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Topic: Quarter tone scale

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Equal tempered

Mathematics of musical scales

Well temperament

Physics of music

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	Musical tuning - Wikipedia, the free encyclopedia
		It is impossible to tune the twelve-note chromatic scale so that all intervals are "perfect"; many different methods with their own various compromises have thus been put forward.
		To do this, eleven perfect fifths in each octave are flattened by a quarter of a syntonic comma, with the remaining fifth being left very sharp (such an unacceptably out-of-tune fifth is known as a wolf interval).
		From this the heptatonic scales consisting of minor, neutral, and major seconds of maqamat are chosen, this system was first promoted by al-Farabi using a 25 tone scale.
	en.wikipedia.org /wiki/Musical_tuning (1293 words)

	Quarter tone -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-21)
		A quarter tone is an (The difference in pitch between two notes) interval half as wide (aurally, or logarithmically) as a (The musical interval between adjacent keys on a keyboard instrument) semitone, which is half a (A musical interval of two semitones) whole tone.
		In (The division of the scale based on an octave that is divided into twelve exactly equal semitones) equal temperament the quarter tone is 50 (A fractional monetary unit of several countries) cents or 2
		In 24 tone equal temperament, or the quarter tone scale, it is the smallest (The act of changing location by raising the foot and setting it down) step.
	www.absoluteastronomy.com /encyclopedia/q/qu/quarter_tone.htm (227 words)

	The Evolution of Scales
		The Arabic scale multiplies its oriental flavor by two Harmonic intervals, one from the 2nd to the 3rd degree, one from the 6th to the 7th.
		The Chinese scale was composed of five whole tones, written on a vertical staff.
		The Chinese were probably the earliest inventors of the scale and notation.
	janpress.freeservers.com /LCscales.htm (524 words)

	Quarter tone - Wikipedia, the free encyclopedia
		Many composers are known for having written music including quarter tones or the quarter tone scale, first proposed by Mikhá'il Mishdgah (Touma 1996, p.16), including:
		Two quarter tones equal a half tone, and three make a three-quarter tone.
		A three-quarter tone may also be considered half of a minor third.
	en.wikipedia.org /wiki/Quarter_tone (148 words)

	Sonic Glossary: Scale
		A scale is a collection of tones traversing the interval of the octave, among which one tone is particularly stable.
		The scales we have seen so far, the whole-tone, the chromatic, and the octatonic, have one characteristic in common: they are all symmetrical, that is, whatever pattern of steps is found in the first half of the scale is duplicated also in its second half.
		Scales that feature this kind of symmetry have an artificial quality, and are far more common in the music of the 20th Century, when composers began actively to search for structures that would enable them to draw out and explore new sonorities.
	www.columbia.edu /ccnmtl/draft/paul/sonic/scale.html (1950 words)

	Equal temperament
		Twelve tone equal temperament was designed to permit the playing of music in all keys with an equal amount of mis-tuning in each, while still approximating just intonation.
		This may be used for atonal music, such as that written with the twelve tone technique or serialism, or tonal music.
		The quarter tone scale or 24-tET is, similarly, based on powers of.
	www.brainyencyclopedia.com /encyclopedia/e/eq/equal_temperament.html (1100 words)

	Articles - Tetrachord (Site not responding. Last check: 2007-10-21)
		The single tone could be placed between the two tetrachords (between perfect fourth and perfect fifth) (termed disjunctive), or it could be placed at either end of the scale (termed conjunctive).
		Scales built on chromatic and enharmonic tetrachords continued to be used in the classical music of the Middle East and India, but in Europe they were maintained only in certain types of folk music.
		Since there are two tetrachords and a major tone in an octave, this creates a 25 tone scale as used in the Arab tone system before the quarter tone scale.
	lastring.com /articles/Tetrachords?mySession=1ce483c72db5cb745dc6c2a... (659 words)

