43ed12: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ED intro}} | |||
43ed12 is very nearly identical to [[12edo]], but with the [[12/1]] rather than the 2/1 being just. The octave is about 0.55 [[cent]]s stretched and the step size is about 100.045 cents. | |||
== Intervals == | == Intervals == | ||
| Line 19: | Line 21: | ||
}} | }} | ||
==See also== | == See also == | ||
* [[7edf|7EDF]] | * [[7edf|7EDF]] – relative ED3/2 | ||
* [[12edo|12EDO]] | * [[12edo|12EDO]] – relative EDO | ||
* [[19ed3|19ED3]] | * [[19ed3|19ED3]] – relative ED3 | ||
* [[28ed5|28ED5]] | * [[28ed5|28ED5]] – relative ED5 | ||
* [[31ed6|31ED6]] | * [[31ed6|31ED6]] – relative ED6 | ||
* [[34ed7|34ED7]] | * [[34ed7|34ED7]] – relative ED7 | ||
* [[40ed10|40ED10]] | * [[40ed10|40ED10]] – relative ED10 | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
Revision as of 13:21, 21 January 2025
| ← 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.
43ed12 is very nearly identical to 12edo, but with the 12/1 rather than the 2/1 being just. The octave is about 0.55 cents stretched and the step size is about 100.045 cents.
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 |
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 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -38.5 | +33.3 | +13.9 | +2.2 | -2.7 | -1.6 | +4.8 | +16.1 | +31.6 | -48.9 | -25.8 |
| Relative (%) | -38.5 | +33.3 | +13.9 | +2.2 | -2.7 | -1.6 | +4.8 | +16.0 | +31.6 | -48.9 | -25.8 | |
| Steps (reduced) |
44 (1) |
46 (3) |
47 (4) |
48 (5) |
49 (6) |
50 (7) |
51 (8) |
52 (9) |
53 (10) |
53 (10) |
54 (11) | |