User:BudjarnLambeth/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 (%) -2.8 +3.0 -5.7 +32.4 +0.2 -11.6 -8.5 +6.0 +29.6 -39.5 -2.7
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 (%) +0.0 +7.5 +0.0 +39.0 +7.5 -3.7 +0.0 +15.0 +39.0 -29.7 +7.5
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 (%) -4.7 +0.0 -9.5 +28.0 -4.7 -17.0 -14.2 +0.0 +23.3 -46.1 -9.5
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 (%) +1.3 +9.6 +2.6 +42.1 +10.9 +0.0 +3.9 +19.2 +43.4 -25.2 +12.2
Steps
(reduced)
5
(5)
8
(8)
10
(10)
12
(12)
13
(13)
14
(0)
15
(1)
16
(2)
17
(3)
17
(3)
18
(4)

Intervals

  • 238.645
  • 477.29
  • 715.934
  • 954.579
  • 1193.224

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