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Line 12: Line 12:
!Approximate ratios
!Approximate ratios
![[17edo]] notation
![[17edo]] notation
![[7L 3s (4/1-equivalent)|7L 3s<4/1>]] 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#, Kbb
|-
|-
|2
|2
Line 27: Line 30:
|[[13/11]], [[7/6]]
|[[13/11]], [[7/6]]
|Eb
|Eb
|Jx, Kb
|-
|-
|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
|-
|-
|4
|4
Line 37: Line 42:
|[[11/8]], [[18/13]], [[32/23]]
|[[11/8]], [[18/13]], [[32/23]]
|^F
|^F
|K#, Lb
|-
|-
|5
|5
Line 42: Line 48:
|[[3/2]], [[32/21]]
|[[3/2]], [[32/21]]
|G
|G
|L
|-
|-
|6
|6
Line 47: Line 54:
|[[13/8]], [[18/11]], [[23/14]]
|[[13/8]], [[18/11]], [[23/14]]
|G#, vA
|G#, vA
|M
|-
|-
|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
|M#, Nb
|-
|-
|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
|-
|-
|9
|9
Line 62: Line 72:
|[[15/7]]
|[[15/7]]
|^C
|^C
|N#, Ob
|-
|-
|10
|10
Line 67: Line 78:
|[[16/7]]
|[[16/7]]
|D
|D
|O
|-
|-
|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
|P#, Qb
|-
|-
|13
|13
Line 82: Line 96:
|[[3/1]]
|[[3/1]]
|F#
|F#
|Q
|-
|-
|14
|14
Line 87: Line 102:
|[[16/5]]
|[[16/5]]
|^G, Ab
|^G, Ab
|Q#, Rb
|-
|-
|15
|15
Line 92: Line 108:
|[[10/3]]
|[[10/3]]
|A
|A
|R
|-
|-
|16
|16
Line 97: Line 114:
|[[11/3]]
|[[11/3]]
|vB
|vB
|R#, Jb
|-
|-
|17
|17
Line 102: Line 120:
|[[4/1]]
|[[4/1]]
|C
|C
|J
|}
|}
[[Category:Macrotonal]]
[[Category:Macrotonal]]
[[Category:Nonoctave]]
[[Category:Nonoctave]]
[[Category:Ed4]]
[[Category:Ed4]]

Revision as of 01:37, 4 April 2023

← 16ed40001/10000 17ed40001/10000 18ed40001/10000 →
Prime factorization 17 (prime)
Step size 141.179 ¢ 
Octave 8\17ed40001/10000 (1129.43 ¢)
(semiconvergent)
Twelfth 13\17ed40001/10000 (1835.33 ¢)
Consistency limit 3
Distinct consistency limit 3

17ed4 is the equal division of the double octave into 17 parts of 141.18 cents each, corresponding to 8.5edo or every second step of 17edo.

Theory

TBA

Approximation of harmonics in 51ed64
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +70.6 -66.7 -0.0 +37.2 +3.9 +19.4 +70.6 +7.9 -33.4 -57.2 -66.7
Relative (%) +50.0 -47.2 -0.0 +26.4 +2.8 +13.7 +50.0 +5.6 -23.6 -40.5 -47.2
Steps
(reduced) 		9
(9) 		13
(13) 		17
(17) 		20
(20) 		22
(22) 		24
(24) 		26
(26) 		27
(27) 		28
(28) 		29
(29) 		30
(30)

Intervals

# Cents Approximate ratios 17edo notation 7L 3s<4/1> notation (J = 1/1)
0 0.00 1/1 C J
1 141.18 13/12, 12/11, 14/13, 25/23 C# J#, Kbb
2 282.36 13/11, 7/6 Eb Jx, Kb
3 423.54 32/25, 9/7, 14/11, 33/26, 23/18 E K
4 564.72 11/8, 18/13, 32/23 ^F K#, Lb
5 705.90 3/2, 32/21 G L
6 847.08 13/8, 18/11, 23/14 G#, vA M
7 988.26 16/9, 7/4, 25/14, 44/25, 23/13 Bb M#, Nb
8 1129.44 25/13, 48/25, 27/14, 64/33, 23/12 B N
9 1270.62 15/7 ^C N#, Ob
10 1411.80 16/7 D O
11 1552.98 12/5, 5/2 vE P
12 1694.16 8/3 F P#, Qb
13 1835.34 3/1 F# Q
14 1976.52 16/5 ^G, Ab Q#, Rb
15 2117.70 10/3 A R
16 2258.88 11/3 vB R#, Jb
17 2400.00 4/1 C J
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