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{{harmonics in cet|50}}
{{harmonics in cet|50}}


{{primes in equal|24|intervals=integer}}
{{harmonics in equal|24|intervals=integer}}


{{Odd harmonics in edo|edo=32}}
{{Odd harmonics in edo|edo=32}}

Revision as of 20:17, 15 January 2022

Approximation of harmonics in 1ed63.1578947368c
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -0.0 -7.2 -0.0 -7.4 -7.2 -21.5 -0.0 -14.4 -7.4 +17.1 -7.2
Relative (%) -0.0 -11.4 -0.0 -11.7 -11.4 -34.0 -0.0 -22.9 -11.7 +27.1 -11.4
Step 19 30 38 44 49 53 57 60 63 66 68


Approximation of harmonics in 1ed88c
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +32.0 +34.0 -24.0 +29.7 -22.0 -24.8 +8.0 -19.9 -26.3 -15.3 +10.0
Relative (%) +36.4 +38.7 -27.3 +33.7 -24.9 -28.2 +9.1 -22.6 -29.9 -17.4 +11.4
Step 14 22 27 32 35 38 41 43 45 47 49


Approximation of harmonics in 1ed50c
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +0.0 -2.0 +0.0 +13.7 -2.0 -18.8 +0.0 -3.9 +13.7 -1.3 -2.0
Relative (%) +0.0 -3.9 +0.0 +27.4 -3.9 -37.7 +0.0 -7.8 +27.4 -2.6 -3.9
Step 24 38 48 56 62 67 72 76 80 83 86


Approximation of harmonics in 24edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +0.0 -2.0 +0.0 +13.7 -2.0 -18.8 +0.0 -3.9 +13.7 -1.3 -2.0
Relative (%) +0.0 -3.9 +0.0 +27.4 -3.9 -37.7 +0.0 -7.8 +27.4 -2.6 -3.9
Steps
(reduced) 		24
(0) 		38
(14) 		48
(0) 		56
(8) 		62
(14) 		67
(19) 		72
(0) 		76
(4) 		80
(8) 		83
(11) 		86
(14)


Approximation of odd harmonics in 32 EDO
Odd harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error absolute (¢) +10.5 -11.3 +6.2 -16.4 +11.2 -15.5 -0.8 +7.5 +2.5 +16.7 +9.2 +14.9 -5.9 -17.1 +17.5
relative (%) +28 -30 +16 -44 +30 -41 -2 +20 +7 +45 +25 +40 -16 -46 +47
Steps (reduced) 51 (19) 74 (10) 90 (26) 101 (5) 111 (15) 118 (22) 125 (29) 131 (3) 136 (8) 141 (13) 145 (17) 149 (21) 152 (24) 155 (27) 159 (31)


Approximation of odd harmonics in 32edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +10.5 -11.3 +6.2 -16.4 +11.2 -15.5 -0.8 +7.5 +2.5 +16.7 +9.2
Relative (%) +28.1 -30.2 +16.5 -43.8 +29.8 -41.4 -2.0 +20.1 +6.6 +44.6 +24.6
Steps
(reduced) 		51
(19) 		74
(10) 		90
(26) 		101
(5) 		111
(15) 		118
(22) 		125
(29) 		131
(3) 		136
(8) 		141
(13) 		145
(17)


Approximation of harmonics in 1ed9/8
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +23.5 -66.8 +46.9 +68.4 -43.3 +97.6 +70.4 +70.4 +91.9 -73.1 -19.8
Relative (%) +11.5 -32.7 +23.0 +33.6 -21.2 +47.9 +34.5 +34.5 +45.1 -35.9 -9.7
Step 6 9 12 14 15 17 18 19 20 20 21


Approximation of odd harmonics in 11edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -47.4 +50.0 +13.0 +14.3 -5.9 +32.2 +2.6 +4.1 +29.8 -34.4 +26.3
Relative (%) -43.5 +45.9 +11.9 +13.1 -5.4 +29.5 +2.4 +3.8 +27.3 -31.5 +24.1
Steps
(reduced) 		17
(6) 		26
(4) 		31
(9) 		35
(2) 		38
(5) 		41
(8) 		43
(10) 		45
(1) 		47
(3) 		48
(4) 		50
(6)


Approximation of prime harmonics in 12edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.0 -2.0 +13.7 +31.2 +48.7 -40.5 -5.0 +2.5 -28.3 -29.6 -45.0
Relative (%) +0.0 -2.0 +13.7 +31.2 +48.7 -40.5 -5.0 +2.5 -28.3 -29.6 -45.0
Steps
(reduced) 		12
(0) 		19
(7) 		28
(4) 		34
(10) 		42
(6) 		44
(8) 		49
(1) 		51
(3) 		54
(6) 		58
(10) 		59
(11)


