11ed7/3: Difference between revisions
Jump to navigation
Jump to search
Hotcrystal0 (talk | contribs) 9edo |
m Re-organize |
||
| Line 3: | Line 3: | ||
{{ED intro}} | {{ED intro}} | ||
== Theory == | |||
11ed7/3 is very nearly identical to [[9edo]], but with the 7/3 instead of the 2/1 being just. The octave is stretched by about 0.167{{cent}}. | 11ed7/3 is very nearly identical to [[9edo]], but with the 7/3 instead of the 2/1 being just. The octave is stretched by about 0.167{{cent}}. | ||
=== Harmonics === | |||
{{Harmonics in equal|11|7|3|columns=11}} | |||
{{Harmonics in equal|11|7|3|columns=12|start=12|collapsed=1|title=Approximation of harmonics in 11ed7/3 (continued)}} | |||
== Intervals == | == Intervals == | ||
{{Interval table}} | {{Interval table}} | ||
Latest revision as of 18:00, 14 May 2026
|
This page is a stub. You can help the Xenharmonic Wiki by expanding it. |
| ← 10ed7/3 | 11ed7/3 | 12ed7/3 → |
(convergent)
11 equal divisions of 7/3 (abbreviated 11ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 11 equal parts of about 133 ¢ each. Each step represents a frequency ratio of (7/3)1/11, or the 11th root of 7/3.
Theory
11ed7/3 is very nearly identical to 9edo, but with the 7/3 instead of the 2/1 being just. The octave is stretched by about 0.167 ¢.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.2 | -35.0 | +0.3 | +14.1 | -34.9 | -35.0 | +0.5 | +63.3 | +14.2 | -17.4 | -34.7 |
| Relative (%) | +0.1 | -26.3 | +0.3 | +10.6 | -26.1 | -26.3 | +0.4 | +47.5 | +10.7 | -13.1 | -26.0 | |
| Steps (reduced) |
9 (9) |
14 (3) |
18 (7) |
21 (10) |
23 (1) |
25 (3) |
27 (5) |
29 (7) |
30 (8) |
31 (9) |
32 (10) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -39.9 | -34.9 | -21.0 | +0.7 | +29.1 | +63.5 | -30.1 | +14.4 | +63.3 | -17.2 | +39.2 | -34.5 |
| Relative (%) | -29.9 | -26.1 | -15.7 | +0.5 | +21.8 | +47.6 | -22.6 | +10.8 | +47.5 | -12.9 | +29.4 | -25.9 | |
| Steps (reduced) |
33 (0) |
34 (1) |
35 (2) |
36 (3) |
37 (4) |
38 (5) |
38 (5) |
39 (6) |
40 (7) |
40 (7) |
41 (8) |
41 (8) | |
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 133.4 | 12/11, 13/12, 14/13, 15/14, 16/15, 17/16 |
| 2 | 266.7 | 7/6, 13/11, 15/13, 19/16, 20/17, 22/19 |
| 3 | 400.1 | 5/4, 14/11, 19/15 |
| 4 | 533.4 | 11/8, 15/11, 18/13, 19/14 |
| 5 | 666.8 | 13/9, 16/11, 19/13, 22/15 |
| 6 | 800.1 | 8/5, 11/7, 19/12, 21/13 |
| 7 | 933.5 | 12/7, 17/10, 19/11, 22/13 |
| 8 | 1066.8 | 11/6, 13/7, 15/8 |
| 9 | 1200.2 | 2/1 |
| 10 | 1333.5 | 13/6, 15/7, 17/8 |
| 11 | 1466.9 | 7/3, 19/8 |