22:28:33: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Overthink (talk | contribs)
create page similarly to 22:26:33
 
Review
Line 1: Line 1:
{{Infobox chord}}
{{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) = [[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.  


{{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]]
[[Category:Major triads]]

Revision as of 10:36, 17 January 2026

Chord information
Harmonics 22:28:33
Subharmonics 1/(42:33:28)
Intervals from root 1/114/113/2
Cents from root 418¢702¢
Step intervals 14/11, 33/28
Step cents 418¢, 284¢
Prime limit 11
Genus 3711 (231)
Intervallic odd limit 33
Otonal odd limit 33
Utonal odd limit 33
Consistent edos (d ≥ 2) 12edo*, 17edo**, 26edo*, 29edo*, …

22:28:33, the pentacircle major triad, is an 11-limit 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, 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 (7 + 6)/(6 + 5) = 13/11. The triad containing this third and the 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 (14/11)⋅(13/11)/(3/2) = 364/363, the minor minthma or gentle comma, is tempered out.

See also