Just intonation: Difference between revisions

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'''Just intonation''' ('''JI''') or '''Rational intonation''' ('''RI''') is an approach to [[musical tuning]] which uses intervals which are found at whole-number ratios of [[Frequency|frequencies]]. Just ~~intervals are precisely those intervals which form different~~ [[~~Harmonic|harmonics~~]] ~~of the same fundamental. (JI multi-note chords formed from harmonics of the same root can be the most concordant chords~~.)

'''Just intonation''' ('''JI''') or '''Rational intonation''' ('''RI''') is an approach to [[musical tuning]] which uses intervals which are found at whole-number ratios of [[Frequency|frequencies]]. Just ratios correspond to the relationships found in the [[harmonic series]].

~~Just~~ intervals achieve concordance 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 where every comprising interval is a concordance.

Low-[[Height|complexity]] JI intervals achieve concordance 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 concordance.

Low-complexity JI intervals and chords also achieve concordance by being the ratios between harmonics of a (possibly unplayed) fundamental even if they do not have harmonic timbre.

In the context of Western music theory prior to the 20th century, the term ''just intonation'' used alone usually refers to [[5-limit]] tuning. ''Extended just intonation'', a term coined by [[Ben Johnston]], usually refers to higher prime limits,<ref>[https://marsbat.space/pdfs/EJItext.pdf Sabat, Marc. ''On Ben Johnston’s Notation and the Performance Practice of Extended Just Intonation'']</ref> such as the [[7-limit]], the [[11-limit]] and the [[13-limit]]. 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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 {{Wikipedia}}
-'''Just intonation''' ('''JI''') or '''Rational intonation''' ('''RI''') is an approach to [[musical tuning]] which uses intervals which are found at whole-number ratios of [[Frequency|frequencies]]. Just intervals are precisely those intervals which form different [[Harmonic|harmonics]] of the same fundamental. (JI multi-note chords formed from harmonics of the same root can be the most concordant chords.)
+'''Just intonation''' ('''JI''') or '''Rational intonation''' ('''RI''') is an approach to [[musical tuning]] which uses intervals which are found at whole-number ratios of [[Frequency|frequencies]]. Just ratios correspond to the relationships found in the [[harmonic series]].
-Just intervals achieve concordance 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 where every comprising interval is a concordance.
+Low-[[Height|complexity]] JI intervals achieve concordance 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 concordance.
+Low-complexity JI intervals and chords also achieve concordance by being the ratios between harmonics of a (possibly unplayed) fundamental even if they do not have harmonic timbre.
 In the context of Western music theory prior to the 20th century, the term ''just intonation'' used alone usually refers to [[5-limit]] tuning. ''Extended just intonation'', a term coined by [[Ben Johnston]], usually refers to higher prime limits,<ref>[https://marsbat.space/pdfs/EJItext.pdf Sabat, Marc. ''On Ben Johnston’s Notation and the Performance Practice of Extended Just Intonation'']</ref> such as the [[7-limit]], the [[11-limit]] and the [[13-limit]]. The practice of just intonation without any particular constraint is sometimes referred to as '''rational intonation''' ('''RI''') or as [[free style JI]].