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{{Infobox ET|51ed64}}
{{Infobox ET}}
<!--Using ED64 as temporary solution until Infobox ET starts working with ED4s-->
{{ED intro}} It corresponds 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]].
 
==Scales and temperaments==
==Theory==
TBA
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
|0.00
|0.00
|[[1/1]]
|[[1/1]]
|C
|J
|-
|-
|1
|1
|141.18
|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
|282.36
|[[13/11]], [[7/6]]
|[[13/11]], [[7/6]]
|Eb
|K
|-
|-
|3
|3
|423.54
|423.54
|[[32/25]], [[9/7]], [[14/11]], [[33/26]], [[23/18]]
|[[32/25]], [[9/7]], [[14/11]], [[33/26]], [[23/18]]
|E
|K#, Lb
|-
|-
|4
|4
|564.72
|564.72
|[[11/8]], [[18/13]], [[32/23]]
|[[11/8]], [[18/13]], [[32/23]]
|^F
|L
|-
|-
|5
|5
|705.90
|705.90
|[[3/2]], [[32/21]]
|[[3/2]], [[32/21]]
|G
|M
|-
|-
|6
|6
|847.08
|847.08
|[[13/8]], [[18/11]], [[23/14]]
|[[13/8]], [[18/11]], [[23/14]]
|G#, vA
|M#, Nb
|-
|-
|7
|7
|988.26
|988.26
|[[16/9]], [[7/4]], [[25/14]], [[44/25]], [[23/13]]
|[[16/9]], [[7/4]], [[25/14]], [[44/25]], [[23/13]]
|Bb
|N
|-
|-
|8
|8
|1129.44
|1129.44
|[[25/13]], [[48/25]], [[27/14]], [[64/33]], [[23/12]]
|[[25/13]], [[48/25]], [[27/14]], [[64/33]], [[23/12]]
|B
|N#, Ob
|-
|-
|9
|9
|1270.62
|1270.62
|[[15/7]]
|[[15/7]]
|^C
|O
|-
|-
|10
|10
|1411.80
|1411.80
|[[16/7]]
|[[9/4]], [[16/7]]
|D
|O#, Pb
|-
|-
|11
|11
|1552.98
|1552.98
|[[12/5]], [[5/2]]
|[[12/5]], [[5/2]]
|vE
|P
|-
|-
|12
|12
|1694.16
|1694.16
|[[8/3]]
|[[8/3]]
|F
|Q
|-
|-
|13
|13
|1835.34
|1835.34
|[[3/1]]
|[[3/1]]
|F#
|Q#, Rb
|-
|-
|14
|14
|1976.52
|1976.52
|[[16/5]]
|[[16/5]]
|^G, Ab
|R
|-
|-
|15
|15
|2117.70
|2117.70
|[[10/3]]
|[[10/3]]
|A
|R#, Sb
|-
|-
|16
|16
|2258.88
|2258.88
|[[11/3]]
|[[11/3]]
|vB
|S
|-
|-
|17
|17
|2400.00
|2400.00
|[[4/1]]
|[[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]]
[[Category:Ed4]]
{{todo|expand}}
Retrieved from "https://en.xen.wiki/w/17ed4"