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Ragisma
In music and tuning, the ragisma is an interval with the ratio of 4375:4374,Haluska, Jan (2003). ''The Mathematical Theory of Tone Systems'', p.xxviii. . ≈0.396 cents (a superparticular ratio). It is usually defined as the difference between the septimal minor third (7:6) and two Bohlen–Pierce small semitones (27:25 ). It is also the difference between minor Bohlen–Pierce diesis (245:243) and septimal semicomma In music, the septimal semicomma, a seven- limit semicomma, is the ratio 126/125 and is equal to approximately 13.79 cents (). It is also called the ''small septimal comma''Haluska, Jan (2003). ''The Mathematical Theory of Tone Systems'', p.xxvi. ... (126:125), as well as the difference between the septimal third tone (28:27) and the greater diesis (648:625). () References {{Intervals, state=expanded 7-limit tuning and intervals Commas (music) 4375:4374 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Superparticular Number
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 simple 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Septimal Minor Third On C
Septimal may refer to: *Septimal chromatic semitone, the interval 21:20, about 84.47 cents *Septimal comma, a small musical interval in just intonation divisible by 7 * Septimal diatonic semitone, the interval 15:14, about 119.44 cents *Septimal diesis, an interval with the ratio of 49:48, about 38.71 cents *Septimal kleisma, an interval of approximately 7.7 cents * Septimal major third, the musical interval with a 9:7 ratio of frequencies *Septimal meantone temperament, the tempering of 7-limit musical intervals by a meantone temperament tuning *Septimal minor third, the musical interval exactly or approximately equal to a 7/6 ratio of frequencies * Septimal quarter tone, an interval with the ratio of 36:35, about 48.77 cents *Septimal semicomma, an interval with the ratio 126/125, about 13.79 cents *Septimal sixth-tone (or jubilisma), an interval with the ratio of 50:49, about 34.98 cents *Septimal tritone, the interval 7:5, about 582.51 ce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Music
Music is the arrangement of sound to create some combination of Musical form, form, harmony, melody, rhythm, or otherwise Musical expression, expressive content. Music is generally agreed to be a cultural universal that is present in all human societies. Definitions of music vary widely in substance and approach. While scholars agree that music is defined by a small number of elements of music, specific elements, there is no consensus as to what these necessary elements are. Music is often characterized as a highly versatile medium for expressing human creativity. Diverse activities are involved in the creation of music, and are often divided into categories of musical composition, composition, musical improvisation, improvisation, and performance. Music may be performed using a wide variety of musical instruments, including the human voice. It can also be composed, sequenced, or otherwise produced to be indirectly played mechanically or electronically, such as via a music box ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Musical Tuning
In music, there are two common meanings for tuning: * #Tuning practice, Tuning practice, the act of tuning an instrument or voice. * #Tuning systems, Tuning systems, the various systems of Pitch (music), 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 A440 (pitch standard), A = 440 Hz. The term "''out of tune''" refers to a pitch/tone that is either too high (Sharp (music), sharp) or too low (Flat (music), 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 method ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interval (music)
In music theory, an interval is a difference in pitch between two sounds. An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord. In Western music, intervals are most commonly differences between notes of a diatonic scale. Intervals between successive notes of a scale are also known as scale steps. The smallest of these intervals is a semitone. Intervals smaller than a semitone are called microtones. They can be formed using the notes of various kinds of non-diatonic scales. Some of the very smallest ones are called commas, and describe small discrepancies, observed in some tuning systems, between enharmonically equivalent notes such as C and D. Intervals can be arbitrarily small, and even imperceptible to the human ear. In physical terms, an interval is the ratio between two sonic fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 temperament, equal tempered perfect fifth () which is 27/12 (about 1.498). If the A above middle C is A440 (Concert A), 440 Hertz, Hz, the perfect fifth above it would be E (musical note), 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#Strobe tuner, electronic tuner). Ratios have an Multiplicative inverse, inverse relationship to string length, for example stopping a string at two-thirds (2:3) its length ... [...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, to check intonation, or to compare the sizes of comparable intervals in different tuning systems. For humans, a single 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, \sqrt 200/math>, at Robert Holford Macdowell Bosanquet's suggestion. Making extensive measurements of musical instruments from around the world, Ellis used cents to report and compare the scales employed, and further described and utilized the system in his 1875 edition of Hermann von Helmholtz's ''On the Sensations of Tone''. It has become the standard me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Septimal Minor Third
