17ed4: Difference between revisions
CompactStar (talk | contribs) No edit summary |
m Removing from Category:Ed4 using Cat-a-lot |
||
| (7 intermediate revisions by 3 users not shown) | |||
| Line 1: | Line 1: | ||
{{Infobox ET | {{Infobox ET}} | ||
{{ED intro}} It corresponds to 8.5edo or every second step of [[17edo]]. | |||
==Theory== | ==Theory== | ||
17ed4 | 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 11: | Line 12: | ||
!Approximate ratios | !Approximate ratios | ||
![[17edo]] notation | ![[17edo]] notation | ||
![[7L 3s (4/1-equivalent)| | ![[7L 3s (4/1-equivalent)|Diaquadic]] notation (J = 1/1) | ||
|- | |- | ||
|0 | |0 | ||
| Line 23: | Line 24: | ||
|[[13/12]], [[12/11]], [[14/13]], [[25/23]] | |[[13/12]], [[12/11]], [[14/13]], [[25/23]] | ||
|C# | |C# | ||
|J#, | |J#, Kb | ||
|- | |- | ||
|2 | |2 | ||
| Line 29: | Line 30: | ||
|[[13/11]], [[7/6]] | |[[13/11]], [[7/6]] | ||
|Eb | |Eb | ||
| | |K | ||
|- | |- | ||
|3 | |3 | ||
| Line 35: | 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 | |K#, Lb | ||
|- | |- | ||
|4 | |4 | ||
| Line 41: | Line 42: | ||
|[[11/8]], [[18/13]], [[32/23]] | |[[11/8]], [[18/13]], [[32/23]] | ||
|^F | |^F | ||
| | |L | ||
|- | |- | ||
|5 | |5 | ||
| Line 47: | Line 48: | ||
|[[3/2]], [[32/21]] | |[[3/2]], [[32/21]] | ||
|G | |G | ||
| | |M | ||
|- | |- | ||
|6 | |6 | ||
| Line 53: | Line 54: | ||
|[[13/8]], [[18/11]], [[23/14]] | |[[13/8]], [[18/11]], [[23/14]] | ||
|G#, vA | |G#, vA | ||
|M | |M#, Nb | ||
|- | |- | ||
|7 | |7 | ||
| Line 59: | 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 65: | 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 | |N#, Ob | ||
|- | |- | ||
|9 | |9 | ||
| Line 71: | Line 72: | ||
|[[15/7]] | |[[15/7]] | ||
|^C | |^C | ||
| | |O | ||
|- | |- | ||
|10 | |10 | ||
|1411.80 | |1411.80 | ||
|[[16/7]] | |[[9/4]], [[16/7]] | ||
|D | |D | ||
|O | |O#, Pb | ||
|- | |- | ||
|11 | |11 | ||
| Line 89: | Line 90: | ||
|[[8/3]] | |[[8/3]] | ||
|F | |F | ||
| | |Q | ||
|- | |- | ||
|13 | |13 | ||
| Line 95: | Line 96: | ||
|[[3/1]] | |[[3/1]] | ||
|F# | |F# | ||
|Q | |Q#, Rb | ||
|- | |- | ||
|14 | |14 | ||
| Line 101: | Line 102: | ||
|[[16/5]] | |[[16/5]] | ||
|^G, Ab | |^G, Ab | ||
| | |R | ||
|- | |- | ||
|15 | |15 | ||
| Line 107: | Line 108: | ||
|[[10/3]] | |[[10/3]] | ||
|A | |A | ||
|R | |R#, Sb | ||
|- | |- | ||
|16 | |16 | ||
| Line 113: | Line 114: | ||
|[[11/3]] | |[[11/3]] | ||
|vB | |vB | ||
| | |S | ||
|- | |- | ||
|17 | |17 | ||
| Line 121: | Line 122: | ||
|J | |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}} | |||