17ed4: Difference between revisions
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{{Infobox ET | {{Infobox ET}} | ||
{{ED intro}} It corresponds to 8.5edo or every second step of [[17edo]]. | |||
==Theory== | |||
17ed4 is the smallest ED4 to contain a diatonic fifth, in this case [[17edo]]'s sharp fifth, and it can be used to generate heptatonic (3L 4s<4/1>) and decatonic ([[7L 3s (4/1-equivalent)|7L 3s<4/1>]]) 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== | ==Intervals== | ||
{|class="wikitable" | {|class="wikitable" | ||
| Line 10: | Line 11: | ||
!Cents | !Cents | ||
!Approximate ratios | !Approximate ratios | ||
![[17edo]] notation | |||
![[7L 3s (4/1-equivalent)|Diaquadic]] notation (J = 1/1) | |||
|- | |- | ||
|0 | |0 | ||
|0. | |0.00 | ||
|[[1/1]] | |[[1/1]] | ||
|C | |||
|J | |||
|- | |- | ||
|1 | |1 | ||
|141. | |141.18 | ||
|[[13/12]], [[12/11]], [[14/13]], [[25/23]] | |[[13/12]], [[12/11]], [[14/13]], [[25/23]] | ||
|C# | |||
|J#, Kb | |||
|- | |- | ||
|2 | |2 | ||
| | |282.36 | ||
|[[13/11]], [[7/6]] | |||
|Eb | |||
|K | |||
|- | |||
|3 | |||
|423.54 | |||
|[[32/25]], [[9/7]], [[14/11]], [[33/26]], [[23/18]] | |||
|E | |||
|K#, Lb | |||
|- | |||
|4 | |||
|564.72 | |||
|[[11/8]], [[18/13]], [[32/23]] | |||
|^F | |||
|L | |||
|- | |||
|5 | |||
|705.90 | |||
|[[3/2]], [[32/21]] | |||
|G | |||
|M | |||
|- | |||
|6 | |||
|847.08 | |||
|[[13/8]], [[18/11]], [[23/14]] | |||
|G#, vA | |||
|M#, Nb | |||
|- | |||
|7 | |||
|988.26 | |||
|[[16/9]], [[7/4]], [[25/14]], [[44/25]], [[23/13]] | |||
|Bb | |||
|N | |||
|- | |||
|8 | |||
|1129.44 | |||
|[[25/13]], [[48/25]], [[27/14]], [[64/33]], [[23/12]] | |||
|B | |||
|N#, Ob | |||
|- | |||
|9 | |||
|1270.62 | |||
|[[15/7]] | |||
|^C | |||
|O | |||
|- | |||
|10 | |||
|1411.80 | |||
|[[9/4]], [[16/7]] | |||
|D | |||
|O#, Pb | |||
|- | |||
|11 | |||
|1552.98 | |||
|[[12/5]], [[5/2]] | |||
|vE | |||
|P | |||
|- | |||
|12 | |||
|1694.16 | |||
|[[8/3]] | |||
|F | |||
|Q | |||
|- | |||
|13 | |||
|1835.34 | |||
|[[3/1]] | |||
|F# | |||
|Q#, Rb | |||
|- | |||
|14 | |||
|1976.52 | |||
|[[16/5]] | |||
|^G, Ab | |||
|R | |||
|- | |||
|15 | |||
|2117.70 | |||
|[[10/3]] | |||
|A | |||
|R#, Sb | |||
|- | |||
|16 | |||
|2258.88 | |||
|[[11/3]] | |||
|vB | |||
|S | |||
|- | |||
|17 | |||
|2400.00 | |||
|[[4/1]] | |||
|C | |||
|J | |||
|} | |} | ||
== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 17 | |||
| num = 4 | |||
| denom = 1 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 17 | |||
| num = 4 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
[[Category:Macrotonal]] | [[Category:Macrotonal]] | ||
[[Category:Nonoctave]] | [[Category:Nonoctave]] | ||
{{todo|expand}} | |||