4:5:6:7:9:11, the harmonic eleventh chord, is a hexad in 11-limit harmony. It can be considered the fundamental otonal consonance of the 11-odd-limit, voiced in a roughly tertian manner. It is an extension of 4:5:6, 4:5:6:7, and 4:5:6:7:9.
| Harmonics
|
4:5:6:7:9:11
|
| Intervals from root
|
1/1–5/4–3/2–7/4–9/4–11/4
|
| Cents from root
|
0¢–386¢–702¢–969¢–1404¢–1751¢
|
| Step intervals
|
5/4, 6/5, 7/6, 9/7, 11/9
|
| Step cents
|
386¢, 316¢, 267¢, 435¢, 347¢
|
| Prime limit
|
11
|
| Genus
|
32⋅5⋅7⋅11 (3465)
|
| Intervallic odd limit
|
11
|
| Otonal odd limit
|
11
|
| Utonal odd limit
|
3465
|
| Consistent edos (d ≥ 1.5)
|
31edo, 46edo, 72edo*
|
|
|
Edo approximations for 4:5:6:7:9:11 ▶
intervals: 5/4, 3/2, 7/4, 9/4, 11/4 · ≤ 60edo, RMS rel. error ≤ 15%
| |
Edo |
Steps |
Cents (¢) |
Absolute errors (¢) |
RMS (¢) |
RMS (%)
|
| ▶ |
22 |
0 7 13 18 26 32 |
0.00 381.82 709.09 981.82 1418.18 1745.45 |
0.00 -4.50 +7.14 +12.99 +14.27 -5.86 |
7.98 |
14.62
|
| ▶ |
31 |
0 10 18 25 36 45 |
0.00 387.10 696.77 967.74 1393.55 1741.94 |
0.00 +0.78 -5.18 -1.08 -10.36 -9.38 |
4.43 |
11.45
|
| ▶ |
41 |
0 13 24 33 48 60 |
0.00 380.49 702.44 965.85 1404.88 1756.10 |
0.00 -5.83 +0.48 -2.97 +0.97 +4.78 |
3.31 |
11.31
|
| ▶ |
46 |
0 15 27 37 54 67 |
0.00 391.30 704.35 965.22 1408.70 1747.83 |
0.00 +4.99 +2.39 -3.61 +4.79 -3.49 |
3.52 |
13.50
|
| ▶ |
58 |
0 19 34 47 68 85 |
0.00 393.10 703.45 972.41 1406.90 1758.62 |
0.00 +6.79 +1.49 +3.59 +2.99 +7.30 |
2.63 |
12.73
|
Related chords
