22:28:33

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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.


Edo approximations for 22:28:33 
intervals: 14/11, 3/2 · ≤ 60edo, RMS rel. error ≤ 15%
  Edo Steps Cents (¢) Absolute errors (¢) RMS (¢) RMS (%)
8 0  3  5 0.00 450.00 750.00 0.00 +32.49 +48.04 20.02 13.34
9 0  3  5 0.00 400.00 666.67 0.00 -17.51 -35.29 14.41 10.80
12 0  4  7 0.00 400.00 700.00 0.00 -17.51  -1.96 7.83 7.83
14 0  5  8 0.00 428.57 685.71 0.00 +11.06 -16.24 11.21 13.08
17 0  6 10 0.00 423.53 705.88 0.00  +6.02  +3.93 2.50 3.54
20 0  7 12 0.00 420.00 720.00 0.00  +2.49 +18.04 7.98 13.31
21 0  7 12 0.00 400.00 685.71 0.00 -17.51 -16.24 7.97 13.95
22 0  8 13 0.00 436.36 709.09 0.00 +18.86  +7.14 7.77 14.25
26 0  9 15 0.00 415.38 692.31 0.00  -2.12  -9.65 4.14 8.97
29 0 10 17 0.00 413.79 703.45 0.00  -3.71  +1.49 2.19 5.29
31 0 11 18 0.00 425.81 696.77 0.00  +8.30  -5.18 5.55 14.34
34 0 12 20 0.00 423.53 705.88 0.00  +6.02  +3.93 2.50 7.07
37 0 13 22 0.00 421.62 713.51 0.00  +4.11 +11.56 4.78 14.75
38 0 13 22 0.00 410.53 694.74 0.00  -6.98  -7.22 3.35 10.60
41 0 14 24 0.00 409.76 702.44 0.00  -7.75  +0.48 3.77 12.89
43 0 15 25 0.00 418.60 697.67 0.00  +1.10  -4.28 2.32 8.31
46 0 16 27 0.00 417.39 704.35 0.00  -0.12  +2.39 1.16 4.43
51 0 18 30 0.00 423.53 705.88 0.00  +6.02  +3.93 2.50 10.61
55 0 19 32 0.00 414.55 698.18 0.00  -2.96  -3.77 1.62 7.43
58 0 20 34 0.00 413.79 703.45 0.00  -3.71  +1.49 2.19 10.58
60 0 21 35 0.00 420.00 700.00 0.00  +2.49  -1.96 1.82 9.10


See also