Otonal
''Otonality'' and ''utonality'' are terms introduced by Harry Partch to describe chords whose pitch classes are the harmonics or subharmonics of a given fixed tone (identity), respectively. For example: , , ,... or , , ,.... Definition An otonality is a collection of pitches which can be expressed in ratios, expressing their relationship to the fixed tone, that have equal denominators and consecutive numerators. For example, , , and (just major chord) form an otonality because they can be written as , , . This in turn can be written as an extended ratio 4:5:6. Every otonality is therefore composed of members of a harmonic series. Similarly, the ratios of a utonality share the same numerator and have consecutive denominators. , , , and () form a utonality, sometimes written as , or as . Every utonality is therefore composed of members of a subharmonic series. This term is used extensively by Harry Partch in ''Genesis of a Music''. An otonality corresponds to ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Otonality And Utonality 5-limit
''Otonality'' and ''utonality'' are terms introduced by Harry Partch to describe chords whose pitch classes are the harmonics or subharmonics of a given fixed tone (identity), respectively. For example: , , ,... or , , ,.... Definition An otonality is a collection of pitches which can be expressed in ratios, expressing their relationship to the fixed tone, that have equal denominators and consecutive numerators. For example, , , and (just major chord) form an otonality because they can be written as , , . This in turn can be written as an extended ratio 4:5:6. Every otonality is therefore composed of members of a harmonic series. Similarly, the ratios of a utonality share the same numerator and have consecutive denominators. , , , and () form a utonality, sometimes written as , or as . Every utonality is therefore composed of members of a subharmonic series. This term is used extensively by Harry Partch in ''Genesis of a Music''. An otonality corresponds to ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Just Intonation
In music, just intonation or pure intonation is the tuning of musical intervals Interval may refer to: Mathematics and physics * Interval (mathematics), a range of numbers ** Partially ordered set#Intervals, its generalization from numbers to arbitrary partially ordered sets * A statistical level of measurement * Interval e ... as whole number ratios (such as 3:2 or 4:3) of Frequency, frequencies. An interval (music), 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 (music), harmonic series of an implied fundamental frequency, 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 (music), fourth. In Western musical practice ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Harry Partch
Harry Partch (June 24, 1901 – September 3, 1974) was an American composer, music theorist, and creator of unique musical instruments. He composed using scales of unequal intervals in just intonation, and was one of the first 20th-century composers in the West to work systematically with microtonal scales, alongside Lou Harrison. He built custom-made instruments in these tunings on which to play his compositions, and described the method behind his theory and practice in his book '' Genesis of a Music'' (1947). Partch composed with scales dividing the octave into 43 unequal tones derived from the natural harmonic series; these scales allowed for more tones of smaller intervals than in standard Western tuning, which uses twelve equal intervals to the octave. To play his music, Partch built many unique instruments, with such names as the Chromelodeon, the Quadrangularis Reversum, and the Zymo-Xyl. Partch described his music as corporeal, and distinguished it from abs ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Tonality Diamond
In music theory and tuning, a tonality diamond is a two-dimensional diagram of ratios in which one dimension is the Otonality and one the Utonality.Rasch, Rudolph (2000). "A Word or Two on the Tunings of Harry Partch", ''Harry Partch: An Anthology of Critical Perspectives'', p.28. Dunn, David, ed. . Thus the n-limit tonality diamond ("limit" here is in the sense of odd limit, not prime limit) is an arrangement in diamond-shape of the set of rational numbers ''r'', 1 \le r < 2, such that the odd part of both the and the of ''r'', when reduced to lowest terms, is less than or equal to the fixed ''n ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Numerary Nexus
In music theory and tuning, a tonality diamond is a two-dimensional diagram of ratios in which one dimension is the Otonality and one the Utonality.Rasch, Rudolph (2000). "A Word or Two on the Tunings of Harry Partch", ''Harry Partch: An Anthology of Critical Perspectives'', p.28. Dunn, David, ed. . Thus the n-limit tonality diamond ("limit" here is in the sense of odd limit, not prime limit) is an arrangement in diamond-shape of the set of rational numbers ''r'', 1 \le r < 2, such that the odd part of both the and the of ''r'', when reduced to lowest terms, is less than or equal to the fixed odd number ''n''. Equivalently, the diamond ma ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Identity (tuning)
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 h ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Bob Gilmore
