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Topic: Just intonation

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	Just intonation - Wikipedia, the free encyclopedia
		In music, just intonation, also called rational intonation, is any musical tuning in which the frequencies of notes are related by whole number ratios; that is, by positive rational numbers.
		Eivind Groven is often considered a just intonation composer but just intonation purists will disagree.
		His tuning system was in fact schismatic temperament, which is indeed capable of far closer approximations to just intonation consonances than 12-note equal temperament or even meantone temperament, but still alters the pure ratios of just intonation slightly in order to achieve a simpler and more flexible system than true just intonation.
	en.wikipedia.org /wiki/Just_intonation (1941 words)

	Musical tuning - Wikipedia, the free encyclopedia
		Just intonation, in which the ratios of the frequencies between all notes are based on relatively low whole numbers, such as 3:2, 5:4 or 7:4; or in which all pitches are based on the harmonic series (music), which are all whole number multiples of a single tone.
		For this reason, just intonation may be less a suitable system for use on keyboard instruments or other instruments where the pitch of individual notes is not flexible.
		For instance, William Sethares shows that the tunings of Balinese gamelans are related to the inharmonic spectra or timbre of their metallophones and the harmonic spectra of stringed instruments such as the rebab, just as just intonation and twelve tone equal temperament are related to the spectra or timbre of harmonic instruments alone.
	en.wikipedia.org /wiki/Tuning (2178 words)

	Just intonation (Site not responding. Last check: 2007-10-22)
		Just intonation is any musical tuning in which the frequencies of note s are related by whole number ratio s.
		Another way of considering just intonation is as being based on members of the harmonic series.
		Music written in just intonation is most often tonal but need not be, some can loosen these boundaries as in some music of Kraig Grady but which is not as atonal as certain pieces by Ben Johnston which are serial.
	www.serebella.com /encyclopedia/article-Just_intonation.html (823 words)

	What is JUST INTONATION? (short version)
		JUST INTONATION is any system of tuning in which all of the intervals can be represented by ratios of whole numbers, with a strongly-implied preference for the smallest numbers compatible with a given musical purpose.
		Just Intonation is not a particular scale, nor is it tied to any particular musical style.
		Just Intonation is not, however, simply a tool for improving the consonance of existing musics; ultimately, it is a method for understanding and navigating through the boundless reaches of the pitch continuum—a method that transcends the musical practices of any particular culture.
	www.justintonation.net /whatisji.html (716 words)

	Just Temperament and Others
		Just temperament refers to a musical scale or musical intervals which maintain exact integer ratios between pitches.
		However, if five cents is taken as the just noticeable difference in pitch, the fifths and fourths of equal temperament are just within that 5¢ margin.
		Expressed in terms of whole number ratios, the ordinary (syntonic or Ptolemaic) comma is the interval between a just major third (5:4) and a Phythagorean ditonic or major third (81:64).
	hyperphysics.phy-astr.gsu.edu /hbase/music/just.html (418 words)

	Pythagorean Tuning - Just Intonation Context
		Justness involves preserving as much as possible the pure ratios of the stable fifths and fourths which make up euphonious trines (Sections 3.1.1, 3.2.1), and also of the unstable intervals with simple ratios, major seconds and minor sevenths (Sections 3.1.3, 3.2.3).
		Given the affinity between Pythagorean just intonation and equal temperament, we should not be surprised that the first recorded approximations to equal temperament in medieval and early Renaissance theory are variations on the Pythagorean scale.
		Just intonation advocates emphasize the importance of striving for absolutely pure and beatless fifths and fourths, and some feel it a substantial compromise even to use synthesizers supporting a Pythagorean scale but able to tune it only to a resolution of the nearest cent or so.
	www.medieval.org /emfaq/harmony/pyth5.html (14527 words)