	HurdAudio: October 2004
		All the intervals of the standard E Flat Ionian Scale (mapped to the octave as per standard practice) are halved to fit within the square-root of 2 (a.k.a.
		Scales replicate their interval patterns at the octave and set-theory is built upon the concept that octaves are "equivalencies" suitable as an orchestration device that adds no new harmonic content.
		Scales replicate their sequence of intervals at the triative and the piano is tuned so that every perfect twelfth (the octave + perfect fifth) is exactly 1901.96 cents apart.
	hurdaudio.blogspot.com /2004_10_01_hurdaudio_archive.html (3831 words)

	MusicYo.com - An Introduction to OB-Tune - What Will I Play Today?
		The scale tone closest to the input is continuously identified.
		Arabic 1: This 17 tone scale is the original Arabic scale adopted from the Pythagorean scale.
		Equal tempered scales with a large number of tones are typically used to play common tonal harmony with greater purity of intervals and chords.
	www.musicyo.com /planet/OBtune_intro.asp (1737 words)

	Musical tuning (Site not responding. Last check: 2007-10-21)
		Musical tuning is the system used to define which tones, or pitcheses, to use when playing music.
		Equal temperament, in which adjacent notes of the scale are all separated by logarithmically equal distances - A harmonized C major scale in equal temperament (.ogg format, 96.9KB)
		Quarter tone scale used in the theory of Arab music tone systems and from which the heptatonic scales consisting of minor, medium, and major seconds of maqamat are chosen
	hallencyclopedia.com /Musical_tuning (1277 words)

	EMI Fret Calculator - Notes on Stretch Compensation
		It is often useful to describe particular scales mathematically, based on the relationships between the frequencies of the pitches that make up the scale.
		The musical intervals that define the scale can then be described in terms of the mathematical relationships between the frequencies of the scale tones.
		The math normally used to describe an equal-tempered scale involves finding a scale factor, which is the constant by which the frequency of each step must be multiplied to arrive at the frequency of the next step.
	www.windworld.com /tools/fretnote.htm (1313 words)

	Scale (Site not responding. Last check: 2007-10-21)
		The term scale denoted an abstract series of tones derived from the system of tuning, presented in ascending order and forming the basis of a given composition of class of compositions.
		The pattern is three consecutive tones, a skipped tone, two consecutive tones, and a skipped tone, or, 1-2-3-5-6.
		The octave is divided into 1,200 equal parts with each of the twelve Western semitones encompassing 100 cents, each whole tone 200 cents, and so on; in a decreasing amount a tempered quarter-tone would comprise 50 cents, an eight-tone 25 cents, and so on (the cent system applied to Thai tuning will be seen subsequently).
	www.seasite.niu.edu /Thai/music/classical/thaitheory/scale.htm (195 words)

	wikien.info: Main_Page (Site not responding. Last check: 2007-10-21)
		Twelve tone equal temperament was introduced in the West to permit the playing of music in all keys with an equal amount of mis-tuning in each, without having to provide more than 12 pitches per octave on instruments, while still roughly approximating just intonation intervals.
		Well-tempermaments were gradually supplanted by equal temperament over the course of the 19th century, and it is in the environment of equal temperament that the new styles of symmetrical tonality and polytonality, atonal music such as that written with the twelve tone technique or serialism, and jazz (at least its piano component) developed and flourished.
		The quarter tone scale or 24-tET is, similarly, based on steps of 50 cents or powers of [\sqrt[24]{2}].
	www.alanaditescili.net /index.php?title=Equal_temperament (1708 words)

	Units: T
		On the standard 12-tone scale, the minor third is approximated by 3 half steps, corresponding to a frequency ratio of 2
		The scale ranges from 0 (object certain to miss the Earth or too small to cause significant damage) to 10 (object certain to hit the Earth and large enough to cause catastrophic damage and global climate disruption).
		On the standard 12-tone scale, the perfect twelfth is approximated as 19 half steps, corresponding to a frequency ratio of 2
	www.unc.edu /~rowlett/units/dictT.html (6833 words)

