22:28:33: Difference between revisions

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'''22:28:33''', the '''pentacircle ~~minthmic major triad''' or '''neogothic~~ major triad''', is an [[11-limit]] {{W|~~Tertian~~ harmony|tertian}} triad. This triad has a brighter quality than the [[4:5:6]] classical major triad, though not as much as the [[14:18:21]] supermajor triad. Here [[14/11]] functions as a [[neogothic]] major third, being between [[5/4]] and [[9/7]], in fact being (5+9)/(4+7), which is the [[mediant]] of 5/4 and 9/7~~. We can similarly find the neogothic minor third by taking the mediant of [[7/6]] and [[6/5]]~~, ~~which is (7+6)/(6+5) = [[13/11]]. The triad containing this third~~ and ~~the~~ [[3/~~2|perfect fifth~~]] ~~is [[22:26:33]], which can be considered~~ the neogothic minor ~~triad. Note that these triads only invert to each other if and only if (14/11)*(13/11)/(3/2) = [[364/363]], the minor minthma or gentle comma, is tempered out~~.

'''22:28:33''', the '''pentacircle major triad''', is an [[11-limit]] {{w|tertian harmony|tertian}} triad. This triad has a brighter quality than the [[4:5:6]] classical major triad, though not as much as the [[14:18:21]] supermajor triad. Here [[14/11]] functions as a [[neogothic major and minor|neogothic]] major third, being between [[5/4]] and [[9/7]], in fact being (5 + 9)/(4 + 7), which is the [[mediant]] of 5/4 and 9/7, and [[33/28]] functions as the corresponding neogothic minor third.

We can find another neogothic minor third by taking the mediant of [[7/6]] and [[6/5]], which is {{nowrap| (7 + 6)/(6 + 5) {{=}} [[13/11]] }}. The triad containing this third and the [[3/2|perfect fifth]] is [[22:26:33]]. Note that these triads are reduced to the [[13-odd-limit]] and invert to each other if and only if {{nowrap| (14/11)⋅(13/11)/(3/2) {{=}} [[364/363]] }}, the minor minthma or gentle comma, is [[tempering out|tempered out]].

== See also ==

* [[28:33:42]] – its inverse

[[Category:Major triads]]

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 {{Infobox chord}}
-'''22:28:33''', the '''pentacircle minthmic major triad''' or '''neogothic major triad''', is an [[11-limit]] {{W|Tertian harmony|tertian}} triad. This triad has a brighter quality than the [[4:5:6]] classical major triad, though not as much as the [[14:18:21]] supermajor triad. Here [[14/11]] functions as a [[neogothic]] major third, being between [[5/4]] and [[9/7]], in fact being (5+9)/(4+7), which is the [[mediant]] of 5/4 and 9/7. We can similarly find the neogothic minor third by taking the mediant of [[7/6]] and [[6/5]], which is (7+6)/(6+5)&nbsp;=&nbsp;[[13/11]]. The triad containing this third and the [[3/2|perfect fifth]] is [[22:26:33]], which can be considered the neogothic minor triad. Note that these triads only invert to each other if and only if (14/11)*(13/11)/(3/2)&nbsp;=&nbsp;[[364/363]], the minor minthma or gentle comma, is tempered out.
+'''22:28:33''', the '''pentacircle major triad''', is an [[11-limit]] {{w|tertian harmony|tertian}} triad. This triad has a brighter quality than the [[4:5:6]] classical major triad, though not as much as the [[14:18:21]] supermajor triad. Here [[14/11]] functions as a [[neogothic major and minor|neogothic]] major third, being between [[5/4]] and [[9/7]], in fact being (5 + 9)/(4 + 7), which is the [[mediant]] of 5/4 and 9/7, and [[33/28]] functions as the corresponding neogothic minor third.
-{{Todo|expand}}
+We can find another neogothic minor third by taking the mediant of [[7/6]] and [[6/5]], which is {{nowrap| (7 + 6)/(6 + 5) {{=}} [[13/11]] }}. The triad containing this third and the [[3/2|perfect fifth]] is [[22:26:33]]. Note that these triads are reduced to the [[13-odd-limit]] and invert to each other if and only if {{nowrap| (14/11)⋅(13/11)/(3/2) {{=}} [[364/363]] }}, the minor minthma or gentle comma, is [[tempering out|tempered out]].
+== See also ==
+* [[28:33:42]] – its inverse
 [[Category:Major triads]]