typically assigned as specialised executive or operations officers for battalion-sized units of 300 to 1,200 soldiers while in some nations, like Germany, majors are often in command of a Company (military unit), company. When used in hyphenated or combined fashion, the term can also imply seniority at other levels of rank, including ''general-major'' or ''major general'', denoting a low-level general officer, and ''sergeant major'', denoting the most senior non-commissioned officer (NCO) of a military unit. The term ''major'' can also be used wit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiplicative Inverse
In mathematics, a multiplicative inverse or reciprocal for a number ''x'', denoted by 1/''x'' or ''x''−1, is a number which when multiplied by ''x'' yields the multiplicative identity, 1. The multiplicative inverse of a fraction ''a''/''b'' is ''b''/''a''. For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4. The reciprocal function, the function ''f''(''x'') that maps ''x'' to 1/''x'', is one of the simplest examples of a function which is its own inverse (an involution). Multiplying by a number is the same as dividing by its reciprocal and vice versa. For example, multiplication by 4/5 (or 0.8) will give the same result as division by 5/4 (or 1.25). Therefore, multiplication by a number followed by multiplication by its reciprocal yields the original number (since the product of the number and its reciprocal is 1). The term ''reciproc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unison
In music, unison is two or more musical parts that sound either the same pitch or pitches separated by intervals of one or more octaves, usually at the same time. ''Rhythmic unison'' is another term for homorhythm. Definition Unison or perfect unison (also called a prime, or perfect prime)Benward & Saker (2003), p. 53. may refer to the (pseudo-) interval formed by a tone and its duplication (in German, ''Unisono'', ''Einklang'', or ''Prime''), for example C–C, as differentiated from the second, C–D, etc. In the unison the two pitches have the ratio of 1:1 or 0 half steps and zero cents. Although two tones in unison are considered to be the same pitch, they are still perceivable as coming from separate sources, whether played on instruments of a different type: ; or of the same type: . This is because a pair of tones in unison come from different locations or can have different "colors" ( timbres), i.e. come from different musical instruments or human voices. Voices wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Musical Instrument
A musical instrument is a device created or adapted to make musical sounds. In principle, any object that produces sound can be considered a musical instrument—it is through purpose that the object becomes a musical instrument. A person who plays a musical instrument is known as an instrumentalist. The history of musical instruments dates to the beginnings of human culture. Early musical instruments may have been used for rituals, such as a horn to signal success on the hunt, or a drum in a religious ceremony. Cultures eventually developed composition and performance of melodies for entertainment. Musical instruments evolved in step with changing applications and technologies. The date and origin of the first device considered a musical instrument is disputed. The oldest object that some scholars refer to as a musical instrument, a simple flute, dates back as far as 50,000 - 60,000 years. Some consensus dates early flutes to about 40,000 years ago. However, most historians ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integer Number
An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign (−1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the Set (mathematics), set of integers is often denoted by the boldface or blackboard bold \mathbb. The set of natural numbers \mathbb is a subset of \mathbb, which in turn is a subset of the set of all rational numbers \mathbb, itself a subset of the real numbers \mathbb. Like the natural numbers, \mathbb is Countable set, countably infinite. An integer may be regarded as a real number that can be written without a fraction, fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, , and are not. The integers form the smallest Group (mathematics), group and the smallest ring (mathematics), ring containing the natural numbers. In algebraic number theory, the integers are sometimes qualified as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Meantone Temperament
Meantone temperament is a musical temperament, that is a tuning system, obtained by narrowing the fifths so that their ratio is slightly less than 3:2 (making them ''narrower'' than a perfect fifth), in order to push the thirds closer to pure. Meantone temperaments are constructed the same way as Pythagorean tuning, as a stack of equal fifths, but it is a ''temperament'' in that the fifths are not pure. Notable meantone temperaments Equal temperament, obtained by making all semitones the same size, each equal to one-twelfth of an octave (with ratio the 12th root of 2 to one (:1), narrows the fifths by about 2 cents or 1/12 of a Pythagorean comma, and produces thirds that are only slightly better than in Pythagorean tuning. Equal temperament is roughly the same as 1/11 comma meantone tuning. Quarter-comma meantone, which tempers the fifths by 1/4 of a syntonic comma, is the best known type of meantone temperament, and the term ''meantone temperament'' is often used to refer t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Just Intonation
