Just intonation: Difference between revisions
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| en = Just intonation | |||
| de = Reine Stimmungen | |||
| es = Entonación Justa | |||
| ja = 純正律 | |||
| ko = 순정률 | |||
| ro = Intervale raționale | |||
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== | {{Wikipedia}} | ||
== | '''Just intonation''' ('''JI''') is an approach to [[musical tuning]] which uses tones whose frequencies are whole-number ratios of a given fundamental [[frequency]]. Just intonation includes the [[harmonic series]], which is the collection of tones found at integer multiples of a fundamental frequency; all just intervals can be found as the interval between two notes in the harmonic series. Just ratios of small numbers, called '''Low-complexity just intonation (LCJI)''' intervals, tend to be the most [[concordant|consonant]] in the sense that their sounds meld together. | ||
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[[ | In the context of Western music theory prior to the 20th century, the term ''just intonation'' used alone usually refers to [[5-limit]] tuning--intervals where the numerators and denominators of any ratio used have no prime factors greater than 5. ''Extended just intonation'', a term coined by [[Ben Johnston]], refers to any tuning in the harmonic series regardless of [[prime limit]].<ref>From Ben Johnston "A Notation System for Extended Just Intonation." ''Maximum Clarity'', 2006, p. 77</ref> In current usage, just intonation typically refers to extended just intonation. The practice of just intonation without any particular constraint is sometimes referred to as '''rational intonation''' ('''RI''') or as [[free style JI]]. | ||
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< | The structure of just intonation has several implications on music composition. [[Wolf interval|Wolf intervals]] and [[Comma|commas]], two kinds of dissonant intervals, may appear between distantly-related pitches. In addition, certain chord progressions are [[Comma pump|comma pumps]], which may cause the [[tonal center]] of a piece to drift up or down in pitch over time. These effects can be treated either as tools to use or as problems to be solved. Examples of approaches that try to solve these problems without greatly restricting the set of available ratios include pitch shifts, [[adaptive just intonation]] and [[temperament]]. Other approaches restrict the space of usable JI intervals in a way that makes these problems arise less frequently. | ||
== Consonance == | |||
LCJI intervals achieve consonance through alignment of [[Partial|partials]] if the interval has [[Harmonic timbre|harmonic timbre]]. In fact, alignment of partials is a stronger effect with harmonic timbre: if partials align at frequency n, they will also align at every multiple of n; and in addition, two notes whose partials align with the same root note will also have partials aligning with each other. This allows for the construction of just-intonation chords of more than two notes where every comprising interval is a consonance. | |||
Low-complexity JI intervals and chords also achieve consonance by being the ratios between harmonics of a (possibly unplayed) fundamental even if they do not have harmonic timbre. | |||
==Ways of using JI== | |||
Here are multiple ways in which musicians and theorists have used just intonation. | |||
[[Free style JI|'''Free style JI''']] <br /> | |||
[[Lou Harrison]] used this term; it means that you choose just-intonation pitches from the set of all possible just intervals (not from a mode or scale) as you use them in music. | |||
'''Harmonic limits and subgroups'''<br /> | |||
[[Harmonic limit|Harmonic limits]] set a limit for the highest prime number in the factorization of any ratio used. [[Subgroup|Subgroups]] name a list of allowable prime numbers used. | |||
'''Restrictions on the denominator or numerator'''<br /> | |||
Some approaches restrict "the denominator to one or very few values"<ref name=":0">From Jacques Dudon, "Differential Coherence", ''1/1'' vol. 11, no. 2: p.1).</ref> (the [[harmonic series]], [[isoharmonic chord]]s, [[AFDO]]s/[[overtone scale]]s, [[primodality]], [[Ringer scale|ringer scales]]), the "numerator to one or a very few values" (the [[subharmonic series]], [[IFDO]]s/undertone scales), or both ([[Tonality diamond|tonality diamonds]]) | |||
'''Mediants'''<br /> | |||
The use of harmonic and arithmetic [[Mediant (operation)|mediants]] as was common with the Ancient Greeks. This can also involve further divisions besides two parts as seen with Ptolemy sometimes using 3 parts. The Chinese have historically used as many as 10 parts. | |||
'''Approximations/alterations of tempered tunings''' <br /> | |||
These are [[Detempering|detemperings]], including [[NEJI]] systems. | |||
'''Other approaches'''<br /> | |||
Other approaches include [http://anaphoria.com/wilsonintroMERU.html Meru scales], [[Tritriadic scale|titriadic scales]], and [[combination product sets|product sets]]. | |||
==Instruments== | |||
{{todo|expand|comment=Expand the instruments section with more examples}} | |||
*The [[Kalimba#Array mbira|array mbira]] was designed by [[Bill Wesley]] as a versatile just intonation instrument, covering a 5 octave range. | |||
*Most of [[Harry Partch]]'s instruments were designed to be for just intonation. | |||
==Music== | |||
{{Main|Music in just intonation}} | |||
== Notation == | |||
There are various [[Musical notation|notation systems]] for just intonation. | |||
==See also== | |||
{{todo|cleanup|inline=1}} | |||
*[[List of approaches to musical tuning]] | |||
*[[Gallery of just intervals]] | |||
*[[Gallery of 12-tone just intonation scales]] | |||
*[[Families of scales]] | |||
*[[boogiewoogiescale|Boogie woogie scale]] | |||
*[[:Category:Just intonation]] | |||
==References== | |||
<references /> | |||
==Further reading== | |||
*[http://www.tonalsoft.com/enc/j/just.aspx Just intonation] on the [[Tonalsoft Encyclopedia]] | |||
*[http://nowitzky.hostwebs.com/justint/ Just Intonation] by Mark Nowitzky | |||
*[http://www.kylegann.com/tuning.html Just Intonation Explained] by Kyle Gann | |||
*[http://www.kylegann.com/Octave.html Anatomy of an Octave] by Kyle Gann | |||
*[http://www.dbdoty.com/Words/What-is-Just-Intonation.html What is Just Intonation?] by David B. Doty | |||
*[http://lumma.org/tuning/faq/#whatisJI What is "just intonation"?] by Carl Lumma | |||
*[http://www.dbdoty.com/Words/werntz.html A Response to Julia Werntz] by David B. Doty | |||
*[http://lumma.org/tuning/gws/commaseq.htm Comma Sequences] by Gene Ward Smith | |||
*[https://casfaculty.case.edu/ross-duffin/just-intonation-in-renaissance-theory-practice/ Just Intonation in Renaissance Theory & Practice] by Ross W. Duffin | |||