Dyadic chord: Difference between revisions
Jubilismic chords are innate because they cannot be mapped justly with pure octaves Tags: Mobile edit Mobile web edit |
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== Innate comma chord == | == Innate comma chord == | ||
An '''innate comma chord''', proposed by [[Kite Giedraitis]], is the type of chord that cannot be mapped to just intonation in a given prime limit and odd limit. However, instead of specifying the targeted JI ratios as in an [[# | An '''innate comma chord''', proposed by [[Kite Giedraitis]], is the type of chord that cannot be mapped to just intonation in a given prime limit and odd limit. However, instead of specifying the targeted JI ratios as in an [[#Essentially tempered dyadic chord|essentially tempered chord]], an innate comma chord describes only the general chord shape: the [[mapped interval]] representations or the [[interval span|sizes]] of its constituent intervals. | ||
For example, the [[augmented triad]] in 5-limit JI is an innate comma chord below the 25-odd-limit, because it is impossible to tune all three major thirds (in the four-note chord doubling the root up an octave) to [[5/4]] or any other 5-limit interval with odd limit below 25: the innate comma here is 128/125 (41¢). In practice, it might be sung or played justly but with a large odd limit (containing [[wolf interval]]s): for example, 1–5/4–8/5–2, or 1–5/4–25/16–2 (or even 1–5/4–25/16–125/64). Or it might be tempered, e.g. in 12edo as 0¢–400¢–800¢–1200¢. In 7-limit JI, one of the major thirds can be tuned to 9/7, reducing the innate comma to 225/224 (only 8¢). This comma can be distributed among the three thirds, tempering each by only a few cents, which is usually close enough to be acceptable. In 11-limit JI, the augmented chord is not an innate comma chord, because it can be tuned justly as 7:9:11:14, a low enough odd limit to "ring". (However, it is debatable whether this chord qualifies as an augmented triad, because the middle [[11/9]] interval is a neutral third rather than a major third.) | For example, the [[augmented triad]] in 5-limit JI is an innate comma chord below the 25-odd-limit, because it is impossible to tune all three major thirds (in the four-note chord doubling the root up an octave) to [[5/4]] or any other 5-limit interval with odd limit below 25: the innate comma here is 128/125 (41¢). In practice, it might be sung or played justly but with a large odd limit (containing [[wolf interval]]s): for example, 1–5/4–8/5–2, or 1–5/4–25/16–2 (or even 1–5/4–25/16–125/64). Or it might be tempered, e.g. in 12edo as 0¢–400¢–800¢–1200¢. In 7-limit JI, one of the major thirds can be tuned to 9/7, reducing the innate comma to 225/224 (only 8¢). This comma can be distributed among the three thirds, tempering each by only a few cents, which is usually close enough to be acceptable. In 11-limit JI, the augmented chord is not an innate comma chord, because it can be tuned justly as 7:9:11:14, a low enough odd limit to "ring". (However, it is debatable whether this chord qualifies as an augmented triad, because the middle [[11/9]] interval is a neutral third rather than a major third.) | ||
== Anomalous saturated suspension == | == Anomalous saturated suspension == | ||
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! Chords !! Associated temperament !! Associated commas | ! Chords !! Associated temperament !! Associated commas | ||
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| [[Jubilismic chords]] || [[Jubilismic]] || [[50/49]] | |||
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| [[Archytas chords]] || [[Archytas]] || [[64/63]] | | [[Archytas chords]] || [[Archytas]] || [[64/63]] | ||
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| [[Diminished seventh chord]] || [[Diminished (temperament)|Diminished]] || [[36/35]], [[50/49]] | | [[Diminished seventh chord]] || [[Diminished (temperament)|Diminished]] || [[36/35]], [[50/49]] | ||
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| [[Augmented triad]] || [[Augmented (temperament)|Augmented]] || [[128/125]] | | [[Augmented triad]] || [[Augmented (temperament)|Augmented]] || [[128/125]] | ||