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96 Equal Temperament
In music, 96 equal temperament, called 96-TET, 96-EDO ("Equal Division of the Octave"), or 96-ET, is the tempered scale derived by dividing the octave into 96 equal steps (equal frequency ratios). Each step represents a frequency ratio of \sqrt 6/math>, or 12.5 cents. Since 96 factors into 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96, it contains all of those temperaments. Most humans can only hear differences of 6 cents on notes that are played sequentially, and this amount varies according to the pitch, so the use of larger divisions of octave can be considered unnecessary. Smaller differences in pitch may be considered vibrato or stylistic devices. History and use 96-EDO was first advocated by Julián Carrillo in 1924, with a 16th-tone piano. It was also advocated more recently by Pascale Criton and Vincent-Olivier Gagnon. Notation Since 96 = 24 × 4, quarter-tone notation can be used and split into four parts. One can split it into four parts like this: C, C, C/C, C, C, ... ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Musical Temperament
In musical tuning, a temperament is a tuning system that slightly compromises the pure intervals of just intonation to meet other requirements. Most modern Western musical instruments are tuned in the equal temperament system. Tempering is the process of altering the size of an interval by making it narrower or wider than pure. "Any plan that describes the adjustments to the sizes of some or all of the twelve fifth intervals in the circle of fifths so that they accommodate pure octaves and produce certain sizes of major thirds is called a ''temperament''." Temperament is especially important for keyboard instruments, which typically allow a player to play only the pitches assigned to the various keys, and lack any way to alter pitch of a note in performance. Historically, the use of just intonation, Pythagorean tuning and meantone temperament meant that such instruments could sound "in tune" in one key, or some keys, but would then have more dissonance in other keys. In the wo ... [...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] |
Semitone
A semitone, also called a 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. 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. from C to C). These are enharmonically equivalent when twelve-tone equal temperament is used, but are not the same thing in meantone temper ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Septimal Diatonic Semitone
In music, a septimal diatonic semitone (or major diatonic semitoneHaluska, Jan (2003). ''The Mathematical Theory of Tone Systems'', p.xxiv & 25. .) is the interval 15:14 . It is about 119.44 cents. The septimal diatonic semitone may be derived from the harmonic series as the interval between the fourteenth and fifteenth harmonics ( B7b and B). The septimal diatonic semitone equals a just diatonic semitone (16:15, or 111.73 cents) plus a septimal kleisma In music, the ratio 225/224 is called the septimal kleisma (). It is a minute comma type interval of approximately 7.7 cents. Factoring it into primes gives 2−5 32 52 7−1, which can be rewritten 2−1 (5/4)2 (9/7). That says t ... (the interval 225:224, or 7.71 cents). See also * Major diatonic semitone (5-limit, 16:15) * Minor diatonic semitone (or septendecimal diatonic semitone, 17:16). References {{music-theory-stub Seconds (music) 7-limit tuning and intervals 0015:0014 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neutral Interval
In music theory, a neutral interval is an interval that is neither a major nor minor, but instead in between. For example, in equal temperament, a major third is 400 cents, a minor third is 300 cents, and a neutral third is 350 cents. A neutral interval inverts to a neutral interval. For example, the inverse of a neutral third is a neutral sixth. Roughly, neutral intervals are a quarter tone sharp from minor intervals and a quarter tone flat from major intervals. In just intonation, as well as in tunings such as 31-ET, 41-ET, or 72-ET, which more closely approximate just intonation, the intervals are closer together. *Neutral second *Neutral third * Neutral sixth * Neutral seventh Second A neutral second or medium second is an interval wider than a minor second and narrower than a major second. Three distinct intervals may be termed neutral seconds: * The intermediate neutral second, called the lesser undecimal neutral second , has a ratio between the higher-freq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Major Second