	ICAD Citations
		After finding that combinations of tones created a confusing display that was difficult to use, the author turned to one signal in which multiple data variables were represented by multiple auditory variables.
		Subjects hearing the same auditory sequence perceived it as two tones if a concurrent visual sequence was presented that was perceived as two moving dots, and one tone if a concurrent visual sequence perceived as a single object was presented.
		Ward presents empirical evidence that the pitch of pure tones is a subjective judgment of the listener, not very consistent across subjects, and whose rate of change is independent of the frequency level of the acoustic source.
	www.icad.org /websiteV2.0/Biblio/complete.html (14569 words)

	Harps.com - Gary Garritan (Site not responding. Last check: 2007-10-21)
		Greeks began to write songs based on these scales and the small lyre harp was ideally suited to play songs in these scales.
		It has 36 nylon strings tuned to the diatonic scale, is played with the fingernails and its sound is bright.
		It was the lack of a full chromatic scale that was identified as the main 'defect' of the harp.
	www.harps.com /history_expanded.html (4694 words)

	Iran Heritage
		Vaziri's quarter-tone theory, which is arrived at by way of a further division of the western equidistant 12-note chromatic scale, is entirely irrelevant to Persian music.
		It would be difficult to accept Vaziri was not aware of the fact that Persian music makes no use of the quarter-tone and that intervals other than the semi-tone and the whole-tone are not achieved through multiples of the quarter-tone.
		He must simply have believed in the desirability of their being adjusted to correspond to an equidistant quarter-tone scale so that a kind of harmony may be imposed upon the music.
	www.iran-heritage.org /interestgroups/AliNaghi.htm (1017 words)

	The Ensemble Sospeso - Richard Barrett (Site not responding. Last check: 2007-10-21)
		Any performer will be able to play a C major scale more quickly and fluently than a quarter-tone scale, and this is the type of thing that interests me a lot.
		Thus the role of improvised music is two-pronged: on the social level, it removes the distance between the audience and the musicians; on the aesthetic level, large scale formal procedures are necessarily rejected, since the music's present moment is the only frame of listening for the listener/musician.
		But there's an emergent quality of large scale form in improvised music: a musician cannot simply determine it, but if the improvisation is succeeding, the formal shapes can emerge are just as interesting, and in their own way, just as involuted, as anything one could dream up in compositional terms.
	www.sospeso.com /contents/articles/barrett_p3.html (1860 words)

	eufonia - hans andré stamm - komponist und orgel virtuose
		Here the introducing organ motives contain descending quarter tones, though which these motives get a weeping expression according to the text ("in sin and misery we are weeping").
		The singing of quarter tones shows to be very difficult even to professional singers and a very good choir like the "Capella Piccola" (conductor: Thomas Reuber).
		This derives from the fact, that the quarter tone is not yet felt as a "discrete" interval, but as a result of intonation correction or as a ornamental motive.
	www.eufonia.de /english/komposition.php (369 words)

	The Austin High Gang
		Actually his tone was bland compared to that of Bix and his style hadn't the rolling quality of the original Wolverines' cornet.
		Besides the growl, that sounded as though he were trying to play two tones at once, Pee Wee played with a sustained rhythmic flow in a tone that was very blue.
		Benny's clarinet on this record has a thin reedy tone, not at all unpleasant but utterly unlike the round limpid tone with which he was to play a few years later.
	www.redhotjazz.com /austinhighgang.html (6883 words)

	Units: S
		In general, 1:n scale means that 1 unit of distance on the map or plan represents n of the same units in fact.
		On the standard 12-tone scale the minor sixth is approximated (roughly) by 8 half steps, corresponding to a frequency ratio of 2
		One sone is the loudness of a pure tone of frequency one kilohertz and strength 40 decibels.
	www.unc.edu /~rowlett/units/dictS.html (10439 words)

	Arab music - Biocrawler definition:Arab music - Biocrawler (Site not responding. Last check: 2007-10-21)
		A tone system (or musical tuning system) with specific interval structures, invented by al-Farabi in the tenth century (p.170).
		The main difference between the western chromatic scale and the Arabic scale is the existence of quarter tones.
		However, while in theory the quarter tone scale or all twenty four tones exist, according to Yūsuf Shawqī (1969) in practice there are many fewer tones (Touma 1996, p.170).
	www.biocrawler.com /biowiki/Classical_Arab_music (1723 words)

