# Ed255/128

An equal division of reduced harmonic 255 (ed255/128) is an equal-step tuning in which the octave-reduced 255th harmonic (255/128) is justly tuned and is divided in a given number of equal steps. 255/128 is very close to the octave, 2/1, but it is slightly flatter. This makes it suitable as an alternative to edos whose consonances are too sharp, such as 5edo.

## 5ed255/128

### Harmonics

Approximation of harmonics in 5ed255/128
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error absolute (¢) -7 +7 -14 +77 +0 -28 -20 +14 +71 -94 -6
relative (%) -3 +3 -6 +32 +0 -12 -9 +6 +30 -40 -3
Steps
(reduced)
5
(0)
8
(3)
10
(0)
12
(2)
13
(3)
14
(4)
15
(0)
16
(1)
17
(2)
17
(2)
18
(3)

5edo, 8edt, 14ed7 for comparison:

Approximation of harmonics in 5edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error absolute (¢) +0 +18 +0 +94 +18 -9 +0 +36 +94 -71 +18
relative (%) +0 +8 +0 +39 +8 -4 +0 +15 +39 -30 +8
Steps
(reduced)
5
(0)
8
(3)
10
(0)
12
(2)
13
(3)
14
(4)
15
(0)
16
(1)
17
(2)
17
(2)
18
(3)
Approximation of harmonics in 8edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error absolute (¢) -11 +0 -23 +67 -11 -40 -34 +0 +55 -110 -23
relative (%) -5 +0 -9 +28 -5 -17 -14 +0 +23 -46 -9
Steps
(reduced)
5
(5)
8
(0)
10
(2)
12
(4)
13
(5)
14
(6)
15
(7)
16
(0)
17
(1)
17
(1)
18
(2)
Approximation of harmonics in 14ed7
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error absolute (¢) +3 +23 +6 +101 +26 +0 +9 +46 +104 -61 +29
relative (%) +1 +10 +3 +42 +11 +0 +4 +19 +43 -25 +12
Steps
(reduced)
5
(5)
8
(8)
10
(10)
12
(12)
13
(13)
14
(0)
15
(1)
16
(2)
17
(3)
17
(3)
18
(4)

• 238.645
• 477.29
• 715.934
• 954.579
• 1193.224

## 6ed255/128

### Harmonics

Approximation of harmonics in 6ed255/128
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error absolute (¢) -6.8 +86.8 -13.6 -2.1 +80.0 +12.0 -20.3 -25.4 -8.9 +25.0 +73.2
relative (%) -3 +44 -7 -1 +40 +6 -10 -13 -4 +13 +37
Steps
(reduced)
6
(0)
10
(4)
12
(0)
14
(2)
16
(4)
17
(5)
18
(0)
19
(1)
20
(2)
21
(3)
22
(4)

6edo for comparison:

Approximation of harmonics in 6edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error absolute (¢) +0.0 +98.0 +0.0 +13.7 +98.0 +31.2 +0.0 -3.9 +13.7 +48.7 +98.0
relative (%) +0 +49 +0 +7 +49 +16 +0 -2 +7 +24 +49
Steps
(reduced)
6
(0)
10
(4)
12
(0)
14
(2)
16
(4)
17
(5)
18
(0)
19
(1)
20
(2)
21
(3)
22
(4)

• 198.871
• 397.741
• 596.612
• 795.483
• 994.353
• 1193.224

## 8ed255/128

### Harmonics

Approximation of harmonics in 8ed255/128
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error absolute (¢) -6.8 +37.0 -13.6 +47.6 +30.3 +61.7 -20.3 +74.1 +40.8 +25.0 +23.5
relative (%) -5 +25 -9 +32 +20 +41 -14 +50 +27 +17 +16
Steps
(reduced)
8
(0)
13
(5)
16
(0)
19
(3)
21
(5)
23
(7)
24
(0)
26
(2)
27
(3)
28
(4)
29
(5)

8edo for comparison:

Approximation of harmonics in 8edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error absolute (¢) +0.0 +48.0 +0.0 +63.7 +48.0 -68.8 +0.0 -53.9 +63.7 +48.7 +48.0
relative (%) +0 +32 +0 +42 +32 -46 +0 -36 +42 +32 +32
Steps
(reduced)
8
(0)
13
(5)
16
(0)
19
(3)
21
(5)
22
(6)
24
(0)
25
(1)
27
(3)
28
(4)
29
(5)

