17ed4: Difference between revisions
Jump to navigation
Jump to search
CompactStar (talk | contribs) No edit summary |
CompactStar (talk | contribs) No edit summary |
||
| Line 1: | Line 1: | ||
{{Infobox ET| | {{Infobox ET|17ed1840616/1678131}} | ||
<!--Using | <!--Using continued fraction convergent of 4^(1/17) until Infobox ET starts working with ED4s--> | ||
'''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== | ||
Revision as of 04:05, 2 May 2023
| ← 16ed1840616/1678131 | 17ed1840616/1678131 | 18ed1840616/1678131 → |
(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 (3L 4s) and decatonic (7L 3s) MOS scales with a period of 4/1. The decatonic scale is the more usable of these two scales, corresponding to an octave-repeating pentatonic scale in terms of step sizes, while the heptatonic scale has too large step sizes, corresponding to an octave-repeating tritonic or tetratonic scale in terms of 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 |