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Septimal Diesis 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 cents ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Septimal Chromatic Semitone
In music, a septimal chromatic semitone or minor semitoneHaluska, Jan (2003). ''The Mathematical Theory of Tone Systems'', p.xxiv. . is the interval 21:20 (). It is about 84.47 cents. The septimal chromatic semitone may be derived from the harmonic series as the interval between the twentieth and twenty-first harmonics. The septimal chromatic semitone equals a just chromatic semitone (25:24) plus a septimal semicomma (126:125). When added to the 15:14 semitone, the 21:20 semitone and 28:27 semitone produce the 9:8 tone (major tone 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 deta ...) and 10:9 tone (minor tone), respectively. References 7-limit tuning and intervals Seconds (music) 0021:0020 {{Music-theory-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Septimal Comma
A septimal comma is a small musical interval in just intonation that contains the number seven in its prime factorization. There is more than one such interval, so the term ''septimal comma'' is ambiguous, but it most commonly refers to the interval 64/63 (27.26 cents). Use of septimal commas introduces new intervals that extend tuning beyond common-practice, extending music to the 7-limit, including the 7/6 septimal minor third, the 7/5 septimal tritone and the 8/7 septimal major second. Composers who made extensive use of these intervals include Harry Partch and Ben Johnston. Johnston uses a "7" as an accidental to indicate a note is lowered 49 cents, or an upside down seven ("ㄥ" or "") to indicate a note is raised 49 cents (36/35).John Fonville. "Ben Johnston's Extended Just Intonation – A Guide for Interpreters", p. 113, '' Perspectives of New Music'', vol. 29, no. 2 (Summer 1991), pp. 106–137. Specific commas The 64/63 septimal comma, also known as '' Archytas' Co ... [...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] |
Septimal Diesis
In music, septimal diesis (or slendro diesis) is an interval with the ratio of 49:48 , which is the difference between the septimal whole tone and the septimal minor third. It is about 35.7 cents wide, which is narrower than a quarter-tone but wider than the septimal comma. It may also be the ratio 36:35, or 48.77 cents. In equal temperament In 12 equal temperament Twelve-tone equal temperament (12-TET) is the musical system that divides the octave into 12 parts, all of which are equally tempered (equally spaced) on a logarithmic scale, with a ratio equal to the 12th root of 2 ( ≈ 1.05946). That resultin ... this interval is not tempered out; the septimal whole tone and septimal minor third are replaced by the normal whole tone and minor third. This makes the diesis a semitone, about twice its "correct" size. The septimal diesis is tempered out by a number of equally tempered tuning systems, including 19-ET, 24-ET and 29-ET; these tunings do not distinguish between ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 that it is the amount that two major thirds of 5/4 and a septimal major third, or supermajor third, of 9/7 exceeds the octave. The septimal kleisma can also be viewed as the difference between the diatonic semitone (16:15) and the 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 f ... (15:14). References {{Intervals, state=expanded 7-limit tuning and intervals Commas (music) 0225:0224 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Septimal Major Third
In music, the septimal major third , also called the supermajor third (by Hermann von Helmholtz among others Hermann L. F. von Helmholtz (2007). ''Sensations of Tone'', p. 187. .) and sometimes '' Bohlen–Pierce third'' is the musical interval exactly or approximately equal to a just 9:7 ratioAndrew Horner, Lydia Ayres (2002). ''Cooking with Csound: Woodwind and Brass Recipes'', p. 131. . "Super-Major Second". of frequencies, or alternately 14:11. It is equal to 435 cents, sharper than a just major third (5:4) by the septimal quarter tone (36:35) (). In 24-TET the septimal major third is approximated by 9 quarter tones, or 450 cents (). Both 24 and 19 equal temperament map the septimal major third and the septimal narrow fourth (21:16) to the same interval. The septimal major third has a characteristic brassy sound which is much less sweet than a pure major third, but is classed as a 9-limit consonance. Together with the root 1:1 and the perfect fifth of 3:2, it makes up the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Septimal Meantone Temperament
In music, septimal meantone temperament, also called ''standard septimal meantone'' or simply ''septimal meantone'', refers to the tempering of 7-limit musical intervals by a meantone temperament tuning in the range from fifths flattened by the amount of fifths for 12 equal temperament to those as flat as 19 equal temperament, with 31 equal temperament being a more or less optimal tuning for both the 5- and 7-limits. Meantone temperament represents a frequency ratio of approximately 5 by means of four fifths, so that the major third, for instance C–E, is obtained from two tones in succession. Septimal meantone represents the frequency ratio of 56 (7 × 23) by ten fifths, so that the interval 7:4 is reached by five successive tones. Hence C–A, not C–B, represents a 7:4 interval in septimal meantone. :*A ≈ B *C — G — D — A — E — B — F — C — G — D — A *C — ≈G — ≈D — ≈A — ≈E — ≈B — ≈F — ≈C — ≈G — ≈D — =B The ... [...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 Quarter Tone
A septimal quarter tone (in music) is an Interval (music), interval with the ratio of 36:35, which is the difference between the septimal minor third and the Just minor third, or about 48.77 Cent (music), cents wide. The name derives from the interval being the 7-limit approximation of a quarter tone. The septimal quarter tone can be viewed either as a musical interval in its own right, or as a septimal comma, comma; if it is tempered out in a given tuning system, the distinction between the two different types of minor thirds is lost. The septimal quarter tone may be derived from the Harmonic series (music), harmonic series as the interval between the thirty-fifth and thirty-sixth harmonics. Composer Ben Johnston (composer), Ben Johnston uses a small seven ("") as an accidental to indicate a note is lowered by 36/35 (≈49 cents), or an upside-down seven ("") to indicate a note is raised by the same amount."Ben Johnston's Extended Just Intonation – A Guide for Interpreters", J ... [...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 Sixth-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] |
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] |
