6:7:8:9 is a subminor add-4 chord in the 7-limit and the 9-odd-limit. In other words, it has a shape similar to a minor add-4 chord, but with a subminor third instead of a minor third.

Chord information
Harmonics 6:7:8:9
Subharmonics 1/(84:72:63:56)
Intervals from root 1/17/64/33/2
Cents from root 267¢498¢702¢
Step intervals 7/6, 8/7, 9/8
Step cents 267¢, 231¢, 204¢
Color name zo add-4 or z,4
Prime limit 7
Genus 327 (63)
Intervallic odd limit 9
Otonal odd limit 9
Utonal odd limit 63
Consistent edos (d ≥ 2) 5edo*, 36edo**, 41edo*, 53edo*, …

It can be constructed by stacking the intervals 7/6, 8/7 and 9/8 in that order, making it a stack of three consecutive superparticular intervals.

It is a subset of 5afdo. It is very approximated very well by 36edo, making it one of the most important consonant tetrads in 36edo harmony.


Edo approximations for 6:7:8:9 
intervals: 7/6, 4/3, 3/2 · ≤ 60edo, RMS rel. error ≤ 15%
  Edo Steps Cents (¢) Absolute errors (¢) RMS (¢) RMS (%)
10 0  2  4  6 0.00 240.00 480.00 720.00 0.00 -26.87 -18.04 +18.04 17.27 14.39
12 0  3  5  7 0.00 300.00 500.00 700.00 0.00 +33.13  +1.96  -1.96 14.41 14.41
14 0  3  6  8 0.00 257.14 514.29 685.71 0.00  -9.73 +16.24 -16.24 12.23 14.27
17 0  4  7 10 0.00 282.35 494.12 705.88 0.00 +15.48  -3.93  +3.93 7.26 10.28
19 0  4  8 11 0.00 252.63 505.26 694.74 0.00 -14.24  +7.22  -7.22 8.00 12.67
22 0  5  9 13 0.00 272.73 490.91 709.09 0.00  +5.86  -7.14  +7.14 5.65 10.35
24 0  5 10 14 0.00 250.00 500.00 700.00 0.00 -16.87  +1.96  -1.96 7.43 14.87
27 0  6 11 16 0.00 266.67 488.89 711.11 0.00  -0.20  -9.16  +9.16 6.47 14.57
31 0  7 13 18 0.00 270.97 503.23 696.77 0.00  +4.10  +5.18  -5.18 4.07 10.51
36 0  8 15 21 0.00 266.67 500.00 700.00 0.00  -0.20  +1.96  -1.96 1.39 4.16
41 0  9 17 24 0.00 263.41 497.56 702.44 0.00  -3.46  -0.48  +0.48 1.54 5.25
46 0 10 19 27 0.00 260.87 495.65 704.35 0.00  -6.00  -2.39  +2.39 3.10 11.89
53 0 12 22 31 0.00 271.70 498.11 701.89 0.00  +4.83  +0.07  -0.07 2.09 9.23
58 0 13 24 34 0.00 268.97 496.55 703.45 0.00  +2.09  -1.49  +1.49 1.39 6.73

See also