41ed4: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ED intro}} It corresponds to 20.5edo, or every second step of [[41edo]]. | |||
The [[Kite Guitar]] (see also [https://kiteguitar.com KiteGuitar.com] and [http://tallkite.com/misc_files/The%20Kite%20Tuning.pdf Kite Tuning]) is a guitar fretting using every other step of 41edo, i.e. 41ed4 or "20½-edo". However, the interval between two adjacent open strings is always an odd number of 41-edosteps. Thus each string only covers 41ed4, but the full edo can be found on every pair of adjacent strings. | The [[Kite Guitar]] (see also [https://kiteguitar.com KiteGuitar.com] and [http://tallkite.com/misc_files/The%20Kite%20Tuning.pdf Kite Tuning]) is a guitar fretting using every other step of 41edo, i.e. 41ed4 or "20½-edo". However, the interval between two adjacent open strings is always an odd number of 41-edosteps. Thus each string only covers 41ed4, but the full edo can be found on every pair of adjacent strings. | ||
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Latest revision as of 14:40, 20 February 2025
| ← 39ed4 | 41ed4 | 43ed4 → |
41 equal divisions of the 4th harmonic (abbreviated 41ed4) is a nonoctave tuning system that divides the interval of 4/1 into 41 equal parts of about 58.5 ¢ each. Each step represents a frequency ratio of 41/41, or the 41st root of 4. It corresponds to 20.5edo, or every second step of 41edo.
The Kite Guitar (see also KiteGuitar.com and Kite Tuning) is a guitar fretting using every other step of 41edo, i.e. 41ed4 or "20½-edo". However, the interval between two adjacent open strings is always an odd number of 41-edosteps. Thus each string only covers 41ed4, but the full edo can be found on every pair of adjacent strings.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 58.5 | 30/29 |
| 2 | 117.1 | |
| 3 | 175.6 | 21/19 |
| 4 | 234.1 | |
| 5 | 292.7 | 13/11 |
| 6 | 351.2 | |
| 7 | 409.8 | 19/15 |
| 8 | 468.3 | 17/13 |
| 9 | 526.8 | 23/17 |
| 10 | 585.4 | 7/5 |
| 11 | 643.9 | |
| 12 | 702.4 | |
| 13 | 761 | |
| 14 | 819.5 | |
| 15 | 878 | |
| 16 | 936.6 | 12/7 |
| 17 | 995.1 | |
| 18 | 1053.7 | 11/6 |
| 19 | 1112.2 | |
| 20 | 1170.7 | |
| 21 | 1229.3 | |
| 22 | 1287.8 | |
| 23 | 1346.3 | |
| 24 | 1404.9 | |
| 25 | 1463.4 | |
| 26 | 1522 | 12/5, 29/12 |
| 27 | 1580.5 | 5/2 |
| 28 | 1639 | |
| 29 | 1697.6 | |
| 30 | 1756.1 | |
| 31 | 1814.6 | |
| 32 | 1873.2 | |
| 33 | 1931.7 | |
| 34 | 1990.2 | 19/6 |
| 35 | 2048.8 | |
| 36 | 2107.3 | |
| 37 | 2165.9 | 7/2 |
| 38 | 2224.4 | |
| 39 | 2282.9 | |
| 40 | 2341.5 | |
| 41 | 2400 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +29.3 | -28.8 | +0.0 | +23.4 | +0.5 | +26.3 | +29.3 | +1.0 | -5.8 | +4.8 | -28.8 |
| Relative (%) | +50.0 | -49.2 | +0.0 | +40.0 | +0.8 | +44.9 | +50.0 | +1.7 | -10.0 | +8.2 | -49.2 | |
| Steps (reduced) |
21 (21) |
32 (32) |
41 (0) |
48 (7) |
53 (12) |
58 (17) |
62 (21) |
65 (24) |
68 (27) |
71 (30) |
73 (32) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +8.3 | -3.0 | -5.3 | +0.0 | +12.1 | -28.3 | -4.8 | +23.4 | -2.5 | -24.5 | +15.6 |
| Relative (%) | +14.1 | -5.1 | -9.1 | +0.0 | +20.7 | -48.3 | -8.3 | +40.0 | -4.3 | -41.8 | +26.7 | |
| Steps (reduced) |
76 (35) |
78 (37) |
80 (39) |
82 (0) |
84 (2) |
85 (3) |
87 (5) |
89 (7) |
90 (8) |
91 (9) |
93 (11) | |