14:21:24

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Chord information
Harmonics 14:21:24
Subharmonics 1/(12:8:7)
Intervals from root 1/13/212/7
Cents from root 702¢933¢
Step intervals 3/2, 8/7
Step cents 702¢, 231¢
Color name ru-6 no-3 or r6no3
Prime limit 7
Genus 37 (21)
Intervallic odd limit 7
Otonal odd limit 21
Utonal odd limit 7
Consistent edos (d ≥ 2) 5edo**, 10edo*, 22edo*, 26edo*, …

14:21:24 is a 7-limit chord found as a subset of the subharmonic sixth chord, 70:84:105:120, or of the septimal major sixth chord, 14:18:21:24. Due to having no fives, it is the first utonal chord that deviates from traditional harmony. As such, it is a candidate for metallic harmony, a form of extraclassical tonality that employs 7 instead of 5 as its other prime.

Its first rotation, 21:24:28, is significant because it consists of the intervals 8/7 and 7/6 stacked on top of each other. The intervals in this chord divide the perfect fourth rather than the perfect fifth, and contrast by 49/48, similarly to how 6/5 and 5/4 contrast by 25/24 in 10:12:15. By swapping the order of 8/7 and 7/6, we get the otonal inverse of 21:24:28, that being 6:7:8.

Another notable setting is the open voicing 7:12:21, which shares the property with 21:24:28 that its intervals, 12/7 and 7/4, contrast by 49/48, but they divide the perfect twelfth instead. Its otonal version is 4:7:12, an open voicing of 4:6:7.

Its second rotation, 12:14:21, is also significant because it functions as the fifthless version of the septimal minor seventh chord, 12:14:18:21.


Edo approximations for 14:21:24 
intervals: 3/2, 12/7 · ≤ 60edo, RMS rel. error ≤ 15%
  Edo Steps Cents (¢) Absolute errors (¢) RMS (¢) RMS (%)
9 0  5  7 0.00 666.67 933.33 0.00 -35.29  +0.20 16.68 12.51
10 0  6  8 0.00 720.00 960.00 0.00 +18.04 +26.87 11.18 9.32
14 0  8 11 0.00 685.71 942.86 0.00 -16.24  +9.73 10.71 12.50
15 0  9 12 0.00 720.00 960.00 0.00 +18.04 +26.87 11.18 13.98
17 0 10 13 0.00 705.88 917.65 0.00  +3.93 -15.48 8.38 11.87
19 0 11 15 0.00 694.74 947.37 0.00  -7.22 +14.24 8.91 14.12
21 0 12 16 0.00 685.71 914.29 0.00 -16.24 -18.84 8.34 14.59
22 0 13 17 0.00 709.09 927.27 0.00  +7.14  -5.86 5.31 9.74
26 0 15 20 0.00 692.31 923.08 0.00  -9.65 -10.05 4.65 10.07
27 0 16 21 0.00 711.11 933.33 0.00  +9.16  +0.20 4.27 9.61
31 0 18 24 0.00 696.77 929.03 0.00  -5.18  -4.10 2.23 5.76
32 0 19 25 0.00 712.50 937.50 0.00 +10.54  +4.37 4.33 11.54
36 0 21 28 0.00 700.00 933.33 0.00  -1.96  +0.20 0.97 2.92
37 0 22 29 0.00 713.51 940.54 0.00 +11.56  +7.41 4.78 14.74
41 0 24 32 0.00 702.44 936.59 0.00  +0.48  +3.46 1.53 5.22
46 0 27 36 0.00 704.35 939.13 0.00  +2.39  +6.00 2.47 9.46
48 0 28 37 0.00 700.00 925.00 0.00  -1.96  -8.13 3.46 13.86
51 0 30 40 0.00 705.88 941.18 0.00  +3.93  +8.05 3.29 13.96
53 0 31 41 0.00 701.89 928.30 0.00  -0.07  -4.83 2.26 9.98
58 0 34 45 0.00 703.45 931.03 0.00  +1.49  -2.09 1.47 7.11