• 149.153
• 298.306
• 447.459
• 596.612
• 745.765
• 894.918
• 1044.071
• 1193.224

## 11ed255/128

### Harmonics

Approximation of harmonics in 11ed255/128
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error absolute (¢) -6.8 +50.6 -13.6 +34.0 +43.8 -6.1 -20.3 -7.3 +27.3 -29.3 +37.0
relative (%) -6 +47 -12 +31 +40 -6 -19 -7 +25 -27 +34
Steps
(reduced)
11
(0)
18
(7)
22
(0)
26
(4)
29
(7)
31
(9)
33
(0)
35
(2)
37
(4)
38
(5)
40
(7)

11edo for comparison:

Approximation of harmonics in 11edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error absolute (¢) +0.0 -47.4 +0.0 +50.0 -47.4 +13.0 +0.0 +14.3 +50.0 -5.9 -47.4
relative (%) +0 -43 +0 +46 -43 +12 +0 +13 +46 -5 -43
Steps
(reduced)
11
(0)
17
(6)
22
(0)
26
(4)
28
(6)
31
(9)
33
(0)
35
(2)
37
(4)
38
(5)
39
(6)

• 108.475
• 216.95
• 325.425
• 433.9
• 542.375
• 650.85
• 759.324
• 867.799
• 976.274
• 1084.749
• 1193.224

## 15ed255/128

### Harmonics

Approximation of harmonics in 15ed255/128
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error absolute (¢) -6.8 +7.2 -13.6 -2.1 +0.4 -27.8 -20.3 +14.4 -8.9 -14.8 -6.3
relative (%) -9 +9 -17 -3 +1 -35 -26 +18 -11 -19 -8
Steps
(reduced)
15
(0)
24
(9)
30
(0)
35
(5)
39
(9)
42
(12)
45
(0)
48
(3)
50
(5)
52
(7)
54
(9)

15edo for comparison:

Approximation of harmonics in 15edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error absolute (¢) +0.0 +18.0 +0.0 +13.7 +18.0 -8.8 +0.0 +36.1 +13.7 +8.7 +18.0
relative (%) +0 +23 +0 +17 +23 -11 +0 +45 +17 +11 +23
Steps
(reduced)
15
(0)
24
(9)
30
(0)
35
(5)
39
(9)
42
(12)
45
(0)
48
(3)
50
(5)
52
(7)
54
(9)

• 79.548
• 159.097
• 238.645
• 318.193
• 397.741
• 477.29
• 556.838
• 636.386
• 715.934
• 795.483
• 875.031
• 954.579
• 1034.128
• 1113.676
• 1193.224

## 17ed255/128

### Harmonics

Approximation of harmonics in 17ed255/128
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error absolute (¢) -6.8 -6.8 -13.6 +21.3 -13.6 +0.3 -20.3 -13.7 +14.5 -10.1 -20.4
relative (%) -10 -10 -19 +30 -19 +0 -29 -19 +21 -14 -29
Steps
(reduced)
17
(0)
27
(10)
34
(0)
40
(6)
44
(10)
48
(14)
51
(0)
54
(3)
57
(6)
59
(8)
61
(10)

17edo for comparison:

Approximation of harmonics in 17edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error absolute (¢) +0.0 +3.9 +0.0 -33.4 +3.9 +19.4 +0.0 +7.9 -33.4 +13.4 +3.9
relative (%) +0 +6 +0 -47 +6 +27 +0 +11 -47 +19 +6
Steps
(reduced)
17
(0)
27
(10)
34
(0)
39
(5)
44
(10)
48
(14)
51
(0)
54
(3)
56
(5)
59
(8)
61
(10)

• 70.19
• 140.379
• 210.569
• 280.759
• 350.948
• 421.138
• 491.328
• 561.517
• 631.707
• 701.897
• 772.086
• 842.276
• 912.466
• 982.655
• 1052.845
• 1123.034
• 1193.224

## 18ed255/128

### Harmonics

Approximation of harmonics in 18ed255/128
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error absolute (¢) -6.8 +20.5 -13.6 -2.1 +13.7 +12.0 -20.3 -25.4 -8.9 +25.0 +6.9
relative (%) -10 +31 -20 -3 +21 +18 -31 -38 -13 +38 +10
Steps
(reduced)
18
(0)
29
(11)
36
(0)
42
(6)
47
(11)
51
(15)
54
(0)
57
(3)
60
(6)
63
(9)
65
(11)

