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]]. | ||
==Theory== | ==Theory== | ||
17ed4 contains [[17edo]]'s sharp fifth, and it can be used to generate heptatonic and decatonic 4/1-repeating MOS scale. The decatonic scale is the more usable of these two scales, with the heptatonic scale having too large step sizes. | |||
==Intervals== | ==Intervals== | ||
{|class="wikitable" | {|class="wikitable" | ||
Revision as of 01:41, 4 April 2023
| ← 16ed40001/10000 | 17ed40001/10000 | 18ed40001/10000 → |
(semiconvergent)
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
17ed4 contains 17edo's sharp fifth, and it can be used to generate heptatonic and decatonic 4/1-repeating MOS scale. The decatonic scale is the more usable of these two scales, with the heptatonic scale having too large step sizes.
Intervals
| # | Cents | Approximate ratios | 17edo notation | 7L 3s<4/1> notation (J = 1/1) |
|---|---|---|---|---|
| 0 | 0.00 | 1/1 | C | J |
| 1 | 141.18 | 13/12, 12/11, 14/13, 25/23 | C# | J#, Kbb |
| 2 | 282.36 | 13/11, 7/6 | Eb | Jx, Kb |
| 3 | 423.54 | 32/25, 9/7, 14/11, 33/26, 23/18 | E | K |
| 4 | 564.72 | 11/8, 18/13, 32/23 | ^F | K#, Lb |
| 5 | 705.90 | 3/2, 32/21 | G | L |
| 6 | 847.08 | 13/8, 18/11, 23/14 | G#, vA | M |
| 7 | 988.26 | 16/9, 7/4, 25/14, 44/25, 23/13 | Bb | M#, Nb |
| 8 | 1129.44 | 25/13, 48/25, 27/14, 64/33, 23/12 | B | N |
| 9 | 1270.62 | 15/7 | ^C | N#, Ob |
| 10 | 1411.80 | 16/7 | D | O |
| 11 | 1552.98 | 12/5, 5/2 | vE | P |
| 12 | 1694.16 | 8/3 | F | P#, Qb |
| 13 | 1835.34 | 3/1 | F# | Q |
| 14 | 1976.52 | 16/5 | ^G, Ab | Q#, Rb |
| 15 | 2117.70 | 10/3 | A | R |
| 16 | 2258.88 | 11/3 | vB | R#, Jb |
| 17 | 2400.00 | 4/1 | C | J |