13edf: Difference between revisions
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m stub mbox, add harmonics, make table collapsible |
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{{Infobox ET}} | {{Infobox ET}} | ||
'''13EDF''' is the [[EDF|equal division of the just perfect fifth]] into 13 parts of 53.9965 [[cent|cents]] each, corresponding to 22.2236 [[edo]]. It is nearly identical to every ninth step of [[200edo]]. | '''13EDF''' is the [[EDF|equal division of the just perfect fifth]] into 13 parts of 53.9965 [[cent|cents]] each, corresponding to 22.2236 [[edo]]. It is nearly identical to every ninth step of [[200edo]]. | ||
==Harmonics== | |||
{{Harmonics in equal|17|3|2|intervals=prime|columns=8}} | |||
{{Harmonics in equal|17|3|2|start=9|intervals=prime|columns=8}} | |||
==Intervals== | ==Intervals== | ||
{| class="wikitable" | {| class="wikitable mw-collapsible" | ||
|+ Intervals of 13edf | |||
|- | |- | ||
! | degree | ! | degree | ||
| Line 144: | Line 149: | ||
| | pythagorean major ninth | | | pythagorean major ninth | ||
|} | |} | ||
{{stub}} | |||
Revision as of 03:32, 21 December 2024
| ← 12edf | 13edf | 14edf → |
13EDF is the equal division of the just perfect fifth into 13 parts of 53.9965 cents each, corresponding to 22.2236 edo. It is nearly identical to every ninth step of 200edo.
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | |
|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.5 | -2.5 | -19.8 | +17.1 | +19.1 | +19.0 | +8.7 | -18.7 |
| Relative (%) | -6.2 | -6.2 | -47.9 | +41.4 | +46.3 | +45.9 | +21.1 | -45.2 | |
| Steps (reduced) |
29 (12) |
46 (12) |
67 (16) |
82 (14) |
101 (16) |
108 (6) |
119 (0) |
123 (4) | |
| Harmonic | 23 | 29 | 31 | 37 | 41 | 43 | 47 | 53 | |
|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -19.1 | -7.5 | +0.9 | -16.3 | +12.4 | +12.5 | -17.6 | -19.1 |
| Relative (%) | -46.2 | -18.1 | +2.3 | -39.6 | +30.0 | +30.4 | -42.6 | -46.3 | |
| Steps (reduced) |
131 (12) |
141 (5) |
144 (8) |
151 (15) |
156 (3) |
158 (5) |
161 (8) |
166 (13) | |
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | exact 1/1 | ||
| 1 | 53.9965 | 33/32 | pseudo-25/24 |
| 2 | 107.9931 | 17/16, 117/110, 16/15 | |
| 3 | 161.9896 | 11/10 | |
| 4 | 215.9862 | 17/15 | |
| 5 | 269.9827 | 7/6 | |
| 6 | 323.9792 | 77/64 | pseudo-6/5 |
| 7 | 377.9758 | 56/45 | pseudo-5/4 |
| 8 | 431.9723 | 9/7 | |
| 9 | 485.9688 | 45/34 | pseudo-4/3 |
| 10 | 539.9654 | 15/11 | |
| 11 | 593.9619 | 55/39, 24/17 | |
| 12 | 647.9585 | 16/11 | |
| 13 | 701.9550 | exact 3/2 | just perfect fifth |
| 14 | 755.9515 | 99/64 | |
| 15 | 809.9481 | 51/32, 8/5 | |
| 16 | 863.9446 | 33/20 | |
| 17 | 917.9412 | 17/10 | |
| 18 | 971.9377 | 7/4 | |
| 19 | 1025.9342 | 29/16 | pseudo-9/5 |
| 20 | 1079.9308 | 28/15 | pseudo-15/8 |
| 21 | 1133.9273 | 52/27, 27/14 | |
| 22 | 1187.9238 | 135/68 | pseudo-octave |
| 23 | 1241.9204 | 45/22 | |
| 24 | 1295.9169 | 19/9, 36/17 | |
| 25 | 1349.9135 | 24/11 | |
| 26 | 1403.9100 | exact 9/4 | pythagorean major ninth |
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