17ed4: Difference between revisions
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'''17ed4''' is the [[Ed4|equal division of the double octave]] into 17 parts of 141.18 [[cent|cents]] each, corresponding to 8.5edo or every second step of [[17edo]]. | '''17ed4''' is the [[Ed4|equal division of the double octave]] into 17 parts of 141.18 [[cent|cents]] each, corresponding to 8.5edo or every second step of [[17edo]]. | ||
==Scales and temperaments== | ==Scales and temperaments== | ||
TBA | TBA | ||
{{Harmonics in equal|51|64}} | |||
==Intervals== | ==Intervals== | ||
{|class="wikitable" | {|class="wikitable" | ||
Revision as of 07:25, 20 March 2023
| ← 50ed64 | 51ed64 | 52ed64 → |
17ed4 is the equal division of the double octave into 17 parts of 141.18 cents each, corresponding to 8.5edo or every second step of 17edo.
Scales and temperaments
TBA
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +70.6 | -66.7 | -0.0 | +37.2 | +3.9 | +19.4 | +70.6 | +7.9 | -33.4 | -57.2 | -66.7 |
| Relative (%) | +50.0 | -47.2 | -0.0 | +26.4 | +2.8 | +13.7 | +50.0 | +5.6 | -23.6 | -40.5 | -47.2 | |
| Steps (reduced) |
9 (9) |
13 (13) |
17 (17) |
20 (20) |
22 (22) |
24 (24) |
26 (26) |
27 (27) |
28 (28) |
29 (29) |
30 (30) | |
Intervals
| # | Cents | Approximate ratios |
|---|---|---|
| 0 | 0.00 | 1/1 |
| 1 | 141.18 | 13/12, 12/11, 14/13, 25/23 |
| 2 | 282.36 | 13/11, 7/6 |
| 3 | 423.54 | 32/25, 9/7, 14/11, 33/26, 23/18 |
| 4 | 564.72 | 11/8, 18/13, 32/23 |
| 5 | 705.90 | 3/2, 32/21 |
| 6 | 847.08 | 13/8, 18/11, 23/14 |
| 7 | 988.26 | 16/9, 7/4, 25/14, 44/25, 23/13 |
| 8 | 1129.44 | 25/13, 48/25, 27/14, 64/33, 23/12 |
| 9 | 1270.62 | 15/7 |
| 10 | 1411.80 | 16/7 |
| 11 | 1552.98 | 12/5, 5/2 |
| 12 | 1694.16 | 8/3 |
| 13 | 1835.34 | 3/1 |
| 14 | 1976.52 | 16/5 |
| 15 | 2117.70 | 10/3 |
| 16 | 2258.88 | 11/3 |
| 17 | 2400.00 | 4/1 |