7ed9/5: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ED intro}} | {{ED intro}} | ||
== Intervals == | == Intervals == | ||
{ | {| class="wikitable mw-collapsible" | ||
|+ | |||
!Step | |||
!Interval (¢) | |||
!JI approximated | |||
!Simplified ratios | |||
|- | |||
|1 | |||
|145.37 | |||
| 37/34, 48/44, 52/48 | |||
| 12/11, 13/12 | |||
|- | |||
|2 | |||
|290.74 | |||
| 19/16, 52/44 | |||
| 13/11 | |||
|- | |||
|3 | |||
|436.11 | |||
| 40/31, 44/34, 52/40 | |||
| 22/17, 13/10 | |||
|- | |||
|4 | |||
|581.48 | |||
| 56/40 | |||
| 7/5 | |||
|- | |||
|5 | |||
|726.85 | |||
| 29/19, 52/34 | |||
| 26/17 | |||
|- | |||
|6 | |||
|872.23 | |||
| 56/34 | |||
| 28/17 | |||
|- | |||
|7 | |||
|1017.60 | |||
| 9/5, 29/16 | |||
| | |||
|- | |||
|8 | |||
|1162.97 | |||
| 31/16, 37/19 | |||
| | |||
|- | |||
|9 | |||
|1308.34 | |||
| 34/16 | |||
| 17/8 | |||
|- | |||
|10 | |||
|1453.71 | |||
| 37/16, 44/19 | |||
| | |||
|- | |||
|11 | |||
|1599.08 | |||
| 40/16, 48/19 | |||
| 5/2 | |||
|- | |||
|12 | |||
|1744.45 | |||
| 44/16, 52/19 | |||
| 11/4 | |||
|- | |||
|13 | |||
|1889.82 | |||
| 3/1, 56/19 | |||
| | |||
|- | |||
|14 | |||
|2035.19 | |||
| 29/9, 52/16 | |||
| 13/4 | |||
|} | |||
The [[subgroup]] interpretation used is 9/5.3.16.19.29.31.34.37.40.44.48.52.56. Other interpretations are possible. Don't forget that fractions can multiply. | |||
== Harmonics == | == Harmonics == | ||
| Line 19: | Line 96: | ||
| collapsed = 1 | | collapsed = 1 | ||
}} | }} | ||
{{stub}} | |||
Latest revision as of 08:28, 22 December 2024
| ← 6ed9/5 | 7ed9/5 | 8ed9/5 → |
(convergent)
7 equal divisions of 9/5 (abbreviated 7ed9/5) is a nonoctave tuning system that divides the interval of 9/5 into 7 equal parts of about 145 ¢ each. Each step represents a frequency ratio of (9/5)1/7, or the 7th root of 9/5.
Intervals
| Step | Interval (¢) | JI approximated | Simplified ratios |
|---|---|---|---|
| 1 | 145.37 | 37/34, 48/44, 52/48 | 12/11, 13/12 |
| 2 | 290.74 | 19/16, 52/44 | 13/11 |
| 3 | 436.11 | 40/31, 44/34, 52/40 | 22/17, 13/10 |
| 4 | 581.48 | 56/40 | 7/5 |
| 5 | 726.85 | 29/19, 52/34 | 26/17 |
| 6 | 872.23 | 56/34 | 28/17 |
| 7 | 1017.60 | 9/5, 29/16 | |
| 8 | 1162.97 | 31/16, 37/19 | |
| 9 | 1308.34 | 34/16 | 17/8 |
| 10 | 1453.71 | 37/16, 44/19 | |
| 11 | 1599.08 | 40/16, 48/19 | 5/2 |
| 12 | 1744.45 | 44/16, 52/19 | 11/4 |
| 13 | 1889.82 | 3/1, 56/19 | |
| 14 | 2035.19 | 29/9, 52/16 | 13/4 |
The subgroup interpretation used is 9/5.3.16.19.29.31.34.37.40.44.48.52.56. Other interpretations are possible. Don't forget that fractions can multiply.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -37.0 | -12.1 | +71.3 | -24.3 | -49.2 | -25.3 | +34.3 | -24.3 | -61.3 | +64.4 | +59.2 |
| Relative (%) | -25.5 | -8.3 | +49.1 | -16.7 | -33.8 | -17.4 | +23.6 | -16.7 | -42.2 | +44.3 | +40.7 | |
| Steps (reduced) |
8 (1) |
13 (6) |
17 (3) |
19 (5) |
21 (0) |
23 (2) |
25 (4) |
26 (5) |
27 (6) |
29 (1) |
30 (2) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +66.0 | -62.3 | -36.4 | -2.8 | +37.7 | -61.3 | -9.5 | +47.0 | -37.4 | +27.4 | -49.6 |
| Relative (%) | +45.4 | -42.9 | -25.0 | -1.9 | +25.9 | -42.2 | -6.6 | +32.4 | -25.7 | +18.9 | -34.1 | |
| Steps (reduced) |
31 (3) |
31 (3) |
32 (4) |
33 (5) |
34 (6) |
34 (6) |
35 (0) |
36 (1) |
36 (1) |
37 (2) |
37 (2) | |
|
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