Just intonation: Difference between revisions

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'''Just intonation''' ('''JI''') is an approach to [[musical tuning]] which uses tones that are found at whole-number ratios of a fundamental [[frequency]]. The collection of all of these tones is called the [[harmonic series]]. Just ratios, such as 3:2 or 4:3, correspond to the interval relationships found in this series. Just ratios of small numbers, called '''Low-complexity just intonation (LCJI)''' intervals, tend to be the most [[concordant]] in the sense that their sounds meld together.

'''Just intonation''' ('''JI''') is an approach to [[musical tuning]] which uses tones that are found at whole-number ratios of a fundamental [[frequency]]. The collection of all of these tones is called the [[harmonic series]]. Just ratios, such as 3:2 or 4:3, correspond to the interval relationships found in this 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.

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 "Three Attacks on a Problem." ''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.

== ~~Concordance~~ ==

== Consonance ==

LCJI 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~~.

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 ~~concordance~~ by being the ratios between harmonics of a (possibly unplayed) fundamental even if they do not have harmonic timbre.

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==

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 {{Wikipedia}}
-'''Just intonation''' ('''JI''') is an approach to [[musical tuning]] which uses tones that are found at whole-number ratios of a fundamental [[frequency]]. The collection of all of these tones is called the [[harmonic series]]. Just ratios, such as 3:2 or 4:3, correspond to the interval relationships found in this series. Just ratios of small numbers, called '''Low-complexity just intonation (LCJI)''' intervals, tend to be the most [[concordant]] in the sense that their sounds meld together.
+'''Just intonation''' ('''JI''') is an approach to [[musical tuning]] which uses tones that are found at whole-number ratios of a fundamental [[frequency]]. The collection of all of these tones is called the [[harmonic series]]. Just ratios, such as 3:2 or 4:3, correspond to the interval relationships found in this 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.
 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 "Three Attacks on a Problem." ''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.
-== Concordance ==
+== Consonance ==
-LCJI 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.
+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 concordance by being the ratios between harmonics of a (possibly unplayed) fundamental even if they do not have harmonic timbre.
+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==