User:MisterShafXen/8ed13/4

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Revision as of 12:29, 24 June 2025 by MisterShafXen (talk | contribs) (Created page with "{{ED intro}} ==Harmonics== {{Harmonics in equal | num = 13 | denom = 4 | steps = 8 | intervals = prime | columns = 20}} {{Harmonics in equal | num = 13 | denom = 4 | steps = 8 | intervals = prime | start = 21 | columns = 20}}")
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8 equal divisions of 13/4 (abbreviated 8ed13/4) is a nonoctave tuning system that divides the interval of 13/4 into 8 equal parts of about 255 ¢ each. Each step represents a frequency ratio of (13/4)1/8, or the 8th root of 13/4.

Harmonics

Approximation of prime harmonics in 8ed13/4
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71
Error Absolute (¢) +75 -116 +19 -53 -70 -104 -59 +4 -72 +37 -79 +125 -52 +120 -34 +13 +83 +25 +118 +17
Relative (%) +29.5 -45.7 +7.6 -20.8 -27.5 -40.9 -23.0 +1.5 -28.2 +14.5 -30.8 +49.1 -20.5 +47.1 -13.2 +5.2 +32.4 +9.8 +46.1 +6.7
Steps
(reduced) 		5
(5) 		7
(7) 		11
(3) 		13
(5) 		16
(0) 		17
(1) 		19
(3) 		20
(4) 		21
(5) 		23
(7) 		23
(7) 		25
(1) 		25
(1) 		26
(2) 		26
(2) 		27
(3) 		28
(4) 		28
(4) 		29
(5) 		29
(5)
Approximation of prime harmonics in 8ed13/4
Harmonic 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173
Error Absolute (¢) -31 +87 +2 -119 -13 -83 -117 +72 +40 -22 +31 -23 -100 -126 +9 -14 -81 +109 +67 +6
Relative (%) -12.1 +34.3 +0.8 -46.6 -5.0 -32.5 -45.8 +28.4 +15.8 -8.7 +12.1 -9.0 -39.4 -49.2 +3.6 -5.4 -31.9 +42.7 +26.2 +2.3
Steps
(reduced) 		29
(5) 		30
(6) 		30
(6) 		30
(6) 		31
(7) 		31
(7) 		31
(7) 		32
(0) 		32
(0) 		32
(0) 		33
(1) 		33
(1) 		33
(1) 		33
(1) 		34
(2) 		34
(2) 		34
(2) 		35
(3) 		35
(3) 		35
(3)
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