48edt: Difference between revisions
Jump to navigation
Jump to search
m Marked page as stub |
m Intro inter harm |
||
| Line 1: | Line 1: | ||
{{Stub}} | {{Stub}} | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{ED intro}} | |||
== Intervals == | |||
{{Interval table}} | |||
== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 48 | |||
| num = 3 | |||
| denom = 1 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 48 | |||
| num = 3 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
Revision as of 04:20, 5 October 2024
|
This page is a stub. You can help the Xenharmonic Wiki by expanding it. |
| ← 47edt | 48edt | 49edt → |
48 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 48edt or 48ed3), is a nonoctave tuning system that divides the interval of 3/1 into 48 equal parts of about 39.6 ¢ each. Each step represents a frequency ratio of 31/48, or the 48th root of 3.
Intervals
| Steps | Cents | Hekts | Approximate ratios |
|---|---|---|---|
| 0 | 0 | 0 | 1/1 |
| 1 | 39.6 | 27.1 | |
| 2 | 79.2 | 54.2 | 22/21, 23/22 |
| 3 | 118.9 | 81.3 | 15/14, 29/27, 31/29 |
| 4 | 158.5 | 108.3 | 23/21 |
| 5 | 198.1 | 135.4 | 19/17, 28/25 |
| 6 | 237.7 | 162.5 | 31/27 |
| 7 | 277.4 | 189.6 | 27/23 |
| 8 | 317 | 216.7 | 6/5 |
| 9 | 356.6 | 243.8 | 27/22 |
| 10 | 396.2 | 270.8 | 29/23 |
| 11 | 435.9 | 297.9 | 9/7 |
| 12 | 475.5 | 325 | 29/22 |
| 13 | 515.1 | 352.1 | 31/23 |
| 14 | 554.7 | 379.2 | 29/21 |
| 15 | 594.4 | 406.3 | 31/22 |
| 16 | 634 | 433.3 | 13/9 |
| 17 | 673.6 | 460.4 | 31/21 |
| 18 | 713.2 | 487.5 | |
| 19 | 752.9 | 514.6 | 17/11 |
| 20 | 792.5 | 541.7 | |
| 21 | 832.1 | 568.8 | 21/13 |
| 22 | 871.7 | 595.8 | |
| 23 | 911.4 | 622.9 | 22/13 |
| 24 | 951 | 650 | 19/11, 26/15 |
| 25 | 990.6 | 677.1 | 23/13 |
| 26 | 1030.2 | 704.2 | |
| 27 | 1069.8 | 731.3 | 13/7 |
| 28 | 1109.5 | 758.3 | |
| 29 | 1149.1 | 785.4 | |
| 30 | 1188.7 | 812.5 | |
| 31 | 1228.3 | 839.6 | |
| 32 | 1268 | 866.7 | 25/12, 27/13 |
| 33 | 1307.6 | 893.8 | |
| 34 | 1347.2 | 920.8 | |
| 35 | 1386.8 | 947.9 | 29/13 |
| 36 | 1426.5 | 975 | |
| 37 | 1466.1 | 1002.1 | 7/3 |
| 38 | 1505.7 | 1029.2 | 31/13 |
| 39 | 1545.3 | 1056.3 | 22/9 |
| 40 | 1585 | 1083.3 | 5/2 |
| 41 | 1624.6 | 1110.4 | 23/9 |
| 42 | 1664.2 | 1137.5 | |
| 43 | 1703.8 | 1164.6 | |
| 44 | 1743.5 | 1191.7 | |
| 45 | 1783.1 | 1218.8 | 14/5 |
| 46 | 1822.7 | 1245.8 | |
| 47 | 1862.3 | 1272.9 | |
| 48 | 1902 | 1300 | 3/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -11.3 | +0.0 | +17.1 | -12.6 | -11.3 | -0.8 | +5.8 | +0.0 | +15.7 | +9.2 | +17.1 |
| Relative (%) | -28.5 | +0.0 | +43.1 | -31.9 | -28.5 | -2.0 | +14.6 | +0.0 | +39.7 | +23.2 | +43.1 | |
| Steps (reduced) |
30 (30) |
48 (0) |
61 (13) |
70 (22) |
78 (30) |
85 (37) |
91 (43) |
96 (0) |
101 (5) |
105 (9) |
109 (13) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.6 | -12.1 | -12.6 | -5.5 | +8.4 | -11.3 | +14.0 | +4.4 | -0.8 | -2.1 | +0.2 |
| Relative (%) | -6.6 | -30.4 | -31.9 | -13.9 | +21.3 | -28.5 | +35.3 | +11.2 | -2.0 | -5.2 | +0.6 | |
| Steps (reduced) |
112 (16) |
115 (19) |
118 (22) |
121 (25) |
124 (28) |
126 (30) |
129 (33) |
131 (35) |
133 (37) |
135 (39) |
137 (41) | |