Twelve Microtonal Etudes for Electronic Music Media
Last updated Easley Blackwood's Twelve Microtonal Etudes for Electronic Music Media, "21 Notes", mm. 1–6Blackwood's notation system for 24 equal temperamentBlackwood's notation system for 21 equal temperament: intervals are notated similarly to those they approximate and there are different enharmonic equivalents.
In the late 1970s, Blackwood won a grant from the National Endowment for the Humanities to investigate the harmonic and modal properties of microtonal tunings. The project culminated in the Microtonal Etudes, composed as illustrations of the tonal possibilities of all the equal tunings from 13 to 24 notes to the octave.[2] He was intrigued by "finding conventional harmonic progressions" in unconventional tunings.[3] "What I was particularly interested in was chord progressions that would give a sensation either of modal coherence or else of tonality. That is to say you can actually identify subdominants, dominants, tonics, and keys."[4]
The Twelve Microtonal Etudes were re-released on compact disc in 1994,[2] accompanied by two additional compositions of Blackwood's in tunings he explored in the Etudes: Fanfare in 19-note Equal Tuning, Op. 28a, and Suite for Guitar in 15-note Equal Tuning, Op. 33. The fanfare, like the etudes, was performed by the composer on Polyfusion synthesizer. The suite was performed by guitarist Jeffrey Kust on an acoustic guitar with a modified fretboard.
Orchestral Arrangement by Matthew Sheeran
In January 2024, an acoustic performance of the Twelve Microtonal Etudes on real orchestral instruments, titled "Acoustic Microtonal," was released by Matthew Sheeran (brother to singer-songwriter Ed Sheeran). The album, featuring the Budapest Scoring Orchestra, was produced by Sheeran, who arranged Blackwood's original compositions for traditional orchestral instruments. The recording was produced by first having the orchestral musicians, whose instruments are typically limited to 12 tone equal temperament, perform "approximated" 12-tone versions of the original etudes on their instruments. These preliminary recordings were then transformed into their intended tunings using the Melodyne electronic retuning software.[5]
↑ Myles Leigh Skinner (2007). Toward a Quarter-tone Syntax: Analyses of Selected Works by Blackwood, Haba, Ives, and Wyschnegradsky, p. 46. ISBN9780542998478.
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.
In music, there are two common meanings for tuning:
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.
Articles related to music include:
In music theory, the circle of fifths is a way of organizing the 12 chromatic pitches as a sequence of perfect fifths.. If C is chosen as a starting point, the sequence is: C, G, D, A, E, B, F♯, C♯, A♭, E♭, B♭, F. Continuing the pattern from F returns the sequence to its starting point of C. This order places the most closely related key signatures adjacent to one another. It is usually illustrated in the form of a circle.
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."
The Bohlen–Pierce scale is a musical tuning and scale, first described in the 1970s, that offers an alternative to the octave-repeating scales typical in Western and other musics, specifically the equal-tempered diatonic scale.
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.
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.
Easley R. Blackwood Jr. was an American professor of music, concert pianist, composer, and the author of books on music theory, including his research into the properties of microtonal tunings and traditional harmony.
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.
In music, the septimal minor third, also called the subminor third or septimal subminor third, 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 have an almost perfect match to this interval. The septimal major sixth, 12/7, is the inverse of this interval.
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.
Mayer Joel Mandelbaum is an American music composer and teacher, best known for his use of microtonal tuning. He wrote the first Ph.D. dissertation on microtonality in 1961. He is married to stained glass artist Ellen Mandelbaum, and is the nephew of Abraham Edel.
The harmonic seventh interval, also known as the septimal minor seventh, or subminor seventh, is one with an exact 7:4 ratio. 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.
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.
A regular diatonic tuning is any musical scale consisting of "tones" (T) and "semitones" (S) arranged in any rotation of the sequence TTSTTTS which adds up to the octave with all the T's being the same size and all the S's the being the same size, with the 'S's being smaller than the 'T's. In such a tuning, then the notes are connected together in a chain of seven fifths, all the same size which makes it a Linear temperament with the tempered fifth as a generator.
In music, 15 equal temperament, called 15-TET, 15-EDO, or 15-ET, is a tempered scale derived by dividing the octave into 15 equal steps. Each step represents a frequency ratio of 15√2, or 80 cents. Because 15 factors into 3 times 5, it can be seen as being made up of three scales of 5 equal divisions of the octave, each of which resembles the Slendro scale in Indonesian gamelan. 15 equal temperament is not a meantone system.
A septimal 1/3-tone 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.
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