19edf: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
'''19EDF''' is the [[EDF|equal division of the just perfect fifth]] into 19 parts of 36.945 [[cent|cents]] each, corresponding to 32.4807 [[edo]] (similar to every second step of [[65edo]]). It tempers out the same commas as 65edo with the addition of |-103/19 65/19> (1.425 cents) resulting from its inexact 4/1. | '''19EDF''' is the [[EDF|equal division of the just perfect fifth]] into 19 parts of 36.945 [[cent|cents]] each, corresponding to 32.4807 [[edo]] (similar to every second step of [[65edo]]). It tempers out the same commas as 65edo with the addition of |-103/19 65/19> (1.425 cents) resulting from its inexact 4/1. | ||
==Harmonics== | |||
{{Harmonics in equal|19|3|2}} | |||
{{Harmonics in equal|19|3|2|start=12|collapsed=1}} | |||
==Intervals== | ==Intervals== | ||
{| class="wikitable" | {| class="wikitable mw-collapsible" | ||
|+ Intervals of 19edf | |||
|- | |- | ||
! | degree | ! | degree | ||
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{{todo|expand}} | |||
Revision as of 08:29, 20 December 2024
| ← 18edf | 19edf | 20edf → |
19EDF is the equal division of the just perfect fifth into 19 parts of 36.945 cents each, corresponding to 32.4807 edo (similar to every second step of 65edo). It tempers out the same commas as 65edo with the addition of |-103/19 65/19> (1.425 cents) resulting from its inexact 4/1.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -17.8 | -17.8 | +1.4 | -15.4 | +1.4 | -6.8 | -16.3 | +1.4 | +3.7 | -13.5 | -16.3 |
| Relative (%) | -48.1 | -48.1 | +3.9 | -41.8 | +3.9 | -18.5 | -44.2 | +3.9 | +10.1 | -36.5 | -44.2 | |
| Steps (reduced) |
32 (13) |
51 (13) |
65 (8) |
75 (18) |
84 (8) |
91 (15) |
97 (2) |
103 (8) |
108 (13) |
112 (17) |
116 (2) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -7.1 | +12.4 | +3.7 | +2.9 | +8.7 | -16.3 | +0.9 | -14.0 | +12.4 | +5.7 | +2.6 |
| Relative (%) | -19.3 | +33.4 | +10.1 | +7.7 | +23.6 | -44.2 | +2.4 | -37.9 | +33.4 | +15.4 | +7.1 | |
| Steps (reduced) |
120 (6) |
124 (10) |
127 (13) |
130 (16) |
133 (0) |
135 (2) |
138 (5) |
140 (7) |
143 (10) |
145 (12) |
147 (14) | |
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | exact 1/1 | ||
| 1 | 36.945 | ||
| 2 | 73.89 | 24/23 | |
| 3 | 110.835 | 16/15 | |
| 4 | 147.78 | 12/11 | |
| 5 | 184.725 | 10/9 | |
| 6 | 221.67 | 25/22 | |
| 7 | 258.615 | 36/31 | |
| 8 | 295.56 | 19/16 | |
| 9 | 332.505 | 63/52, 40/33 | |
| 10 | 369.45 | 26/21 | |
| 11 | 406.395 | 24/19, 19/15 | |
| 12 | 443.34 | 31/24 | |
| 13 | 480.285 | 33/25 | |
| 14 | 517.23 | 27/20 | |
| 15 | 554.175 | 11/8 | |
| 16 | 591.12 | 45/32 | |
| 17 | 628.065 | 23/16 | |
| 18 | 665.01 | 22/15 | |
| 19 | 701.955 | exact 3/2 | just perfect fifth |
| 20 | 738.9 | ||
| 21 | 775.845 | ||
| 22 | 812.79 | 8/5 | |
| 23 | 849.735 | 18/11 | |
| 24 | 886.68 | 5/3 | |
| 25 | 923.625 | ||
| 26 | 960.57 | ||
| 27 | 997.515 | 16/9 | |
| 28 | 1034.46 | 20/11 | |
| 29 | 1071.405 | 13/7 | |
| 30 | 1108.35 | 36/19 | |
| 31 | 1145.295 | 31/16 | |
| 32 | 1182.24 | ||
| 33 | 1219.185 | ||
| 34 | 1256.13 | ||
| 35 | 1293.075 | ||
| 36 | 1330.02 | ||
| 37 | 1366.965 | ||
| 38 | 1403.91 | exact 9/4 | |