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Otonality And Utonality
''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 t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Major Third
In classical music, a third is a musical interval encompassing three staff positions (see Interval number for more details), and the major third () is a third spanning four semitones. Forte, Allen (1979). ''Tonal Harmony in Concept and Practice'', p.8. Holt, Rinehart, and Winston. Third edition . "A large 3rd, or ''major 3rd'' (M3) encompassing four half steps." Along with the minor third, the major third is one of two commonly occurring thirds. It is qualified as ''major'' because it is the larger of the two: the major third spans four semitones, the minor third three. For example, the interval from C to E is a major third, as the note E lies four semitones above C, and there are three staff positions from C to E. Diminished and augmented thirds span the same number of staff positions, but consist of a different number of semitones (two and five). The major third may be derived from the harmonic series as the interval between the fourth and fifth harmonics. The maj ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tuva
Tuva (; russian: Тува́) or Tyva ( tyv, Тыва), officially the Republic of Tuva (russian: Респу́блика Тыва́, r=Respublika Tyva, p=rʲɪˈspublʲɪkə tɨˈva; tyv, Тыва Республика, translit=Tyva Respublika ), is a federal subject of Russia (a republic, also defined in the Constitution of the Russian Federation as a state). The Tuvan Republic lies at the geographical center of Asia, in southern Siberia. The republic borders the Altai Republic, the Republic of Khakassia, Krasnoyarsk Krai, Irkutsk Oblast, and the Republic of Buryatia in Russia and Mongolia to the south. Tuva has a population of 307,930 ( 2010 census). Its capital is the city of Kyzyl. From 1921 to 1944, Tuva constituted a sovereign, independent, but partially recognized nation, acknowledged only by its neighbors the Soviet Union and Mongolia. It was known officially as Tannu Tuva until 1926 and thereafter as the Tuvan People's Republic. A majority of the population are ethni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brass Instrument
A brass instrument is a musical instrument that produces sound by sympathetic vibration of air in a tubular resonator in sympathy with the vibration of the player's lips. Brass instruments are also called labrosones or labrophones, from Latin and Greek elements meaning 'lip' and 'sound'. There are several factors involved in producing different pitches on a brass instrument. Slides, valves, crooks (though they are rarely used today), or keys are used to change vibratory length of tubing, thus changing the available harmonic series, while the player's embouchure, lip tension and air flow serve to select the specific harmonic produced from the available series. The view of most scholars (see organology) is that the term "brass instrument" should be defined by the way the sound is made, as above, and not by whether the instrument is actually made of brass. Thus one finds brass instruments made of wood, like the alphorn, the cornett, the serpent and the didgeridoo, while some ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
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] |
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] |
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] |
Septimal Minor Third
In music, the septimal minor third, also called the subminor third (e.g., by Ellis), is the musical interval exactly or approximately equal to a 7/6 ratio of frequencies. In terms of cents, it is 267 cents, a quartertone of size 36/35 flatter than a just minor third of 6/5. In 24-tone equal temperament five quarter tones approximate the septimal minor third at 250 cents (). A septimal minor third is almost exactly two-ninths of an octave, and thus all divisions of the octave into multiples of nine (72 equal temperament being the most notable) have an almost perfect match to this interval. The septimal major sixth, 12/7, is the inverse of this interval. The septimal minor third may be derived in the harmonic series from the seventh harmonic, and as such is in inharmonic ratios with all notes in the regular 12TET scale, with the exception of the fundamental and the octave. It has a darker but generally pleasing character when compared to the 6/5 third. A triad formed by using ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Septimal Tritone
A septimal tritone is a tritone (about one half of an octave) that involves the factor seven. There are two that are inverses. The lesser septimal tritone (also Huygens' tritone) is the musical interval with ratio 7:5 (582.51 cents). The greater septimal tritone (also Euler's tritone), is an interval with ratio 10:7 (617.49 cents). They are also known as the sub-fifth and super-fourth, or subminor fifth and supermajor fourth, respectively. The 7:5 interval (diminished fifth) is equal to a 6:5 minor third plus a 7:6 subminor third. The 10:7 interval (augmented fourth) is equal to a 5:4 major third plus an 8:7 supermajor second, or a 9:7 supermajor third plus a 10:9 major second. The difference between these two is the septimal sixth tone (50:49, 34.98 cents) . 12 equal temperament and 22 equal temperament do not distinguish between these tritones; 19 equal temperament does distinguish them but doesn't match them closely. 31 equal temperament and 41 equal temperament both disti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Septimal Minor Seventh
The harmonic seventh interval, also known as the septimal minor seventh, or subminor seventh, is one with an exact 7:4 ratio (about 969 cents). This is somewhat narrower than and is, "particularly sweet", "sweeter in quality" than an "ordinary" just minor seventh, which has an intonation ratio of 9:5 (about 1018 cents). The harmonic seventh arises from the harmonic series as the interval between the fourth harmonic (second octave of the fundamental) and the seventh harmonic; in that octave, harmonics 4, 5, 6, and 7 constitute a purely consonant major chord with added seventh (root position). When played on the natural horn, as a compromise the note is often adjusted to 16:9 of the root (for C maj7, the substituted note is B, 996.09 cents), but some pieces call for the pure harmonic seventh, including Britten's ''Serenade for Tenor, Horn and Strings''. Composer Ben Johnston uses a small "7" as an accidental to indicate a note is lowered 49 cents ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
