17ed4: Difference between revisions
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!Cents | !Cents | ||
!Approximate ratios | !Approximate ratios | ||
![[17edo]] notation | |||
|- | |- | ||
|0 | |0 | ||
|0.00 | |0.00 | ||
|[[1/1]] | |[[1/1]] | ||
|C | |||
|- | |- | ||
|1 | |1 | ||
|141.18 | |141.18 | ||
|[[13/12]], [[12/11]], [[14/13]], [[25/23]] | |[[13/12]], [[12/11]], [[14/13]], [[25/23]] | ||
|C# | |||
|- | |- | ||
|2 | |2 | ||
|282.36 | |282.36 | ||
|[[13/11]], [[7/6]] | |[[13/11]], [[7/6]] | ||
|Eb | |||
|- | |- | ||
|3 | |3 | ||
|423.54 | |423.54 | ||
|[[32/25]], [[9/7]], [[14/11]], [[33/26]], [[23/18]] | |[[32/25]], [[9/7]], [[14/11]], [[33/26]], [[23/18]] | ||
|E | |||
|- | |- | ||
|4 | |4 | ||
|564.72 | |564.72 | ||
|[[11/8]], [[18/13]], [[32/23]] | |[[11/8]], [[18/13]], [[32/23]] | ||
|^F | |||
|- | |- | ||
|5 | |5 | ||
|705.90 | |705.90 | ||
|[[3/2]], [[32/21]] | |[[3/2]], [[32/21]] | ||
|G | |||
|- | |- | ||
|6 | |6 | ||
|847.08 | |847.08 | ||
|[[13/8]], [[18/11]], [[23/14]] | |[[13/8]], [[18/11]], [[23/14]] | ||
|G#, vA | |||
|- | |- | ||
|7 | |7 | ||
|988.26 | |988.26 | ||
|[[16/9]], [[7/4]], [[25/14]], [[44/25]], [[23/13]] | |[[16/9]], [[7/4]], [[25/14]], [[44/25]], [[23/13]] | ||
|Bb | |||
|- | |- | ||
|8 | |8 | ||
|1129.44 | |1129.44 | ||
|[[25/13]], [[48/25]], [[27/14]], [[64/33]], [[23/12]] | |[[25/13]], [[48/25]], [[27/14]], [[64/33]], [[23/12]] | ||
|B | |||
|- | |- | ||
|9 | |9 | ||
|1270.62 | |1270.62 | ||
|[[15/7]] | |[[15/7]] | ||
|^C | |||
|- | |- | ||
|10 | |10 | ||
|1411.80 | |1411.80 | ||
|[[16/7]] | |[[16/7]] | ||
|D | |||
|- | |- | ||
|11 | |11 | ||
|1552.98 | |1552.98 | ||
|[[12/5]], [[5/2]] | |[[12/5]], [[5/2]] | ||
|vE | |||
|- | |- | ||
|12 | |12 | ||
|1694.16 | |1694.16 | ||
|[[8/3]] | |[[8/3]] | ||
|F | |||
|- | |- | ||
|13 | |13 | ||
|1835.34 | |1835.34 | ||
|[[3/1]] | |[[3/1]] | ||
|F# | |||
|- | |- | ||
|14 | |14 | ||
|1976.52 | |1976.52 | ||
|[[16/5]] | |[[16/5]] | ||
|^G, Ab | |||
|- | |- | ||
|15 | |15 | ||
|2117.70 | |2117.70 | ||
|[[10/3]] | |[[10/3]] | ||
|A | |||
|- | |- | ||
|16 | |16 | ||
|2258.88 | |2258.88 | ||
|[[11/3]] | |[[11/3]] | ||
|vB | |||
|- | |- | ||
|17 | |17 | ||
|2400.00 | |2400.00 | ||
|[[4/1]] | |[[4/1]] | ||
|C | |||
|} | |} | ||
[[Category:Macrotonal]] | [[Category:Macrotonal]] | ||
[[Category:Nonoctave]] | [[Category:Nonoctave]] | ||
[[Category:Ed4]] | [[Category:Ed4]] | ||
Revision as of 21:42, 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.
Theory
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 | 17edo notation |
|---|---|---|---|
| 0 | 0.00 | 1/1 | C |
| 1 | 141.18 | 13/12, 12/11, 14/13, 25/23 | C# |
| 2 | 282.36 | 13/11, 7/6 | Eb |
| 3 | 423.54 | 32/25, 9/7, 14/11, 33/26, 23/18 | E |
| 4 | 564.72 | 11/8, 18/13, 32/23 | ^F |
| 5 | 705.90 | 3/2, 32/21 | G |
| 6 | 847.08 | 13/8, 18/11, 23/14 | G#, vA |
| 7 | 988.26 | 16/9, 7/4, 25/14, 44/25, 23/13 | Bb |
| 8 | 1129.44 | 25/13, 48/25, 27/14, 64/33, 23/12 | B |
| 9 | 1270.62 | 15/7 | ^C |
| 10 | 1411.80 | 16/7 | D |
| 11 | 1552.98 | 12/5, 5/2 | vE |
| 12 | 1694.16 | 8/3 | F |
| 13 | 1835.34 | 3/1 | F# |
| 14 | 1976.52 | 16/5 | ^G, Ab |
| 15 | 2117.70 | 10/3 | A |
| 16 | 2258.88 | 11/3 | vB |
| 17 | 2400.00 | 4/1 | C |