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== | ==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 12: | Line 12: | ||
!Approximate ratios | !Approximate ratios | ||
![[17edo]] notation | ![[17edo]] notation | ||
![[7L 3s (4/1-equivalent)|Diaquadic]] notation (J = 1/1) | |||
|- | |- | ||
|0 | |0 | ||
| Line 17: | Line 18: | ||
|[[1/1]] | |[[1/1]] | ||
|C | |C | ||
|J | |||
|- | |- | ||
|1 | |1 | ||
| Line 22: | Line 24: | ||
|[[13/12]], [[12/11]], [[14/13]], [[25/23]] | |[[13/12]], [[12/11]], [[14/13]], [[25/23]] | ||
|C# | |C# | ||
|J#, Kb | |||
|- | |- | ||
|2 | |2 | ||
| Line 27: | Line 30: | ||
|[[13/11]], [[7/6]] | |[[13/11]], [[7/6]] | ||
|Eb | |Eb | ||
|K | |||
|- | |- | ||
|3 | |3 | ||
| Line 32: | Line 36: | ||
|[[32/25]], [[9/7]], [[14/11]], [[33/26]], [[23/18]] | |[[32/25]], [[9/7]], [[14/11]], [[33/26]], [[23/18]] | ||
|E | |E | ||
|K#, Lb | |||
|- | |- | ||
|4 | |4 | ||
| Line 37: | Line 42: | ||
|[[11/8]], [[18/13]], [[32/23]] | |[[11/8]], [[18/13]], [[32/23]] | ||
|^F | |^F | ||
|L | |||
|- | |- | ||
|5 | |5 | ||
| Line 42: | Line 48: | ||
|[[3/2]], [[32/21]] | |[[3/2]], [[32/21]] | ||
|G | |G | ||
|M | |||
|- | |- | ||
|6 | |6 | ||
| Line 47: | Line 54: | ||
|[[13/8]], [[18/11]], [[23/14]] | |[[13/8]], [[18/11]], [[23/14]] | ||
|G#, vA | |G#, vA | ||
|M#, Nb | |||
|- | |- | ||
|7 | |7 | ||
| Line 52: | Line 60: | ||
|[[16/9]], [[7/4]], [[25/14]], [[44/25]], [[23/13]] | |[[16/9]], [[7/4]], [[25/14]], [[44/25]], [[23/13]] | ||
|Bb | |Bb | ||
|N | |||
|- | |- | ||
|8 | |8 | ||
| Line 57: | Line 66: | ||
|[[25/13]], [[48/25]], [[27/14]], [[64/33]], [[23/12]] | |[[25/13]], [[48/25]], [[27/14]], [[64/33]], [[23/12]] | ||
|B | |B | ||
|N#, Ob | |||
|- | |- | ||
|9 | |9 | ||
| Line 62: | Line 72: | ||
|[[15/7]] | |[[15/7]] | ||
|^C | |^C | ||
|O | |||
|- | |- | ||
|10 | |10 | ||
|1411.80 | |1411.80 | ||
|[[16/7]] | |[[9/4]], [[16/7]] | ||
|D | |D | ||
|O#, Pb | |||
|- | |- | ||
|11 | |11 | ||
| Line 72: | Line 84: | ||
|[[12/5]], [[5/2]] | |[[12/5]], [[5/2]] | ||
|vE | |vE | ||
|P | |||
|- | |- | ||
|12 | |12 | ||
| Line 77: | Line 90: | ||
|[[8/3]] | |[[8/3]] | ||
|F | |F | ||
|Q | |||
|- | |- | ||
|13 | |13 | ||
| Line 82: | Line 96: | ||
|[[3/1]] | |[[3/1]] | ||
|F# | |F# | ||
|Q#, Rb | |||
|- | |- | ||
|14 | |14 | ||
| Line 87: | Line 102: | ||
|[[16/5]] | |[[16/5]] | ||
|^G, Ab | |^G, Ab | ||
|R | |||
|- | |- | ||
|15 | |15 | ||
| Line 92: | Line 108: | ||
|[[10/3]] | |[[10/3]] | ||
|A | |A | ||
|R#, Sb | |||
|- | |- | ||
|16 | |16 | ||
| Line 97: | Line 114: | ||
|[[11/3]] | |[[11/3]] | ||
|vB | |vB | ||
|S | |||
|- | |- | ||
|17 | |17 | ||
| Line 102: | Line 120: | ||
|[[4/1]] | |[[4/1]] | ||
|C | |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}} | |||