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 is the smallest ED4 to contain a diatonic fifth, in this cas [[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. | 17ed4 is the smallest ED4 to contain a diatonic fifth, in this cas [[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 22: | Line 22: | ||
|[[13/12]], [[12/11]], [[14/13]], [[25/23]] | |[[13/12]], [[12/11]], [[14/13]], [[25/23]] | ||
|C# | |C# | ||
|J#, | |J#, Kb | ||
|- | |- | ||
|2 | |2 | ||
| Line 28: | Line 28: | ||
|[[13/11]], [[7/6]] | |[[13/11]], [[7/6]] | ||
|Eb | |Eb | ||
| | |K | ||
|- | |- | ||
|3 | |3 | ||
| Line 34: | Line 34: | ||
|[[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 40: | Line 40: | ||
|[[11/8]], [[18/13]], [[32/23]] | |[[11/8]], [[18/13]], [[32/23]] | ||
|^F | |^F | ||
| | |L | ||
|- | |- | ||
|5 | |5 | ||
| Line 46: | Line 46: | ||
|[[3/2]], [[32/21]] | |[[3/2]], [[32/21]] | ||
|G | |G | ||
| | |M | ||
|- | |- | ||
|6 | |6 | ||
| Line 52: | Line 52: | ||
|[[13/8]], [[18/11]], [[23/14]] | |[[13/8]], [[18/11]], [[23/14]] | ||
|G#, vA | |G#, vA | ||
|M | |M#, Nb | ||
|- | |- | ||
|7 | |7 | ||
| Line 58: | Line 58: | ||
|[[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 64: | Line 64: | ||
|[[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 70: | Line 70: | ||
|[[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 88: | Line 88: | ||
|[[8/3]] | |[[8/3]] | ||
|F | |F | ||
| | |Q | ||
|- | |- | ||
|13 | |13 | ||
| Line 94: | Line 94: | ||
|[[3/1]] | |[[3/1]] | ||
|F# | |F# | ||
|Q | |Q#, Rb | ||
|- | |- | ||
|14 | |14 | ||
| Line 100: | Line 100: | ||
|[[16/5]] | |[[16/5]] | ||
|^G, Ab | |^G, Ab | ||
| | |R | ||
|- | |- | ||
|15 | |15 | ||
| Line 106: | Line 106: | ||
|[[10/3]] | |[[10/3]] | ||
|A | |A | ||
|R | |R#, Sb | ||
|- | |- | ||
|16 | |16 | ||
| Line 112: | Line 112: | ||
|[[11/3]] | |[[11/3]] | ||
|vB | |vB | ||
| | |S | ||
|- | |- | ||
|17 | |17 | ||