22:26:33: Difference between revisions

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{{Infobox chord}}
{{Infobox chord}}
'''22:26:33''', the '''major minthmic minor triad''' or '''neogothic minor triad''', is a [[13-limit]] {{W|Tertian harmony|tertian}} triad. This triad has a darker quality than the [[10:12:15]] classical minor triad, though not as much as the [[6:7:9]] subminor triad. Here [[13/11]] functions as a [[neogothic]] minor third, being between [[7/6]] and [[6/5]], in fact being (7+6)/(6+5), which is the [[mediant]] of 7/6 and 6/5. We can similarly find the neogothic major third by taking the mediant of [[5/4]] and [[9/7]], which is (5+9)/(4+7) = [[14/11]]. The triad containing this third and the [[3/2|perfect fifth]] is [[22:28:33]], which can be considered the neogothic major 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.
'''22:26:33''', the '''major minthmic minor triad''', is a [[13-limit]] {{w|tertian harmony|tertian}} triad. This triad has a darker quality than the [[10:12:15]] classical minor triad, though not as much as the [[6:7:9]] subminor triad. Here [[13/11]] functions as a [[neogothic major and minor|neogothic]] minor third, being between [[7/6]] and [[6/5]], in fact being (7 + 6)/(6 + 5), which is the [[mediant]] of 7/6 and 6/5, and [[33/26]] functions as the corresponding neogothic major third.  


{{Todo|expand}}
We can find another neogothic major third by taking the mediant of [[5/4]] and [[9/7]], which is {{nowrap| (5 + 9)/(4 + 7) {{=}} [[14/11]] }}. The triad containing this third and the [[3/2|perfect fifth]] is [[22:28:33]]. 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 ==
* [[26:33:39]] – its inverse


[[Category:Minor triads]]
[[Category:Minor triads]]

Latest revision as of 10:36, 17 January 2026

Chord information
Harmonics 22:26:33
Subharmonics 1/(39:33:26)
Intervals from root 1/113/113/2
Cents from root 289¢702¢
Step intervals 13/11, 33/26
Step cents 289¢, 413¢
Prime limit 13
Genus 31113 (429)
Intervallic odd limit 33
Otonal odd limit 33
Utonal odd limit 39
Consistent edos (d ≥ 2) 12edo*, 17edo*, 29edo***, 38edo*, …

22:26:33, the major minthmic minor triad, is a 13-limit tertian triad. This triad has a darker quality than the 10:12:15 classical minor triad, though not as much as the 6:7:9 subminor triad. Here 13/11 functions as a neogothic minor third, being between 7/6 and 6/5, in fact being (7 + 6)/(6 + 5), which is the mediant of 7/6 and 6/5, and 33/26 functions as the corresponding neogothic major third.

We can find another neogothic major third by taking the mediant of 5/4 and 9/7, which is (5 + 9)/(4 + 7) = 14/11. The triad containing this third and the perfect fifth is 22:28:33. 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