6:7:9: Difference between revisions

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'''6:7:9''', the ''subminor triad'' or ''septimal minor triad'', is a triad in the [[7-limit]] sometimes used in place of a [[minor triad]]. It appears as a minor triad in the [[5L 2s|diatonic scale]] of [[superpyth]], as [[64/63]] being tempered out means [[32/27]] is equated with [[7/6]]. This is in contrast to [[meantone]], where 32/27 is equated with [[6/5]], and thus the minor triad becomes [[10:12:15]].

6:7:9 is the second-simplest [[otonal]] {{w|tertian harmony|tertian}} triad, past [[4:5:6]], and is thus very [[consonant]]. The inverse of 6:7:9 is [[14:18:21]], the supermajor triad. These triads can be used in the same way as the 5-limit ones, leading to a septimal version of tertian harmony. However, this has a number of issues. First of all, [[14:18:21]] may sound unstable due to its relatively high otonal complexity. In addition, the [[7/6]] and [[9/7]] intervals differ by [[54/49]], an interval of 168 [[cent]]s, unlike [[5/4]] and [[6/5]], which differ by [[25/24]], an interval only about 71 cents in size. This means the 6:7:9 and 14:18:21 chords don't contrast as well as the 5-limit 4:5:6 and 10:12:15 chords. Another important fact is that the 6:7:9 chord doesn't contain the root, though it is a subchord of [[4:5:6:7:9]] which does. ~~These triads~~ are nonetheless useful in tertian harmony, bringing new flavors not found in the 5-limit.

6:7:9 is the second-simplest [[otonal]] {{w|tertian harmony|tertian}} triad, past [[4:5:6]], and is thus very [[consonant]]. The inverse of 6:7:9 is [[14:18:21]], the supermajor triad. These triads can be used in the same way as the 5-limit ones, leading to a septimal version of tertian harmony. However, this has a number of issues. First of all, [[14:18:21]] may sound unstable due to its relatively high otonal complexity. In addition, the [[7/6]] and [[9/7]] intervals differ by [[54/49]], an interval of 168 [[cent]]s, unlike [[5/4]] and [[6/5]], which differ by [[25/24]], an interval only about 71 cents in size. This means the 6:7:9 and 14:18:21 chords don't contrast as well as the 5-limit 4:5:6 and 10:12:15 chords. Another important fact is that the 6:7:9 chord doesn't contain the root, though it is a subchord of [[4:5:6:7:9]] which does.

The 6:7:9 triad and its inverse 14:18:21 are nonetheless useful in tertian harmony, bringing new flavors not found in the 5-limit.

== See also ==

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 '''6:7:9''', the ''subminor triad'' or ''septimal minor triad'', is a triad in the [[7-limit]] sometimes used in place of a [[minor triad]]. It appears as a minor triad in the [[5L 2s|diatonic scale]] of [[superpyth]], as [[64/63]] being tempered out means [[32/27]] is equated with [[7/6]]. This is in contrast to [[meantone]], where 32/27 is equated with [[6/5]], and thus the minor triad becomes [[10:12:15]].
-:7:9 is the second-simplest [[otonal]] {{w|tertian harmony|tertian}} triad, past [[4:5:6]], and is thus very [[consonant]]. The inverse of 6:7:9 is [[14:18:21]], the supermajor triad. These triads can be used in the same way as the 5-limit ones, leading to a septimal version of tertian harmony. However, this has a number of issues. First of all, [[14:18:21]] may sound unstable due to its relatively high otonal complexity. In addition, the [[7/6]] and [[9/7]] intervals differ by [[54/49]], an interval of 168 [[cent]]s, unlike [[5/4]] and [[6/5]], which differ by [[25/24]], an interval only about 71 cents in size. This means the 6:7:9 and 14:18:21 chords don't contrast as well as the 5-limit 4:5:6 and 10:12:15 chords. Another important fact is that the 6:7:9 chord doesn't contain the root, though it is a subchord of [[4:5:6:7:9]] which does. These triads are nonetheless useful in tertian harmony, bringing new flavors not found in the 5-limit.
+:7:9 is the second-simplest [[otonal]] {{w|tertian harmony|tertian}} triad, past [[4:5:6]], and is thus very [[consonant]]. The inverse of 6:7:9 is [[14:18:21]], the supermajor triad. These triads can be used in the same way as the 5-limit ones, leading to a septimal version of tertian harmony. However, this has a number of issues. First of all, [[14:18:21]] may sound unstable due to its relatively high otonal complexity. In addition, the [[7/6]] and [[9/7]] intervals differ by [[54/49]], an interval of 168 [[cent]]s, unlike [[5/4]] and [[6/5]], which differ by [[25/24]], an interval only about 71 cents in size. This means the 6:7:9 and 14:18:21 chords don't contrast as well as the 5-limit 4:5:6 and 10:12:15 chords. Another important fact is that the 6:7:9 chord doesn't contain the root, though it is a subchord of [[4:5:6:7:9]] which does.
+The 6:7:9 triad and its inverse 14:18:21 are nonetheless useful in tertian harmony, bringing new flavors not found in the 5-limit.
 == See also ==