	Reasons for Using Just Intonation
		So they think that nature-worshipping just intonationists go to absurd lengths to be mathematically accurate beyond the ear's capacity to care, and that we do so in search of pure, beatless consonances - and that consequently we apparently like our music all simple and pretty and full of major triads and uninteresting.
		For me the great thing about just intonation is not that everything is consonant and beats don't exist, but that you have a tremendous range from having no beats at all to extreme WOWOWOWOWOW beat conglomerations.
		Just intonation, for me, represents the ability to use every note with an intense awareness of its harmonic interconnectedness with every other note.
	www.kylegann.com /JIreasons.html (1577 words)

	Intonation
		Intonation is an area that requires a good musician to keep his mind and ears open.
		"Just" intonation is the development of the scale based on the organic generation of tones as they occur in the natural harmonic series.
		I consider the use of just intonation in the ensemble to be absolutely paramount to tempered tuning, but the extent to which one alters pitch can be an issue of taste.
	www.woodwind.org /clarinet/Equipment/Intonation.html (2748 words)

	Just intonation (Site not responding. Last check: 2007-10-22)
		Intervals used are then capable ofgreater consonant, but consonance is not always emphasized or a goal in musicwritten with just intonation.
		It is possible to tune the familiar diatonic scale or chromatic scale in just intonation but many other justly tuned scales havealso been used.
		Music written in just intonation is most often tonal but need not be,some can loosen these boundaries as in some music of Kraig Grady but which is not as atonal as certain pieces by Ben Johnston which are serial.
	www.therfcc.org /just-intonation-19441.html (691 words)

	Peterson Tuners Forum 2006 - "perfect" intonation vs. just intonation
		In the just scale, a perfect fifth is defined as two frequencies with a ratio of 3 to 2, e.g.
		All of the intervals in the just scale are defined in terms of small, whole numbers, so the harmonics of the upper note in an interval coincide, as much as possible, with the harmonics of the lower note.
		I was hoping there might be somewhere something like Peterson's just intonation chart that would show: to get a perfect major 7th in the key of C lower the 7th 2.58 cents.
	www.petersontuners.com /forum/topic.asp?TOPIC_ID=251 (2282 words)

	Just Intonation
		Just Intonation (or JI) uses the actual uncompromised intervals which our ears perceive to be consonant. ; In short, small whole number ratios. ; The table on the right lists of most of the intervals that our ears hear as consonant. ; Specifically, the simplest 13 odd-limit ratios within an octave and their inversions.
		The ear will "correct" for small deviations from consonant intervals, thus 301/200 will be heard as a slightly out of tune 3/2 and still sound consonant. ; Consonant ratios generally involve numerators and denominators which are multiples of primes no greater than 13 but the definition seems to vary a bit from person to person.
		Designing just intonation scales is particularly fun for people who enjoy playing with numbers, particularly integers, and their relationships to each other in terms of ratios, powers, and common divisors.
	www.organicdesign.org /peterson/tuning/ji.html (603 words)

	Just Intonation the Harmonic Piano: Michael Harrison composer and pianist
		It is the first piano tuned in Just Intonation with the flexibility to modulate to multiple key centers at the press of a pedal.
		Just intonation is the basis for the music of ancient Greece, as well as other cultures, including those of India, Persia, China, and Japan.
		Just intonation is also vital to the "a cappella" music of the West, from Gregorian chant and renaissance polyphony, to "barbershop" harmonies.
	www.michaelharrison.com /harmonic-piano.html (979 words)

	MTO 2.6: Walker, A Defense of Just Intonation
		ABSTRACT: Just intonation is commonly dismissed as an impractical, utopian system which could not have had any role to play in the performance of Renaissance vocal polyphony.
		Roger Wibberley, posting to mto-talk, 21 Aug 1996 "Re: Wibberley, MTO 2.5"; the issue of just intonation in Renaissance polyphony was one of the topics of the mto-talk discussion that followed the publication of Wibberley's article "Josquin's Ave Maria: Musica Ficta versus mode" in MTO 2.5.
		The New Grove entry on Just Intonation, by Mark Lindley, is conceptually skewed in just this manner: from half-way through the first paragraph, to the end of its two-page spread, keyboard instruments are the sole subject matter (with a passing reference to the guitar, another fixed-pitch instrument).
	mto.societymusictheory.org /issues/mto.96.2.6/mto.96.2.6.walker.html (5440 words)