Bob Gilmore (6 June 1961 – 2 January 2015) was a musicologist, educator and keyboard player. Born in Larne, Northern Ireland, he spent his early years in Carrickfergus. He studied music at York University, England, then at Queen's University Belfast (PhD. 1992), and, on a Fulbright Scholarship, at the University of California, San Diego. He is best known for his books on American music: he wrote ''Harry Partch: A Biography'' (Yale University Press, 1998) and edited with an introduction ''"Maximum Clarity" and Other Writings on Music'' (University of Illinois Press, 2006—collected writings by Ben Johnston), both of which were recipients of the Deems Taylor Award from ASCAP. He also wrote extensively on the American experimental tradition, microtonal music and spectral music, including the work of such figures as James Tenney, Horațiu Rădulescu, Claude Vivier, and Frank Denyer. He wrote on the work of younger Irish composers including Deirdre Gribbin, Donnacha Dennehy and ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Harmonic Series (music)
A harmonic series (also overtone series) is the sequence of harmonics, musical tones, or pure tones whose frequency is an integer multiple of a ''fundamental frequency''. Pitched musical instruments are often based on an acoustic resonator such as a string or a column of air, which oscillates at numerous modes simultaneously. At the frequencies of each vibrating mode, waves travel in both directions along the string or air column, reinforcing and canceling each other to form standing waves. Interaction with the surrounding air causes audible sound waves, which travel away from the instrument. Because of the typical spacing of the resonances, these frequencies are mostly limited to integer multiples, or harmonics, of the lowest frequency, and such multiples form the harmonic series. The musical pitch of a note is usually perceived as the lowest partial present (the fundamental frequency), which may be the one created by vibration over the full length of the string or air co ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Audio Frequency
An audio frequency or audible frequency (AF) is a periodic vibration whose frequency is audible to the average human. The SI unit of frequency is the hertz (Hz). It is the property of sound that most determines pitch. The generally accepted standard hearing range for humans is 20 to 20,000 Hz. In air at atmospheric pressure, these represent sound waves with wavelengths of to . Frequencies below 20 Hz are generally felt rather than heard, assuming the amplitude of the vibration is great enough. High frequencies are the first to be affected by hearing loss due to age or prolonged exposure to very loud noises. Sound frequencies above 20 kHz are called ultrasonic. Frequencies and descriptions See also *Absolute threshold of hearing *Hypersonic effect, controversial claim for human perception above 20,000 Hz *Loudspeaker *Musical acoustics *Piano key frequencies *Scientific pitch notation *Whistle register The whistle register (also called the flute regi ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Arithmetic Series
An arithmetic progression or arithmetic sequence () is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common difference of 2. If the initial term of an arithmetic progression is a and the common difference of successive members is d, then the n-th term of the sequence (a_n) is given by: :a_n = a + (n - 1)d, If there are ''m'' terms in the AP, then a_m represents the last term which is given by: :a_m = a + (m - 1)d. A finite portion of an arithmetic progression is called a finite arithmetic progression and sometimes just called an arithmetic progression. The sum of a finite arithmetic progression is called an arithmetic series. Sum Computation of the sum 2 + 5 + 8 + 11 + 14. When the sequence is reversed and added to itself term by term, the resulting sequence has a single repeated value in it, equal to the sum of the first and last numbers ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Subharmonic Series
In music, the undertone series or subharmonic series is a sequence of notes that results from inverting the intervals of the overtone series. While overtones naturally occur with the physical production of music on instruments, undertones must be produced in unusual ways. While the overtone series is based upon arithmetic multiplication of frequencies, resulting in a harmonic series, the undertone series is based on arithmetic division. Nattiez shows the undertone series on E, as Riemann (''Handbuch der Harmonielehre'', 10th ed., 1929, p. 4) and D'Indy (''Cours de composition musicale'', vol. I, 1912, p. 100) had done. Terminology The hybrid term ''subharmonic'' is used in music in a few different ways. In its pure sense, the term ''subharmonic'' refers strictly to any member of the subharmonic series (, , , , etc.). When the subharmonic series is used to refer to frequency relationships, it is written with f representing some highest known reference frequency (, , , , etc. ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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String Instrument
String instruments, stringed instruments, or chordophones are musical instruments that produce sound from vibrating strings when a performer plays or sounds the strings in some manner. Musicians play some string instruments by plucking the strings with their fingers or a plectrum—and others by hitting the strings with a light wooden hammer or by rubbing the strings with a bow. In some keyboard instruments, such as the harpsichord, the musician presses a key that plucks the string. Other musical instruments generate sound by striking the string. With bowed instruments, the player pulls a rosined horsehair bow across the strings, causing them to vibrate. With a hurdy-gurdy, the musician cranks a wheel whose rosined edge touches the strings. Bowed instruments include the string section instruments of the orchestra in Western classical music (violin, viola, cello and double bass) and a number of other instruments (e.g., viols and gambas used in early music from the Baro ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |