140:180:210:252:315

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140:180:210:252:315 is the subharmonic ninth chord. It is a septimal dominant ninth chord. It is the inverse of 4:5:6:7:9, and can serve as the fundamental utonal consonance of the 9-odd-limit, with many chords being a subset of it or one of its inversions. Its otonal inverse, 4:5:6:7:9, can also be seen as a fundamental chord, and subsets can be taken out of it as well. The 1/(9:7:6:5:4) chord can be modified to get its otonal inverse by inflecting both the third and seventh down by 36/35, so the third becomes 5/4 and the seventh 7/4.

Chord information
Harmonics 140:180:210:252:315
Subharmonics 1/(9:7:6:5:4)
Intervals from root 1/19/73/29/59/4
Cents from root 435¢702¢1018¢1404¢
Step intervals 9/7, 7/6, 6/5, 5/4
Step cents 435¢, 267¢, 316¢, 386¢
Color names sub-9 or s9
ru gu-7 add-9 or r,g7,9
Prime limit 7
Genus 3257 (315)
Intervallic odd limit 9
Otonal odd limit 315
Utonal odd limit 9
Consistent edos (d ≥ 1.5) 31edo, 41edo*, 46edo, 53edo, …


Edo approximations for 140:180:210:252:315 
intervals: 9/7, 3/2, 9/5, 9/4 · ≤ 60edo, RMS rel. error ≤ 15%
  Edo Steps Cents (¢) Absolute errors (¢) RMS (¢) RMS (%)
12 0  4  7 10 14 0.00 400.00 700.00 1000.00 1400.00 0.00 -35.08 -1.96 -17.60  -3.91 13.22 13.22
19 0  7 11 16 22 0.00 442.11 694.74 1010.53 1389.47 0.00  +7.02 -7.22  -7.07 -14.44 7.29 11.54
22 0  8 13 19 26 0.00 436.36 709.09 1036.36 1418.18 0.00  +1.28 +7.14 +18.77 +14.27 7.28 13.34
27 0 10 16 23 32 0.00 444.44 711.11 1022.22 1422.22 0.00  +9.36 +9.16  +4.63 +18.31 6.07 13.67
31 0 11 18 26 36 0.00 425.81 696.77 1006.45 1393.55 0.00  -9.28 -5.18 -11.14 -10.36 4.14 10.70
41 0 15 24 35 48 0.00 439.02 702.44 1024.39 1404.88 0.00  +3.94 +0.48  +6.79  +0.97 2.58 8.80
46 0 17 27 39 54 0.00 443.48 704.35 1017.39 1408.70 0.00  +8.39 +2.39  -0.20  +4.79 3.22 12.35
53 0 19 31 45 62 0.00 430.19 701.89 1018.87 1403.77 0.00  -4.90 -0.07  +1.27  -0.14 2.13 9.41
58 0 21 34 49 68 0.00 434.48 703.45 1013.79 1406.90 0.00  -0.60 +1.49  -3.80  +2.99 2.28 11.02

See also