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 ratios correspond to the relationships found in the [[harmonic series]].

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]].

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 features or as problems to be solved. Examples of approaches that try to solve these problems include pitch shifts, [[adaptive just intonation]] and [[temperament]].

== 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~~]].~~

==Ways of using JI==

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 features or as problems to be solved. Examples of approaches that try to solve these problems include pitch shifts, [[adaptive just intonation]] and [[temperament]].

~~==Just intonation in use~~==

Here are multiple ways in which musicians and theorists have used just intonation.

@@ Line 11: / Line 11: @@
 '''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]].
+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]].
+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 features or as problems to be solved. Examples of approaches that try to solve these problems include pitch shifts, [[adaptive just intonation]] and [[temperament]].
+== 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]].
+==Ways of using JI==
-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 features or as problems to be solved. Examples of approaches that try to solve these problems include pitch shifts, [[adaptive just intonation]] and [[temperament]].
-==Just intonation in use==
 Here are multiple ways in which musicians and theorists have used just intonation.