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 ~~rational~~ ratios of [[Frequency|frequencies]].

'''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 intervals ~~are precisely those intervals which~~ 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. Just intervals are also precisely those intervals which achieve concordance by melding with each other by forming different [[Harmonic|harmonics]] of the same unplayed root. (JI multi-note chords formed from harmonics of the same root can be the most concordant chords.)

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.

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 rational ratios of [[Frequency|frequencies]].
+'''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 intervals are precisely those intervals which 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. Just intervals are also precisely those intervals which achieve concordance by melding with each other by forming different [[Harmonic|harmonics]] of the same unplayed root. (JI multi-note chords formed from harmonics of the same root can be the most concordant chords.)
+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.
 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]].