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An equal temperament is a musical temperament or tuning system that approximates just intervals by dividing an octave into steps such that the ratio of the frequencies of any adjacent pair of notes is the same. This system yields pitch steps perceived as equal in size, due to the logarithmic changes in pitch frequency.
In music, just intonation or pure intonation is the tuning of musical intervals as whole number ratios of frequencies. An interval tuned in this way is said to be pure, and is called a just interval. Just intervals consist of tones from a single harmonic series of an implied fundamental. For example, in the diagram, if the notes G3 and C4 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.
Meantone temperaments are musical temperaments, that is a variety of tuning systems, obtained by narrowing the fifths so that their ratio is slightly less than 3:2, in order to push the thirds closer to pure. Meantone temperaments are constructed similarly to Pythagorean tuning, as a stack of equal fifths, but they are temperaments in that the fifths are not pure.
Microtonal or microtonality is the use in music of microtones—intervals smaller than a semitone, also called "microintervals". It may also be extended to include any music using intervals not found in the customary Western tuning of twelve equal intervals per octave. In other words, a microtone may be thought of as a note that falls "between the keys" of a piano tuned in equal temperament.
In jazz and blues, a blue note is a note that—for expressive purposes—is sung or played at a slightly different pitch from standard. Typically the alteration is between a quartertone and a semitone, but this varies depending on the musical context.
Xenharmonic music is music that uses a tuning system that is unlike the 12-tone equal temperament scale. It was named by Ivor Darreg, from the Greek Xenos meaning both foreign and hospitable. He stated that it was "intended to include just intonation and such temperaments as the 5-, 7-, and 11-tone, along with the higher-numbered really-microtonal systems as far as one wishes to go."
A schismatic temperament is a musical tuning system that results from tempering the schisma of 32805:32768 to a unison. It is also called the schismic temperament, Helmholtz temperament, or quasi-Pythagorean temperament.
In music, the schisma (also spelled skhisma) is the interval between the syntonic comma (81:80) and the Pythagorean comma ( 531 441 : 524 288 ), which is slightly larger. It equals 5 × 38 / 215 or 32 805 : 32 768 ≈ 1.00113, which corresponds to 1.9537 cents. It may also be defined as:
A quarter tone is a pitch halfway between the usual notes of a chromatic scale or an interval about half as wide as a semitone, which itself is half a whole tone. Quarter tones divide the octave by 50 cents each, and have 24 different pitches.
Adriaan Daniël Fokker was a Dutch physicist. He worked in the fields of special relativity and statistical mechanics. He was the inventor of the Fokker organ, a 31-tone equal-tempered (31-TET) organ.
In music, 72 equal temperament, called twelfth-tone, 72-TET, 72-EDO, or 72-ET, is the tempered scale derived by dividing the octave into twelfth-tones, or in other words 72 equal steps. Each step represents a frequency ratio of 72√2, or 16+2⁄3 cents, which divides the 100 cent "halftone" into 6 equal parts and is thus a "twelfth-tone". Since 72 is divisible by 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72, 72-EDO includes all those equal temperaments. Since it contains so many temperaments, 72-EDO contains at the same time tempered semitones, third-tones, quartertones and sixth-tones, which makes it a very versatile temperament.
12 equal temperament (12-ET) is the musical system that divides the octave into 12 parts, all of which are equally tempered on a logarithmic scale, with a ratio equal to the 12th root of 2. That resulting smallest interval, 1⁄12 the width of an octave, is called a semitone or half step.
In music, 31 equal temperament, 31-ET, which can also be abbreviated 31-TET or 31-EDO, also known as tricesimoprimal, is the tempered scale derived by dividing the octave into 31 equal-sized steps. Each step represents a frequency ratio of 31√2, or 38.71 cents.
In music, 19 equal temperament, called 19 TET, 19 EDO, 19-ED2 or 19 ET, is the tempered scale derived by dividing the octave into 19 equal steps. Each step represents a frequency ratio of 19√2, or 63.16 cents.
Twelve Microtonal Etudes for Electronic Music Media, Op. 28, is a set of pieces in various microtonal equal temperaments composed and released on LP in 1980 by American composer Easley Blackwood Jr.
In music, septimal 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.
A septimal quarter tone is an 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 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 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 as the interval between the thirty-fifth and thirty-sixth harmonics.
The Huygens-Fokker Foundation is a "centre for microtonal music" founded on February 15, 1960, housed in the Muziekgebouw aan 't IJ, and named for Christiaan Huygens and Adriaan Fokker. The Foundation's library possesses a large archive of correspondence, scores, books, and other publications. The Foundation presents frequent concerts presenting contemporary, early, popular, and improvised microtonal music. They maintain contact with other organizations dedicated to microtonality including Tonalsoft, the Harry Partch Institute, the Logos Foundation, and individuals such as Kyle Gann. They published the journal Thirty-One and presented MicroFest Amsterdam 2011. They house the 31-tone Fokker organ with new MIDI-connections in the BAM Hall. The current director is Sander Germanus.
In music, 96 equal temperament, called 96-TET, 96-EDO, or 96-ET, is the tempered scale derived by dividing the octave into 96 equal steps. Each step represents a frequency ratio of , 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.
References
- 1 2 Randel, Don. Harvard Dictionary of Music. p. 546.
- ↑ J. Mandelbaum, Multiple division of the octave and the tonal resources of the 19-tone equal temperament , PhD thesis, Indiana University, (1961)
- ↑ "Stichting Huygens-Fokker: Joel Mandelbaum". Archived from the original on 2007-11-04. Retrieved 2007-11-12.
- ↑ Douglas Keislar; Easley Blackwood; John Eaton; Lou Harrison; Ben Johnston; Joel Mandelbaum; William Schottstaedt (Winter 1991). "Six American Composers on Nonstandard Tunnings". Perspectives of New Music . 29 (1): 176–211. doi:10.2307/833076. JSTOR 833076.