	Alois Hába (Site not responding. Last check: 2007-10-21)
		Alois Hába (June 21, 1893 - November 18, 1973) was a Czech composer primarily known for his microtonal compositions, especially using the quarter tone scale, though he used others such as sixth-tones and twelfth-tones.
		He was supported by Josef Suk and with his help was able to found a microtonal department of teaching and research at the Prague Conservatory in 1924.
		He also commissioned quarter and sixth tone instruments such as trumpets and pianos.
	www.free-download-soft.com /info/audio-converters.html (122 words)

	Iranian Classical Music (Site not responding. Last check: 2007-10-21)
		Each dastagah has an associated eight note scale, and each tone in the scale has a special significance, with one note being designated the analogue of the tonic in Western diatonic music.
		The modal structure (the eight tone scale) of Shur is presented in figure 1:
		Note that the scale does not span an octave per se, as it is bound by a b semi-flat on its lower end and by a b-flat on the upper end.
	www.iranchamber.com /music/articles/iranian_classical_music.php (1448 words)

	[No title]
		As a performer with a reputation, he could bring the practical art to bear upon the discussions.So whilst he was more thorough than the Greeks in handling the physical bases of sound, he could also make valuable contributions to physiological accoustics, i.e.
		The instrument's frets (dasateen, aPersian word) gave a "pre-Islamic scale." It was a quarter-tone scale which was developed by dividing a string into forty equal parts.
		Although Al-Farabi's instrument did not have the following scale, yet the theoretical division mentioned previously would produce a scale which expressed in cycliccents, would be: Fret Nut 2nd 4th 6th 8th 10thCent 0 89 182 281 386 498.
	www.pharaohsentertainment.com /main/music.html (1837 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		Major mode: One of the modes of the diatonic scale, oriented around C as the tonic; characterized by the interval between the first and third notes containing 4 semitones, as opposed to 3 in the minor mode (26)
		Minor mode: One of the modes of the diatonic scale, oriented around A as the tonic; characterized by the interval between the first and third notes containing 3 semitones, as opposed to 4 in the major (26)
		Quarter-tone scale: A 24-note scale, used in the 20th century, consisting of all the semitones of the chromatic scale and all quarter tones in between the semitones (319)
	bcs.bedfordstmartins.com /listen/content/cat_090/gls_menu.asp?... (6084 words)

	Art of the States: Three Quarter-Tone Pieces for Two Pianos
		He would pick out quarter-tone tunes and try to get the family to sing them, but I remember he gave that up except as a means of punishment -- though we got to like some of the tunes which kept to the usual scale and had quarter-tone notes thrown in...
		He meticulously considered theories of quarter-tones, and produced tables of quarter-tone scale possibilities.
		if an addition of a series of smaller tone divisions is to be added to our semi-tone system "to help round out our souls," how much of a fight will the ears have to put up?' He concluded about the stacked chords he constructed, '...
	www.artofthestates.org /cgi-bin/piece.pl?pid=255 (1506 words)

	Skytopia : Tuning & Music Scales Theory - Why are there 12 notes in Equal temperament?
		Some have argued that the importance of the number 12 in music is thanks to the fact that the 12 equal tempered pitches approximate many simple ratios such as 4/3 or 5/4 very closely, but this surely isn't the full story, since other numbers (such as 19) are quite good at this too.
		Others have argued how successive powers of 3 will 'complete' the scale after 12 iterations (the basis behind Pythagorean tuning), but this can't be the full story, since the twelfth iteration (3^12 or 3^-12) - known infamously as the 'wolf' note - is a fraction over (or under) the octave.
		All chromatic scale tunings have this 'problem' or 'idiosyncrasy', and so strictly speaking, literally hundreds (or even thousands) of harmonic partials are simultaneously 'clashing' with other fundamentals and their countless harmonics in a tune.
	www.skytopia.com /project/scale.html (9996 words)

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