	Historic Music Tuning Problem, just intonation, pure harmony
		Just intonation refers to music in which the scale intervals are precisely tuned to the pure harmonics of the natural overtone series.
		Pure harmonic tuning, known as just intonation, is based on these fractions and these relationships to each other.
		Keyboards and frets digitized musical intonation, dividing the natural continuum of tones into distinct points that were not meant to change.
	www.justonic.com /history.htm (1051 words)

	Just Intonation Tutorial, Part 6
		This is ideal for exploring some of the outer reaches of just intonation, as well as other tuning systems.
		A just intonation system based on a series of minor sevenths stacked on top of one another like a barber pole, for example, can produce some exotic effects.
		In principle, any full-featured sampler can be tuned to just intonation, because you can assign a separate sample to each key and then tune each key up or down as needed.
	www.musicwords.net /musictech/justtutor/justtutor6.htm (1582 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		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.
		These mappings from equal temperament to just intonation are by no means unique.
		A further extension of 12-tET is 72-tET, which though not a meantone tuning, approximates most just intonation intervals, including non-traditional ones like 7/4, 9/7, 11/5, 11/6 and 11/7, much better.
	www.worldhistory.com /wiki/J/Just-intonation.htm (946 words)

	Just Intonation Tutorial Part 1
		Just intonation is a general term for a variety of tuning systems -- ways of tuning the notes of the scale in relation to one another.
		Just intonation is a tool that allows us to explore the emotional qualities of intervals in greater depth than is possible with the conventional method of tuning the scale.
		In a certain sense, just intonation is simple and natural.
	www.musicwords.net /musictech/justtutor/justtutor1.htm (519 words)

	Harmonic Lattice Diagrams, (c) 1998 by Joseph L. Monzo - Ho java applet
		Thinking of just intonation in terms of subdividing a string produces problems for the JI music theory.
		Subsequent theorists were no longer limited to conceiving of just scales as string subdivision.; Instead, they could now view just intonation scales as cyclic groups generated by mathematical functions operating on sets of integers.
		His breakthrough: the realization that just scales construction could be reformulated as mathematical functions operating on subsets of the integers.
	sonic-arts.org /monzo/lattices/ming.htm (662 words)

	Just Intonation: Two Definitions
		It states that just intonation is a method of tuning intervals and scales based exclusively on rational numbers.
		It states that just intonation is a method of tuning based on the intervals of the harmonic series.
		Finally, with the exception of Western instruments influenced by keyboard and fretted instruments tuned in 12-tone equal temperament, most musicians in the world tune their instruments in just intonation, or based on intervals that have rational identities.
	www.chrysalis-foundation.org /just_intonation.htm (1842 words)

	NWCForum - Equal Temperance and Just Intonation
		Just intonation might not be so good for polyphony, but I've never heard a keyboard tuned to this.
		Just intonation is, in fact, not a very practical tuning system, especially for fixed interval instruments like keyboard instruments and the tuning of these is inevitably a compromise.
		But when I was reading up on the Just Intonation tuning system it made a real connection for me. As you might imagine, as an engineer, I have on more then one occasion found myself working in the proximity of some piece of plant that is emitting a highly resonant low hum.
	www.noteworthysoftware.com /nwcforum/4785.htm (4849 words)

	just intonation - Hutchinson encyclopedia article about just intonation (Site not responding. Last check: 2007-10-22)
		In music, singing or instrumental playing in what is said to be the pure natural scale, not that artificially fixed on keyboard instruments by equal temperament.
		I accepted the invitation with a worldly grin and a perfectly just intonation, because I really didn't care what I did.
		This information should not be considered complete, up to date, and is not intended to be used in place of a visit, consultation, or advice of a legal, medical, or any other professional.
	encyclopedia.farlex.com /just+intonation (118 words)

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