Just intonation: Difference between revisions

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]]. 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.

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://web.archive.org/web/20240315224927/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]].

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]], usually refers to higher prime limits,<ref>[https://web.archive.org/web/20240315224927/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 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.

@@ 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]]. 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.
-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://web.archive.org/web/20240315224927/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]].
+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]], usually refers to higher prime limits,<ref>[https://web.archive.org/web/20240315224927/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 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.