18edo for comparison:

Approximation of harmonics in 18edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error absolute (¢) +0.0 +31.4 +0.0 +13.7 +31.4 +31.2 +0.0 -3.9 +13.7 -18.0 +31.4
relative (%) +0 +47 +0 +21 +47 +47 +0 -6 +21 -27 +47
Steps
(reduced)
18
(0)
29
(11)
36
(0)
42
(6)
47
(11)
51
(15)
54
(0)
57
(3)
60
(6)
62
(8)
65
(11)

• 66.29
• 132.58
• 198.871
• 265.161
• 331.451
• 397.741
• 464.032
• 530.322
• 596.612
• 662.902
• 729.193
• 795.483
• 861.773
• 928.063
• 994.353
• 1060.644
• 1126.934
• 1193.224

## 27ed255/128

### Harmonics

Approximation of harmonics in 27ed255/128
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error absolute (¢) -6.8 -1.6 -13.6 -2.1 -8.4 -10.1 -20.3 -3.3 -8.9 +2.9 -15.2
relative (%) -15 -4 -31 -5 -19 -23 -46 -7 -20 +6 -34
Steps
(reduced)
27
(0)
43
(16)
54
(0)
63
(9)
70
(16)
76
(22)
81
(0)
86
(5)
90
(9)
94
(13)
97
(16)

27edo for comparison:

Approximation of harmonics in 27edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error absolute (¢) +0.0 +9.2 +0.0 +13.7 +9.2 +9.0 +0.0 +18.3 +13.7 -18.0 +9.2
relative (%) +0 +21 +0 +31 +21 +20 +0 +41 +31 -40 +21
Steps
(reduced)
27
(0)
43
(16)
54
(0)
63
(9)
70
(16)
76
(22)
81
(0)
86
(5)
90
(9)
93
(12)
97
(16)

• 44.193
• 88.387
• 132.58
• 176.774
• 220.967
• 265.161
• 309.354
• 353.548
• 397.741
• 441.935
• 486.128
• 530.322
• 574.515
• 618.709
• 662.902
• 707.096
• 751.289
• 795.483
• 839.676
• 883.87
• 928.063
• 972.257
• 1016.45
• 1060.644
• 1104.837
• 1149.031
• 1193.224

## 39ed255/128

### Harmonics

Approximation of harmonics in 39ed255/128
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error absolute (¢) -6.8 -5.0 -13.6 -2.1 -11.8 -3.3 +10.3 -10.1 -8.9 +9.7 +12.0
relative (%) -22 -16 -44 -7 -39 -11 +34 -33 -29 +32 +39
Steps
(reduced)
39
(0)
62
(23)
78
(0)
91
(13)
101
(23)
110
(32)
118
(1)
124
(7)
130
(13)
136
(19)
141
(24)

19edo for comparison:

Approximation of harmonics in 39edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error absolute (¢) +0.0 +5.7 +0.0 +13.7 +5.7 -15.0 +0.0 +11.5 +13.7 +2.5 +5.7
relative (%) +0 +19 +0 +44 +19 -49 +0 +37 +44 +8 +19
Steps
(reduced)
39
(0)
62
(23)
78
(0)
91
(13)
101
(23)
109
(31)
117
(0)
124
(7)
130
(13)
135
(18)
140
(23)

## 49ed255/128

### Harmonics

Approximation of harmonics in 49ed255/128
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error absolute (¢) -6.8 -2.5 +10.8 -10.2 -9.3 -8.3 +4.0 -5.1 +7.3 -11.6 +8.3
relative (%) -28 -10 +44 -42 -38 -34 +17 -21 +30 -47 +34
Steps
(reduced)
49
(0)
78
(29)
99
(1)
114
(16)
127
(29)
138
(40)
148
(1)
156
(9)
164
(17)
170
(23)
177
(30)

19edo for comparison:

Approximation of harmonics in 49edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error absolute (¢) +0.0 +8.2 +0.0 +5.5 +8.2 +10.8 +0.0 -8.0 +5.5 +11.9 +8.2
relative (%) +0 +34 +0 +23 +34 +44 +0 -33 +23 +49 +34
Steps
(reduced)
49
(0)
78
(29)
98
(0)
114
(16)
127
(29)
138
(40)
147
(0)
155
(8)
163
(16)
170
(23)
176
(29)