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Created page with "'''40EDT''' is the equal division of the third harmonic into 40 parts of 47.5489 cents each, corresponding to 25.2372 edo. It is related to the regular te..." Tags: Mobile edit Mobile web edit |
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'''40EDT''' is the [[Edt|equal division of the third harmonic]] into 40 parts of 47.5489 [[cent|cents]] each, corresponding to 25.2372 [[edo]]. It is related to the regular temperament which tempers out |440 -219 -40> in the 5-limit, which is supported by 101, 429, 530, 959, 1388, 1817, 2246 and 2347 EDOs. | {{Infobox ET}} | ||
'''40EDT''' is the [[Edt|equal division of the third harmonic]] into 40 parts of 47.5489 [[cent|cents]] each, corresponding to 25.2372 [[edo]]. It is related to the regular temperament which tempers out |440 -219 -40> in the 5-limit, which is supported by [[101edo|101]], [[429edo|429]], [[530edo|530]], [[959edo|959]], [[1388edo|1388]], [[1817edo|1817]], [[2246edo|2246]] and [[2347edo|2347]] EDOs. | |||
== Intervals == | |||
{{Interval table}} | |||
== Harmonics== | |||
{{Harmonics in equal | |||
| steps = 40 | |||
| num = 3 | |||
| denom = 1 | |||
| intervals = prime | |||
}} | |||
{{Harmonics in equal | |||
| steps = 40 | |||
| num = 3 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
| intervals = prime | |||
}} | |||
{{stub}} | |||
Latest revision as of 19:22, 1 August 2025
| ← 39edt | 40edt | 41edt → |
40EDT is the equal division of the third harmonic into 40 parts of 47.5489 cents each, corresponding to 25.2372 edo. It is related to the regular temperament which tempers out |440 -219 -40> in the 5-limit, which is supported by 101, 429, 530, 959, 1388, 1817, 2246 and 2347 EDOs.
Intervals
| Steps | Cents | Hekts | Approximate ratios |
|---|---|---|---|
| 0 | 0 | 0 | 1/1 |
| 1 | 47.5 | 32.5 | |
| 2 | 95.1 | 65 | 18/17, 19/18, 20/19 |
| 3 | 142.6 | 97.5 | 13/12 |
| 4 | 190.2 | 130 | 19/17 |
| 5 | 237.7 | 162.5 | 23/20 |
| 6 | 285.3 | 195 | 13/11, 20/17 |
| 7 | 332.8 | 227.5 | 17/14, 23/19 |
| 8 | 380.4 | 260 | |
| 9 | 427.9 | 292.5 | 9/7, 23/18 |
| 10 | 475.5 | 325 | |
| 11 | 523 | 357.5 | 19/14, 23/17, 27/20 |
| 12 | 570.6 | 390 | 18/13 |
| 13 | 618.1 | 422.5 | 10/7 |
| 14 | 665.7 | 455 | 28/19 |
| 15 | 713.2 | 487.5 | |
| 16 | 760.8 | 520 | 14/9, 17/11 |
| 17 | 808.3 | 552.5 | |
| 18 | 855.9 | 585 | 18/11, 23/14 |
| 19 | 903.4 | 617.5 | |
| 20 | 951 | 650 | 19/11 |
| 21 | 998.5 | 682.5 | |
| 22 | 1046.1 | 715 | 11/6 |
| 23 | 1093.6 | 747.5 | |
| 24 | 1141.2 | 780 | 27/14, 29/15 |
| 25 | 1188.7 | 812.5 | |
| 26 | 1236.3 | 845 | |
| 27 | 1283.8 | 877.5 | 21/10, 23/11 |
| 28 | 1331.4 | 910 | 13/6, 28/13 |
| 29 | 1378.9 | 942.5 | 20/9 |
| 30 | 1426.5 | 975 | |
| 31 | 1474 | 1007.5 | 7/3 |
| 32 | 1521.6 | 1040 | |
| 33 | 1569.1 | 1072.5 | |
| 34 | 1616.7 | 1105 | 28/11 |
| 35 | 1664.2 | 1137.5 | |
| 36 | 1711.8 | 1170 | |
| 37 | 1759.3 | 1202.5 | |
| 38 | 1806.9 | 1235 | 17/6 |
| 39 | 1854.4 | 1267.5 | |
| 40 | 1902 | 1300 | 3/1 |
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -11.3 | +0.0 | +19.1 | +7.1 | -14.6 | -18.5 | -7.4 | -9.8 | -7.7 | +18.9 | -1.4 |
| Relative (%) | -23.7 | +0.0 | +40.1 | +15.0 | -30.6 | -38.9 | -15.6 | -20.6 | -16.2 | +39.8 | -3.0 | |
| Steps (reduced) |
25 (25) |
40 (0) |
59 (19) |
71 (31) |
87 (7) |
93 (13) |
103 (23) |
107 (27) |
114 (34) |
123 (3) |
125 (5) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -22.4 | -10.0 | +2.7 | -8.7 | +21.1 | -21.9 | +15.4 | -4.3 | -9.6 | -10.2 | -4.3 |
| Relative (%) | -47.2 | -21.0 | +5.6 | -18.2 | +44.3 | -46.1 | +32.5 | -9.1 | -20.2 | -21.4 | -9.0 | |
| Steps (reduced) |
131 (11) |
135 (15) |
137 (17) |
140 (20) |
145 (25) |
148 (28) |
150 (30) |
153 (33) |
155 (35) |
156 (36) |
159 (39) | |
|
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