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47ed4 | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
47ed4 does very well on the 4.7.10.13 subgroup, and is an excellent tuning of [[Nelinda#Xenharmonic Systems for Nelinda|Nelindic]] temperament. | |||
== Intervals == | |||
{{Interval table}} | |||
== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 47 | |||
| num = 4 | |||
| denom = 1 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 47 | |||
| num = 4 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
[[Category:Nelindic]] | [[Category:Nelindic]] | ||
[[Category:94edo]] | [[Category:94edo]] | ||
{{todo|expand}} | |||
Latest revision as of 21:18, 31 July 2025
| ← 45ed4 | 47ed4 | 49ed4 → |
47 equal divisions of the 4th harmonic (abbreviated 47ed4) is a nonoctave tuning system that divides the interval of 4/1 into 47 equal parts of about 51.1 ¢ each. Each step represents a frequency ratio of 41/47, or the 47th root of 4.
47ed4 does very well on the 4.7.10.13 subgroup, and is an excellent tuning of Nelindic temperament.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 51.1 | |
| 2 | 102.1 | 18/17 |
| 3 | 153.2 | 23/21 |
| 4 | 204.3 | |
| 5 | 255.3 | 22/19 |
| 6 | 306.4 | |
| 7 | 357.4 | |
| 8 | 408.5 | 19/15 |
| 9 | 459.6 | 17/13 |
| 10 | 510.6 | |
| 11 | 561.7 | 18/13, 29/21 |
| 12 | 612.8 | |
| 13 | 663.8 | 22/15 |
| 14 | 714.9 | |
| 15 | 766 | |
| 16 | 817 | |
| 17 | 868.1 | |
| 18 | 919.1 | 29/17 |
| 19 | 970.2 | |
| 20 | 1021.3 | |
| 21 | 1072.3 | 13/7 |
| 22 | 1123.4 | 21/11 |
| 23 | 1174.5 | |
| 24 | 1225.5 | |
| 25 | 1276.6 | 23/11, 25/12 |
| 26 | 1327.7 | |
| 27 | 1378.7 | |
| 28 | 1429.8 | |
| 29 | 1480.9 | |
| 30 | 1531.9 | 17/7 |
| 31 | 1583 | 5/2 |
| 32 | 1634 | 18/7 |
| 33 | 1685.1 | |
| 34 | 1736.2 | |
| 35 | 1787.2 | 14/5 |
| 36 | 1838.3 | |
| 37 | 1889.4 | |
| 38 | 1940.4 | |
| 39 | 1991.5 | 19/6 |
| 40 | 2042.6 | |
| 41 | 2093.6 | |
| 42 | 2144.7 | 31/9 |
| 43 | 2195.7 | |
| 44 | 2246.8 | 11/3 |
| 45 | 2297.9 | |
| 46 | 2348.9 | |
| 47 | 2400 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +25.5 | -12.6 | +0.0 | +22.2 | +12.9 | +1.4 | +25.5 | -25.2 | -3.3 | -15.1 | -12.6 |
| Relative (%) | +50.0 | -24.7 | +0.0 | +43.5 | +25.3 | +2.7 | +50.0 | -49.3 | -6.5 | -29.7 | -24.7 | |
| Steps (reduced) |
24 (24) |
37 (37) |
47 (0) |
55 (8) |
61 (14) |
66 (19) |
71 (24) |
74 (27) |
78 (31) |
81 (34) |
84 (37) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.0 | -24.1 | +9.6 | +0.0 | -2.8 | +0.3 | +8.9 | +22.2 | -11.2 | +10.4 | -15.5 |
| Relative (%) | +4.0 | -47.3 | +18.8 | +0.0 | -5.5 | +0.7 | +17.4 | +43.5 | -21.9 | +20.3 | -30.4 | |
| Steps (reduced) |
87 (40) |
89 (42) |
92 (45) |
94 (0) |
96 (2) |
98 (4) |
100 (6) |
102 (8) |
103 (9) |
105 (11) |
106 (12) | |