In Western music theory, a major second (sometimes also called whole tone or a whole step) is a second spanning two semitones (). A second is a musical interval encompassing two adjacent staff positions (see Interval number for more details). For example, the interval from C to D is a major second, as the note D lies two semitones above C, and the two notes are notated on adjacent staff positions. Diminished, minor and augmented seconds are notated on adjacent staff positions as well, but consist of a different number of semitones (zero, one, and three). The major second is the interval that occurs between the first and second degrees of a major scale, the tonic and the supertonic. On a musical keyboard, a major second is the interval between two keys separated by one key, counting white and black keys alike. On a guitar string, it is the interval separated by two frets. In moveable-do solfège, it is the interval between ''do'' and ''re''. It is considered a melo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Septimal Whole Tone
In music, the septimal whole tone, septimal major second, or supermajor second is the musical interval exactly or approximately equal to an 8/7 ratio of frequencies.Andrew Horner, Lydia Ayres (2002). ''Cooking with Csound: Woodwind and Brass Recipes'', p.131. . "Super-Major Second". It is about 231 cents wide in just intonation.Leta E. Miller, Fredric Lieberman (2006). ''Lou Harrison'', p.72. . 24 equal temperament does not match this interval particularly well, its nearest representation being at 250 cents, approximately 19 cents sharp. The septimal whole tone may be derived from the harmonic series as the interval between the seventh and eighth harmonics and the term ''septimal'' refers to the fact that it utilizes the seventh harmonic. It can also be thought of as the octave inversion of the 7/4 interval, the harmonic seventh. No close approximation to this interval exists in the standard 12 equal temperament used in most modern western music. The very simple 5 equal ... [...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] |
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] |
Augmented Second
In classical music from Western culture, an augmented second is an interval that, in equal temperament, is sonically equivalent to a minor third, spanning three semitones, and is created by widening a major second by a chromatic semitone.Benward & Saker (2003). ''Music: In Theory and Practice, Vol. I'', p.54. . Specific example of an A2 not given but general example of major intervals described. For instance, the interval from C to D is a major second, two semitones wide, and the interval from C to D is an augmented second, spanning three semitones. Usage Augmented seconds occur in many scales, most importantly the harmonic minor and its various modes. They also occur in the various Gypsy scales (which consist almost entirely of augmented and minor seconds). In harmonic minor scales, the augmented second occurs between the sixth and seventh scale degrees. For example, in the scale of A harmonic minor, the notes F and G form the interval of an augmented second. This distinguish ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minor Third
In music theory, a minor third is a musical interval that encompasses three half steps, or semitones. Staff notation represents the minor third as encompassing three staff positions (see: interval number). The minor third is one of two commonly occurring thirds. It is called ''minor'' because it is the smaller of the two: the major third spans an additional semitone. For example, the interval from A to C is a minor third, as the note C lies three semitones above A. Coincidentally, there are three staff positions from A to C. Diminished and augmented thirds span the same number of staff positions, but consist of a different number of semitones (two and five). The minor third is a skip melodically. Notable examples of ascending minor thirds include the opening two notes of " Greensleeves" and of " Light My Fire". The minor third may be derived from the harmonic series as the interval between the fifth and sixth harmonics, or from the 19th harmonic. The minor third is co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neutral Third
A neutral third is a musical interval wider than a minor third but narrower than a major third , named by Jan Pieter Land in 1880. Land makes reference to the neutral third attributed to Zalzal (8th c.), described by Al-Farabi (10th c.) as corresponding to a ratio of 27:22 (354.5 cents) and by Avicenna (Ibn Sina, 11th c.) as 39:32 (342.5 cents). The Zalzalian third may have been a mobile interval. Three distinct intervals may be termed neutral thirds: * The ''undecimal neutral third'' has a ratio of 11:9 between the frequencies of the two tones, or about 347.41 cents . This ratio is the mathematical mediant of the major third 5/4 and the minor third 6/5, and as such, has the property that if harmonic notes of frequency ''f'' and (11/9) ''f'' are played together, the beat frequency of the 5th harmonic of the lower pitch against the 4th of the upper, i.e. , 5 f - 4 (11/9) f, = (1/9) f, is the same as the beat frequency of the 6th harmonic of the lower pitch against the 5t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
