43ed12
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| ← 42ed12 | 43ed12 | 44ed12 → |
(convergent)
(convergent)
43 equal divisions of the 12th harmonic (abbreviated 43ed12) is a nonoctave tuning system that divides the interval of 12/1 into 43 equal parts of about 100 ¢ each. Each step represents a frequency ratio of 121/43, or the 43rd root of 12.
Theory
43ed12 is very nearly identical to 12edo, but with the 12th harmonic rather than the octave being just. The octave is about 0.546 cents stretched.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.5 | -1.1 | +1.1 | +15.0 | -0.5 | +32.7 | +1.6 | -2.2 | +15.5 | -49.5 | +0.0 |
| Relative (%) | +0.5 | -1.1 | +1.1 | +15.0 | -0.5 | +32.7 | +1.6 | -2.2 | +15.5 | -49.4 | +0.0 | |
| Steps (reduced) |
12 (12) |
19 (19) |
24 (24) |
28 (28) |
31 (31) |
34 (34) |
36 (36) |
38 (38) |
40 (40) |
41 (41) |
43 (0) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -38.5 | +33.3 | +13.9 | +2.2 | -2.7 | -1.6 | +4.8 | +16.1 | +31.6 | -48.9 | -25.8 | +0.5 |
| Relative (%) | -38.5 | +33.3 | +13.9 | +2.2 | -2.7 | -1.6 | +4.8 | +16.0 | +31.6 | -48.9 | -25.8 | +0.5 | |
| Steps (reduced) |
44 (1) |
46 (3) |
47 (4) |
48 (5) |
49 (6) |
50 (7) |
51 (8) |
52 (9) |
53 (10) |
53 (10) |
54 (11) |
55 (12) | |
Subsets and supersets
43ed12 is the 14th prime ed12. It does not contain any nontrivial subset ed12's.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 100 | 17/16, 18/17, 19/18 |
| 2 | 200.1 | 9/8, 28/25 |
| 3 | 300.1 | 19/16, 25/21 |
| 4 | 400.2 | 24/19, 29/23 |
| 5 | 500.2 | 4/3 |
| 6 | 600.3 | 17/12, 24/17 |
| 7 | 700.3 | 3/2 |
| 8 | 800.4 | 19/12, 27/17 |
| 9 | 900.4 | 27/16 |
| 10 | 1000.5 | 16/9, 25/14 |
| 11 | 1100.5 | 17/9 |
| 12 | 1200.5 | 2/1 |
| 13 | 1300.6 | 17/8 |
| 14 | 1400.6 | 9/4 |
| 15 | 1500.7 | 19/8 |
| 16 | 1600.7 | |
| 17 | 1700.8 | 8/3 |
| 18 | 1800.8 | 17/6 |
| 19 | 1900.9 | 3/1 |
| 20 | 2000.9 | 19/6 |
| 21 | 2101 | 27/8 |
| 22 | 2201 | 25/7 |
| 23 | 2301 | |
| 24 | 2401.1 | 4/1 |
| 25 | 2501.1 | 17/4 |
| 26 | 2601.2 | 9/2 |
| 27 | 2701.2 | 19/4 |
| 28 | 2801.3 | |
| 29 | 2901.3 | 16/3 |
| 30 | 3001.4 | 17/3 |
| 31 | 3101.4 | 6/1 |
| 32 | 3201.5 | 19/3 |
| 33 | 3301.5 | 27/4 |
| 34 | 3401.5 | |
| 35 | 3501.6 | |
| 36 | 3601.6 | 8/1 |
| 37 | 3701.7 | 17/2 |
| 38 | 3801.7 | 9/1 |
| 39 | 3901.8 | 19/2 |
| 40 | 4001.8 | |
| 41 | 4101.9 | |
| 42 | 4201.9 | |
| 43 | 4302 | 12/1 |