Septimal may refer to: *Septimal chromatic semitone, the interval 21:20, about 84.47 cents *Septimal comma, a small musical interval in just intonation divisible by 7 *Septimal diatonic semitone, the interval 15:14, about 119.44 cents *Septimal diesis, an interval with the ratio of 49:48, about 38.71 cents *Septimal kleisma, an interval of approximately 7.7 cents *Septimal major third, the musical interval with a 9:7 ratio of frequencies *Septimal meantone temperament, the tempering of 7-limit musical intervals by a meantone temperament tuning *Septimal minor third, the musical interval exactly or approximately equal to a 7/6 ratio of frequencies *Septimal quarter tone, an interval with the ratio of 36:35, about 48.77 cents *Septimal semicomma, an interval with the ratio 126/125, about 13.79 cents *Septimal sixth-tone (or jubilisma), an interval with the ratio of 50:49, about 34.98 cents *Septimal tritone, the interval 7:5, about 582.51 cents ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bohlen–Pierce Scale
The Bohlen–Pierce scale (BP scale) is a musical musical tuning, tuning and scale (music), scale, first described in the 1970s, that offers an alternative to the octave-repeating scales typical in Classical music, Western and other musics, specifically the equal temperament, equal-tempered diatonic scale. The interval 3:1 (often called by a new name, ''tritave'') serves as the fundamental harmonic ratio, replacing the diatonic scale's 2:1 (the octave) with a perfect twelfth (an octave higher than a perfect fifth). For any pitch that is part of the BP scale, all pitches one or more tritaves higher or lower are part of the system as well, and are considered equivalent. The BP scale divides the tritave into 13 steps, either Equal temperament, equal tempered (the most popular form), or in a Just intonation, justly tuned version. Compared with octave-repeating scales, the BP scale's interval (music), intervals are more consonance and dissonance, consonant with certain types of acous ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Just Minor Second
A semitone, also called a minor second, half step, or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically. It is defined as the interval between two adjacent notes in a 12-tone scale (or half of a whole step), visually seen on a keyboard as the distance between two keys that are adjacent to each other. For example, C is adjacent to C; the interval between them is a semitone. In a 12-note approximately equally divided scale, any interval can be defined in terms of an appropriate number of semitones (e.g. a whole tone or major second is 2 semitones wide, a major third 4 semitones, and a perfect fifth 7 semitones). In music theory, a distinction is made between a diatonic semitone, or minor second (an interval encompassing two different staff positions, e.g. from C to D) and a chromatic semitone or augmented unison (an interval between two notes at the same staff position, e.g. f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Septimal Semicomma
In music, the septimal semicomma, a seven- limit semicomma, is the ratio 126/125 and is equal to approximately 13.79 cents (). It is also called the ''small septimal comma''Haluska, Jan (2003). ''The Mathematical Theory of Tone Systems'', p.xxvi. . and the ''starling comma'' after its use in starling temperament. Factored into primes it is: 2*3^2*5^*7 Or as simple just intervals: (6/5)^3*(7/6)*(2/1)^ Thus it is the difference between three minor thirds of 6/5 plus a septimal minor third of 7/6 and an octave (2/1). This comma is important to certain tuning systems, such as septimal meantone temperament. A diminished seventh chord consisting of three minor thirds and a subminor third making up an octave is possible in such systems. This characteristic feature of these tuning systems is known as the ''septimal semicomma diminished seventh chord''. In equal temperament It is tempered out in 19 equal temperament and 31 equal temperament, but not in 22 equal temperament, 34 equa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Septimal Third Tone
A septimal 1/3-tone (in music) is an interval with the ratio of 28:27, which is the difference between the perfect fourth and the supermajor third. It is about 62.96 cents wide. The septimal 1/3-tone can be viewed either as a musical interval in its own right, or as a comma; if it is tempered out in a given tuning system, the distinction between these two intervals is lost. The septimal 1/3-tone may be derived from the harmonic series as the interval between the twenty-seventh and twenty-eighth harmonics. It may be considered a diesis. The septimal 1/3-tone, along with the septimal diesis is tempered out by five-tone equal temperament, and equal temperaments which divide the octave into a small multiple of 5 steps, such as 15-TET and 25-TET. This family of scales is known as Blackwood temperament in honor of Easley Blackwood, Jr., who first analyzed 10-note subsets of 15-TET that take advantage of the temperament. When added to the 15:14 semitone, the 21:20 semitone ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