Approximation of odd harmonics in 13edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +36.5 -17.1 -45.7 -19.3 +2.5 -9.8 +19.4 -12.6 -20.6 -9.2 +17.9
Relative (%) +39.5 -18.5 -49.6 -20.9 +2.7 -10.6 +21.0 -13.7 -22.3 -10.0 +19.4
Steps
(reduced) 		21
(8) 		30
(4) 		36
(10) 		41
(2) 		45
(6) 		48
(9) 		51
(12) 		53
(1) 		55
(3) 		57
(5) 		59
(7)


Approximation of prime harmonics in 15edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.0 +18.0 +13.7 -8.8 +8.7 +39.5 -25.0 +22.5 +11.7 +10.4 -25.0
Relative (%) +0.0 +22.6 +17.1 -11.0 +10.9 +49.3 -31.2 +28.1 +14.7 +13.0 -31.3
Steps
(reduced) 		15
(0) 		24
(9) 		35
(5) 		42
(12) 		52
(7) 		56
(11) 		61
(1) 		64
(4) 		68
(8) 		73
(13) 		74
(14)


Approximation of odd harmonics in 18edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +31.4 +13.7 +31.2 -3.9 -18.0 +26.1 -21.6 +28.4 -30.8 -4.1 -28.3
Relative (%) +47.1 +20.5 +46.8 -5.9 -27.0 +39.2 -32.4 +42.6 -46.3 -6.2 -42.4
Steps
(reduced) 		29
(11) 		42
(6) 		51
(15) 		57
(3) 		62
(8) 		67
(13) 		70
(16) 		74
(2) 		76
(4) 		79
(7) 		81
(9)


Approximation of harmonics in 13edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -29.6 +0.0 -59.1 -6.5 -29.6 -3.8 +57.6 +0.0 -36.1 -54.8 -59.1
Relative (%) -20.2 +0.0 -40.4 -4.5 -20.2 -2.6 +39.4 +0.0 -24.7 -37.5 -40.4
Steps
(reduced) 		8
(8) 		13
(0) 		16
(3) 		19
(6) 		21
(8) 		23
(10) 		25
(12) 		26
(0) 		27
(1) 		28
(2) 		29
(3)


Approximation of harmonics in 12ed7/4
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +11.0 +35.7 +22.1 +39.4 -34.0 +22.1 +33.1 -9.3 -30.3 -33.8 -23.0
Relative (%) +13.7 +44.2 +27.3 +48.8 -42.1 +27.3 +41.0 -11.6 -37.5 -41.9 -28.5
Steps
(reduced) 		15
(3) 		24
(0) 		30
(6) 		35
(11) 		38
(2) 		42
(6) 		45
(9) 		47
(11) 		49
(1) 		51
(3) 		53
(5)


Approximation of harmonics in 12ed16/9
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -37.9 +7.2 +7.2 +35.9 -30.7 +34.5 -30.7 +14.4 -2.0 -0.9 +14.4
Relative (%) -45.7 +8.7 +8.7 +43.3 -37.0 +41.5 -37.0 +17.4 -2.4 -1.1 +17.4
Steps
(reduced) 		14
(2) 		23
(11) 		29
(5) 		34
(10) 		37
(1) 		41
(5) 		43
(7) 		46
(10) 		48
(0) 		50
(2) 		52
(4)


Approximation of harmonics in 19edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +1.2 +0.0 +2.5 +16.6 +1.2 +34.7 +3.7 +0.0 +17.8 -47.1 +2.5
Relative (%) +1.2 +0.0 +2.5 +16.6 +1.2 +34.6 +3.7 +0.0 +17.8 -47.1 +2.5
Steps
(reduced) 		12
(12) 		19
(0) 		24
(5) 		28
(9) 		31
(12) 		34
(15) 		36
(17) 		38
(0) 		40
(2) 		41
(3) 		43
(5)


Approximation of harmonics in 7edf
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +3.4 +3.4 +6.7 +21.5 +6.7 +40.7 +10.1 +6.7 +24.9 -39.9 +10.1
Relative (%) +3.3 +3.3 +6.7 +21.4 +6.7 +40.6 +10.0 +6.7 +24.8 -39.8 +10.0
Steps
(reduced) 		12
(5) 		19
(5) 		24
(3) 		28
(0) 		31
(3) 		34
(6) 		36
(1) 		38
(3) 		40
(5) 		41
(6) 		43
(1)


Approximation of harmonics in 28ed5
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -5.9 -11.2 -11.7 +0.0 -17.1 +14.6 -17.6 -22.5 -5.9 +28.2 -23.0
Relative (%) -5.9 -11.3 -11.8 +0.0 -17.2 +14.6 -17.7 -22.6 -5.9 +28.3 -23.1
Steps
(reduced) 		12
(12) 		19
(19) 		24
(24) 		28
(0) 		31
(3) 		34
(6) 		36
(8) 		38
(10) 		40
(12) 		42
(14) 		43
(15)
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