Kees (Cornelis) van Prooijen (born 7 August 1952) is a creator of computer art. [1] Although it does not bear his name, he independently discovered the Bohlen-Pierce scale, [2] [3] a non-octave-repeating scale based on the tritave and spectra containing odd harmonics, in 1978. Van Prooijen came across the scale through an investigation of continued fractions. [4] [5] [6]
He also invented the Kees height, or an "expressibility" measure for complexity of just intonation pitch classes. [7] [8]
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An equal temperament is a musical temperament or tuning system, which approximates just intervals by dividing an octave into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, which gives an equal perceived step size as pitch is perceived roughly as the logarithm of frequency.
In music theory, limit or harmonic limit is a way of characterizing the harmony found in a piece or genre of music, or the harmonies that can be made using a particular scale. The term limit was introduced by Harry Partch, who used it to give an upper bound on the complexity of harmony; hence the name.
A combination tone is a psychoacoustic phenomenon of an additional tone or tones that are artificially perceived when two real tones are sounded at the same time. Their discovery is credited to the violinist Giuseppe Tartini and so they are also called Tartini tones.
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 Xenia, hospitable, and Xenos foreign. 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 pseudo-octave, pseudooctave, or paradoxical octave in music is an interval whose frequency ratio is not 2:1, that of the octave, but is perceived or treated as equivalent to this ratio, and whose pitches are considered equivalent to each other as with octave equivalency.
Curtis Roads is an American composer, author and computer programmer. He composes electronic and electroacoustic music, specializing in granular and pulsar synthesis.
Otonality and utonality are terms introduced by Harry Partch to describe chords whose pitch classes are the harmonics or subharmonics of a given fixed tone (identity), respectively. For example: 1/1, 2/1, 3/1,... or 1/1, 1/2, 1/3,....
An Otonality is that set of pitches generated by the numerical factors (...identities)...over a numerical constant in the denominator. Conversely, a Utonality is the inversion of an Otonality, a set of pitches with a numerical constant in the numerator over the numerical factors...in the denominator.
George Secor was an American composer from Chicago. He was the discoverer of miracle temperament and eponym of the secor.
Twelve-tone equal temperament 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, intonation is the pitch accuracy of a musician or musical instrument. Intonation may be flat, sharp, or both, successively or simultaneously.
A neutral third is a musical interval wider than a minor third play (help·info) but narrower than a major third play (help·info), named by Jan Pieter Land in 1880. Land makes reference to the neutral third attributed to Zalzal, described by Al-Farabi as corresponding to a ratio of 27:22 and by Avicenna as 39:32. The Zalzalian third may have been a mobile interval.
In music, 41 equal temperament, abbreviated 41-TET, 41-EDO, or 41-ET, is the tempered scale derived by dividing the octave into 41 equally sized steps. Play (help·info) Each step represents a frequency ratio of 21/41, or 29.27 cents, an interval close in size to the septimal comma. 41-ET can be seen as a tuning of the schismatic, magic and miracle temperaments. It is the second smallest equal temperament, after 29-ET, whose perfect fifth is closer to just intonation than that of 12-ET. In other words, is a better approximation to the ratio than either or .
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.
The δ (delta) scale is a non-octave repeating musical scale. It may be regarded as the beta scale's reciprocal, since it is "as far 'down' the circle from α as β is 'up'". As such it would split the minor second into eight equal parts of approximately 14 cents each Play (help·info). This would total approximately 85.7 steps per octave.
Heinz P. Bohlen was a microwave electronics and communications engineer.
The 833 cents scale is a musical tuning and scale proposed by Heinz Bohlen based on combination tones, an interval of 833.09 cents, and, coincidentally, the Fibonacci sequence. The golden ratio is , which as a musical interval is 833.09 cents. In the 833 cents scale this interval is taken as an alternative to the octave as the interval of repetition, however the golden ratio is not regarded as an equivalent interval. Other music theorists such as Walter O'Connell, in his 1993 "The Tonality of the Golden Section", and Loren Temes appear to have also created this scale prior to Bohlen's discovery of it.
A12 is a non-octave-repeating scale or musical tuning featuring twelve steps to the tritave. As twelve steps to the octave is based on a triad of harmonics 4:5:6, Play (help·info) A12 is based on a triad of harmonics 4:7:10. Discovered by Heinz Bohlen between 1972 and 1973, it was named "A12" by Enrique Moreno. Bohlen considered this scale less logically consistent than the Bohlen–Pierce scale, which has thirteen steps in the twelfth.
Sean Archibald, also known as Sevish, is a British electronic music composer from London. Described by Aaron Krister Johnson as "a well-known creative force in the world of online microtonal music," he is most known for his compositions which combine aspects of electronic dance music with microtonality. As a child Archibald was inspired by music in video games such as Chrono Trigger, Streets of Rage, and Sonic the Hedgehog. He would then go on to discover microtonality as a teenager by listening to gamelan music and Aphex Twin. At age 16 he began officially releasing music online and released his first solo album at age 20. He first gained notoriety in the microtonal music scene with his 2010 release, Golden Hour. Sevish's 2011 xenharmonic dance album, Subversio, created in collaboration with Tony Dubshot and Jacky Ligon was described by Andrew Hugill as "dub meets microtonal tunings."