In music, just intonation or pure intonation is the tuning of musical intervals as whole number ratios (such as 3:2 or 4:3) of frequencies. An interval tuned in this way is said to be pure, and is called a just interval. Just intervals (and chords created by combining them) consist of tones from a single harmonic series of an implied fundamental. For example, in the diagram, if the notes G3 and C4 (labelled 3 and 4) are tuned as members of the harmonic series of the lowest C, their frequencies will be 3 and 4 times the fundamental frequency. The interval ratio between C4 and G3 is therefore 4:3, a just fourth. In Western musical practice, instruments are rarely tuned using only pure intervals—the desire for different keys to have identical intervals in Western music makes this impractical. Some instruments of fixed pitch, such as electric pianos, are commonly tuned using equal temperament, in which all intervals other than octaves consist of irrational-number freq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pythagorean Tuning
Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are based on the ratio 3:2.Bruce Benward and Marilyn Nadine Saker (2003). ''Music: In Theory and Practice'', seventh edition, 2 vols. (Boston: McGraw-Hill). Vol. I: p. 56. . This ratio, also known as the " pure" perfect fifth, is chosen because it is one of the most consonant and easiest to tune by ear and because of importance attributed to the integer 3. As Novalis put it, "The musical proportions seem to me to be particularly correct natural proportions." Alternatively, it can be described as the tuning of the syntonic temperament in which the generator is the ratio 3:2 (i.e., the untempered perfect fifth), which is ≈702 cents wide. The system dates to Ancient Mesopotamia; see . The system is named, and has been widely misattributed, to Ancient Greeks, notably Pythagoras (sixth century BC) by modern authors of music theory, while Ptolemy, and later Boethius, ascribed th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tuning System
In music, there are two common meanings for tuning: * Tuning practice, the act of tuning an instrument or voice. * Tuning systems, the various systems of pitches used to tune an instrument, and their theoretical bases. Tuning practice 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. The term "''out of tune''" refers to a pitch/tone that is either too high ( sharp) or too low ( flat) in relation to a given reference pitch. While an instrument might be in tune relative to its own range of notes, it may not be considered 'in tune' if it does not match the chosen reference pitch. Some instruments become 'out of tune' with temperature, humidity, damage, or simply time, and must be readjusted or repaired. Different methods of sound production require different methods of adjustment: * Tuning to a pitch with one's vo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cent (music)
The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each. Typically, cents are used to express small intervals, or to compare the sizes of comparable intervals in different tuning systems, and in fact the interval of one cent is too small to be perceived between successive notes. Cents, as described by Alexander John Ellis, follow a tradition of measuring intervals by logarithms that began with Juan Caramuel y Lobkowitz in the 17th century. Ellis chose to base his measures on the hundredth part of a semitone, , at Robert Holford Macdowell Bosanquet's suggestion. He made extensive measurements of musical instruments from around the world, using cents extensively to report and compare the scales employed, and further described and employed the system in his 1875 edition of Hermann von Helmholtz's ''On the Sensations of Tone''. It has become the standard method of representin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
7-limit
7-limit or septimal tunings and intervals are musical instrument tunings that have a limit of seven: the largest prime factor contained in the interval ratios between pitches is seven. Thus, for example, 50:49 is a 7-limit interval, but 14:11 is not. For example, the greater just minor seventh, 9:5 () is a 5-limit ratio, the harmonic seventh has the ratio 7:4 and is thus a septimal interval. Similarly, the septimal chromatic semitone, 21:20, is a septimal interval as 21÷7=3. The harmonic seventh is used in the barbershop seventh chord and music. () Compositions with septimal tunings include La Monte Young's ''The Well-Tuned Piano'', Ben Johnston's String Quartet No. 4, Lou Harrison's ''Incidental Music for Corneille's Cinna'', and Michael Harrison's ''Revelation: Music in Pure Intonation''. The Great Highland bagpipe is tuned to a ten-note seven-limit scale: 1:1, 9:8, 5:4, 4:3, 27:20, 3:2, 5:3, 7:4, 16:9, 9:5. In the 2nd century Ptolemy described the sept ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Limit (music)
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; hence the name. The harmonic series and the evolution of music 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 (see emancipation of the dissonance). In medieval music, only chords made of octaves and perfect fifths (involving relationships among the first three harmonics) were considered consonant. In the West, triadic harmony arose ( contenance angloise) around the time of the Renaissance, and triads quickly became the fundamental building blocks of Western music. The major and minor thirds of these triads invoke relationships among the first five ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
