20ed11/5
Jump to navigation
Jump to search
Prime factorization
22 × 5
Step size
68.2502¢
Octave
18\20ed11/5 (1228.5¢) (→9\10ed11/5)
Twelfth
28\20ed11/5 (1911.01¢) (→7\5ed11/5)
Consistency limit
3
Distinct consistency limit
2
| ← 19ed11/5 | 20ed11/5 | 21ed11/5 → |
20ed11/5 is the equal division of the neutral ninth into 20 parts of 68.3 cents each.
Temperaments
20ed11/5 tempers out 2093663/2088025 and 54925/54043 in the no-twos-or-threes 17-limit which means it supports catfish temperament, which can be viewed as the no-twos-or-threes-analog of meantone. However, its 13/11 approximation is quite flat (closer to a subminor third) which affects the quality of the 11:13:17 chord, one of the most consonant no-twos-or-threes chords.
Intervals
| # | Cents | Approximate ratios | Catfish nonatonic notation (J = 1/1) |
|---|---|---|---|
| 0 | 0.0 | 1/1 | J |
| 1 | 68.3 | 28/27, 27/26, 26/25, 25/24 | J#, Kb |
| 2 | 136.5 | 14/13, 27/25, 13/12 | K |
| 3 | 204.8 | 9/8 | K#, Lb |
| 4 | 273.0 | 7/6, 75/64 | L |
| 5 | 341.3 | 17/14, 39/32, 11/9 | L#, Mb |
| 6 | 409.5 | 14/11,81/64, 19/15 | M |
| 7 | 477.8 | 21/16, 33/25 | M#, Nb |
| 8 | 546.0 | 11/8, 15/11, 48/35 | N |
| 9 | 614.3 | 10/7, 121/85 | N# |
| 10 | 682.5 | 3/2, 40/27 | Ob |
| 11 | 750.1 | 17/11, 49/32 | O |
| 12 | 819.0 | 8/5, 21/13 | O#, Pb |
| 13 | 887.3 | 5/3, 38/23 | P |
| 14 | 955.5 | 7/4, 26/15 | P#, Qb |
| 15 | 1023.8 | 9/5, 29/16, 20/11 | Q |
| 16 | 1092.0 | 15/8, 32/17 | Q#, Rb |
| 17 | 1160.3 | 49/25, 35/18 | R |
| 18 | 1228.5 | 2/1 | R# |
| 19 | 1296.8 | 15/7 | Jb |
| 20 | 1365.0 | 11/5 | J |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +28.5 | +9.1 | -11.2 | +11.9 | -30.7 | -24.6 | +17.3 | +18.1 | -27.8 | +11.9 | -2.2 |
| Relative (%) | +41.8 | +13.3 | -16.5 | +17.5 | -45.0 | -36.0 | +25.3 | +26.5 | -40.7 | +17.5 | -3.2 | |
| Steps (reduced) |
18 (18) |
28 (8) |
35 (15) |
41 (1) |
45 (5) |
49 (9) |
53 (13) |
56 (16) |
58 (18) |
61 (1) |
63 (3) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -4.3 | +3.9 | +21.0 | -22.5 | +9.1 | -21.6 | +21.3 | +0.7 | -15.5 | -27.8 | +31.7 |
| Relative (%) | -6.2 | +5.8 | +30.8 | -32.9 | +13.3 | -31.7 | +31.1 | +1.0 | -22.7 | -40.7 | +46.5 | |
| Steps (reduced) |
65 (5) |
67 (7) |
69 (9) |
70 (10) |
72 (12) |
73 (13) |
75 (15) |
76 (16) |
77 (17) |
78 (18) |
80 (0) | |